Existence of entire solutions of some non-linear differential-difference equations.

PubMed

Chen, Minfeng; Gao, Zongsheng; Du, Yunfei

2017-01-01

In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation [Formula: see text], where [Formula: see text], [Formula: see text] are two non-constant polynomials, [Formula: see text], m , n are positive integers and satisfy [Formula: see text] except for [Formula: see text], [Formula: see text].

A direct method of solution for the Fokas-Lenells derivative nonlinear Schrödinger equation: I. Bright soliton solutions

NASA Astrophysics Data System (ADS)

Matsuno, Yoshimasa

2012-06-01

We develop a direct method of solution for finding the bright N-soliton solution of the Fokas-Lenells derivative nonlinear Schrödinger equation. The construction of the solution is performed by means of a purely algebraic procedure using an elementary theory of determinants and does not rely on the inverse scattering transform method. We present two different expressions of the solution both of which are expressed as a ratio of determinants. We then investigate the properties of the solutions and find several new features. Specifically, we derive the formula for the phase shift caused by the collisions of bright solitons.

Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian.

PubMed

Shen, Liejun

2018-01-01

The present study is concerned with the following fractional p -Laplacian equation involving a critical Sobolev exponent of Kirchhoff type: [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are constants, and [Formula: see text] is the fractional p -Laplacian operator with [Formula: see text] and [Formula: see text]. For suitable [Formula: see text], the above equation possesses at least two nontrivial solutions by variational method for any [Formula: see text]. Moreover, we regard [Formula: see text] and [Formula: see text] as parameters to obtain convergent properties of solutions for the given problem as [Formula: see text] and [Formula: see text], respectively.

Variational estimate method for solving autonomous ordinary differential equations

NASA Astrophysics Data System (ADS)

Mungkasi, Sudi

2018-04-01

In this paper, we propose a method for solving first-order autonomous ordinary differential equation problems using a variational estimate formulation. The variational estimate is constructed with a Lagrange multiplier which is chosen optimally, so that the formulation leads to an accurate solution to the problem. The variational estimate is an integral form, which can be computed using a computer software. As the variational estimate is an explicit formula, the solution is easy to compute. This is a great advantage of the variational estimate formulation.

The theory of nonstationary thermophoresis of a solid spherical particle

NASA Astrophysics Data System (ADS)

Kuzmin, M. K.; Yalamov, Yu. I.

2007-06-01

The theory of nonstationary thermophoresis of a solid spherical particle in a viscous gaseous medium is presented. The theory is constructed on the solutions of fluid-dynamics and thermal problems, each of which is split into stationary and strictly nonstationary parts. The solution of the stationary parts of the problems gives the final formula for determining the stationary component of the thermophoretic velocity of this particle. To determine the nonstationary component of the thermophoretic velocity of the particle, the corresponding formula in the space of Laplace transforms is derived. The limiting value theorems from operational calculus are used for obtaining the dependence of the nonstationary component of the thermophoretic velocity of the spherical particle on the strictly nonstationary temperature gradient for large and small values of time. The factors determining the thermophoretic velocity of the particle under investigation are determined.

5D Lovelock gravity: New exact solutions with torsion

NASA Astrophysics Data System (ADS)

Cvetković, B.; Simić, D.

2016-10-01

Five-dimensional Lovelock gravity is investigated in the first order formalism. A new class of exact solutions is constructed: the Bañados, Teitelboim, Zanelli black rings with and without torsion. We show that our solution with torsion exists in a different sector of the Lovelock gravity, as compared to the Lovelock Chern-Simons sector or the one investigated by Canfora et al. The conserved charges of the solutions are found using Nester's formula, and the results are confirmed by the canonical method. We show that the theory linearized around the background with torsion possesses two additional degrees of freedom with respect to general relativity.

Special solutions to Chazy equation

NASA Astrophysics Data System (ADS)

Varin, V. P.

2017-02-01

We consider the classical Chazy equation, which is known to be integrable in hypergeometric functions. But this solution has remained purely existential and was never used numerically. We give explicit formulas for hypergeometric solutions in terms of initial data. A special solution was found in the upper half plane H with the same tessellation of H as that of the modular group. This allowed us to derive some new identities for the Eisenstein series. We constructed a special solution in the unit disk and gave an explicit description of singularities on its natural boundary. A global solution to Chazy equation in elliptic and theta functions was found that allows parametrization of an arbitrary solution to Chazy equation. The results have applications to analytic number theory.

Transit-time and age distributions for nonlinear time-dependent compartmental systems.

PubMed

Metzler, Holger; Müller, Markus; Sierra, Carlos A

2018-02-06

Many processes in nature are modeled using compartmental systems (reservoir/pool/box systems). Usually, they are expressed as a set of first-order differential equations describing the transfer of matter across a network of compartments. The concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions. Until now, explicit formulas for transit-time and age distributions of nonlinear time-dependent compartmental systems were not available. We compute densities for these types of systems under the assumption of well-mixed compartments. Assuming that a solution of the nonlinear system is available at least numerically, we show how to construct a linear time-dependent system with the same solution trajectory. We demonstrate how to exploit this solution to compute transit-time and age distributions in dependence on given start values and initial age distributions. Furthermore, we derive equations for the time evolution of quantiles and moments of the age distributions. Our results generalize available density formulas for the linear time-independent case and mean-age formulas for the linear time-dependent case. As an example, we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time-dependent input signal which represents fossil fuel additions. We derive time-dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business-as-usual scenario.

Lagrange thermodynamic potential and intrinsic variables for He-3 He-4 dilute solutions

NASA Technical Reports Server (NTRS)

Jackson, H. W.

1983-01-01

For a two-fluid model of dilute solutions of He-3 in liquid He-4, a thermodynamic potential is constructed that provides a Lagrangian for deriving equations of motion by a variational procedure. This Lagrangian is defined for uniform velocity fields as a (negative) Legendre transform of total internal energy, and its primary independent variables, together with their thermodynamic conjugates, are identified. Here, similarities between relations in classical physics and quantum statistical mechanics serve as a guide for developing an alternate expression for this function that reveals its character as the difference between apparent kinetic energy and intrinsic internal energy. When the He-3 concentration in the mixtures tends to zero, this expression reduces to Zilsel's formula for the Lagrangian for pure liquid He-4. An investigation of properties of the intrinsic internal energy leads to the introduction of intrinsic chemical potentials along with other intrinsic variables for the mixtures. Explicit formulas for these variables are derived for a noninteracting elementary excitation model of the fluid. Using these formulas and others also derived from quantum statistical mechanics, another equivalent expression for the Lagrangian is generated.

On the initial value problem for the wave equation in Friedmann-Robertson-Walker space-times.

PubMed

Abbasi, Bilal; Craig, Walter

2014-09-08

The propagator W ( t 0 , t 1 )( g , h ) for the wave equation in a given space-time takes initial data ( g ( x ), h ( x )) on a Cauchy surface {( t , x ) :  t = t 0 } and evaluates the solution ( u ( t 1 , x ),∂ t u ( t 1 , x )) at other times t 1 . The Friedmann-Robertson-Walker space-times are defined for t 0 , t 1 >0, whereas for t 0 →0, there is a metric singularity. There is a spherical means representation for the general solution of the wave equation with the Friedmann-Robertson-Walker background metric in the three spatial dimensional cases of curvature K =0 and K =-1 given by S. Klainerman and P. Sarnak. We derive from the expression of their representation three results about the wave propagator for the Cauchy problem in these space-times. First, we give an elementary proof of the sharp rate of time decay of solutions with compactly supported data. Second, we observe that the sharp Huygens principle is not satisfied by solutions, unlike in the case of three-dimensional Minkowski space-time (the usual Huygens principle of finite propagation speed is satisfied, of course). Third, we show that for 0< t 0 < t the limit, [Formula: see text] exists, it is independent of h ( x ), and for all reasonable initial data g ( x ), it gives rise to a well-defined solution for all t >0 emanating from the space-time singularity at t =0. Under reflection t →- t , the Friedmann-Robertson-Walker metric gives a space-time metric for t <0 with a singular future at t =0, and the same solution formulae hold. We thus have constructed solutions u ( t , x ) of the wave equation in Friedmann-Robertson-Walker space-times which exist for all [Formula: see text] and [Formula: see text], where in conformally regularized coordinates, these solutions are continuous through the singularity t =0 of space-time, taking on specified data u (0,⋅)= g (⋅) at the singular time.

Numerical method for solving the nonlinear four-point boundary value problems

NASA Astrophysics Data System (ADS)

Lin, Yingzhen; Lin, Jinnan

2010-12-01

In this paper, a new reproducing kernel space is constructed skillfully in order to solve a class of nonlinear four-point boundary value problems. The exact solution of the linear problem can be expressed in the form of series and the approximate solution of the nonlinear problem is given by the iterative formula. Compared with known investigations, the advantages of our method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Meanwhile we present the convergent theorem, complexity analysis and error estimation. The performance of the new method is illustrated with several numerical examples.

Free boundary skin current MHD (magnetohydrodynamic) equilibria

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reusch, M.F.

1988-02-01

Function theoretic methods in the complex plane are used to develop simple parametric hodograph formulae which generate sharp boundary equilibria of arbitrary shape. The related method of Gorenflo and Merkel is discussed. A numerical technique for the construction of solutions, based on one of the methods is presented. A study is made of the bifurcations of an equilibrium of general form. 28 refs., 9 figs.

Asymptotically spacelike warped anti-de Sitter spacetimes in generalized minimal massive gravity

NASA Astrophysics Data System (ADS)

Setare, M. R.; Adami, H.

2017-06-01

In this paper we show that warped AdS3 black hole spacetime is a solution of the generalized minimal massive gravity (GMMG) and introduce suitable boundary conditions for asymptotically warped AdS3 spacetimes. Then we find the Killing vector fields such that transformations generated by them preserve the considered boundary conditions. We calculate the conserved charges which correspond to the obtained Killing vector fields and show that the algebra of the asymptotic conserved charges is given as the semi direct product of the Virasoro algebra with U(1) current algebra. We use a particular Sugawara construction to reconstruct the conformal algebra. Thus, we are allowed to use the Cardy formula to calculate the entropy of the warped black hole. We demonstrate that the gravitational entropy of the warped black hole exactly coincides with what we obtain via Cardy’s formula. As we expect, the warped Cardy formula also gives us exactly the same result as we obtain from the usual Cardy’s formula. We calculate mass and angular momentum of the warped black hole and then check that obtained mass, angular momentum and entropy to satisfy the first law of the black hole mechanics. According to the results of this paper we believe that the dual theory of the warped AdS3 black hole solution of GMMG is a warped CFT.

Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of Al-Salam Carlitz I polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.; Ahmed, H. M.

2005-12-01

Two formulae expressing explicitly the derivatives and moments of Al-Salam-Carlitz I polynomials of any degree and for any order in terms of Al-Salam-Carlitz I themselves are proved. Two other formulae for the expansion coefficients of general-order derivatives Dpqf(x), and for the moments xellDpqf(x), of an arbitrary function f(x) in terms of its original expansion coefficients are also obtained. Application of these formulae for solving q-difference equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Al-Salam-Carlitz I polynomials and any system of basic hypergeometric orthogonal polynomials, belonging to the q-Hahn class, is described.

Analysis of the numerical differentiation formulas of functions with large gradients

NASA Astrophysics Data System (ADS)

Tikhovskaya, S. V.

2017-10-01

The solution of a singularly perturbed problem corresponds to a function with large gradients. Therefore the question of interpolation and numerical differentiation of such functions is relevant. The interpolation based on Lagrange polynomials on uniform mesh is widely applied. However, it is known that the use of such interpolation for the function with large gradients leads to estimates that are not uniform with respect to the perturbation parameter and therefore leads to errors of order O(1). To obtain the estimates that are uniform with respect to the perturbation parameter, we can use the polynomial interpolation on a fitted mesh like the piecewise-uniform Shishkin mesh or we can construct on uniform mesh the interpolation formula that is exact on the boundary layer components. In this paper the numerical differentiation formulas for functions with large gradients based on the interpolation formulas on the uniform mesh, which were proposed by A.I. Zadorin, are investigated. The formulas for the first and the second derivatives of the function with two or three interpolation nodes are considered. Error estimates that are uniform with respect to the perturbation parameter are obtained in the particular cases. The numerical results validating the theoretical estimates are discussed.

Systems of nonlinear algebraic equations with positive solutions.

PubMed

Ciurte, Anca; Nedevschi, Sergiu; Rasa, Ioan

2017-01-01

We are concerned with the positive solutions of an algebraic system depending on a parameter [Formula: see text] and arising in economics. For [Formula: see text] we prove that the system has at least a solution. For [Formula: see text] we give three proofs of the existence and a proof of the uniqueness of the solution. Brouwer's theorem and inequalities involving convex functions are essential tools in our proofs.

Free boundary skin current magnetohydrodynamic equilibria

NASA Astrophysics Data System (ADS)

Reusch, Michael F.

1988-10-01

Function theoretic methods in the complex plane are used to develop simple parametric hodograph formulas that generate sharp boundary equilibria of arbitrary shape. The related method of Gorenflo [Z. Angew. Math. Phys. 16, 279 (1965)] and Merkel (Ph.D. thesis, University of Munich, 1965) is discussed. A numerical technique for the construction of solutions, based on one of the methods, is presented. A study is made of the bifurcations of an equilibrium of general form.

An integrated assessment instrument: Developing and validating instrument for facilitating critical thinking abilities and science process skills on electrolyte and nonelectrolyte solution matter

NASA Astrophysics Data System (ADS)

Astuti, Sri Rejeki Dwi; Suyanta, LFX, Endang Widjajanti; Rohaeti, Eli

2017-05-01

The demanding of assessment in learning process was impact by policy changes. Nowadays, assessment is not only emphasizing knowledge, but also skills and attitudes. However, in reality there are many obstacles in measuring them. This paper aimed to describe how to develop integrated assessment instrument and to verify instruments' validity such as content validity and construct validity. This instrument development used test development model by McIntire. Development process data was acquired based on development test step. Initial product was observed by three peer reviewer and six expert judgments (two subject matter experts, two evaluation experts and two chemistry teachers) to acquire content validity. This research involved 376 first grade students of two Senior High Schools in Bantul Regency to acquire construct validity. Content validity was analyzed used Aiken's formula. The verifying of construct validity was analyzed by exploratory factor analysis using SPSS ver 16.0. The result show that all constructs in integrated assessment instrument are asserted valid according to content validity and construct validity. Therefore, the integrated assessment instrument is suitable for measuring critical thinking abilities and science process skills of senior high school students on electrolyte solution matter.

Sasa-Satsuma higher-order nonlinear Schrödinger equation and its bilinearization and multisoliton solutions.

PubMed

Gilson, C; Hietarinta, J; Nimmo, J; Ohta, Y

2003-07-01

Higher-order and multicomponent generalizations of the nonlinear Schrödinger equation are important in various applications, e.g., in optics. One of these equations, the integrable Sasa-Satsuma equation, has particularly interesting soliton solutions. Unfortunately, the construction of multisoliton solutions to this equation presents difficulties due to its complicated bilinearization. We discuss briefly some previous attempts and then give the correct bilinearization based on the interpretation of the Sasa-Satsuma equation as a reduction of the three-component Kadomtsev-Petviashvili hierarchy. In the process, we also get bilinearizations and multisoliton formulas for a two-component generalization of the Sasa-Satsuma equation (the Yajima-Oikawa-Tasgal-Potasek model), and for a (2+1)-dimensional generalization.

Automating FEA programming

NASA Technical Reports Server (NTRS)

Sharma, Naveen

1992-01-01

In this paper we briefly describe a combined symbolic and numeric approach for solving mathematical models on parallel computers. An experimental software system, PIER, is being developed in Common Lisp to synthesize computationally intensive and domain formulation dependent phases of finite element analysis (FEA) solution methods. Quantities for domain formulation like shape functions, element stiffness matrices, etc., are automatically derived using symbolic mathematical computations. The problem specific information and derived formulae are then used to generate (parallel) numerical code for FEA solution steps. A constructive approach to specify a numerical program design is taken. The code generator compiles application oriented input specifications into (parallel) FORTRAN77 routines with the help of built-in knowledge of the particular problem, numerical solution methods and the target computer.

Topological and statistical properties of nonlinear force-free fields

NASA Astrophysics Data System (ADS)

Mangalam, A.; Prasad, A.

2018-01-01

We use our semi-analytic solution of the nonlinear force-free field equation to construct three-dimensional magnetic fields that are applicable to the solar corona and study their statistical properties for estimating the degree of braiding exhibited by these fields. We present a new formula for calculating the winding number and compare it with the formula for the crossing number. The comparison is shown for a toy model of two helices and for realistic cases of nonlinear force-free fields; conceptually the formulae are nearly the same but the resulting distributions calculated for a given topology can be different. We also calculate linkages, which are useful topological quantities that are independent measures of the contribution of magnetic braiding to the total free energy and relative helicity of the field. Finally, we derive new analytical bounds for the free energy and relative helicity for the field configurations in terms of the linking number. These bounds will be of utility in estimating the braided energy available for nano-flares or for eruptions.

A time-domain method for prediction of noise radiated from supersonic rotating sources in a moving medium

NASA Astrophysics Data System (ADS)

Huang, Zhongjie; Siozos-Rousoulis, Leonidas; De Troyer, Tim; Ghorbaniasl, Ghader

2018-02-01

This paper presents a time-domain method for noise prediction of supersonic rotating sources in a moving medium. The proposed approach can be interpreted as an extensive time-domain solution for the convected permeable Ffowcs Williams and Hawkings equation, which is capable of avoiding the Doppler singularity. The solution requires special treatment for construction of the emission surface. The derived formula can explicitly and efficiently account for subsonic uniform constant flow effects on radiated noise. Implementation of the methodology is realized through the Isom thickness noise case and high-speed impulsive noise prediction from helicopter rotors.

Stochastic theory of fatigue corrosion

NASA Astrophysics Data System (ADS)

Hu, Haiyun

1999-10-01

A stochastic theory of corrosion has been constructed. The stochastic equations are described giving the transportation corrosion rate and fluctuation corrosion coefficient. In addition the pit diameter distribution function, the average pit diameter and the most probable pit diameter including other related empirical formula have been derived. In order to clarify the effect of stress range on the initiation and growth behaviour of pitting corrosion, round smooth specimen were tested under cyclic loading in 3.5% NaCl solution.

Thermal Analysis of Reinforced Concrete Tank for Conditioning Wood by FEM Method

NASA Astrophysics Data System (ADS)

Błaszczyński, Tomasz; Babiak, Michał; Wielentejczyk, Przemysław

2017-10-01

The article introduces the analysis of a RC tank for conditioning wood carried out using the FEM (Finite Element Method). A temperature gradient distribution increase resulting from the influence of hot liquid filling the tank was defined. Values of gradients in border sections of the tank walls and the bottom were defined on the basis of the isotherm method. The obtained results were compared with empirical formulas from literature. Strength analyses were also carried out. Additionally, the problematic aspects of elongated monolithic tanks for liquids were introduced, especially regarding large temperature gradients and the means of necessary technical solutions. The use of the FEM method for designing engineering objects is, nowadays, an irreplaceable solution. In the case of the discussed tank, a spatial model of the construction mapping its actual performance was constructed in order to correctly estimate the necessary dimensions of wall and bottom sections, as well as reinforcement.

A climate-based malaria model with the use of bed nets.

PubMed

Wang, Xiunan; Zhao, Xiao-Qiang

2018-07-01

Insecticide-treated bed nets (ITNs) are among the most important and effective intervention measures against malaria. In order to investigate the impact of bed net use on disease control, we formulate a periodic vector-bias malaria model incorporating the juvenile stage of mosquitoes and the use of ITNs. We derive the vector reproduction ratio [Formula: see text] and the basic reproduction ratio [Formula: see text]. We show that the global dynamics of the model is completely determined by these two reproduction ratios. More precisely, the mosquito-free periodic solution is globally attractive if [Formula: see text]; the unique disease-free periodic solution is globally attractive if [Formula: see text] and [Formula: see text]; and the model admits a unique positive periodic solution and it is globally attractive if [Formula: see text] and [Formula: see text]. Numerically, we study the malaria transmission case in Port Harcourt, Nigeria. Our findings show that the use of ITNs has a positive effect on reducing [Formula: see text], and that malaria may be eliminated from this area if over 75% of the human population were to use ITNs. The simulation about the long term behavior of solutions has good agreement with the obtained analytic result. Moreover, we find that the ignorance of the vector-bias effect may result in underestimation of the basic reproduction ratio [Formula: see text]. Another notable result is that the infection risk would be underestimated if the basic reproduction ratio [Formula: see text] of the time-averaged autonomous system were used.

A new frequency domain analytical solution of a cascade of diffusive channels for flood routing

NASA Astrophysics Data System (ADS)

Cimorelli, Luigi; Cozzolino, Luca; Della Morte, Renata; Pianese, Domenico; Singh, Vijay P.

2015-04-01

Simplified flood propagation models are often employed in practical applications for hydraulic and hydrologic analyses. In this paper, we present a new numerical method for the solution of the Linear Parabolic Approximation (LPA) of the De Saint Venant equations (DSVEs), accounting for the space variation of model parameters and the imposition of appropriate downstream boundary conditions. The new model is based on the analytical solution of a cascade of linear diffusive channels in the Laplace Transform domain. The time domain solutions are obtained using a Fourier series approximation of the Laplace Inversion formula. The new Inverse Laplace Transform Diffusive Flood Routing model (ILTDFR) can be used as a building block for the construction of real-time flood forecasting models or in optimization models, because it is unconditionally stable and allows fast and fairly precise computation.

Analyticity in Time and Smoothing Effect of Solutions to Nonlinear Schrödinger Equations

NASA Astrophysics Data System (ADS)

Hayashi, Nakao; Kato, Keiichi

In this paper we consider analyticity in time and smoothing effect of solutions to nonlinear Schrödinger equations where . We prove that if φ satisfies then there exists a unique solution of (1) and positive constants T, C0, C1 such that is analytic in time and space variables for and and has an analytic continuation on and In the case the condition (2) can be relaxed as follows: where m= 0 if n= 1, p= 1, m= 1 if n= 2, and m= 1 if n= 3, p= 1.

A High Frequency Model of Cascade Noise

NASA Technical Reports Server (NTRS)

Envia, Edmane

1998-01-01

Closed form asymptotic expressions for computing high frequency noise generated by an annular cascade in an infinite duct containing a uniform flow are presented. There are two new elements in this work. First, the annular duct mode representation does not rely on the often-used Bessel function expansion resulting in simpler expressions for both the radial eigenvalues and eigenfunctions of the duct. In particular, the new representation provides an explicit approximate formula for the radial eigenvalues obviating the need for solutions of the transcendental annular duct eigenvalue equation. Also, the radial eigenfunctions are represented in terms of exponentials eliminating the numerical problems associated with generating the Bessel functions on a computer. The second new element is the construction of an unsteady response model for an annular cascade. The new construction satisfies the boundary conditions on both the cascade and duct walls simultaneously adding a new level of realism to the noise calculations. Preliminary results which demonstrate the effectiveness of the new elements are presented. A discussion of the utility of the asymptotic formulas for calculating cascade discrete tone as well as broadband noise is also included.

An Edge-Based Method for the Incompressible Navier-Stokes Equations on Polygonal Meshes

NASA Astrophysics Data System (ADS)

Wright, Jeffrey A.; Smith, Richard W.

2001-05-01

A pressure-based method is presented for discretizing the unsteady incompressible Navier-Stokes equations using hybrid unstructured meshes. The edge-based data structure and assembly procedure adopted lead naturally to a strictly conservative discretization, which is valid for meshes composed of n-sided polygons. Particular attention is given to the construction of a pressure-velocity coupling procedure which is supported by edge data, resulting in a relatively simple numerical method that is consistent with the boundary and initial conditions required by the incompressible Navier-Stokes equations. Edge formulas are presented for assembling the momentum equations, which are based on an upwind-biased linear reconstruction of the velocity field. Similar formulas are presented for assembling the pressure equation. The method is demonstrated to be second-order accurate in space and time for two Navier-Stokes problems admitting an exact solution. Results for several other well-known problems are also presented, including lid-driven cavity flow, impulsively started cylinder flow, and unsteady vortex shedding from a circular cylinder. Although the method is by construction minimalist, it is shown to be accurate and robust for the problems considered.

How are population-based funding formulae for healthcare composed? A comparative analysis of seven models.

PubMed

Penno, Erin; Gauld, Robin; Audas, Rick

2013-11-08

Population-based funding formulae act as an important means of promoting equitable health funding structures. To evaluate how policy makers in different jurisdictions construct health funding formulae and build an understanding of contextual influences underpinning formula construction we carried out a comparative analysis of key components of funding formulae across seven high-income and predominantly publically financed health systems: New Zealand, England, Scotland, the Netherlands, the state of New South Wales in Australia, the Canadian province of Ontario, and the city of Stockholm, Sweden. Core components from each formula were summarised and key similarities and differences evaluated from a compositional perspective. We categorised approaches to constructing funding formulae under three main themes: identifying factors which predict differential need amongst populations; adjusting for cost factors outside of needs factors; and engaging in normative correction of allocations for 'unmet' need. We found significant congruence in the factors used to guide need and cost adjustments. However, there is considerable variation in interpretation and implementation of these factors. Despite broadly similar frameworks, there are distinct differences in the composition of the formulae across the seven health systems. Ultimately, the development of funding formulae is a dynamic process, subject to availability of data reflecting health needs, the influence of wider socio-political objectives and health system determinants.

Integration by parts and Pohozaev identities for space-dependent fractional-order operators

NASA Astrophysics Data System (ADS)

Grubb, Gerd

2016-08-01

Consider a classical elliptic pseudodifferential operator P on Rn of order 2a (0 < a < 1) with even symbol. For example, P = A(x , D) a where A (x , D) is a second-order strongly elliptic differential operator; the fractional Laplacian (- Δ) a is a particular case. For solutions u of the Dirichlet problem on a bounded smooth subset Ω ⊂Rn, we show an integration-by-parts formula with a boundary integral involving (d-a u)|∂Ω, where d (x) = dist (x , ∂ Ω). This extends recent results of Ros-Oton, Serra and Valdinoci, to operators that are x-dependent, nonsymmetric, and have lower-order parts. We also generalize their formula of Pohozaev-type, that can be used to prove unique continuation properties, and nonexistence of nontrivial solutions of semilinear problems. An illustration is given with P =(- Δ +m2) a. The basic step in our analysis is a factorization of P, P ∼P-P+, where we set up a calculus for the generalized pseudodifferential operators P± that come out of the construction.

Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Frederickson, Paul O.

1990-01-01

High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.

Effect of blood flow on near-the-wall mass transport of drugs and other bioactive agents: a simple formula to estimate boundary layer concentrations.

PubMed

Rugonyi, Sandra

2008-04-01

Transport of bioactive agents through the blood is essential for cardiovascular regulatory processes and drug delivery. Bioactive agents and other solutes infused into the blood through the wall of a blood vessel or released into the blood from an area in the vessel wall spread downstream of the infusion/release region and form a thin boundary layer in which solute concentration is higher than in the rest of the blood. Bioactive agents distributed along the vessel wall affect endothelial cells and regulate biological processes, such as thrombus formation, atherogenesis, and vascular remodeling. To calculate the concentration of solutes in the boundary layer, researchers have generally used numerical simulations. However, to investigate the effect of blood flow, infusion rate, and vessel geometry on the concentration of different solutes, many simulations are needed, leading to a time-consuming effort. In this paper, a relatively simple formula to quantify concentrations in a tube downstream of an infusion/release region is presented. Given known blood-flow rates, tube radius, solute diffusivity, and the length of the infusion region, this formula can be used to quickly estimate solute concentrations when infusion rates are known or to estimate infusion rates when solute concentrations at a point downstream of the infusion region are known. The developed formula is based on boundary layer theory and physical principles. The formula is an approximate solution of the advection-diffusion equations in the boundary layer region when solute concentration is small (dilute solution), infusion rate is modeled as a mass flux, and there is no transport of solute through the wall or chemical reactions downstream of the infusion region. Wall concentrations calculated using the formula developed in this paper were compared to the results from finite element models. Agreement between the results was within 10%. The developed formula could be used in experimental procedures to evaluate drug efficacy, in the design of drug-eluting stents, and to calculate rates of release of bioactive substances at active surfaces using downstream concentration measurements. In addition to being simple and fast to use, the formula gives accurate quantifications of concentrations and infusion rates under steady-state and oscillatory flow conditions, and therefore can be used to estimate boundary layer concentrations under physiological conditions.

On corrected formula for irradiated graphene quantum conductivity

NASA Astrophysics Data System (ADS)

Firsova, N. E.

2017-09-01

Graphene membrane irradiated by weak activating periodic electric field in terahertz range is considered. The corrected formula for the graphene quantum conductivity is found. The obtained formula gives complex conjugate results when radiation polarization direction is clockwise or it is opposite clockwise. The found formula allows us to see that the graphene membrane is an oscillating contour. Its eigen frequency coincides with a singularity point of the conductivity and depends on the electrons concentration. So the graphene membrane could be used as an antenna or a transistor and its eigen frequency could be tuned by doping in a large terahertz-infrared frequency range. The obtained formula allows us also to calculate the graphene membrane quantum inductivity and capacitance. The found dependence on electrons concentration is consistent with experiments. The method of the proof is based on study of the time-dependent density matrix. The exact solution of von Neumann equation for density matrix is found for our case in linear approximation on the external field. On this basis the induced current is studied and then the formula for quantum conductivity as a function of external field frequency and temperature is obtained. The method of the proof suggested in this paper could be used to study other problems. The found formula for quantum conductivity can be used to correct the SPPs Dispersion Relation and for the description of radiation process. It would be useful to take the obtained results into account when constructing devices containing graphene membrane nanoantenna. Such project could make it possible to create wireless communications among nanosystems. This would be promising research area of energy harvesting applications.

Infinite time interval backward stochastic differential equations with continuous coefficients.

PubMed

Zong, Zhaojun; Hu, Feng

2016-01-01

In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704-718, 2013).

Higher-order jump conditions for conservation laws

NASA Astrophysics Data System (ADS)

Oksuzoglu, Hakan

2018-04-01

The hyperbolic conservation laws admit discontinuous solutions where the solution variables can have finite jumps in space and time. The jump conditions for conservation laws are expressed in terms of the speed of the discontinuity and the state variables on both sides. An example from the Gas Dynamics is the Rankine-Hugoniot conditions for the shock speed. Here, we provide an expression for the acceleration of the discontinuity in terms of the state variables and their spatial derivatives on both sides. We derive a jump condition for the shock acceleration. Using this general expression, we show how to obtain explicit shock acceleration formulas for nonlinear hyperbolic conservation laws. We start with the Burgers' equation and check the derived formula with an analytical solution. We next derive formulas for the Shallow Water Equations and the Euler Equations of Gas Dynamics. We will verify our formulas for the Euler Equations using an exact solution for the spherically symmetric blast wave problem. In addition, we discuss the potential use of these formulas for the implementation of shock fitting methods.

Darboux Transformation and N-soliton Solution for Extended Form of Modified Kadomtsev—Petviashvili Equation with Variable-Coefficient

NASA Astrophysics Data System (ADS)

Luo, Xing-Yu; Chen, Yong

2016-08-01

The extended form of modified Kadomtsev—Petviashvili equation with variable-coefficient is investigated in the framework of Painlevé analysis. The Lax pairs are obtained by analysing two Painlevé branches of this equation. Starting with the Lax pair, the N-times Darboux transformation is constructed and the N-soliton solution formula is given, which contains 2n free parameters and two arbitrary functions. Furthermore, with different combinations of the parameters, several types of soliton solutions are calculated from the first order to the third order. The regularity conditions are discussed in order to avoid the singularity of the solutions. Moreover, we construct the generalized Darboux transformation matrix by considering a special limiting process and find a rational-type solution for this equation. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos. 11275072 and 11435005, Doctoral Program of Higher Education of China under Grant No. 20120076110024, The Network Information Physics Calculation of basic research innovation research group of China under Grant No. 61321064, Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, Shanghai Minhang District talents of high level scientific research project

On static black holes solutions in Einstein and Einstein-Gauss-Bonnet gravity with topology [Formula: see text].

PubMed

Dadhich, Naresh; Pons, Josep M

We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with the topology of the product of two spheres, [Formula: see text], in higher dimensions. There is an unusual new feature of the Gauss-Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of [Formula: see text]. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for [Formula: see text] is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature.

Differential invariants in nonclassical models of hydrodynamics

NASA Astrophysics Data System (ADS)

Bublik, Vasily V.

2017-10-01

In this paper, differential invariants are used to construct solutions for equations of the dynamics of a viscous heat-conducting gas and the dynamics of a viscous incompressible fluid modified by nanopowder inoculators. To describe the dynamics of a viscous heat-conducting gas, we use the complete system of Navier—Stokes equations with allowance for heat fluxes. Mathematical description of the dynamics of liquid metals under high-energy external influences (laser radiation or plasma flow) includes, in addition to the Navier—Stokes system of an incompressible viscous fluid, also heat fluxes and processes of nonequilibrium crystallization of a deformable fluid. Differentially invariant solutions are a generalization of partially invariant solutions, and their active study for various models of continuous medium mechanics is just beginning. Differentially invariant solutions can also be considered as solutions with differential constraints; therefore, when developing them, the approaches and methods developed by the science schools of academicians N. N. Yanenko and A. F. Sidorov will be actively used. In the construction of partially invariant and differentially invariant solutions, there are overdetermined systems of differential equations that require a compatibility analysis. The algorithms for reducing such systems to involution in a finite number of steps are described by Cartan, Finikov, Kuranishi, and other authors. However, the difficultly foreseeable volume of intermediate calculations complicates their practical application. Therefore, the methods of computer algebra are actively used here, which largely helps in solving this difficult problem. It is proposed to use the constructed exact solutions as tests for formulas, algorithms and their software implementations when developing and creating numerical methods and computational program complexes. This combination of effective numerical methods, capable of solving a wide class of problems, with analytical methods makes it possible to make the results of mathematical modeling more accurate and reliable.

Comments on new multiple-brane solutions based on Hata-Kojita duality in open string field theory

NASA Astrophysics Data System (ADS)

Masuda, Toru

2014-05-01

Recently, Hata and Kojita proposed a new energy formula for a class of solutions in Witten's open string field theory based on a novel symmetry of correlation functions they found. Their energy formula can be regarded as a generalization of the conventional energy formula by Murata and Schnabl. Following their proposal, we investigate their new ansatz for the classical solution representing double D-branes. We present a regularized definition of this solution and show that the solution satisfies the equation of motion when it is contracted with the solution itself and when it is contracted with any states in the Fock space. However, the Ellwood invariant and the boundary state of the solution are the same as those for the perturbative vacuum. This result disagrees with an expectation from the Ellwood conjecture.

SART-Type Half-Threshold Filtering Approach for CT Reconstruction.

PubMed

Yu, Hengyong; Wang, Ge

2014-01-01

The [Formula: see text] regularization problem has been widely used to solve the sparsity constrained problems. To enhance the sparsity constraint for better imaging performance, a promising direction is to use the [Formula: see text] norm (0 < p < 1) and solve the [Formula: see text] minimization problem. Very recently, Xu et al. developed an analytic solution for the [Formula: see text] regularization via an iterative thresholding operation, which is also referred to as half-threshold filtering. In this paper, we design a simultaneous algebraic reconstruction technique (SART)-type half-threshold filtering framework to solve the computed tomography (CT) reconstruction problem. In the medical imaging filed, the discrete gradient transform (DGT) is widely used to define the sparsity. However, the DGT is noninvertible and it cannot be applied to half-threshold filtering for CT reconstruction. To demonstrate the utility of the proposed SART-type half-threshold filtering framework, an emphasis of this paper is to construct a pseudoinverse transforms for DGT. The proposed algorithms are evaluated with numerical and physical phantom data sets. Our results show that the SART-type half-threshold filtering algorithms have great potential to improve the reconstructed image quality from few and noisy projections. They are complementary to the counterparts of the state-of-the-art soft-threshold filtering and hard-threshold filtering.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

Analysis of water sorption isotherms of amorphous food materials by solution thermodynamics with relevance to glass transition: evaluation of plasticizing effect of water by the thermodynamic parameters.

PubMed

Shimazaki, Eriko; Tashiro, Akiko; Kumagai, Hitomi; Kumagai, Hitoshi

2017-04-01

Relation between the thermodynamic parameters obtained from water sorption isotherms and the degree of reduction in the glass transition temperature (T g ), accompanied by water sorption, was quantitatively studied. Two well-known glassy food materials namely, wheat gluten and maltodextrin were used as samples. The difference between the chemical potential of water in a solution and that of pure water ([Formula: see text]), the difference between the chemical potential of solid in a solution and that of a pure solid ([Formula: see text]), and the change in the integral Gibbs free energy ([Formula: see text]) were obtained by analyzing the water sorption isotherms using solution thermodynamics. The parameter [Formula: see text] correlated well with ΔT g (≡T g  - T g0 ; where T g0 is the glass transition temperature of dry material), which had been taken to be an index of plasticizing effect. This indicates that plasticizing effect of water on foods can be evaluated through the parameter [Formula: see text].

Green operators for low regularity spacetimes

NASA Astrophysics Data System (ADS)

Sanchez Sanchez, Yafet; Vickers, James

2018-02-01

In this paper we define and construct advanced and retarded Green operators for the wave operator on spacetimes with low regularity. In order to do so we require that the spacetime satisfies the condition of generalised hyperbolicity which is equivalent to well-posedness of the classical inhomogeneous problem with zero initial data where weak solutions are properly supported. Moreover, we provide an explicit formula for the kernel of the Green operators in terms of an arbitrary eigenbasis of H 1 and a suitable Green matrix that solves a system of second order ODEs.

A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

NASA Astrophysics Data System (ADS)

Xu, Jiuping; Li, Jun

2002-09-01

In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

Removal kinetics for gaseous NO and SO2 by an aqueous NaClO2 solution mist in a wet electrostatic precipitator.

PubMed

Park, Hyun-Woo; Park, Dong-Wha

2017-04-01

Removal kinetics for NO and SO 2 by NaClO 2 solution mist were investigated in a wet electrostatic precipitator. By varying the molar concentrations of NO, SO 2 , and NaClO 2 , the removal rates of NO and SO 2 confirmed to range from 34.8 to 72.9 mmol/m 3  s and 36.6 to 84.7 mmol/m 3  s, respectively, at a fixed gas residence time of 0.25 s. The rate coefficients of NO and SO 2 were calculated to be 0.679 (mmol/m 3 ) -0.33  s -1 and 1.401 (mmol/m 3 ) -0.1  s -1 based on the rates of the individual removal of NO and SO 2 . Simultaneous removal of NO and SO 2 investigated after the evaluation of removal rates for their individual treatment was performed. At a short gas residence time, SO 2 gas removed more quickly by a mist of NaClO 2 solution than NO gas in simultaneous removal experiments. This is because SO 2 gas, which has a relatively high solubility in solution, was absorbed more rapidly at the gas-liquid interface than NO gas. NO and SO 2 gases were absorbed as nitrite [Formula: see text] and sulfite [Formula: see text] ions, respectively, by the NaClO 2 solution mist at the gas-liquid interface. Then, [Formula: see text] and [Formula: see text] were oxidized to nitrate [Formula: see text] and sulfate [Formula: see text], respectively, by reactions with [Formula: see text], ClO 2 , HClO, and ClO in the liquid phase.

A New Newton-Like Iterative Method for Roots of Analytic Functions

ERIC Educational Resources Information Center

Otolorin, Olayiwola

2005-01-01

A new Newton-like iterative formula for the solution of non-linear equations is proposed. To derive the formula, the convergence criteria of the one-parameter iteration formula, and also the quasilinearization in the derivation of Newton's formula are reviewed. The result is a new formula which eliminates the limitations of other methods. There is…

Influence of spin and charge fluctuations on spectra of the two-dimensional Hubbard model.

PubMed

Sherman, A

2018-05-16

The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions [Formula: see text], temperatures [Formula: see text] and electron concentrations [Formula: see text] with t the intersite hopping constant. For all considered U the system exhibits a transition to the long-range antiferromagnetic order at [Formula: see text]. At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the U-T plane, the curve separating metallic solutions passes from [Formula: see text] at the highest temperatures to U  =  2t at [Formula: see text] for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low T, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for [Formula: see text] to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for [Formula: see text]. For [Formula: see text] and [Formula: see text] doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband. Obtained spectra feature waterfalls and Fermi arcs, which are similar to those observed in hole-doped cuprates.

A simple equation to estimate body fat percentage in children with overweightness or obesity: a retrospective study.

PubMed

Cortés-Castell, Ernesto; Juste, Mercedes; Palazón-Bru, Antonio; Monge, Laura; Sánchez-Ferrer, Francisco; Rizo-Baeza, María Mercedes

2017-01-01

Dual-energy X-ray absorptiometry (DXA) provides separate measurements of fat mass, fat-free mass and bone mass, and is a quick, accurate, and safe technique, yet one that is not readily available in routine clinical practice. Consequently, we aimed to develop statistical formulas to predict fat mass (%) and fat mass index (FMI) with simple parameters (age, sex, weight and height). We conducted a retrospective observational cross-sectional study in 416 overweight or obese patients aged 4-18 years that involved assessing adiposity by DXA (fat mass percentage and FMI), body mass index (BMI), sex and age. We randomly divided the sample into two parts (construction and validation). In the construction sample, we developed formulas to predict fat mass and FMI using linear multiple regression models. The formulas were validated in the other sample, calculating the intraclass correlation coefficient via bootstrapping. The fat mass percentage formula had a coefficient of determination of 0.65. This value was 0.86 for FMI. In the validation, the constructed formulas had an intraclass correlation coefficient of 0.77 for fat mass percentage and 0.92 for FMI. Our predictive formulas accurately predicted fat mass and FMI with simple parameters (BMI, sex and age) in children with overweight and obesity. The proposed methodology could be applied in other fields. Further studies are needed to externally validate these formulas.

A note on a corrector formula for the numerical solution of ordinary differential equations

NASA Technical Reports Server (NTRS)

Chien, Y.-C.; Agrawal, K. M.

1979-01-01

A new corrector formula for predictor-corrector methods for numerical solutions of ordinary differential equations is presented. Two considerations for choosing corrector formulas are given: (1) the coefficient in the error term and (2) its stability properties. The graph of the roots of an equation plotted against its stability region, of different values, is presented along with the tables that correspond to various corrector equations, including Hamming's and Milne and Reynolds'.

SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling.

PubMed

Luchko, Tyler; Blinov, Nikolay; Limon, Garrett C; Joyce, Kevin P; Kovalenko, Andriy

2016-11-01

Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing ([Formula: see text] for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining [Formula: see text] compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to [Formula: see text]. Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple [Formula: see text] correction improved agreement with experiment from [Formula: see text] to [Formula: see text], despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.

Universal formula for the holographic speed of sound

NASA Astrophysics Data System (ADS)

Anabalón, Andrés; Andrade, Tomás; Astefanesei, Dumitru; Mann, Robert

2018-06-01

We consider planar hairy black holes in five dimensions with a real scalar field in the Breitenlohner-Freedman window and derive a universal formula for the holographic speed of sound for any mixed boundary conditions of the scalar field. As an example, we numerically construct the most general class of planar black holes coupled to a single scalar field in the consistent truncation of type IIB supergravity that preserves the SO (3) × SO (3) R-symmetry group of the gauge theory. For this particular family of solutions, we find that the speed of sound exceeds the conformal value. From a phenomenological point of view, the fact that the conformal bound can be violated by choosing the right mixed boundary conditions is relevant for the existence of neutron stars with a certain mass-size relationship for which a large value of the speed of sound codifies a stiff equation of state. In the way, we also shed light on a puzzle regarding the appearance of the scalar charges in the first law. Finally, we generalize the formula of the speed of sound to arbitrary dimensional scalar-metric theories whose parameters lie within the Breitenlohner-Freedman window.

Frechet derivatives for shallow water ocean acoustic inverse problems

NASA Astrophysics Data System (ADS)

Odom, Robert I.

2003-04-01

For any inverse problem, finding a model fitting the data is only half the problem. Most inverse problems of interest in ocean acoustics yield nonunique model solutions, and involve inevitable trade-offs between model and data resolution and variance. Problems of uniqueness and resolution and variance trade-offs can be addressed by examining the Frechet derivatives of the model-data functional with respect to the model variables. Tarantola [Inverse Problem Theory (Elsevier, Amsterdam, 1987), p. 613] published analytical formulas for the basic derivatives, e.g., derivatives of pressure with respect to elastic moduli and density. Other derivatives of interest, such as the derivative of transmission loss with respect to attenuation, can be easily constructed using the chain rule. For a range independent medium the analytical formulas involve only the Green's function and the vertical derivative of the Green's function for the medium. A crucial advantage of the analytical formulas for the Frechet derivatives over numerical differencing is that they can be computed with a single pass of any program which supplies the Green's function. Various derivatives of interest in shallow water ocean acoustics are presented and illustrated by an application to the sensitivity of measured pressure to shallow water sediment properties. [Work supported by ONR.

Radon transport model into a porous ground layer of finite capacity

NASA Astrophysics Data System (ADS)

Parovik, Roman

2017-10-01

The model of radon transfer is considered in a porous ground layer of finite power. With the help of the Laplace integral transformation, a numerical solution of this model is obtained which is based on the construction of a generalized quadrature formula of the highest degree of accuracy for the transition to the original - the function of solving this problem. The calculated curves are constructed and investigated depending on the diffusion and advection coefficients.The work was a mathematical model that describes the effect of the sliding attachment (stick-slip), taking into account hereditarity. This model can be regarded as a mechanical model of earthquake preparation. For such a model was proposed explicit finite- difference scheme, on which were built the waveform and phase trajectories hereditarity effect of stick-slip.

Generalized enhanced suffix array construction in external memory.

PubMed

Louza, Felipe A; Telles, Guilherme P; Hoffmann, Steve; Ciferri, Cristina D A

2017-01-01

Suffix arrays, augmented by additional data structures, allow solving efficiently many string processing problems. The external memory construction of the generalized suffix array for a string collection is a fundamental task when the size of the input collection or the data structure exceeds the available internal memory. In this article we present and analyze [Formula: see text] [introduced in CPM (External memory generalized suffix and [Formula: see text] arrays construction. In: Proceedings of CPM. pp 201-10, 2013)], the first external memory algorithm to construct generalized suffix arrays augmented with the longest common prefix array for a string collection. Our algorithm relies on a combination of buffers, induced sorting and a heap to avoid direct string comparisons. We performed experiments that covered different aspects of our algorithm, including running time, efficiency, external memory access, internal phases and the influence of different optimization strategies. On real datasets of size up to 24 GB and using 2 GB of internal memory, [Formula: see text] showed a competitive performance when compared to [Formula: see text] and [Formula: see text], which are efficient algorithms for a single string according to the related literature. We also show the effect of disk caching managed by the operating system on our algorithm. The proposed algorithm was validated through performance tests using real datasets from different domains, in various combinations, and showed a competitive performance. Our algorithm can also construct the generalized Burrows-Wheeler transform of a string collection with no additional cost except by the output time.

Constrained minimization problems for the reproduction number in meta-population models.

PubMed

Poghotanyan, Gayane; Feng, Zhilan; Glasser, John W; Hill, Andrew N

2018-02-14

The basic reproduction number ([Formula: see text]) can be considerably higher in an SIR model with heterogeneous mixing compared to that from a corresponding model with homogeneous mixing. For example, in the case of measles, mumps and rubella in San Diego, CA, Glasser et al. (Lancet Infect Dis 16(5):599-605, 2016. https://doi.org/10.1016/S1473-3099(16)00004-9 ), reported an increase of 70% in [Formula: see text] when heterogeneity was accounted for. Meta-population models with simple heterogeneous mixing functions, e.g., proportionate mixing, have been employed to identify optimal vaccination strategies using an approach based on the gradient of the effective reproduction number ([Formula: see text]), which consists of partial derivatives of [Formula: see text] with respect to the proportions immune [Formula: see text] in sub-groups i (Feng et al. in J Theor Biol 386:177-187, 2015.  https://doi.org/10.1016/j.jtbi.2015.09.006 ; Math Biosci 287:93-104, 2017.  https://doi.org/10.1016/j.mbs.2016.09.013 ). These papers consider cases in which an optimal vaccination strategy exists. However, in general, the optimal solution identified using the gradient may not be feasible for some parameter values (i.e., vaccination coverages outside the unit interval). In this paper, we derive the analytic conditions under which the optimal solution is feasible. Explicit expressions for the optimal solutions in the case of [Formula: see text] sub-populations are obtained, and the bounds for optimal solutions are derived for [Formula: see text] sub-populations. This is done for general mixing functions and examples of proportionate and preferential mixing are presented. Of special significance is the result that for general mixing schemes, both [Formula: see text] and [Formula: see text] are bounded below and above by their corresponding expressions when mixing is proportionate and isolated, respectively.

Objective assessment based on motion-related metrics and technical performance in laparoscopic suturing.

PubMed

Sánchez-Margallo, Juan A; Sánchez-Margallo, Francisco M; Oropesa, Ignacio; Enciso, Silvia; Gómez, Enrique J

2017-02-01

The aim of this study is to present the construct and concurrent validity of a motion-tracking method of laparoscopic instruments based on an optical pose tracker and determine its feasibility as an objective assessment tool of psychomotor skills during laparoscopic suturing. A group of novice ([Formula: see text] laparoscopic procedures), intermediate (11-100 laparoscopic procedures) and experienced ([Formula: see text] laparoscopic procedures) surgeons performed three intracorporeal sutures on an ex vivo porcine stomach. Motion analysis metrics were recorded using the proposed tracking method, which employs an optical pose tracker to determine the laparoscopic instruments' position. Construct validation was measured for all 10 metrics across the three groups and between pairs of groups. Concurrent validation was measured against a previously validated suturing checklist. Checklists were completed by two independent surgeons over blinded video recordings of the task. Eighteen novices, 15 intermediates and 11 experienced surgeons took part in this study. Execution time and path length travelled by the laparoscopic dissector presented construct validity. Experienced surgeons required significantly less time ([Formula: see text]), travelled less distance using both laparoscopic instruments ([Formula: see text]) and made more efficient use of the work space ([Formula: see text]) compared with novice and intermediate surgeons. Concurrent validation showed strong correlation between both the execution time and path length and the checklist score ([Formula: see text] and [Formula: see text], [Formula: see text]). The suturing performance was successfully assessed by the motion analysis method. Construct and concurrent validity of the motion-based assessment method has been demonstrated for the execution time and path length metrics. This study demonstrates the efficacy of the presented method for objective evaluation of psychomotor skills in laparoscopic suturing. However, this method does not take into account the quality of the suture. Thus, future works will focus on developing new methods combining motion analysis and qualitative outcome evaluation to provide a complete performance assessment to trainees.

On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2004-01-01

Formulae expressing explicitly the Jacobi coefficients of a general-order derivative (integral) of an infinitely differentiable function in terms of its original expansion coefficients, and formulae for the derivatives (integrals) of Jacobi polynomials in terms of Jacobi polynomials themselves are stated. A formula for the Jacobi coefficients of the moments of one single Jacobi polynomial of certain degree is proved. Another formula for the Jacobi coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its original expanded coefficients is also given. A simple approach in order to construct and solve recursively for the connection coefficients between Jacobi-Jacobi polynomials is described. Explicit formulae for these coefficients between ultraspherical and Jacobi polynomials are deduced, of which the Chebyshev polynomials of the first and second kinds and Legendre polynomials are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Jacobi and Hermite-Jacobi are developed.

Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

PubMed Central

Song, Junqiang; Leng, Hongze; Lu, Fengshun

2014-01-01

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303

Asymptotics of a Class of Solutions to the Cylindrical Toda Equations

NASA Astrophysics Data System (ADS)

Tracy, Craig A.; Widom, Harold

The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, , have the representation where Kk$ are integral operators. This class includes the n-periodic cylindrical Toda equations. For n=2 our results reduce to the previously computed asymptotics of the 2D radial sinh-Gordon equation and for n=3 (and with an additional symmetry constraint) they reduce to earlier results for the radial Bullough-Dodd equation. Both of these special cases are examples of Painlevé III and have arisen in various applications. The asymptotics of are derived by computing the small t asymptotics where explicit formulas are given for the quantities ak and bk. The method consists of showing that the resolvent operator of Kk has an approximation in terms of resolvents of certain Wiener-Hopf operators, for which there are explicit integral formulas.

ON THE NUMBER OF SOLUTIONS OF THE EQUATION x^k = a IN THE SYMMETRIC GROUP S_n

NASA Astrophysics Data System (ADS)

Pavlov, A. I.

1981-04-01

This paper consists of three sections. In the first a formula is given for the number N_n^{(k)}(a) of solutions of the equation x^k = a in S_n depending on the cyclic structure of the permutation a. In the second an asymptotic formula is given for the quantity M_n^{(k)} = \\max_{a \\in S_n} N_n^{(k)}(a) for a fixed k \\geq 2 as n \\to \\infty. In the third an asymptotic formula is found for the cardinality of the set of permutations a such that the equation x^k = a has a unique solution. Bibliography: 5 titles.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

PubMed

Wu, Yang; Kelly, Damien P

2014-12-12

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method for the parameter estimation on geographically weighted ordinal logistic regression model (GWOLR)

NASA Astrophysics Data System (ADS)

Saputro, Dewi Retno Sari; Widyaningsih, Purnami

2017-08-01

In general, the parameter estimation of GWOLR model uses maximum likelihood method, but it constructs a system of nonlinear equations, making it difficult to find the solution. Therefore, an approximate solution is needed. There are two popular numerical methods: the methods of Newton and Quasi-Newton (QN). Newton's method requires large-scale time in executing the computation program since it contains Jacobian matrix (derivative). QN method overcomes the drawback of Newton's method by substituting derivative computation into a function of direct computation. The QN method uses Hessian matrix approach which contains Davidon-Fletcher-Powell (DFP) formula. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is categorized as the QN method which has the DFP formula attribute of having positive definite Hessian matrix. The BFGS method requires large memory in executing the program so another algorithm to decrease memory usage is needed, namely Low Memory BFGS (LBFGS). The purpose of this research is to compute the efficiency of the LBFGS method in the iterative and recursive computation of Hessian matrix and its inverse for the GWOLR parameter estimation. In reference to the research findings, we found out that the BFGS and LBFGS methods have arithmetic operation schemes, including O(n2) and O(nm).

Fast rotating neutron stars with realistic nuclear matter equation of state

NASA Astrophysics Data System (ADS)

Cipolletta, F.; Cherubini, C.; Filippi, S.; Rueda, J. A.; Ruffini, R.

2015-07-01

We construct equilibrium configurations of uniformly rotating neutron stars for selected relativistic mean-field nuclear matter equations of state (EOS). We compute, in particular, the gravitational mass (M ), equatorial (Req) and polar (Rpol) radii, eccentricity, angular momentum (J ), moment of inertia (I ) and quadrupole moment (M2) of neutron stars stable against mass shedding and secular axisymmetric instability. By constructing the constant frequency sequence f =716 Hz of the fastest observed pulsar, PSR J1748-2446ad, and constraining it to be within the stability region, we obtain a lower mass bound for the pulsar, Mmin=[1.2 - 1.4 ]M⊙ , for the EOS employed. Moreover, we give a fitting formula relating the baryonic mass (Mb) and gravitational mass of nonrotating neutron stars, Mb/M⊙=M /M⊙+(13 /200 )(M /M⊙)2 [or M /M⊙=Mb/M⊙-(1 /20 )(Mb/M⊙)2], which is independent of the EOS. We also obtain a fitting formula, although not EOS independent, relating the gravitational mass and the angular momentum of neutron stars along the secular axisymmetric instability line for each EOS. We compute the maximum value of the dimensionless angular momentum, a /M ≡c J /(G M2) (or "Kerr parameter"), (a /M )max≈0.7 , found to be also independent of the EOS. We then compare and contrast the quadrupole moment of rotating neutron stars with the one predicted by the Kerr exterior solution for the same values of mass and angular momentum. Finally, we show that, although the mass quadrupole moment of realistic neutron stars never reaches the Kerr value, the latter is closely approached from above at the maximum mass value, as physically expected from the no-hair theorem. In particular, the stiffer the EOS, the closer the mass quadrupole moment approaches the value of the Kerr solution.

The Lorentzian distance formula in noncommutative geometry

NASA Astrophysics Data System (ADS)

Franco, Nicolas

2018-02-01

For almost twenty years, a search for a Lorentzian version of the well-known Connes’ distance formula has been undertaken. Several authors have contributed to this search, providing important milestones, and the time has now come to put those elements together in order to get a valid and functional formula. This paper presents a historical review of the construction and the proof of a Lorentzian distance formula suitable for noncommutative geometry.

Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields.

DTIC Science & Technology

perturbation formulas of Groebner (1960) and Alexseev (1961) for the solution of ordinary differential equations. These formulas are generalized and...iteration methods are given, which include the Methods of Picard, Groebner -Knapp, Poincare, Chen, as special cases. Chapter 3 generalizes an iterated

The new model of the Big Bang and the Universe expansion. A comparison with modern observational data and cosmological theories

NASA Astrophysics Data System (ADS)

Kraiko, A. N.; Valiyev, Kh. F.

2016-10-01

The new model of the Big Bang and the Universe expansion is constructed. It is based on solutions in classical and in relativistic statements of problem on the dispersion into the void of the gas compressed into a point or in a finite, but for further negligible, volume. If to restrict in relativistic statement gas speed value v by the speed of light (υ =| v |

Solution of the wave equation for open surfaces involving a line integral over the edge. [for supersonic propeller noise prediction

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

A simple mathematical model of a stationary source distribution for the supersonic-propeller noise-prediction formula of Farassat (1983) is developed to test the validity of the formula solutions. The conventional thickness source term is used in place of the Isom thickness formula; the relative importance of the line and surface integrals in the solutions is evaluated; and the numerical results are compared with those obtained with a conventional retarded-time solution in tables. Good agreement is obtained over elevation angles from 10 to 90 deg, and the line-integral contribution is found to be significant at all elevation angles and of the same order of magnitude as the surface-integral contribution at angles less than 30 deg. The amplitude-normalized directivity patterns for the four cases computed (x = 1.5 or 10; k = 5.0 or 50) are presented graphically.

A Malaria Transmission Model with Temperature-Dependent Incubation Period.

PubMed

Wang, Xiunan; Zhao, Xiao-Qiang

2017-05-01

Malaria is an infectious disease caused by Plasmodium parasites and is transmitted among humans by female Anopheles mosquitoes. Climate factors have significant impact on both mosquito life cycle and parasite development. To consider the temperature sensitivity of the extrinsic incubation period (EIP) of malaria parasites, we formulate a delay differential equations model with a periodic time delay. We derive the basic reproduction ratio [Formula: see text] and establish a threshold type result on the global dynamics in terms of [Formula: see text], that is, the unique disease-free periodic solution is globally asymptotically stable if [Formula: see text]; and the model system admits a unique positive periodic solution which is globally asymptotically stable if [Formula: see text]. Numerically, we parameterize the model with data from Maputo Province, Mozambique, and simulate the long-term behavior of solutions. The simulation result is consistent with the obtained analytic result. In addition, we find that using the time-averaged EIP may underestimate the basic reproduction ratio.

Formulae and Flow-Diagrams

ERIC Educational Resources Information Center

Willson, William Wynne

1977-01-01

The author recommends the use of flow charting to help students understand the manipulation of algebraic formulae. He identifies some problems with flow charts and suggests an alternative method of constructing flow diagrams. (SD)

Geometrically derived difference formulae for the numerical integration of trajectory problems

NASA Technical Reports Server (NTRS)

Mcleod, R. J. Y.; Sanz-Serna, J. M.

1981-01-01

The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested.

Existence of weak solutions to degenerate p-Laplacian equations and integral formulas

NASA Astrophysics Data System (ADS)

Chua, Seng-Kee; Wheeden, Richard L.

2017-12-01

We study the problem of solving some general integral formulas and then apply the conclusions to obtain results about the existence of weak solutions of various degenerate p-Laplacian equations. We adapt Variational Calculus methods and the Mountain Pass Lemma without the Palais-Smale condition, and we use an abstract version of Lions' Concentration Compactness Principle II.

Correlation Relation for the Membrane Transport ParametersL(p), σ, and ω.

PubMed

Kargol, A; Kargol, M; Przestalski, S

1997-12-01

We derive a formula for the correlation of the three practical transportparameters L(p), σ, and ω appearing in Kedem-Katchalskyequations. It has a form ω = KL(p)/v(s)(1-σ), where K = 0.0306 is a universal constant independent ofthe choice of a membrane and a solute. It can be used to calculate the valueof any of these parameters, provided the other two and the molar volume[Formula: see text] of the solute are known. The formula couldbe very useful, in particular when measurements of the parameters aredifficult or even impossible.

A reaction-diffusion malaria model with seasonality and incubation period.

PubMed

Bai, Zhenguo; Peng, Rui; Zhao, Xiao-Qiang

2018-07-01

In this paper, we propose a time-periodic reaction-diffusion model which incorporates seasonality, spatial heterogeneity and the extrinsic incubation period (EIP) of the parasite. The basic reproduction number [Formula: see text] is derived, and it is shown that the disease-free periodic solution is globally attractive if [Formula: see text], while there is an endemic periodic solution and the disease is uniformly persistent if [Formula: see text]. Numerical simulations indicate that prolonging the EIP may be helpful in the disease control, while spatial heterogeneity of the disease transmission coefficient may increase the disease burden.

New non-naturally reductive Einstein metrics on exceptional simple Lie groups

NASA Astrophysics Data System (ADS)

Chen, Huibin; Chen, Zhiqi; Deng, Shaoqiang

2018-01-01

In this article, we construct several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are found through the decomposition arising from generalized Wallach spaces. Using the decomposition corresponding to the two involutions, we calculate the non-zero coefficients in the formulas of the components of Ricci tensor with respect to the given metrics. The Einstein metrics are obtained as solutions of a system of polynomial equations, which we manipulate by symbolic computations using Gröbner bases. In particular, we discuss the concrete numbers of non-naturally reductive Einstein metrics for each case up to isometry and homothety.

N-fold Darboux Transformation for Integrable Couplings of AKNS Equations

NASA Astrophysics Data System (ADS)

Yu, Jing; Chen, Shou-Ting; Han, Jing-Wei; Ma, Wen-Xiu

2018-04-01

For the integrable couplings of Ablowitz-Kaup-Newell-Segur (ICAKNS) equations, N-fold Darboux transformation (DT) TN, which is a 4 × 4 matrix, is constructed in this paper. Each element of this matrix is expressed by a ratio of the (4N + 1)-order determinant and 4N-order determinant of eigenfunctions. By making use of these formulae, the determinant expressions of N-transformed new solutions p [N], q [N], r [N] and s [N] are generated by this N-fold DT. Furthermore, when the reduced conditions q = ‑p* and s = ‑r* are chosen, we obtain determinant representations of N-fold DT and N-transformed solutions for the integrable couplings of nonlinear Schrödinger (ICNLS) equations. Starting from the zero seed solutions, one-soliton solutions are explicitly given as an example. Supported by the National Natural Science Foundation of China under Grant Nos. 61771174, 11371326, 11371361, 11301454, and 11271168, Natural Science Fund for Colleges and Universities of Jiangsu Province of China under Grant No. 17KJB110020, and General Research Project of Department of Education of Zhejiang Province (Y201636538)

Unconventional Expressions: Productive Syntax in the L2 Acquisition of Formulaic Language

ERIC Educational Resources Information Center

Bardovi-Harlig, Kathleen; Stringer, David

2017-01-01

This article presents a generative analysis of the acquisition of formulaic language as an alternative to current usage-based proposals. One influential view of the role of formulaic expressions in second language (L2) development is that they are a bootstrapping mechanism into the L2 grammar; an initial repertoire of constructions allows for…

A structured population model with diffusion in structure space.

PubMed

Pugliese, Andrea; Milner, Fabio

2018-05-09

A structured population model is described and analyzed, in which individual dynamics is stochastic. The model consists of a PDE of advection-diffusion type in the structure variable. The population may represent, for example, the density of infected individuals structured by pathogen density x, [Formula: see text]. The individuals with density [Formula: see text] are not infected, but rather susceptible or recovered. Their dynamics is described by an ODE with a source term that is the exact flux from the diffusion and advection as [Formula: see text]. Infection/reinfection is then modeled moving a fraction of these individuals into the infected class by distributing them in the structure variable through a probability density function. Existence of a global-in-time solution is proven, as well as a classical bifurcation result about equilibrium solutions: a net reproduction number [Formula: see text] is defined that separates the case of only the trivial equilibrium existing when [Formula: see text] from the existence of another-nontrivial-equilibrium when [Formula: see text]. Numerical simulation results are provided to show the stabilization towards the positive equilibrium when [Formula: see text] and towards the trivial one when [Formula: see text], result that is not proven analytically. Simulations are also provided to show the Allee effect that helps boost population sizes at low densities.

Integer Solutions of Binomial Coefficients

ERIC Educational Resources Information Center

Gilbertson, Nicholas J.

2016-01-01

A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation…

Correlation between crystallographic anisotropy and dendritic orientation selection of binary magnesium alloys.

PubMed

Du, Jinglian; Guo, Zhipeng; Zhang, Ang; Yang, Manhong; Li, Mei; Xiong, Shoumei

2017-10-19

Both synchrotron X-ray tomography and EBSD characterization revealed that the preferred growth directions of magnesium alloy dendrite change as the type and amount of solute elements. Such growth behavior was further investigated by evaluating the orientation-dependent surface energy and the subsequent crystallographic anisotropy via ab-initio calculations based on density functional theory and hcp lattice structure. It was found that for most binary magnesium alloys, the preferred growth direction of the α-Mg dendrite in the basal plane is always [Formula: see text], and independent on either the type or concentration of the additional elements. In non-basal planes, however, the preferred growth direction is highly dependent on the solute concentration. In particular, for Mg-Al alloys, this direction changes from [Formula: see text] to [Formula: see text] as the Al-concentration increased, and for Mg-Zn alloys, this direction changes from [Formula: see text] to [Formula: see text] or [Formula: see text] as the Zn-content varied. Our results provide a better understanding on the dendritic orientation selection and morphology transition of magnesium alloys at the atomic level.

Simultaneous removal of SO2 and NOx from flue gas by wet scrubbing using a urea solution.

PubMed

Li, Ge; Wang, Baodong; Xu, Wayne Qiang; Li, Yonglong; Han, Yifan; Sun, Qi

2018-03-27

Nitrogen oxides (NO x ) and sulfur dioxide (SO 2 ) are major air pollutants, so simultaneously removing them from gases emitted during fossil fuel combustion in stationary systems is important. Wet denitrification using urea is used for a wide range of systems. Additives have strong effects on wet denitrification using urea, and different mechanisms are involved and different effects found using different additives. In this study, the effects of different additives, initial urea concentrations, reaction temperatures, initial pH values, gas flow rates, and reaction times on the simultaneous desulfurization and denitrification efficiencies achieved using wet denitrification using urea were studied in single factor experiment. The optimum reaction conditions for desulfurization and denitrification were found. Desulfurization and denitrification efficiencies of 97.5% and 96.3%, respectively, were achieved at a KMnO 4 concentration 5 mmol/L, a reaction temperature of 70°C, initial urea solution pH 8, a urea concentration of 9%, and a gas flow rate of 40 L/h. The concentrations of the desulfurization and denitrification reaction products in the solution were determined. NO x was mainly transformed into N 2 , and the [Formula: see text] and [Formula: see text] concentrations in the solution became very low. The reactions involved in SO 2 and NO x removal using urea were analyzed from the thermodynamic viewpoint. Increasing the temperature was not conducive to the reactions but increased the rate constant, so an optimum temperature was determined. The simultaneous desulfurization and denitrification kinetics were calculated. The urea consumption and [Formula: see text], [Formula: see text], and [Formula: see text] generation reactions were all zero order. The [Formula: see text] generation rate was greater than the [Formula: see text] generation rate. The simultaneous desulfurization and denitrification process and mechanism were studied. The results provide reference data for performing flue gas desulfurization and denitrification in factories.

Circularly polarized few-cycle optical rogue waves: rotating reduced Maxwell-Bloch equations.

PubMed

Xu, Shuwei; Porsezian, K; He, Jingsong; Cheng, Yi

2013-12-01

The rotating reduced Maxwell-Bloch (RMB) equations, which describe the propagation of few-cycle optical pulses in a transparent media with two isotropic polarized electronic field components, are derived from a system of complete Maxwell-Bloch equations without using the slowly varying envelope approximations. Two hierarchies of the obtained rational solutions, including rogue waves, which are also called few-cycle optical rogue waves, of the rotating RMB equations are constructed explicitly through degenerate Darboux transformation. In addition to the above, the dynamical evolution of the first-, second-, and third-order few-cycle optical rogue waves are constructed with different patterns. For an electric field E in the three lower-order rogue waves, we find that rogue waves correspond to localized large amplitude oscillations of the polarized electric fields. Further a complementary relationship of two electric field components of rogue waves is discussed in terms of analytical formulas as well as numerical figures.

Transport of a decay chain in homogenous porous media: analytical solutions.

PubMed

Bauer, P; Attinger, S; Kinzelbach, W

2001-06-01

With the aid of integral transforms, analytical solutions for the transport of a decay chain in homogenous porous media are derived. Unidirectional steady-state flow and radial steady-state flow in single and multiple porosity media are considered. At least in Laplace domain, all solutions can be written in closed analytical formulae. Partly, the solutions can also be inverted analytically. If not, analytical calculation of the steady-state concentration distributions, evaluation of temporal moments and numerical inversion are still possible. Formulae for several simple boundary conditions are given and visualized in this paper. The derived novel solutions are widely applicable and are very useful for the validation of numerical transport codes.

The inventions technology on water resources to support environmental engineering based infrastructure

NASA Astrophysics Data System (ADS)

Sunjoto, S.

2017-03-01

Since the Stockholm Declaration, declared on the United Nation Conference on the Human Environment in Sweden on 5-16 June 1972 and attended the 113 country delegations, all the infrastructure construction should comply the sustainable development. As a consequence, almost research and studies were directing to the environmental aspect of construction including on water resources engineering. This paper will present the inventions which are very useful for the design of infrastructure, especially on the Groundwater engineering. This field has been rapidly developed since the publication of the well known law of flow through porous materials by Henri Darcy in 1856 on his book "Les fontaine publiques de la ville de Dijon". This law states that the discharge through porous media is proportional to the product of the hydraulic gradient, the cross-sectional area normal to the flow and the coefficient of permeability of the material. Forchheimer in 1930 developed a breakthrough formula by simplifying solution in a steady state flow condition especially in the case of radial flow to compute the permeability coefficient of casing hole or tube test with zero inflow discharge. The outflow discharge on the holes is equal to shape factor of tip of casing (F) multiplied by coefficient of permeability of soils (K) and multiplied by hydraulic head (H). In 1988, Sunjoto derived an equation in unsteady state flow condition based on this formula. In 2002, Sunjoto developed several formulas of shape factor as the parameters of the equation. In the beginning this formula is implemented to compute for the dimension of recharge well as the best method of water conservation for the urban area. After a long research this formula can be implemented to compute the drawdown on pumping or coefficient of permeability of soil by pumping test. This method can substitute the former methods like Theis (1935), Cooper-Jacob (1946), Chow (1952), Glover (1966), Papadopulos-Cooper (1967), Todd (1980), Singh (2000) etc. The advantages of Sunjoto's equation compared to the former methods that it is simpler in equation, easier to compute, doesn't need graphical support, is accurate in result and doesn't need observation well in pumping test, due to its need on drawdown on well function duration of pumping data only.

Weak convergence to isotropic complex [Formula: see text] random measure.

PubMed

Wang, Jun; Li, Yunmeng; Sang, Liheng

2017-01-01

In this paper, we prove that an isotropic complex symmetric α -stable random measure ([Formula: see text]) can be approximated by a complex process constructed by integrals based on the Poisson process with random intensity.

Gravitational vacuum condensate stars.

PubMed

Mazur, Pawel O; Mottola, Emil

2004-06-29

A new final state of gravitational collapse is proposed. By extending the concept of Bose-Einstein condensation to gravitational systems, a cold, dark, compact object with an interior de Sitter condensate p(v) = -rho(v) and an exterior Schwarzschild geometry of arbitrary total mass M is constructed. These regions are separated by a shell with a small but finite proper thickness l of fluid with equation of state p = +rho, replacing both the Schwarzschild and de Sitter classical horizons. The new solution has no singularities, no event horizons, and a global time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of the order k(B)lMc/Planck's over 2 pi, instead of the Bekenstein-Hawking entropy formula, S(BH) = 4 pi k(B)GM(2)/Planck's over 2 pi c. Hence, unlike black holes, the new solution is thermodynamically stable and has no information paradox.

Accuracy of analytic energy level formulas applied to hadronic spectroscopy of heavy mesons

NASA Technical Reports Server (NTRS)

Badavi, Forooz F.; Norbury, John W.; Wilson, John W.; Townsend, Lawrence W.

1988-01-01

Linear and harmonic potential models are used in the nonrelativistic Schroedinger equation to obtain article mass spectra for mesons as bound states of quarks. The main emphasis is on the linear potential where exact solutions of the S-state eigenvalues and eigenfunctions and the asymptotic solution for the higher order partial wave are obtained. A study of the accuracy of two analytical energy level formulas as applied to heavy mesons is also included. Cornwall's formula is found to be particularly accurate and useful as a predictor of heavy quarkonium states. Exact solution for all partial waves of eigenvalues and eigenfunctions for a harmonic potential is also obtained and compared with the calculated discrete spectra of the linear potential. Detailed derivations of the eigenvalues and eigenfunctions of the linear and harmonic potentials are presented in appendixes.

Scalar hairy black holes and scalarons in the isolated horizons formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corichi, Alejandro; Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, A. Postal 61-3, Morelia, Michoacan, 58090; Nucamendi, Ulises

The Isolated Horizons (IH) formalism, together with a simple phenomenological model for colored black holes has been used to predict nontrivial formulas that relate the ADM mass of the solitons and hairy Black Holes of Gravity-Matter system on the one hand, and several horizon properties of the black holes in the other. In this article, the IH formalism is tested numerically for spherically symmetric solutions to an Einstein-Higgs system where hairy black holes were recently found to exist. It is shown that the mass formulas still hold and that, by appropriately extending the current model, one can account for themore » behavior of the horizon properties of these new solutions. An empirical formula that approximates the ADM mass of hairy solutions is put forward, and some of its properties are analyzed.« less

The symbolic computation of series solutions to ordinary differential equations using trees (extended abstract)

NASA Technical Reports Server (NTRS)

Grossman, Robert

1991-01-01

Algorithms previously developed by the author give formulas which can be used for the efficient symbolic computation of series expansions to solutions of nonlinear systems of ordinary differential equations. As a by product of this analysis, formulas are derived which relate to trees to the coefficients of the series expansions, similar to the work of Leroux and Viennot, and Lamnabhi, Leroux and Viennot.

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

Precise and versatile formula for birefringent filters

NASA Astrophysics Data System (ADS)

Shao, Zhongxing

1996-07-01

In an investigation of extraordinary-(E-) ray behavior and the index of refraction for E waves in a uniaxial crystal, a precise and versatile formula for birefringent filters, based on the exact construction of the optical path difference, is set up with neither the approximation Delta n = no - ne less than or equals no (or n e), nor the ambiguity sin( theta )/sin(rw) = ne. The exact construction gives the correct variation of the position and the dimension in each path, yielding the path difference while the filter is tuning. The formula is applicable not only to a filter with its optical axis parallel to the entrance surface (FAPS) but also to a filter with its axis inclined to the surface (FAIS). Also, the formula indicates that a FAIS allows laser wavelengths to be tuned over a wider range than does a FAPS. The origin of the wider range is interpreted to be the greater variation in the index for the FAIS while the filter is tuning. With the help of the formula we design a FAIS for tuning a cw 42.25.Lc.

Distributed modeling of diffusive solute transport in peritoneal dialysis.

PubMed

Waniewski, Jacek

2002-01-01

The diffusive transport between blood and an ex-tissue medium (dialysis fluid) is evaluated using a mathematical model that takes into account the (quasicontinuous) distribution of capillaries within the tissue at various distances from the tissue surface, and includes diffusive-convective transport through the capillary wall and lymphatic absorption from the tissue. General formulas for solute penetration depth, lambda, and for the diffusive mass transport coefficient for the transport between blood and dialysis fluid, K(BD), are provided in terms of local transport coefficients for capillary wall, tissue, and lymphatic absorption. For pure diffusive transport between blood and dialysis fluid and thick tissue layers (i.e., if the solute penetration depth is much lower than the tissue thickness) these formulas yield previously known expressions. It is shown that apparent tissue layers, with widths lambdaTBL and lambdaT, respectively, may be defined according to the values of local transport parameters in such a way that K(BD) is equal to the solute clearance K(TBL) from the tissue by blood and lymph for a layer with width lambdaTBL or to the solute clearance K(T) from blood to dialysate by diffusion through the tissue layer with width lambdaT. For tissue layers with width much higher than the penetration depth: lambdaT approximately = lambdaTBL approximately = lambda. These characteristic width lengths depend on the transport parameters (and thus on the size) of solutes. Effective blood flow, which may be related to the exchange of the solute between blood and dialysate, is defined using an analogy to the extraction/absorption coefficients for blood-tissue exchange. Various approximations for the distributed model formula for diffusive mass transport coefficient (K(BD)) are possible. The appropriate range for their application is obtained from the general formula.

Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation.

PubMed

Mohamad, Ahmad Qushairi; Khan, Ilyas; Ismail, Zulkhibri; Shafie, Sharidan

2016-01-01

Non-coaxial rotation has wide applications in engineering devices, e.g. in food processing such as mixer machines and stirrers with a two-axis kneader, in cooling turbine blades, jet engines, pumps and vacuum cleaners, in designing thermal syphon tubes, and in geophysical flows. Therefore, this study aims to investigate unsteady free convection flow of viscous fluid due to non-coaxial rotation and fluid at infinity over an oscillating vertical plate with constant wall temperature. The governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time ( t ), the Grashof number ( Gr ), the Prandtl number ([Formula: see text]), and the phase angle ([Formula: see text]). Skin friction and the Nusselt number are also evaluated. The exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver-Stehfest algorithm. The interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time ( t ), the Grashof number ( Gr ), the Prandtl number ([Formula: see text]), and the phase angle ([Formula: see text]).

An approximate formula for recalescence in binary eutectic alloys

NASA Technical Reports Server (NTRS)

Ohsaka, K.; Trinh, E. H.

1993-01-01

In alloys, solidification takes place along various paths which may be ascertained via phase diagrams; while there would be no single formula applicable to all alloys, an approximate formula for a specific solidification path would be useful in estimating the fraction of the solid formed during recalescence. A formulation is here presented of recalescence in binary eutectic alloys. This formula is applied to Ag-Cu alloys which are of interest in containerless solidification, due to their formation of supersaturated solutions.

Protection zone in a diffusive predator-prey model with Beddington-DeAngelis functional response.

PubMed

He, Xiao; Zheng, Sining

2017-07-01

In any reaction-diffusion system of predator-prey models, the population densities of species are determined by the interactions between them, together with the influences from the spatial environments surrounding them. Generally, the prey species would die out when their birth rate is too low, the habitat size is too small, the predator grows too fast, or the predation pressure is too high. To save the endangered prey species, some human interference is useful, such as creating a protection zone where the prey could cross the boundary freely but the predator is prohibited from entering. This paper studies the existence of positive steady states to a predator-prey model with reaction-diffusion terms, Beddington-DeAngelis type functional response and non-flux boundary conditions. It is shown that there is a threshold value [Formula: see text] which characterizes the refuge ability of prey such that the positivity of prey population can be ensured if either the prey's birth rate satisfies [Formula: see text] (no matter how large the predator's growth rate is) or the predator's growth rate satisfies [Formula: see text], while a protection zone [Formula: see text] is necessary for such positive solutions if [Formula: see text] with [Formula: see text] properly large. The more interesting finding is that there is another threshold value [Formula: see text], such that the positive solutions do exist for all [Formula: see text]. Letting [Formula: see text], we get the third threshold value [Formula: see text] such that if [Formula: see text], prey species could survive no matter how large the predator's growth rate is. In addition, we get the fourth threshold value [Formula: see text] for negative [Formula: see text] such that the system admits positive steady states if and only if [Formula: see text]. All these results match well with the mechanistic derivation for the B-D type functional response recently given by Geritz and Gyllenberg (J Theoret Biol 314:106-108, 2012). Finally, we obtain the uniqueness of positive steady states for [Formula: see text] properly large, as well as the asymptotic behavior of the unique positive steady state as [Formula: see text].

Equivalence of quantum Boltzmann equation and Kubo formula for dc conductivity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Su, Z.B.; Chen, L.Y.

1990-02-01

This paper presents a derivation of the quantum Boltzmann equation for linear dc transport with a correction term to Mahan-Hansch's equations and derive a formal solution to it. Based on this formal solution, the authors find the electric conductivity can be expressed as the retarded current-current correlation. Therefore, the authors explicitly demonstrate the equivalence of the two most important theoretical methods: quantum Boltzmann equation and Kubo formula.

Neutron scattering on solitons in quasi-one-dimensional systems

NASA Astrophysics Data System (ADS)

Fedyanin, V. K.

1983-05-01

In the framework of the model of an ideal lattice gas of solitons, we obtain the following general formula for the dynamic neutron scattering form factor: S(q, w) = N¯S 1(q, w) , S(q, w) = {p‧(ν 0)δ 22}/{2πqZ 1h }f 2(qδ(ν 0 Here q = k‧ - k and w = E‧ - E are the neutron momentum and energy transfer, respectively, ν0 = wq-1, δ(ν) is the soliton width of velocity ν, p‧( ν0) = d p/d ν| ν0 , p(ν) is the soliton momentum, E(p(ν)) is the soliton energy, N¯ is the average number of solitons at θ = kδT = β-1 and is constructed from the soliton non-linear differential equations. The derivation of the formula is essentially based on (i) specific dependence of these solutions on ξ = x - vt, and (ii) generalization of the averaging over the soliton ensemble, proposed in ref. [1]. The specifi properties of the scattering spectra of polypeptides, DNA molecules and magnetics as functions of the temperature and interaction parameters and of external fields are discussed on the basis of this formula. The contribution to S(q, w) for “slow” solitons in magnetics has been calculated in [2, 3]. (For each concrete model the authors were forced to formulate anew the way of calculation, to assume the small size of ν, etc.)

Approximate formulas for elasticity of the Tornquist functions and some their advantages

NASA Astrophysics Data System (ADS)

Issin, Meyram

2017-09-01

In this article functions of demand for prime necessity, second necessity and luxury goods depending on the income are considered. These functions are called Tornquist functions. By means of the return model the demand for prime necessity goods and second necessity goods are approximately described. Then on the basis of a method of the smallest squares approximate formulas for elasticity of these Tornquist functions are received. To receive an approximate formula for elasticity of function of demand for luxury goods, the linear asymptotic formula is constructed for this function. Some benefits of approximate formulas for elasticity of Tornquist functions are specified.

Analysis and testing of numerical formulas for the initial value problem

NASA Technical Reports Server (NTRS)

Brown, R. L.; Kovach, K. R.; Popyack, J. L.

1980-01-01

Three computer programs for evaluating and testing numerical integration formulas used with fixed stepsize programs to solve initial value systems of ordinary differential equations are described. A program written in PASCAL SERIES, takes as input the differential equations and produces a FORTRAN subroutine for the derivatives of the system and for computing the actual solution through recursive power series techniques. Both of these are used by STAN, a FORTRAN program that interactively displays a discrete analog of the Liapunov stability region of any two dimensional subspace of the system. The derivatives may be used by CLMP, a FORTRAN program, to test the fixed stepsize formula against a good numerical result and interactively display the solutions.

Methods and formulas for calculating the strength of plate and shell constructions as used in airplane design

NASA Technical Reports Server (NTRS)

Heck, O S; Ebner, H

1936-01-01

This report is a compilation of previously published articles on formulas and methods of calculation for the determination of the strength and stability of plate and shell construction as employed in airplane design. In particular, it treats the problem of isotropic, orthotopic, and stiffened rectangular plates, thin curved panels, and circular cylinders under various loading conditions. The purpose of appending the pertinent literature references following the subjects discussed was to facilitate a comprehensive study of the treated problems.

Error behavior of multistep methods applied to unstable differential systems

NASA Technical Reports Server (NTRS)

Brown, R. L.

1977-01-01

The problem of modeling a dynamic system described by a system of ordinary differential equations which has unstable components for limited periods of time is discussed. It is shown that the global error in a multistep numerical method is the solution to a difference equation initial value problem, and the approximate solution is given for several popular multistep integration formulas. Inspection of the solution leads to the formulation of four criteria for integrators appropriate to unstable problems. A sample problem is solved numerically using three popular formulas and two different stepsizes to illustrate the appropriateness of the criteria.

A two-dimensional solution of the FW-H equation for rectilinear motion of sources

NASA Astrophysics Data System (ADS)

Bozorgi, Alireza; Siozos-Rousoulis, Leonidas; Nourbakhsh, Seyyed Ahmad; Ghorbaniasl, Ghader

2017-02-01

In this paper, a subsonic solution of the two-dimensional Ffowcs Williams and Hawkings (FW-H) equation is presented for calculation of noise generated by sources moving with constant velocity in a medium at rest or in a moving medium. The solution is represented in the frequency domain and is valid for observers located far from the noise sources. In order to verify the validity of the derived formula, three test cases are considered, namely a monopole, a dipole, and a quadrupole source in a medium at rest or in motion. The calculated results well coincide with the analytical solutions, validating the applicability of the formula to rectilinear subsonic motion problems.

Tutoring math platform accessible for visually impaired people.

PubMed

Maćkowski, Michał Sebastian; Brzoza, Piotr Franciszek; Spinczyk, Dominik Roland

2018-04-01

There are many problems with teaching and assessing impaired students in higher education, especially in technical science, where the knowledge is represented mostly by structural information like: math formulae, charts, graphs, etc. Developing e-learning platform for distance education solves this problem only partially due to the lack of accessibility for the blind. The proposed method is based on the decomposition of the typical mathematical exercise into a sequence of elementary sub-exercises. This allows for interactive resolving of math exercises and assessment of the correctness of exercise solutions at every stage. The presented methods were prepared and evaluated by visually impaired people and students. The article presents the accessible interactive tutoring platform for math teaching and assessment, and experience in exploring it. The results of conducted research confirm good understanding of math formulae described according to elaborated rules. Regardless of the level of complexity of the math formulae the level of math formulae understanding is higher for alternative structural description. The proposed solution enables alternative descriptions of math formulae. Based on the research results, the tool for computer-aided interactive learning of mathematics adapted to the needs of the blind has been designed, implemented and deployed as a platform for on-site and online and distance learning. The designed solution can be very helpful in overcoming many barriers that occur while teaching impaired students. Copyright © 2017 Elsevier Ltd. All rights reserved.

Visible and UV photo-detection in ZnO nanostructured thin films via simple tuning of solution method.

PubMed

Khokhra, Richa; Bharti, Bandna; Lee, Heung-No; Kumar, Rajesh

2017-11-08

This study demonstrates significant visible light photo-detection capability of pristine ZnO nanostructure thin films possessing substantially high percentage of oxygen vacancies [Formula: see text] and zinc interstitials [Formula: see text], introduced by simple tuning of economical solution method. The demonstrated visible light photo-detection capability, in addition to the inherent UV light detection ability of ZnO, shows great dependency of [Formula: see text] and [Formula: see text] with the nanostructure morphology. The dependency was evaluated by analyzing the presence/percentage of [Formula: see text] and [Formula: see text] using photoluminescence (PL) and X-ray photoelectron spectroscopy (XPS) measurements. Morphologies of ZnO viz. nanoparticles (NPs), nanosheets (NSs) and nanoflowers (NFs), as a result of tuning of synthesis method contended different concentrations of defects, demonstrated different photo-detection capabilities in the form of a thin film photodetector. The photo-detection capability was investigated under different light excitations (UV; 380~420 nm, white ; λ > 420 nm and green; 490~570 nm). The as fabricated NSs photodetector possessing comparatively intermediate percentage of [Formula: see text] ~ 47.7% and [Formula: see text] ~ 13.8% exhibited superior performance than that of NPs and NFs photodetectors, and ever reported photodetectors fabricated by using pristine ZnO nanostructures in thin film architecture. The adopted low cost and simplest approach makes the pristine ZnO-NSs applicable for wide-wavelength applications in optoelectronic devices.

Geopotential coefficient determination and the gravimetric boundary value problem: A new approach

NASA Technical Reports Server (NTRS)

Sjoeberg, Lars E.

1989-01-01

New integral formulas to determine geopotential coefficients from terrestrial gravity and satellite altimetry data are given. The formulas are based on the integration of data over the non-spherical surface of the Earth. The effect of the topography to low degrees and orders of coefficients is estimated numerically. Formulas for the solution of the gravimetric boundary value problem are derived.

A Mathematical Model of Anthrax Transmission in Animal Populations.

PubMed

Saad-Roy, C M; van den Driessche, P; Yakubu, Abdul-Aziz

2017-02-01

A general mathematical model of anthrax (caused by Bacillus anthracis) transmission is formulated that includes live animals, infected carcasses and spores in the environment. The basic reproduction number [Formula: see text] is calculated, and existence of a unique endemic equilibrium is established for [Formula: see text] above the threshold value 1. Using data from the literature, elasticity indices for [Formula: see text] and type reproduction numbers are computed to quantify anthrax control measures. Including only herbivorous animals, anthrax is eradicated if [Formula: see text]. For these animals, oscillatory solutions arising from Hopf bifurcations are numerically shown to exist for certain parameter values with [Formula: see text] and to have periodicity as observed from anthrax data. Including carnivores and assuming no disease-related death, anthrax again goes extinct below the threshold. Local stability of the endemic equilibrium is established above the threshold; thus, periodic solutions are not possible for these populations. It is shown numerically that oscillations in spore growth may drive oscillations in animal populations; however, the total number of infected animals remains about the same as with constant spore growth.

The DOZZ formula from the path integral

NASA Astrophysics Data System (ADS)

Kupiainen, Antti; Rhodes, Rémi; Vargas, Vincent

2018-05-01

We present a rigorous proof of the Dorn, Otto, Zamolodchikov, Zamolodchikov formula (the DOZZ formula) for the 3 point structure constants of Liouville Conformal Field Theory (LCFT) starting from a rigorous probabilistic construction of the functional integral defining LCFT given earlier by the authors and David. A crucial ingredient in our argument is a probabilistic derivation of the reflection relation in LCFT based on a refined tail analysis of Gaussian multiplicative chaos measures.

ESTIMATING THE RADIUS OF THE CONVECTIVE CORE OF MAIN-SEQUENCE STARS FROM OBSERVED OSCILLATION FREQUENCIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Wuming, E-mail: yangwuming@bnu.edu.cn, E-mail: yangwuming@ynao.ac.cn

The determination of the size of the convective core of main-sequence stars is usually dependent on the construction of models of stars. Here we introduce a method to estimate the radius of the convective core of main-sequence stars with masses between about 1.1 and 1.5 M {sub ⊙} from observed frequencies of low-degree p -modes. A formula is proposed to achieve the estimation. The values of the radius of the convective core of four known stars are successfully estimated by the formula. The radius of the convective core of KIC 9812850 estimated by the formula is 0.140 ± 0.028 Rmore » {sub ⊙}. In order to confirm this prediction, a grid of evolutionary models was computed. The value of the convective-core radius of the best-fit model of KIC 9812850 is 0.149 R {sub ⊙}, which is in good agreement with that estimated by the formula from observed frequencies. The formula aids in understanding the interior structure of stars directly from observed frequencies. The understanding is not dependent on the construction of models.« less

Thermodynamics of new black hole solutions in the Einstein-Maxwell-dilaton gravity

NASA Astrophysics Data System (ADS)

Dehghani, M.

In the present work, thermodynamics of the new black hole solutions to the four-dimensional Einstein-Maxwell-dilaton gravity theory have been studied. The dilaton potential, as the solution to the scalar field equations, has been constructed out by a linear combination of three Liouville-type potentials. Three new classes of charged dilatonic black hole solutions, as the exact solutions to the coupled equations of gravitational, electromagnetic and scalar fields, have been introduced. The conserved charge and mass of the new black holes have been calculated by utilizing Gauss's electric law and Abbott-Deser mass proposal, respectively. Also, the temperature, entropy and the electric potential of these new classes of charged dilatonic black holes have been calculated, making use of the geometrical approaches. Through a Smarr-type mass formula, the intensive parameters of the black holes have been calculated and validity of the first law of black hole thermodynamics has been confirmed. A thermal stability or phase transition analysis has been performed, making use of the canonical ensemble method. The heat capacity of the new black holes has been calculated and the points of type one- and type two-phase transitions as well as the ranges at which the new charged dilatonic black holes are locally stable have been determined, precisely.

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

An Analysis of Waves Underlying Grid Cell Firing in the Medial Enthorinal Cortex.

PubMed

Bonilla-Quintana, Mayte; Wedgwood, Kyle C A; O'Dea, Reuben D; Coombes, Stephen

2017-08-25

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an [Formula: see text] current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo (Philos. Trans. R. Soc. Lond. B, Biol. Sci. 369:20120523, 2013) showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the [Formula: see text] current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in [Formula: see text] resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the [Formula: see text] current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions.

Numerical solution of second order ODE directly by two point block backward differentiation formula

NASA Astrophysics Data System (ADS)

Zainuddin, Nooraini; Ibrahim, Zarina Bibi; Othman, Khairil Iskandar; Suleiman, Mohamed; Jamaludin, Noraini

2015-12-01

Direct Two Point Block Backward Differentiation Formula, (BBDF2) for solving second order ordinary differential equations (ODEs) will be presented throughout this paper. The method is derived by differentiating the interpolating polynomial using three back values. In BBDF2, two approximate solutions are produced simultaneously at each step of integration. The method derived is implemented by using fixed step size and the numerical results that follow demonstrate the advantage of the direct method as compared to the reduction method.

Sensitivity of Optimal Solutions to Control Problems for Second Order Evolution Subdifferential Inclusions.

PubMed

Bartosz, Krzysztof; Denkowski, Zdzisław; Kalita, Piotr

In this paper the sensitivity of optimal solutions to control problems described by second order evolution subdifferential inclusions under perturbations of state relations and of cost functionals is investigated. First we establish a new existence result for a class of such inclusions. Then, based on the theory of sequential [Formula: see text]-convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. The abstract scheme works provided we can establish two properties: the Kuratowski convergence of solution sets for the state relations and some complementary [Formula: see text]-convergence of the cost functionals. Then these two properties are implemented in the considered case.

Corridor of existence of thermodynamically consistent solution of the Ornstein-Zernike equation.

PubMed

Vorob'ev, V S; Martynov, G A

2007-07-14

We obtain the exact equation for a correction to the Ornstein-Zernike (OZ) equation based on the assumption of the uniqueness of thermodynamical functions. We show that this equation is reduced to a differential equation with one arbitrary parameter for the hard sphere model. The compressibility factor within narrow limits of this parameter variation can either coincide with one of the formulas obtained on the basis of analytical solutions of the OZ equation or assume all intermediate values lying in a corridor between these solutions. In particular, we find the value of this parameter when the thermodynamically consistent compressibility factor corresponds to the Carnahan-Stirling formula.

An invariant asymptotic formula for solutions of second-order linear ODE's

NASA Technical Reports Server (NTRS)

Gingold, H.

1988-01-01

An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).

On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations.

PubMed

Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio

2015-01-01

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P[Formula: see text]) equation or its fourth-order analogue P[Formula: see text]. As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

Relative Bioavailability of Apixaban Solution or Crushed Tablet Formulations Administered by Mouth or Nasogastric Tube in Healthy Subjects.

PubMed

Song, Yan; Wang, Xiaoli; Perlstein, Itay; Wang, Jessie; Badawy, Sherif; Frost, Charles; LaCreta, Frank

2015-08-01

Crushed tablet and solution formulations of apixaban administered orally or via a nasogastric tube (NGT) may be useful in patients unable to swallow solid dose formulations. It is important to understand whether new formulations and/or methods of administration impact apixaban bioavailability and pharmacokinetic properties. These studies evaluated the relative bioavailability (Frel) of apixaban solution administered orally; oral solution administered via NGT flushed with either 5% dextrose in water (D5W) or with infant formula; oral solution via NGT with a nutritional supplement; and crushed tablet suspended in D5W and administered via NGT. Three open-label, randomized, crossover studies were conducted in healthy adults (study 1: apixaban 10-mg tablet [reference] versus oral solution, both administered PO; study 2: apixaban 5-mg oral solution PO [reference] versus oral solution via NGT flushed with either D5W or infant formula; study 3: apixaban 5-mg oral solution PO [reference] versus apixaban 5-mg oral solution via NGT with a nutritional supplement and versus crushed tablet suspended in D5W and administered via NGT). Point estimates and 90% CIs of the geometric mean ratios (GMRs; test/reference) were generated for Cmax and AUC. Adverse events were recorded throughout each study. Frel of the oral solution was 105% versus tablet, and Frel for oral solution via NGT with D5W flush, infant formula flush, nutritional supplement, and crushed tablet via NGT versus oral solution administration were 96.7%, 92.2%, 81.3%, and 95.1%, respectively. The 90% CIs of the GMRs of all AUCs met the bioequivalence criterion except that of the nutritional supplement (0.766-0.863). The corresponding GMRs for Cmax were 0.977, 0.953, 0.805, 0.682, and 0.884. For the solution via NGT flushed with D5W and for the crushed tablet, the 90% CIs of the Cmax GMRs met the bioequivalence criterion. Apixaban was well tolerated in all 3 studies; most adverse events were mild. Comparable Frel was observed for oral apixaban solution, tablet, NGT administration of solution flushed with D5W and infant formula, and NGT administration of crushed tablet suspension. Exposure was less when oral solution was administered via NGT with nutritional supplement. These results support several alternative methods of administering apixaban that may be useful in certain clinical situations. ClinicalTrials.gov identifiers: NCT02034565, NCT02034578, and NCT02034591. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Using Paperclips to Explain Empirical Formulas to Students

ERIC Educational Resources Information Center

Nassiff, Peter; Czerwinski, Wendy A.

2014-01-01

Early in their chemistry education, students learn to do empirical formula calculations by rote without an understanding of the historical context behind them or the reason why their calculations work. In these activities, students use paperclip "atoms", construct a series of simple compounds representing real molecules, and discover,…

Design, parametrization, and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules.

PubMed

Blumthaler, Ingrid; Oberst, Ulrich

2012-03-01

Control design belongs to the most important and difficult tasks of control engineering and has therefore been treated by many prominent researchers and in many textbooks, the systems being generally described by their transfer matrices or by Rosenbrock equations and more recently also as behaviors. Our approach to controller design uses, in addition to the ideas of our predecessors on coprime factorizations of transfer matrices and on the parametrization of stabilizing compensators, a new mathematical technique which enables simpler design and also new theorems in spite of the many outstanding results of the literature: (1) We use an injective cogenerator signal module ℱ over the polynomial algebra [Formula: see text] (F an infinite field), a saturated multiplicatively closed set T of stable polynomials and its quotient ring [Formula: see text] of stable rational functions. This enables the simultaneous treatment of continuous and discrete systems and of all notions of stability, called T-stability. We investigate stabilizing control design by output feedback of input/output (IO) behaviors and study the full feedback IO behavior, especially its autonomous part and not only its transfer matrix. (2) The new technique is characterized by the permanent application of the injective cogenerator quotient signal module [Formula: see text] and of quotient behaviors [Formula: see text] of [Formula: see text]-behaviors B. (3) For the control tasks of tracking, disturbance rejection, model matching, and decoupling and not necessarily proper plants we derive necessary and sufficient conditions for the existence of proper stabilizing compensators with proper and stable closed loop behaviors, parametrize all such compensators as IO behaviors and not only their transfer matrices and give new algorithms for their construction. Moreover we solve the problem of pole placement or spectral assignability for the complete feedback behavior. The properness of the full feedback behavior ensures the absence of impulsive solutions in the continuous case, and that of the compensator enables its realization by Kalman state space equations or elementary building blocks. We note that every behavior admits an IO decomposition with proper transfer matrix, but that most of these decompositions do not have this property, and therefore we do not assume the properness of the plant. (4) The new technique can also be applied to more general control interconnections according to Willems, in particular to two-parameter feedback compensators and to the recent tracking framework of Fiaz/Takaba/Trentelman. In contrast to these authors, however, we pay special attention to the properness of all constructed transfer matrices which requires more subtle algorithms.

A penalized quantitative structure-property relationship study on melting point of energetic carbocyclic nitroaromatic compounds using adaptive bridge penalty.

PubMed

Al-Fakih, A M; Algamal, Z Y; Lee, M H; Aziz, M

2018-05-01

A penalized quantitative structure-property relationship (QSPR) model with adaptive bridge penalty for predicting the melting points of 92 energetic carbocyclic nitroaromatic compounds is proposed. To ensure the consistency of the descriptor selection of the proposed penalized adaptive bridge (PBridge), we proposed a ridge estimator ([Formula: see text]) as an initial weight in the adaptive bridge penalty. The Bayesian information criterion was applied to ensure the accurate selection of the tuning parameter ([Formula: see text]). The PBridge based model was internally and externally validated based on [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], the Y-randomization test, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and the applicability domain. The validation results indicate that the model is robust and not due to chance correlation. The descriptor selection and prediction performance of PBridge for the training dataset outperforms the other methods used. PBridge shows the highest [Formula: see text] of 0.959, [Formula: see text] of 0.953, [Formula: see text] of 0.949 and [Formula: see text] of 0.959, and the lowest [Formula: see text] and [Formula: see text]. For the test dataset, PBridge shows a higher [Formula: see text] of 0.945 and [Formula: see text] of 0.948, and a lower [Formula: see text] and [Formula: see text], indicating its better prediction performance. The results clearly reveal that the proposed PBridge is useful for constructing reliable and robust QSPRs for predicting melting points prior to synthesizing new organic compounds.

Event generator tunes obtained from underlying event and multiparton scattering measurements.

PubMed

Khachatryan, V; Sirunyan, A M; Tumasyan, A; Adam, W; Asilar, E; Bergauer, T; Brandstetter, J; Brondolin, E; Dragicevic, M; Erö, J; Friedl, M; Frühwirth, R; Ghete, V M; Hartl, C; Hörmann, N; Hrubec, J; Jeitler, M; Knünz, V; König, A; Krammer, M; Krätschmer, I; Liko, D; Matsushita, T; Mikulec, I; Rabady, D; Rahbaran, B; Rohringer, H; Schieck, J; Schöfbeck, R; Strauss, J; Treberer-Treberspurg, W; Waltenberger, W; Wulz, C-E; Mossolov, V; Shumeiko, N; Suarez Gonzalez, J; Alderweireldt, S; Cornelis, T; De Wolf, E A; Janssen, X; Knutsson, A; Lauwers, J; Luyckx, S; Van De Klundert, M; Van Haevermaet, H; Van Mechelen, P; Van Remortel, N; Van Spilbeeck, A; Abu Zeid, S; Blekman, F; D'Hondt, J; Daci, N; De Bruyn, I; Deroover, K; Heracleous, N; Keaveney, J; Lowette, S; Moreels, L; Olbrechts, A; Python, Q; Strom, D; Tavernier, S; Van Doninck, W; Van Mulders, P; Van Onsem, G P; Van Parijs, I; Barria, P; Brun, H; Caillol, C; Clerbaux, B; De Lentdecker, G; Fasanella, G; Favart, L; Grebenyuk, A; Karapostoli, G; Lenzi, T; Léonard, A; Maerschalk, T; Marinov, A; Perniè, L; Randle-Conde, A; Seva, T; Vander Velde, C; Yonamine, R; Vanlaer, P; Yonamine, R; Zenoni, F; Zhang, F; Adler, V; Beernaert, K; Benucci, L; Cimmino, A; Crucy, S; Dobur, D; Fagot, A; Garcia, G; Gul, M; Mccartin, J; Ocampo Rios, A A; Poyraz, D; Ryckbosch, D; Salva, S; Sigamani, M; Tytgat, M; Van Driessche, W; Yazgan, E; Zaganidis, N; Basegmez, S; Beluffi, C; Bondu, O; Brochet, S; Bruno, G; Caudron, A; Ceard, L; Da Silveira, G G; Delaere, C; Favart, D; Forthomme, L; Giammanco, A; Hollar, J; Jafari, A; Jez, P; Komm, M; Lemaitre, V; Mertens, A; Musich, M; Nuttens, C; Perrini, L; Pin, A; Piotrzkowski, K; Popov, A; Quertenmont, L; Selvaggi, M; Vidal Marono, M; Beliy, N; Hammad, G H; Júnior, W L Aldá; Alves, F L; Alves, G A; Brito, L; Correa Martins Junior, M; Hamer, M; Hensel, C; Moraes, A; Pol, M E; Rebello Teles, P; Belchior Batista Das Chagas, E; Carvalho, W; Chinellato, J; Custódio, A; Da Costa, E M; De Jesus Damiao, D; De Oliveira Martins, C; 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Rank, D; Rossin, R; Shchutska, L; Snowball, M; Sperka, D; Terentyev, N; Thomas, L; Wang, J; Wang, S; Yelton, J; Hewamanage, S; Linn, S; Markowitz, P; Martinez, G; Rodriguez, J L; Adams, J R; Ackert, A; Adams, T; Askew, A; Bein, S; Bochenek, J; Diamond, B; Haas, J; Hagopian, S; Hagopian, V; Johnson, K F; Khatiwada, A; Prosper, H; Weinberg, M; Baarmand, M M; Bhopatkar, V; Colafranceschi, S; Hohlmann, M; Kalakhety, H; Noonan, D; Roy, T; Yumiceva, F; Adams, M R; Apanasevich, L; Berry, D; Betts, R R; Bucinskaite, I; Cavanaugh, R; Evdokimov, O; Gauthier, L; Gerber, C E; Hofman, D J; Kurt, P; O'Brien, C; Sandoval Gonzalez, L D; Silkworth, C; Turner, P; Varelas, N; Wu, Z; Zakaria, M; Bilki, B; Clarida, W; Dilsiz, K; Durgut, S; Gandrajula, R P; Haytmyradov, M; Khristenko, V; Merlo, J-P; Mermerkaya, H; Mestvirishvili, A; Moeller, A; Nachtman, J; Ogul, H; Onel, Y; Ozok, F; Penzo, A; Snyder, C; Tiras, E; Wetzel, J; Yi, K; Anderson, I; Anderson, I; Barnett, B A; Blumenfeld, B; Eminizer, N; Fehling, D; 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New sets of parameters ("tunes") for the underlying-event (UE) modelling of the pythia8, pythia6 and herwig++ Monte Carlo event generators are constructed using different parton distribution functions. Combined fits to CMS UE proton-proton ([Formula: see text]) data at [Formula: see text] and to UE proton-antiproton ([Formula: see text]) data from the CDF experiment at lower [Formula: see text], are used to study the UE models and constrain their parameters, providing thereby improved predictions for proton-proton collisions at 13[Formula: see text]. In addition, it is investigated whether the values of the parameters obtained from fits to UE observables are consistent with the values determined from fitting observables sensitive to double-parton scattering processes. Finally, comparisons are presented of the UE tunes to "minimum bias" (MB) events, multijet, and Drell-Yan ([Formula: see text] lepton-antilepton+jets) observables at 7 and 8[Formula: see text], as well as predictions for MB and UE observables at 13[Formula: see text].

Mass Distribution and Gravitational Potential of the Milky Way

NASA Astrophysics Data System (ADS)

Ninković, Slobodan

2017-04-01

Models of mass distribution in the Milky Way are discussed where those yielding the potential analytically are preferred. It is noted that there are three main contributors to the Milky Way potential: bulge, disc and dark halo. In the case of the disc the Miyamoto-Nagai formula, as simple enough, has shown as a very good solution, but it has not been able to satisfy all requirements. Therefore, improvements, such as adding new terms or combining several Miyamoto-Nagai terms, have been attempted. Unlike the disc, in studying the bulge and dark halo the flattening is usually neglected, which offers the possibility of obtaining an exact solution of the Poisson equation. It is emphasized that the Hernquist formula, used very often for the bulge potential, is a special case of another formula and the properties of that formula are analysed. In the case of the dark halo, the slopes of its cumulative mass for the inner and outer parts are explained through a new formalism presented here for the first time.

Stiffness Matrix of Thin-Walled Open Bar Subject to Bending, Bending Torsion and Shift of Cross Section Middle Surface

NASA Astrophysics Data System (ADS)

Panasenko, N. N.; Sinelschikov, A. V.

2017-11-01

One of the main stages in the analysis of complex 3D structures and engineering constructions made of thin-walled open bars using FEM is a stiffness matrix developing. Taking into account middle surface shear deformation caused by the work of tangential stresses in the formula to calculate a potential energy of thin-walled open bars, the authors obtain an important correction at calculation of the bar deformation and fundamental frequencies. The results of the analysis of the free end buckling of a cantilever H-bar under plane bending differ from exact solution by 0.53%. In the course of comparison of the obtained results with the cantilever bar buckling regardless the middle surface shear deformation, an increase made 16.6%. The stiffness matrix of a thin-walled open bar developed in the present work can be integrated into any software suite using FEM for the analysis of complex 3-D structures and engineering constructions with n-freedoms.

Efficient construction of exchange and correlation potentials by inverting the Kohn-Sham equations.

PubMed

Kananenka, Alexei A; Kohut, Sviataslau V; Gaiduk, Alex P; Ryabinkin, Ilya G; Staroverov, Viktor N

2013-08-21

Given a set of canonical Kohn-Sham orbitals, orbital energies, and an external potential for a many-electron system, one can invert the Kohn-Sham equations in a single step to obtain the corresponding exchange-correlation potential, vXC(r). For orbitals and orbital energies that are solutions of the Kohn-Sham equations with a multiplicative vXC(r) this procedure recovers vXC(r) (in the basis set limit), but for eigenfunctions of a non-multiplicative one-electron operator it produces an orbital-averaged potential. In particular, substitution of Hartree-Fock orbitals and eigenvalues into the Kohn-Sham inversion formula is a fast way to compute the Slater potential. In the same way, we efficiently construct orbital-averaged exchange and correlation potentials for hybrid and kinetic-energy-density-dependent functionals. We also show how the Kohn-Sham inversion approach can be used to compute functional derivatives of explicit density functionals and to approximate functional derivatives of orbital-dependent functionals.

Analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric

NASA Astrophysics Data System (ADS)

Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

2017-09-01

We construct an analytical approximation for the numerical black hole metric of P. Kanti et al. [Phys. Rev. D 54, 5049 (1996), 10.1103/PhysRevD.54.5049] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a compactified radial coordinate, used here, converges slowly when the dilaton coupling approaches its extremal values, but for a black hole far from the extremal state, the analytical formula has a maximal relative error of a fraction of one percent already within the third order of the continued fraction expansion. The suggested analytical representation of the numerical black hole metric is relatively compact and a good approximation in the whole space outside the black hole event horizon. Therefore, it can serve in the same way as an exact solution when analyzing particles' motion, perturbations, quasinormal modes, Hawking radiation, accreting disks, and many other problems in the vicinity of a black hole. In addition, we construct the approximate analytical expression for the dilaton field.

A multilayer perceptron solution to the match phase problem in rule-based artificial intelligence systems

NASA Technical Reports Server (NTRS)

Sartori, Michael A.; Passino, Kevin M.; Antsaklis, Panos J.

1992-01-01

In rule-based AI planning, expert, and learning systems, it is often the case that the left-hand-sides of the rules must be repeatedly compared to the contents of some 'working memory'. The traditional approach to solve such a 'match phase problem' for production systems is to use the Rete Match Algorithm. Here, a new technique using a multilayer perceptron, a particular artificial neural network model, is presented to solve the match phase problem for rule-based AI systems. A syntax for premise formulas (i.e., the left-hand-sides of the rules) is defined, and working memory is specified. From this, it is shown how to construct a multilayer perceptron that finds all of the rules which can be executed for the current situation in working memory. The complexity of the constructed multilayer perceptron is derived in terms of the maximum number of nodes and the required number of layers. A method for reducing the number of layers to at most three is also presented.

Quasi-local conserved charges in Lorenz-diffeomorphism covariant theory of gravity

NASA Astrophysics Data System (ADS)

Adami, H.; Setare, M. R.

2016-04-01

In this paper, using the combined Lorenz-diffeomorphism symmetry, we find a general formula for the quasi-local conserved charge of the covariant gravity theories in a first order formalism of gravity. We simplify the general formula for the Lovelock theory of gravity. Afterwards, we apply the obtained formula on BHT gravity to obtain the energy and angular momentum of the rotating OTT black hole solution in the context of this theory.

Functional Screening of the Cronobacter sakazakii BAA-894 Genome reveals a role for ProP (ESA_02131) in carnitine uptake.

PubMed

Feeney, Audrey; Sleator, Roy D

2015-01-01

Cronobacter sakazakii is a neonatal pathogen responsible for up to 80% of fatalities in infected infants. Low birth weight infants and neonates infected with C. sakazakii suffer necrotizing enterocolitis, bacteraemia and meningitis. The mode of transmission most often associated with infection is powdered infant formula (PIF) which, with an aw of ∼0.2, is too low to allow most microorganisms to persist. Survival of C. sakazakii in environments subject to extreme hyperosmotic stress has previously been attributed to the uptake of compatible solutes including proline and betaine. Herein, we report the construction and screening of a C. sakazakii genome bank and the identification of ProP (ESA_02131) as a carnitine uptake system.

Data on electrical energy conservation using high efficiency motors for the confidence bounds using statistical techniques.

PubMed

Shaikh, Muhammad Mujtaba; Memon, Abdul Jabbar; Hussain, Manzoor

2016-09-01

In this article, we describe details of the data used in the research paper "Confidence bounds for energy conservation in electric motors: An economical solution using statistical techniques" [1]. The data presented in this paper is intended to show benefits of high efficiency electric motors over the standard efficiency motors of similar rating in the industrial sector of Pakistan. We explain how the data was collected and then processed by means of formulas to show cost effectiveness of energy efficient motors in terms of three important parameters: annual energy saving, cost saving and payback periods. This data can be further used to construct confidence bounds for the parameters using statistical techniques as described in [1].

Conserved charges of minimal massive gravity coupled to scalar field

NASA Astrophysics Data System (ADS)

Setare, M. R.; Adami, H.

2018-02-01

Recently, the theory of topologically massive gravity non-minimally coupled to a scalar field has been proposed, which comes from the Lorentz-Chern-Simons theory (JHEP 06, 113, 2015), a torsion-free theory. We extend this theory by adding an extra term which makes the torsion to be non-zero. We show that the BTZ spacetime is a particular solution to this theory in the case where the scalar field is constant. The quasi-local conserved charge is defined by the concept of the generalized off-shell ADT current. Also a general formula is found for the entropy of the stationary black hole solution in context of the considered theory. The obtained formulas are applied to the BTZ black hole solution in order to obtain the energy, the angular momentum and the entropy of this solution. The central extension term, the central charges and the eigenvalues of the Virasoro algebra generators for the BTZ black hole solution are thus obtained. The energy and the angular momentum of the BTZ black hole using the eigenvalues of the Virasoro algebra generators are calculated. Also, using the Cardy formula, the entropy of the BTZ black hole is found. It is found that the results obtained in two different ways exactly match, just as expected.

Oscillatory Reduction in Option Pricing Formula Using Shifted Poisson and Linear Approximation

NASA Astrophysics Data System (ADS)

Nur Rachmawati, Ro'fah; Irene; Budiharto, Widodo

2014-03-01

Option is one of derivative instruments that can help investors improve their expected return and minimize the risks. However, the Black-Scholes formula is generally used in determining the price of the option does not involve skewness factor and it is difficult to apply in computing process because it produces oscillation for the skewness values close to zero. In this paper, we construct option pricing formula that involve skewness by modified Black-Scholes formula using Shifted Poisson model and transformed it into the form of a Linear Approximation in the complete market to reduce the oscillation. The results are Linear Approximation formula can predict the price of an option with very accurate and successfully reduce the oscillations in the calculation processes.

A counter-rotating vortex pair in inviscid fluid

NASA Astrophysics Data System (ADS)

Habibah, Ummu; Fukumoto, Yasuhide

2017-12-01

We study the motion of a counter-rotating vortex pair with the circulations ±Γ move in incompressible fluid. The assumption is made that the core is very thin, that is the core radius σ is much smaller than the vortex radius d such that ɛ = σ/d ≪ 1. With this condition, the method of matched asymptotic expansion is employed. The solutions of the Navier-Stokes equations and the Biot-Savart law, regarding the inner and outer solutions respectively, are constructed in the form of a small parameter. An asymptotic expansion of the Biot-Savart law near the vortex core provides with the matching condition for an asymptotic expansion for limiting the Navier-Stokes equations for large radius r. The general formula of an anti-parallel vortex pair is established. At leading order O(ɛ0), we apply the special case in inviscid fluid, the Rankine vortex, a circular vortex of uniform vorticity. Furthermore at leading order O(ɛ5) we show the traveling speed of a vortex pair.

Uniformly rotating, axisymmetric, and triaxial quark stars in general relativity

NASA Astrophysics Data System (ADS)

Zhou, Enping; Tsokaros, Antonios; Rezzolla, Luciano; Xu, Renxin; Uryū, Kōji

2018-01-01

Quasiequilibrium models of uniformly rotating axisymmetric and triaxial quark stars are computed in a general-relativistic gravity scenario. The Isenberg-Wilson-Mathews (IWM) formulation is employed and the Compact Object Calculator (cocal) code is extended to treat rotating stars with finite surface density and new equations of state (EOSs). Besides the MIT bag model for quark matter which is composed of deconfined quarks, we examine a new EOS proposed by Lai and Xu that is based on quark clustering and results in a stiff EOS that can support masses up to 3.3 M⊙ in the case we considered. We perform convergence tests for our new code to evaluate the effect of finite surface density in the accuracy of our solutions and construct sequences of solutions for both small and high compactness. The onset of secular instability due to viscous dissipation is identified and possible implications are discussed. An estimate of the gravitational wave amplitude and luminosity based on quadrupole formulas is presented and comparison with neutron stars is discussed.

The reliable solution and computation time of variable parameters logistic model

NASA Astrophysics Data System (ADS)

Wang, Pengfei; Pan, Xinnong

2018-05-01

The study investigates the reliable computation time (RCT, termed as T c) by applying a double-precision computation of a variable parameters logistic map (VPLM). Firstly, by using the proposed method, we obtain the reliable solutions for the logistic map. Secondly, we construct 10,000 samples of reliable experiments from a time-dependent non-stationary parameters VPLM and then calculate the mean T c. The results indicate that, for each different initial value, the T cs of the VPLM are generally different. However, the mean T c trends to a constant value when the sample number is large enough. The maximum, minimum, and probable distribution functions of T c are also obtained, which can help us to identify the robustness of applying a nonlinear time series theory to forecasting by using the VPLM output. In addition, the T c of the fixed parameter experiments of the logistic map is obtained, and the results suggest that this T c matches the theoretical formula-predicted value.

On HPM approximation for the perihelion precession angle in general relativity

NASA Astrophysics Data System (ADS)

Shchigolev, Victor; Bezbatko, Dmitrii

2017-03-01

In this paper, the homotopy perturbation method (HPM) is applied for calculating the perihelion precession angle of planetary orbits in General Relativity. The HPM is quite efficient and is practically well suited for use in many astrophysical and cosmological problems. For our purpose, we applied HPM to the approximate solutions for the orbits in order to calculate the perihelion shift. On the basis of the main idea of HPM, we construct the appropriate homotopy that leads to the problem of solving the set of linear algebraic equations. As a result, we obtain a simple formula for the angle of precession avoiding any restrictions on the smallness of physical parameters. First of all, we consider the simple examples of the Schwarzschild metric and the Reissner - Nordström spacetime of a charged star for which the approximate geodesics solutions are known. Furthermore, the implementation of HPM has allowed us to readily obtain the precession angle for the orbits in the gravitational field of Kiselev black hole.

Constructing Matching Texts in Two Languages: The Application of Propositional Analysis.

ERIC Educational Resources Information Center

Valdes, Guadalupe; And Others

1984-01-01

Discusses how current procedures for selecting/constructing equivalent texts may lead to error because of their specific limitations; proposes the utilization of micro-propositional analysis coupled with word-frequency lists and readability formulas for constructing "matching" texts; presents some procedures which researchers working in…

A submicron device to rectify a square-wave angular velocity.

PubMed

Moradian, A; Miri, M F

2011-02-01

We study a system composed of two thick dielectric disks separated by a thin layer of an electrolyte solution. Initially both plates have the same surface charge distribution. The surface charge distribution has no rotational symmetry. We show that the top plate experiences a torque [Formula: see text]([Formula: see text]) if it rotates about its axis by an angle [Formula: see text] . The torque can be controlled by varying the electrolyte concentration, the separation and the surface charge density of the plates. For a specific example of charged rods attached to the plates, we find [Formula: see text]([Formula: see text]) [Formula: see text] sin(4[Formula: see text]) . We also study the dynamics of the system. We consider the case where the angular velocity of the bottom disk is a square-wave signal. We find that the average angular velocity of the top disk is not zero.

A Formula for Factoring.

ERIC Educational Resources Information Center

Roebuck, Kay I. Meeks

1997-01-01

Suggests use of the quadratic formula to build understanding that connections between factors and solutions to equations work both ways. Making use of natural connections among concepts allows students to work more efficiently. Presents four sample problems showing the roots of equations. Messy quadratic equations with rational roots can be solved…

Covariant n/sup 2/-plet mass formulas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davidson, A.

Using a generalized internal symmetry group analogous to the Lorentz group, we have constructed a covariant n/sup 2/-plet mass operator. This operator is built as a scalar matrix in the (n;n*) representation, and its SU(n) breaking parameters are identified as intrinsic boost ones. Its basic properties are: covariance, Hermiticity, positivity, charge conjugation, quark contents, and a self-consistent n/sup 2/-1, 1 mixing. The GMO and the Okubo formulas are obtained by considering two different limits of the same generalized mass formula.

Smarr formula for Lovelock black holes: A Lagrangian approach

NASA Astrophysics Data System (ADS)

Liberati, Stefano; Pacilio, Costantino

2016-04-01

The mass formula for black holes can be formally expressed in terms of a Noether charge surface integral plus a suitable volume integral, for any gravitational theory. The integrals can be constructed as an application of Wald's formalism. We apply this formalism to compute the mass and the Smarr formula for static Lovelock black holes. Finally, we propose a new prescription for Wald's entropy in the case of Lovelock black holes, which takes into account topological contributions to the entropy functional.

New algorithms to compute the nearness symmetric solution of the matrix equation.

PubMed

Peng, Zhen-Yun; Fang, Yang-Zhi; Xiao, Xian-Wei; Du, Dan-Dan

2016-01-01

In this paper we consider the nearness symmetric solution of the matrix equation AXB = C to a given matrix [Formula: see text] in the sense of the Frobenius norm. By discussing equivalent form of the considered problem, we derive some necessary and sufficient conditions for the matrix [Formula: see text] is a solution of the considered problem. Based on the idea of the alternating variable minimization with multiplier method, we propose two iterative methods to compute the solution of the considered problem, and analyze the global convergence results of the proposed algorithms. Numerical results illustrate the proposed methods are more effective than the existing two methods proposed in Peng et al. (Appl Math Comput 160:763-777, 2005) and Peng (Int J Comput Math 87: 1820-1830, 2010).

Soil fluoride fractions and their bioavailability to tea plants (Camellia sinensis L.).

PubMed

Yi, Xiaoyun; Qiao, Sha; Ma, Lifeng; Wang, Jie; Ruan, Jianyun

2017-10-01

Drinking teas containing high fluoride (F) imposes fluorosis risk. The soil F bioavailability is an important factor influencing its uptake and contents in teas. The present work was conducted to investigate F fractions in soil and their bioavailability to tea plants. Tea seedlings were cultivated on 6 typical soils treated with a mixture consisting of dolomite, lime, peat and KCl at variable rates in the pot experiment. Soils and young shoots were collected in pairs from 63 sites of 21 plantations in a field experiment. Soil fluoride was sequentially separated into hot water soluble [Formula: see text], exchangeable [Formula: see text] (by 1 mol L -1 MgCl 2 , pH = 7.0), F bound to Mn and Fe hydroxides [F (oxides,s) ], and organic matter [F (OM,s) ] or extracted independently by water [Formula: see text] or 0.01 mol L -1 CaCl 2 solution [Formula: see text]. Averaged [Formula: see text], [Formula: see text], F (oxides,s) and F (OM,s) accounted for 51, 14, 5 and 30 % of the total sequential extracts, respectively. There were significant correlations among [Formula: see text], [Formula: see text] and F (OM,s) . Fluoride contents in leaves correlated with [Formula: see text] (r = 0.71, p < 0.001), [Formula: see text] (r = 0.93, p < 0.001) and F (OM,s) (r = 0.69, p < 0.01) but not other fractions in the pot experiment and with [Formula: see text] (r = 0.43-0.57, p < 0.001) and [Formula: see text] (r = 0.42-0.79, p < 0.001) in the field experiment. It was concluded that 0.01 M CaCl 2 extractable fluoride can be a good indicator of soil F bioavailability to tea plants. The significant correlations among some of the F fractions suggested that F in solution, AlF complexes (AlF 2 + , AlF 2+ ) and those bound to organic matter likely represent the available pools to tea plants.

EFL Learners' Grammatical Awareness through Accumulating Formulaic Sequences of Morphological Structure (-ing)

ERIC Educational Resources Information Center

Kashiwagi, Kazuko; Ito, Yukiko

2017-01-01

Even young EFL learners who have not yet learned L2 grammar will notice language patterns if, when retrieving exemplars ("item-based patterns"), they succeed in making form-meaning connections (FMCs). Item-based patterns, termed formulaic sequences (FS), serve as a basis for creative constructions. Although learners are implicitly…

Teaching Flower Structure & Floral Formulae--A Mix of the Real & Virtual Worlds

ERIC Educational Resources Information Center

Burrows, Geoff

2010-01-01

The study of flower structure is essential in plant identification and in understanding sexual reproduction in plants, pollination syndromes, plant breeding, and fruit structure. Thus, study of flower structure and construction of floral formulae are standard parts of first-year university botany and biology courses. These activities involve…

27 CFR 21.59 - Formula No. 32.

Code of Federal Regulations, 2014 CFR

2014-04-01

....Collodion, U.S.P. 311.Ethyl cellulose compounds (dehydration). 332.Processing miscellaneous food products... solutions. 481.Photoengraving and rotogravure solutions and dyes. (2) As a raw material: 522.Ethyl chloride...

27 CFR 21.59 - Formula No. 32.

Code of Federal Regulations, 2013 CFR

2013-04-01

....Collodion, U.S.P. 311.Ethyl cellulose compounds (dehydration). 332.Processing miscellaneous food products... solutions. 481.Photoengraving and rotogravure solutions and dyes. (2) As a raw material: 522.Ethyl chloride...

27 CFR 21.59 - Formula No. 32.

Code of Federal Regulations, 2012 CFR

2012-04-01

....Collodion, U.S.P. 311.Ethyl cellulose compounds (dehydration). 332.Processing miscellaneous food products... solutions. 481.Photoengraving and rotogravure solutions and dyes. (2) As a raw material: 522.Ethyl chloride...

Numerical treatment for solving two-dimensional space-fractional advection-dispersion equation using meshless method

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Sun, Fengxin; Wei, Qi; Wang, Jufeng

2018-02-01

Space-fractional advection-dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann-Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

Assessing the cariogenic potential of some infant formulas, milk and sugar solutions.

PubMed

Bowen, W H; Pearson, S K; Rosalen, P L; Miguel, J C; Shih, A Y

1997-07-01

Using a desalivated rat model, the authors found that several commonly used infant formulas had significant cariogenic potential. Sucrose was by far the most cariogenic and cows' milk the least cariogenic of all the products examined. The data show that dental practitioners and other health care professionals should discourage the use of sugar in baby bottles and provide information on which formulas are least likely to induce caries when continuous bottle feeding is unavoidable.

Observed changes in the Earth's dynamic oblateness from GRACE data and geophysical models.

PubMed

Sun, Y; Ditmar, P; Riva, R

A new methodology is proposed to estimate changes in the Earth's dynamic oblateness ([Formula: see text] or equivalently, [Formula: see text]) on a monthly basis. The algorithm uses monthly Gravity Recovery and Climate Experiment (GRACE) gravity solutions, an ocean bottom pressure model and a glacial isostatic adjustment (GIA) model. The resulting time series agree remarkably well with a solution based on satellite laser ranging (SLR) data. Seasonal variations of the obtained time series show little sensitivity to the choice of GRACE solutions. Reducing signal leakage in coastal areas when dealing with GRACE data and accounting for self-attraction and loading effects when dealing with water redistribution in the ocean is crucial in achieving close agreement with the SLR-based solution in terms of de-trended solutions. The obtained trend estimates, on the other hand, may be less accurate due to their dependence on the GIA models, which still carry large uncertainties.

Estimation of wind erosion from construction of a railway in arid northwest China

USDA-ARS?s Scientific Manuscript database

A state-of-the-art wind erosion simulation model, the Wind Erosion Prediction System and the United States Environmental Protection Agency’s AP-42 emission factors formula, were combined together to evaluate wind-blown dust emissions from various construction units from a railway construction projec...

Correlation Structure of Fractional Pearson Diffusions.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-09-01

The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of Mittag-Leffler functions. That formula shows that fractional Pearson diffusions are long range dependent, with a correlation that falls off like a power law, whose exponent equals the order of the fractional derivative.

27 CFR 21.49 - Formula No. 23-H.

Code of Federal Regulations, 2014 CFR

2014-04-01

... biocides. 450.Cleaning solutions (including household detergents). (2) Miscellaneous uses: 812.Product... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Formula No. 23-H. 21.49 Section 21.49 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT...

27 CFR 21.49 - Formula No. 23-H.

Code of Federal Regulations, 2012 CFR

2012-04-01

... biocides. 450.Cleaning solutions (including household detergents). (2) Miscellaneous uses: 812.Product... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Formula No. 23-H. 21.49 Section 21.49 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT...

27 CFR 21.49 - Formula No. 23-H.

Code of Federal Regulations, 2011 CFR

2011-04-01

... biocides. 450.Cleaning solutions (including household detergents). (2) Miscellaneous uses: 812.Product... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 23-H. 21.49 Section 21.49 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT...

27 CFR 21.49 - Formula No. 23-H.

Code of Federal Regulations, 2013 CFR

2013-04-01

... biocides. 450.Cleaning solutions (including household detergents). (2) Miscellaneous uses: 812.Product... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Formula No. 23-H. 21.49 Section 21.49 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT...

Improving ESL Writing Using an Online Formulaic Sequence Word-Combination Checker

ERIC Educational Resources Information Center

Grami, G. M. A.; Alkazemi, B. Y.

2016-01-01

Writing correct English sentences can be challenging. Furthermore, writing correct formulaic sequences can be especially difficult because accepted combinations do not follow clear rules governing which words appear together in a sequence. One solution is to provide examples of correct usage accompanied by statistical feedback from web-based…

The Factorability of Quadratics: Motivation for More Techniques

ERIC Educational Resources Information Center

Bosse, Michael J.; Nandakumar, N. R.

2005-01-01

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

A Solution Space for a System of Null-State Partial Differential Equations: Part 4

NASA Astrophysics Data System (ADS)

Flores, Steven M.; Kleban, Peter

2015-01-01

This article is the last of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). The system comprises 2 N null-state equations and three conformal Ward identities that govern CFT correlation functions of 2 N one-leg boundary operators. In the first two articles (Flores and Kleban in Commun Math Phys, 2012; Flores and Kleban, in Commun Math Phys, 2014), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. Using these results in the third article (Flores and Kleban, in Commun Math Phys, 2013), we prove that dim and is spanned by (real-valued) solutions constructed with the Coulomb gas (contour integral) formalism of CFT. In this article, we use these results to prove some facts concerning the solution space . First, we show that each of its elements equals a sum of at most two distinct Frobenius series in powers of the difference between two adjacent points (unless is odd, in which case a logarithmic term may appear). This establishes an important element in the operator product expansion for one-leg boundary operators, assumed in CFT. We also identify particular elements of , which we call connectivity weights, and exploit their special properties to conjecture a formula for the probability that the curves of a multiple-SLE process join in a particular connectivity. This leads to new formulas for crossing probabilities of critical lattice models inside polygons with a free/fixed side-alternating boundary condition, which we derive in Flores et al. (Partition functions and crossing probabilities for critical systems inside polygons, in preparation). Finally, we propose a reason for why the exceptional speeds [certain values that appeared in the analysis of the Coulomb gas solutions in Flores and Kleban (Commun Math Phys, 2013)] and the minimal models of CFT are connected.

Combinatorial Formulas for Characteristic Classes, and Localization of Secondary Topological Invariants.

NASA Astrophysics Data System (ADS)

Smirnov, Mikhail

1995-01-01

The problems solved in this thesis originated from combinatorial formulas for characteristic classes. This thesis deals with Chern-Simons classes, their generalizations and related algebraic and analytic problems. (1) In this thesis, I describe a new class of algebras whose elements contain Chern and generalized Chern -Simons classes. There is a Poisson bracket in these algebras, similar to the bracket in Kontsevich's noncommutative symplectic geometry (Kon). I prove that the Poisson bracket gives rise to a graded Lie algebra containing differential forms representing Chern and Chern-Simons classes. This is a new result. I describe algebraic analogs of the dilogarithm and higher polylogarithms in the algebra corresponding to Chern-Simons classes. (2) I study the properties of this bracket. It is possible to write the exterior differential and other operations in the algebra using this bracket. The bracket of any two Chern classes is zero and the bracket of a Chern class and a Chern-Simons class is d-closed. The construction developed here easily gives explicit formulas for known secondary classes and makes it possible to construct new ones. (3) I develop an algebraic model for the action of the gauge group and describe how elements of algebra corresponding to the secondary characteristic classes change under this action (see theorem 3 page xi). (4) It is possible give new explicit formulas for cocycles on a gauge group of a bundle and for the corresponding cocycles on the Lie algebra of the gauge group. I use formulas for secondary characteristic classes and an algebraic approach developed in chapter 1. I also use the work of Faddeev, Reiman and Semyonov-Tian-Shanskii (FRS) on cocycles as quantum anomalies. (5) I apply the methods of differential geometry of formal power series to construct universal characteristic and secondary characteristic classes. Given a pair of gauge equivalent connections using local formulas I obtain dilogarithmic and trilogarithmic analogs of Chern-Simons classes.

27 CFR 21.41 - Formula No. 13-A.

Code of Federal Regulations, 2014 CFR

2014-04-01

...). 241.Collodion, U.S.P. 331.Processing pectin. 332.Processing other food products. 342.Processing... and preserving solutions. 481.Photoengraving and rotogravure solutions and dyes. (2) As a raw material...

27 CFR 21.41 - Formula No. 13-A.

Code of Federal Regulations, 2012 CFR

2012-04-01

...). 241.Collodion, U.S.P. 331.Processing pectin. 332.Processing other food products. 342.Processing... and preserving solutions. 481.Photoengraving and rotogravure solutions and dyes. (2) As a raw material...

AN EMPIRICAL FORMULA FOR THE DISTRIBUTION FUNCTION OF A THIN EXPONENTIAL DISC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharma, Sanjib; Bland-Hawthorn, Joss

2013-08-20

An empirical formula for a Shu distribution function that reproduces a thin disc with exponential surface density to good accuracy is presented. The formula has two free parameters that specify the functional form of the velocity dispersion. Conventionally, this requires the use of an iterative algorithm to produce the correct solution, which is computationally taxing for applications like Markov Chain Monte Carlo model fitting. The formula has been shown to work for flat, rising, and falling rotation curves. Application of this methodology to one of the Dehnen distribution functions is also shown. Finally, an extension of this formula to reproducemore » velocity dispersion profiles that are an exponential function of radius is also presented. Our empirical formula should greatly aid the efficient comparison of disc models with large stellar surveys or N-body simulations.« less

Flowing to higher dimensions: a new strongly-coupled phase on M2 branes

DOE PAGES

Pilch, Krzysztof; Tyukov, Alexander; Warner, Nicholas P.

2015-11-24

We describe a one-parameter family of new holographic RG flows that start from AdS 4 × S 7 and go to AdS 5ˆ×B6, where B6 is conformal to a Kahler manifold and AdS 5ˆ is Poincaré AdS 5 with one spatial direction compactified and fibered over B6. The new solutions “flow up dimensions,” going from the (2 + 1)-dimensional conformal field theory on M2 branes in the UV to a (3 + 1)-dimensional field theory on intersecting M5 branes in the infra-red. The M2 branes completely polarize into M5 branes along the flow and the Poincare sections of the AdSmore » 5ˆ are the (3 + 1)-dimensional common intersection of the M5 branes. The emergence of the extra dimension in the infra-red suggests a new strongly-coupled phase of the M2 brane and ABJM theories in which charged solitons are becoming massless. The flow solution is first analyzed by finding a four-dimensional N=2 supersymmetric flow in N=8 gauged supergravity. This is then generalized to a one parameter family of non-supersymmetric flows. The infra-red limit of the solutions appears to be quite singular in four dimensions but the uplift to eleven-dimensional supergravity is remarkable and regular (up to orbifolding). Our construction is a non-trivial application of the recently derived uplift formulae for fluxes, going well beyond the earlier constructions of stationary points solutions. As a result, the eleven-dimensional supersymmetry is also analyzed and shows how, for the supersymmetric flow, the M2-brane supersymmetry in the UV is polarized entirely into M5-brane supersymmetry in the infra-red.« less

Flowing to higher dimensions: a new strongly-coupled phase on M2 branes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pilch, Krzysztof; Tyukov, Alexander; Warner, Nicholas P.

We describe a one-parameter family of new holographic RG flows that start from AdS 4 × S 7 and go to AdS 5ˆ×B6, where B6 is conformal to a Kahler manifold and AdS 5ˆ is Poincaré AdS 5 with one spatial direction compactified and fibered over B6. The new solutions “flow up dimensions,” going from the (2 + 1)-dimensional conformal field theory on M2 branes in the UV to a (3 + 1)-dimensional field theory on intersecting M5 branes in the infra-red. The M2 branes completely polarize into M5 branes along the flow and the Poincare sections of the AdSmore » 5ˆ are the (3 + 1)-dimensional common intersection of the M5 branes. The emergence of the extra dimension in the infra-red suggests a new strongly-coupled phase of the M2 brane and ABJM theories in which charged solitons are becoming massless. The flow solution is first analyzed by finding a four-dimensional N=2 supersymmetric flow in N=8 gauged supergravity. This is then generalized to a one parameter family of non-supersymmetric flows. The infra-red limit of the solutions appears to be quite singular in four dimensions but the uplift to eleven-dimensional supergravity is remarkable and regular (up to orbifolding). Our construction is a non-trivial application of the recently derived uplift formulae for fluxes, going well beyond the earlier constructions of stationary points solutions. As a result, the eleven-dimensional supersymmetry is also analyzed and shows how, for the supersymmetric flow, the M2-brane supersymmetry in the UV is polarized entirely into M5-brane supersymmetry in the infra-red.« less

Catalysis and chemical mechanisms of calcite dissolution in seawater.

PubMed

Subhas, Adam V; Adkins, Jess F; Rollins, Nick E; Naviaux, John; Erez, Jonathan; Berelson, William M

2017-07-18

Near-equilibrium calcite dissolution in seawater contributes significantly to the regulation of atmospheric [Formula: see text] on 1,000-y timescales. Despite many studies on far-from-equilibrium dissolution, little is known about the detailed mechanisms responsible for calcite dissolution in seawater. In this paper, we dissolve 13 C-labeled calcites in natural seawater. We show that the time-evolving enrichment of [Formula: see text] in solution is a direct measure of both dissolution and precipitation reactions across a large range of saturation states. Secondary Ion Mass Spectrometer profiles into the 13 C-labeled solids confirm the presence of precipitated material even in undersaturated conditions. The close balance of precipitation and dissolution near equilibrium can alter the chemical composition of calcite deeper than one monolayer into the crystal. This balance of dissolution-precipitation shifts significantly toward a dissolution-dominated mechanism below about [Formula: see text] Finally, we show that the enzyme carbonic anhydrase (CA) increases the dissolution rate across all saturation states, and the effect is most pronounced close to equilibrium. This finding suggests that the rate of hydration of [Formula: see text] is a rate-limiting step for calcite dissolution in seawater. We then interpret our dissolution data in a framework that incorporates both solution chemistry and geometric constraints on the calcite solid. Near equilibrium, this framework demonstrates a lowered free energy barrier at the solid-solution interface in the presence of CA. This framework also indicates a significant change in dissolution mechanism at [Formula: see text], which we interpret as the onset of homogeneous etch pit nucleation.

Analysis of mixing conditions and multistage irradiation impact on NOx removal efficiency in the electron beam flue gas treatment process.

PubMed

Pawelec, Andrzej; Dobrowolski, Andrzej

2017-01-01

In the process of electron beam flue gas treatment (EBFGT), most energy is spent on NO x removal. The dose distribution in the reactor is not uniform and the flue gas flow pattern plays an important role in the process efficiency. It was found that proper construction of the reactor may increase the energy efficiency of the process. The impact of the number of irradiation stages and mixing conditions on NO x removal efficiency was investigated for an ideal case and a practical solution was presented and compared with previously known EBFGT reactor constructions. The research was performed by means of computational fluid dynamics methods in combination with empirical Wittig formula. Two versions of dose distribution were taken for calculations. The results of the research show that for an ideal case, application of multistage irradiation and interstage mixing may reduce the energy consumption in the process by up to 39%. On the other side, simulation of reactor construction modification for two-stage irradiation results in 25% energy consumption reduction. The results of presented case study may be applied for improving the existing reactors and proper design of future installations.

Exact recovery of sparse multiple measurement vectors by [Formula: see text]-minimization.

PubMed

Wang, Changlong; Peng, Jigen

2018-01-01

The joint sparse recovery problem is a generalization of the single measurement vector problem widely studied in compressed sensing. It aims to recover a set of jointly sparse vectors, i.e., those that have nonzero entries concentrated at a common location. Meanwhile [Formula: see text]-minimization subject to matrixes is widely used in a large number of algorithms designed for this problem, i.e., [Formula: see text]-minimization [Formula: see text] Therefore the main contribution in this paper is two theoretical results about this technique. The first one is proving that in every multiple system of linear equations there exists a constant [Formula: see text] such that the original unique sparse solution also can be recovered from a minimization in [Formula: see text] quasi-norm subject to matrixes whenever [Formula: see text]. The other one is showing an analytic expression of such [Formula: see text]. Finally, we display the results of one example to confirm the validity of our conclusions, and we use some numerical experiments to show that we increase the efficiency of these algorithms designed for [Formula: see text]-minimization by using our results.

Optimizing highly noncoplanar VMAT trajectories: the NoVo method.

PubMed

Langhans, Marco; Unkelbach, Jan; Bortfeld, Thomas; Craft, David

2018-01-16

We introduce a new method called NoVo (Noncoplanar VMAT Optimization) to produce volumetric modulated arc therapy (VMAT) treatment plans with noncoplanar trajectories. While the use of noncoplanar beam arrangements for intensity modulated radiation therapy (IMRT), and in particular high fraction stereotactic radiosurgery (SRS), is common, noncoplanar beam trajectories for VMAT are less common as the availability of treatment machines handling these is limited. For both IMRT and VMAT, the beam angle selection problem is highly nonconvex in nature, which is why automated beam angle selection procedures have not entered mainstream clinical usage. NoVo determines a noncoplanar VMAT solution (i.e. the simultaneous trajectories of the gantry and the couch) by first computing a [Formula: see text] solution (beams from every possible direction, suitably discretized) and then eliminating beams by examing fluence contributions. Also all beam angles are scored via geometrical considerations only to find out the usefulness of the whole beam space in a very short time. A custom path finding algorithm is applied to find an optimized, continuous trajectory through the most promising beam angles using the calculated score of the beam space. Finally, using this trajectory a VMAT plan is optimized. For three clinical cases, a lung, brain, and liver case, we compare NoVo to the ideal [Formula: see text] solution, nine beam noncoplanar IMRT, coplanar VMAT, and a recently published noncoplanar VMAT algorithm. NoVo comes closest to the [Formula: see text] solution considering the lung case (brain and liver case: second), as well as improving the solution time by using geometrical considerations, followed by a time effective iterative process reducing the [Formula: see text] solution. Compared to a recently published noncoplanar VMAT algorithm, using NoVo the computation time is reduced by a factor of 2-3 (depending on the case). Compared to coplanar VMAT, NoVo reduces the objective function value by 24%, 49% and 6% for the lung, brain and liver cases, respectively.

Exact Closed-form Solutions for Lamb's Problem

NASA Astrophysics Data System (ADS)

Feng, Xi; Zhang, Haiming

2018-04-01

In this article, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem, for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's (1974) integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson (1974), which strongly confirms the correctness of our explicit formulas. It is hoped that in due time, these formulas may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.

Exact closed-form solutions for Lamb's problem

NASA Astrophysics Data System (ADS)

Feng, Xi; Zhang, Haiming

2018-07-01

In this paper, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson, which strongly confirms the correctness of our explicit formulae. It is hoped that in due time, these formulae may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.

Light-quark and gluon jet discrimination in [Formula: see text] collisions at [Formula: see text] with the ATLAS detector.

PubMed

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Schaarschmidt, J; Schacht, P; Schaefer, D; Schaefer, R; Schaepe, S; Schaetzel, S; Schäfer, U; Schaffer, A C; Schaile, D; Schamberger, R D; Scharf, V; Schegelsky, V A; Scheirich, D; Schernau, M; Scherzer, M I; Schiavi, C; Schieck, J; Schillo, C; Schioppa, M; Schlenker, S; Schmidt, E; Schmieden, K; Schmitt, C; Schmitt, C; Schmitt, S; Schneider, B; Schnellbach, Y J; Schnoor, U; Schoeffel, L; Schoening, A; Schoenrock, B D; Schorlemmer, A L S; Schott, M; Schouten, D; Schovancova, J; Schram, M; Schramm, S; Schreyer, M; Schroeder, C; Schuh, N; Schultens, M J; Schultz-Coulon, H-C; Schulz, H; Schumacher, M; Schumm, B A; Schune, Ph; Schwartzman, A; Schwegler, Ph; Schwemling, Ph; Schwienhorst, R; Schwindling, J; Schwindt, T; Schwoerer, M; Sciacca, F G; Scifo, E; Sciolla, G; Scott, W G; Scuri, F; Scutti, F; Searcy, J; Sedov, G; Sedykh, E; Seidel, S C; Seiden, A; Seifert, F; Seixas, J M; Sekhniaidze, G; Sekula, S J; Selbach, K E; Seliverstov, D M; Sellers, G; Semprini-Cesari, N; Serfon, C; Serin, L; Serkin, L; Serre, T; Seuster, R; Severini, H; Sforza, F; Sfyrla, A; Shabalina, E; Shamim, M; Shan, L Y; Shank, J T; Shao, Q T; Shapiro, M; Shatalov, P B; Shaw, K; Sherwood, P; Shimizu, S; Shimmin, C O; Shimojima, M; Shiyakova, M; Shmeleva, A; Shochet, M J; Short, D; Shrestha, S; Shulga, E; Shupe, M A; Shushkevich, S; Sicho, P; Sidorov, D; Sidoti, A; Siegert, F; Sijacki, Dj; Silbert, O; Silva, J; Silver, Y; Silverstein, D; Silverstein, S B; Simak, V; Simard, O; Simic, Lj; Simion, S; Simioni, E; Simmons, B; Simoniello, R; Simonyan, M; Sinervo, P; Sinev, N B; Sipica, V; Siragusa, G; Sircar, A; Sisakyan, A N; Sivoklokov, S Yu; Sjölin, J; Sjursen, T B; Skottowe, H P; Skovpen, K Yu; Skubic, P; Slater, M; Slavicek, T; Sliwa, K; Smakhtin, V; Smart, B H; Smestad, L; Smirnov, S Yu; Smirnov, Y; Smirnova, L N; Smirnova, O; Smizanska, M; Smolek, K; Snesarev, A A; Snidero, G; Snow, J; Snyder, S; Sobie, R; Socher, F; Sodomka, J; Soffer, A; Soh, D A; Solans, C A; Solar, M; Solc, J; Soldatov, E Yu; Soldevila, U; Solfaroli Camillocci, E; Solodkov, A A; Solovyanov, O V; Solovyev, V; Sommer, P; Song, H Y; Soni, N; Sood, A; Sopczak, A; Sopko, V; Sopko, B; Sorin, V; Sosebee, M; Soualah, R; Soueid, P; Soukharev, A M; South, D; Spagnolo, S; Spanò, F; Spearman, W R; Spighi, R; Spigo, G; Spousta, M; Spreitzer, T; Spurlock, B; Denis, R D St; Staerz, S; Stahlman, J; Stamen, R; Stanecka, E; Stanek, R W; Stanescu, C; Stanescu-Bellu, M; Stanitzki, M M; Stapnes, S; Starchenko, E A; Stark, J; Staroba, P; Starovoitov, P; Staszewski, R; Stavina, P; Steele, G; Steinberg, P; Stekl, I; Stelzer, B; Stelzer, H J; Stelzer-Chilton, O; Stenzel, H; Stern, S; Stewart, G A; Stillings, J A; Stockton, M C; Stoebe, M; Stoicea, G; Stolte, P; Stonjek, S; Stradling, A R; Straessner, A; Stramaglia, M E; Strandberg, J; Strandberg, S; Strandlie, A; Strauss, E; Strauss, M; Strizenec, P; Ströhmer, R; Strom, D M; Stroynowski, R; Stucci, S A; Stugu, B; Styles, N A; Su, D; Su, J; Subramania, Hs; Subramaniam, R; Succurro, A; Sugaya, Y; Suhr, C; Suk, M; Sulin, V V; Sultansoy, S; Sumida, T; Sun, X; Sundermann, J E; Suruliz, K; Susinno, G; Sutton, M R; Suzuki, Y; Svatos, M; Swedish, S; Swiatlowski, M; Sykora, I; Sykora, T; Ta, D; Tackmann, K; Taenzer, J; Taffard, A; Tafirout, R; Taiblum, N; Takahashi, Y; Takai, H; Takashima, R; Takeda, H; Takeshita, T; Takubo, Y; Talby, M; Talyshev, A A; Tam, J Y C; Tamsett, M C; Tan, K G; Tanaka, J; Tanaka, R; Tanaka, S; Tanaka, S; Tanasijczuk, A J; Tani, K; Tannoury, N; Tapprogge, S; Tarem, S; Tarrade, F; Tartarelli, G F; Tas, P; Tasevsky, M; Tashiro, T; Tassi, E; Tavares Delgado, A; Tayalati, Y; Taylor, F E; Taylor, G N; Taylor, W; Teischinger, F A; Teixeira Dias Castanheira, M; Teixeira-Dias, P; Temming, K K; Ten Kate, H; Teng, P K; Terada, S; Terashi, K; Terron, J; Terzo, S; Testa, M; Teuscher, R J; Therhaag, J; Theveneaux-Pelzer, T; Thoma, S; Thomas, J P; Thomas-Wilsker, J; Thompson, E N; Thompson, P D; Thompson, P D; Thompson, A S; Thomsen, L A; Thomson, E; Thomson, M; Thong, W M; Thun, R P; Tian, F; Tibbetts, M J; Tikhomirov, V O; Tikhonov, Yu A; Timoshenko, S; Tiouchichine, E; Tipton, P; Tisserant, S; Todorov, T; Todorova-Nova, S; Toggerson, B; Tojo, J; Tokár, S; Tokushuku, K; Tollefson, K; Tomlinson, L; Tomoto, M; Tompkins, L; Toms, K; Topilin, N D; Torrence, E; Torres, H; Torró Pastor, E; Toth, J; Touchard, F; Tovey, D R; Tran, H L; Trefzger, T; Tremblet, L; Tricoli, A; Trigger, I M; Trincaz-Duvoid, S; Tripiana, M F; Triplett, N; Trischuk, W; Trocmé, B; Troncon, C; Trottier-McDonald, M; Trovatelli, M; True, P; Trzebinski, M; Trzupek, A; Tsarouchas, C; Tseng, J C-L; Tsiareshka, P V; Tsionou, D; Tsipolitis, G; Tsirintanis, N; Tsiskaridze, S; Tsiskaridze, V; Tskhadadze, E G; Tsukerman, I I; Tsulaia, V; Tsuno, S; Tsybychev, D; Tudorache, A; Tudorache, V; Tuna, A N; Tupputi, S A; Turchikhin, S; Turecek, D; Turk Cakir, I; Turra, R; Tuts, P M; Tykhonov, A; Tylmad, M; Tyndel, M; Uchida, K; Ueda, I; Ueno, R; Ughetto, M; Ugland, M; Uhlenbrock, M; Ukegawa, F; Unal, G; Undrus, A; Unel, G; Ungaro, F C; Unno, Y; Urbaniec, D; Urquijo, P; Usai, G; Usanova, A; Vacavant, L; Vacek, V; Vachon, B; Valencic, N; Valentinetti, S; Valero, A; Valery, L; Valkar, S; Valladolid Gallego, E; Vallecorsa, S; Valls Ferrer, J A; Van Berg, R; Van Der Deijl, P C; van der Geer, R; van der Graaf, H; Van Der Leeuw, R; van der Ster, D; van Eldik, N; van Gemmeren, P; Van Nieuwkoop, J; van Vulpen, I; van Woerden, M C; Vanadia, M; Vandelli, W; Vanguri, R; Vaniachine, A; Vankov, P; Vannucci, F; Vardanyan, G; Vari, R; Varnes, E W; Varol, T; Varouchas, D; Vartapetian, A; Varvell, K E; Vazeille, F; Vazquez Schroeder, T; Veatch, J; Veloso, F; Veneziano, S; Ventura, A; Ventura, D; Venturi, M; Venturi, N; Venturini, A; Vercesi, V; Verducci, M; Verkerke, W; Vermeulen, J C; Vest, A; Vetterli, M C; Viazlo, O; Vichou, I; Vickey, T; Vickey Boeriu, O E; Viehhauser, G H A; Viel, S; Vigne, R; Villa, M; Villaplana Perez, M; Vilucchi, E; Vincter, M G; Vinogradov, V B; Virzi, J; Vivarelli, I; Vives Vaque, F; Vlachos, S; Vladoiu, D; Vlasak, M; Vogel, A; Vokac, P; Volpi, G; Volpi, M; von der Schmitt, H; von Radziewski, H; von Toerne, E; Vorobel, V; Vorobev, K; Vos, M; Voss, R; Vossebeld, J H; Vranjes, N; Vranjes Milosavljevic, M; Vrba, V; Vreeswijk, M; Vu Anh, T; Vuillermet, R; Vukotic, I; Vykydal, Z; Wagner, W; Wagner, P; Wahrmund, S; Wakabayashi, J; Walder, J; Walker, R; Walkowiak, W; Wall, R; Waller, P; Walsh, B; Wang, C; Wang, C; Wang, F; Wang, H; Wang, H; Wang, J; Wang, J; Wang, K; Wang, R; Wang, S M; Wang, T; Wang, X; Wanotayaroj, C; Warburton, A; Ward, C P; Wardrope, D R; Warsinsky, M; Washbrook, A; Wasicki, C; Watanabe, I; Watkins, P M; Watson, A T; Watson, I J; Watson, M F; Watts, G; Watts, S; Waugh, B M; Webb, S; Weber, M S; Weber, S W; Webster, J S; Weidberg, A R; Weigell, P; Weinert, B; Weingarten, J; Weiser, C; Weits, H; Wells, P S; Wenaus, T; Wendland, D; Weng, Z; Wengler, T; Wenig, S; Wermes, N; Werner, M; Werner, P; Wessels, M; Wetter, J; Whalen, K; White, A; White, M J; White, R; White, S; Whiteson, D; Wicke, D; Wickens, F J; Wiedenmann, W; Wielers, M; Wienemann, P; Wiglesworth, C; Wiik-Fuchs, L A M; Wijeratne, P A; Wildauer, A; Wildt, M A; Wilkens, H G; Will, J Z; Williams, H H; Williams, S; Willis, C; Willocq, S; Wilson, J A; Wilson, A; Wingerter-Seez, I; Winklmeier, F; Wittgen, M; Wittig, T; Wittkowski, J; Wollstadt, S J; Wolter, M W; Wolters, H; Wosiek, B K; Wotschack, J; Woudstra, M J; Wozniak, K W; Wright, M; Wu, M; Wu, S L; Wu, X; Wu, Y; Wulf, E; Wyatt, T R; Wynne, B M; Xella, S; Xiao, M; Xu, D; Xu, L; Yabsley, B; Yacoob, S; Yamada, M; Yamaguchi, H; Yamaguchi, Y; Yamamoto, A; Yamamoto, K; Yamamoto, S; Yamamura, T; Yamanaka, T; Yamauchi, K; Yamazaki, Y; Yan, Z; Yang, H; Yang, H; Yang, U K; Yang, Y; Yanush, S; Yao, L; Yao, W-M; Yasu, Y; Yatsenko, E; Yau Wong, K H; Ye, J; Ye, S; Yen, A L; Yildirim, E; Yilmaz, M; Yoosoofmiya, R; Yorita, K; Yoshida, R; Yoshihara, K; Young, C; Young, C J S; Youssef, S; Yu, D R; Yu, J; Yu, J M; Yu, J; Yuan, L; Yurkewicz, A; Zabinski, B; Zaidan, R; Zaitsev, A M; Zaman, A; Zambito, S; Zanello, L; Zanzi, D; Zaytsev, A; Zeitnitz, C; Zeman, M; Zemla, A; Zengel, K; Zenin, O; Ženiš, T; Zerwas, D; Zevi Della Porta, G; Zhang, D; Zhang, F; Zhang, H; Zhang, J; Zhang, L; Zhang, X; Zhang, Z; Zhao, Z; Zhemchugov, A; Zhong, J; Zhou, B; Zhou, L; Zhou, N; Zhu, C G; Zhu, H; Zhu, J; Zhu, Y; Zhuang, X; Zibell, A; Zieminska, D; Zimine, N I; Zimmermann, C; Zimmermann, R; Zimmermann, S; Zimmermann, S; Zinonos, Z; Ziolkowski, M; Zobernig, G; Zoccoli, A; Zur Nedden, M; Zurzolo, G; Zutshi, V; Zwalinski, L

A likelihood-based discriminant for the identification of quark- and gluon-initiated jets is built and validated using 4.7 fb[Formula: see text] of proton-proton collision data at [Formula: see text] [Formula: see text] collected with the ATLAS detector at the LHC. Data samples with enriched quark or gluon content are used in the construction and validation of templates of jet properties that are the input to the likelihood-based discriminant. The discriminating power of the jet tagger is established in both data and Monte Carlo samples within a systematic uncertainty of [Formula: see text] 10-20 %. In data, light-quark jets can be tagged with an efficiency of [Formula: see text] while achieving a gluon-jet mis-tag rate of [Formula: see text] in a [Formula: see text] range between [Formula: see text] and [Formula: see text] for jets in the acceptance of the tracker. The rejection of gluon-jets found in the data is significantly below what is attainable using a Pythia 6 Monte Carlo simulation, where gluon-jet mis-tag rates of 10 % can be reached for a 50 % selection efficiency of light-quark jets using the same jet properties.

On the Flow of a Compressible Fluid by the Hodograph Method. II - Fundamental Set of Particular Flow Solutions of the Chaplygin Differential Equation

NASA Technical Reports Server (NTRS)

Garrick, I. E.; Kaplan, Carl

1944-01-01

The differential equation of Chaplygin's jet problem is utilized to give a systematic development of particular solutions of the hodograph flow equations, which extends the treatment of Chaplygin into the supersonic range and completes the set of particular solutions. The particular solutions serve to place on a reasonable basis the use of velocity correction formulas for the comparison of incompressible and compressible flows. It is shown that the geometric-mean type of velocity correction formula introduced in part I has significance as an over-all type of approximation in the subsonic range. A brief review of general conditions limiting the potential flow of an adiabatic compressible fluid is given and application is made to the particular solutions, yielding conditions for the existence of singular loci in the supersonic range. The combining of particular solutions in accordance with prescribed boundary flow conditions is not treated in the present paper.

Derivation of formulas for root-mean-square errors in location, orientation, and shape in triangulation solution of an elongated object in space

NASA Technical Reports Server (NTRS)

Long, S. A. T.

1974-01-01

Formulas are derived for the root-mean-square (rms) displacement, slope, and curvature errors in an azimuth-elevation image trace of an elongated object in space, as functions of the number and spacing of the input data points and the rms elevation error in the individual input data points from a single observation station. Also, formulas are derived for the total rms displacement, slope, and curvature error vectors in the triangulation solution of an elongated object in space due to the rms displacement, slope, and curvature errors, respectively, in the azimuth-elevation image traces from different observation stations. The total rms displacement, slope, and curvature error vectors provide useful measure numbers for determining the relative merits of two or more different triangulation procedures applicable to elongated objects in space.

An empirical relationship for homogenization in single-phase binary alloy systems

NASA Technical Reports Server (NTRS)

Unnam, J.; Tenney, D. R.; Stein, B. A.

1979-01-01

A semiempirical formula is developed for describing the extent of interaction between constituents in single-phase binary alloy systems with planar, cylindrical, or spherical interfaces. The formula contains two parameters that are functions of mean concentration and interface geometry of the couple. The empirical solution is simple, easy to use, and does not involve sequential calculations, thereby allowing quick estimation of the extent of interactions without lengthy calculations. Results obtained with this formula are in good agreement with those from a finite-difference analysis.

Ultrathin nanoporous membranes for insulator-based dielectrophoresis.

PubMed

Mukaibo, Hitomi; Wang, Tonghui; Perez-Gonzalez, Victor H; Getpreecharsawas, Jirachai; Wurzer, Jack; Lapizco-Encinas, Blanca H; McGrath, James L

2018-06-08

Insulator-based dielectrophoresis (iDEP) is a simple, scalable mechanism that can be used for directly manipulating particle trajectories in pore-based filtration and separation processes. However, iDEP manipulation of nanoparticles presents unique challenges as the dielectrophoretic force [Formula: see text] exerted on the nanoparticles can easily be overshadowed by opposing kinetic forces. In this study, a molecularly thin, SiN-based nanoporous membrane (NPN) is explored as a breakthrough technology that enhances [Formula: see text] By numerically assessing the gradient of the electric field square [Formula: see text]-a common measure for [Formula: see text] magnitude-it was found that the unique geometrical features of NPN (pore tapering, sharp pore corner and ultrathin thickness) act in favor of intensifying the overall [Formula: see text] A comparative study indicated that [Formula: see text] generated in NPN are four orders of magnitude larger than track-etched polycarbonate membranes with comparable pore size. The stronger [Formula: see text] suggests that iDEP can be conducted under lower voltage bias with NPN: reducing joule heating concerns and enabling solutions to have higher ionic strength. Enabling higher ionic strength solutions may also extend the opportunities of iDEP applications under physiologically relevant conditions. This study also highlights the effects of [Formula: see text] induced by the ion accumulation along charged surfaces (electric-double layer (EDL)). EDL-based [Formula: see text] exists along the entire charged surface, including locations where geometry-based iDEP is negligible. The high surface-to-volume ratio of NPN offers a unique platform for exploiting such EDL-based DEP systems. The EDL-based [Formula: see text] was also found to offset the geometry-based [Formula: see text] but this effect was easily circumvented by reducing the EDL thickness (e.g. increasing the ionic strength from 0.1 to 100 mM). The results from this study imply the potential application of iDEP as a direct, in-operando antifouling mechanism for ultrafiltration technology, and also as an active tuning mechanism to control the cut-off size limit for continuous selectivity of nanomembrane-based separations.

Developing Student's Notion of Measurement Unit for Area

ERIC Educational Resources Information Center

Yuberta, Kurnia Rahmi; Zulkardi; Hartono, Yusuf; van Galen, Frans

2011-01-01

Many researchers found that students have difficulties in understanding area measurement. Students mostly focus on applying formula to find the area of certain shapes without knowing what the area is and why the formula works. It is important for the students to know what attribute being measured and to construct the unit for area measurement.…

Elementary kinematical model of thermal diffusion in liquids and gases.

PubMed

Brenner, Howard

2006-09-01

An elementary hydrodynamic and Brownian motion model of the thermal diffusivity D(T) of a restricted class of binary liquid mixtures, previously proposed by the author, is given a more transparent derivation than originally, exposing thereby the strictly kinematic-hydrodynamic nature of an important class of thermodiffusion separation phenomena. Moreover, it is argued that the solvent's thermometric diffusivity alpha appearing in that theory as one of the two fundamental parameters governing D(T) should be replaced by the solvent's (isothermal) self-diffusivity D(S). In addition, a corrective multiplier of O(1) is inserted to reflect the general physicochemical noninertness of the solute relative to the solvent, thus enhancing the applicability of the resulting formula D(T)=lambdaD(S)beta to "nonideal" solutions. Here, beta is the solvent's thermal expansivity and lambda is a term of O(1), insensitive to the physicochemical nature of the solute (thus rendering D(T) primarily dependent upon only the properties of the solvent). This formula is, on the basis of its derivation, presumably valid only under certain idealized, albeit well-defined, circumstances. This occurs when the solute molecules are: (i) large compared with those of the solvent; and (ii) present only in small proportions relative to those of the solvent. When the solute is physicochemically inert, it is expected that lambda=1. When these conditions are met, the resulting thermal diffusivity of the mixture is, in theory, independent of any and all properties of the solute. Moreover, because beta is algebraically signed, the thermal diffusivity can either by positive or negative, according as the solvent expands or contracts upon being heated. This formula for D(T) is compared with available experimental data for selected binary liquid mixtures. Reasonable agreement is found in almost all circumstances with lambda near unity, the more so the higher the temperature, especially when the solute-solvent mixture properties closely approximate those where agreement would be expected and conversely. Finally, it is pointed out that for the restricted circumstances described, the formula D(T)=lambdaD(S)beta is equally credible for gases. Here, based on gas-kinetic theory, it is possible to furnish the theoretical value of lambda. Overall, while spanning a range of about five orders of magnitude, the D(T) values given by this elementary formula are shown to apply with reasonable accuracy to: (i) liquids (including circumstances for which D(T) is negative) as well as gases; (ii) all combinations of solvents and solutes tested (the latter including, for example, polymer molecules and metallic colloidal particles); and (iii) all sizes of solute molecules, from angstroms to submicron.

Few-cycle optical rogue waves: complex modified Korteweg-de Vries equation.

PubMed

He, Jingsong; Wang, Lihong; Li, Linjing; Porsezian, K; Erdélyi, R

2014-06-01

In this paper, we consider the complex modified Korteweg-de Vries (mKdV) equation as a model of few-cycle optical pulses. Using the Lax pair, we construct a generalized Darboux transformation and systematically generate the first-, second-, and third-order rogue wave solutions and analyze the nature of evolution of higher-order rogue waves in detail. Based on detailed numerical and analytical investigations, we classify the higher-order rogue waves with respect to their intrinsic structure, namely, fundamental pattern, triangular pattern, and ring pattern. We also present several new patterns of the rogue wave according to the standard and nonstandard decomposition. The results of this paper explain the generalization of higher-order rogue waves in terms of rational solutions. We apply the contour line method to obtain the analytical formulas of the length and width of the first-order rogue wave of the complex mKdV and the nonlinear Schrödinger equations. In nonlinear optics, the higher-order rogue wave solutions found here will be very useful to generate high-power few-cycle optical pulses which will be applicable in the area of ultrashort pulse technology.

A 2-D numerical simulation study on longitudinal solute transport and longitudinal dispersion coefficient

NASA Astrophysics Data System (ADS)

Zhang, Wei

2011-07-01

The longitudinal dispersion coefficient, DL, is a fundamental parameter of longitudinal solute transport models: the advection-dispersion (AD) model and various deadzone models. Since DL cannot be measured directly, and since its calibration using tracer test data is quite expensive and not always available, researchers have developed various methods, theoretical or empirical, for estimating DL by easier available cross-sectional hydraulic measurements (i.e., the transverse velocity profile, etc.). However, for known and unknown reasons, DL cannot be satisfactorily predicted using these theoretical/empirical formulae. Either there is very large prediction error for theoretical methods, or there is a lack of generality for the empirical formulae. Here, numerical experiments using Mike21, a software package that implements one of the most rigorous two-dimensional hydrodynamic and solute transport equations, for longitudinal solute transport in hypothetical streams, are presented. An analysis of the evolution of simulated solute clouds indicates that the two fundamental assumptions in Fischer's longitudinal transport analysis may be not reasonable. The transverse solute concentration distribution, and hence the longitudinal transport appears to be controlled by a dimensionless number ?, where Q is the average volumetric flowrate, Dt is a cross-sectional average transverse dispersion coefficient, and W is channel flow width. A simple empirical ? relationship may be established. Analysis and a revision of Fischer's theoretical formula suggest that ɛ influences the efficiency of transverse mixing and hence has restraining effect on longitudinal spreading. The findings presented here would improve and expand our understanding of longitudinal solute transport in open channel flow.

Students' Difficulties with Applying a Familiar Formula in an Unfamiliar Context

ERIC Educational Resources Information Center

Hoch, Maureen; Dreyfus, Tommy

2005-01-01

This paper discusses problems many tenth grade students have when asked to apply a familiar formula in an unfamiliar context: specifically factoring a compound expression. Some of their attempts at solution are presented and discussed in terms of structure sense. (Contains 1 table.) [For complete proceedings, see ED496848.

Synthesis and preliminary biological evaluations of (+)-isocampholenic acid-derived amides.

PubMed

Grošelj, Uroš; Golobič, Amalija; Knez, Damijan; Hrast, Martina; Gobec, Stanislav; Ričko, Sebastijan; Svete, Jurij

2016-08-01

The synthesis of two novel (+)-isocampholenic acid-derived amines has been realized starting from commercially available (1S)-(+)-10-camphorsulfonic acid. The novel amines as well as (+)-isocampholenic acid have been used as building blocks in the construction of a library of amides using various aliphatic, aromatic, and amino acid-derived coupling partners using BPC and CDI as activating agents. Amide derivatives have been assayed against several enzymes that hold potential for the development of new drugs to battle bacterial infections and Alzheimer's disease. Compounds 20c and 20e showed promising selective sub-micromolar inhibition of human butyrylcholinesterase [Formula: see text] ([Formula: see text] values [Formula: see text] and [Formula: see text], respectively).

Lyapunov dimension formula for the global attractor of the Lorenz system

NASA Astrophysics Data System (ADS)

Leonov, G. A.; Kuznetsov, N. V.; Korzhemanova, N. A.; Kusakin, D. V.

2016-12-01

The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of parameters, including classical values, was analytically obtained first by G.A. Leonov in 2002. Leonov used the construction technique of special Lyapunov-type functions, which was developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters, of the system, such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values including all parameters, which satisfy the classical physical limitations.

Nonequilibrium electrophoresis of an ion-selective microgranule for weak and moderate external electric fields

NASA Astrophysics Data System (ADS)

Frants, E. A.; Ganchenko, G. S.; Shelistov, V. S.; Amiroudine, S.; Demekhin, E. A.

2018-02-01

Electrokinetics and the movement of charge-selective micro-granules in an electrolyte solution under the influence of an external electric field are investigated theoretically. Straightforward perturbation analysis is applied to a thin electric double layer and a weak external field, while a numerical solution is used for moderate electric fields. The asymptotic solution enables the determination of the salt concentration, electric charge distribution, and electro-osmotic velocity fields. It may also be used to obtain a simple analytical formula for the electrophoretic velocity in the case of quasi-equilibrium electrophoresis (electrophoresis of the first kind). This formula differs from the famous Helmholtz-Smoluchowski relation, which applies to dielectric microparticles, but not to ion-selective granules. Numerical calculations are used to validate the derived formula for weak external electric fields, but for moderate fields, nonlinear effects lead to a significant increase in electrophoretic mobility and to a transition from quasi-equilibrium electrophoresis of the first kind to nonequilibrium electrophoresis of the second kind. Theoretical results are successfully compared with experimental data.

A Solution Space for a System of Null-State Partial Differential Equations: Part 3

NASA Astrophysics Data System (ADS)

Flores, Steven M.; Kleban, Peter

2015-01-01

This article is the third of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations (PDEs) in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE κ ). The system comprises 2 N null-state equations and three conformal Ward identities that govern CFT correlation functions of 2 N one-leg boundary operators. In the first two articles (Flores and Kleban, in Commun Math Phys, arXiv:1212.2301, 2012; Commun Math Phys, arXiv:1404.0035, 2014), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. Extending these results, we prove in this article that dim and entirely consists of (real-valued) solutions constructed with the CFT Coulomb gas (contour integral) formalism. In order to prove this claim, we show that a certain set of C N such solutions is linearly independent. Because the formulas for these solutions are complicated, we prove linear independence indirectly. We use the linear injective map of Lemma 15 in Flores and Kleban (Commun Math Phys, arXiv:1212.2301, 2012) to send each solution of the mentioned set to a vector in , whose components we find as inner products of elements in a Temperley-Lieb algebra. We gather these vectors together as columns of a symmetric matrix, with the form of a meander matrix. If the determinant of this matrix does not vanish, then the set of C N Coulomb gas solutions is linearly independent. And if this determinant does vanish, then we construct an alternative set of C N Coulomb gas solutions and follow a similar procedure to show that this set is linearly independent. The latter situation is closely related to CFT minimal models. We emphasize that, although the system of PDEs arises in CFT in away that is typically non-rigorous, our treatment of this system here and in Flores and Kleban (Commun Math Phys, arXiv:1212.2301, 2012; Commun Math Phys, arXiv:1404.0035, 2014; Commun Math Phys, arXiv:1405.2747, 2014) is completely rigorous.

Analytical studies on holographic superconductor in the probe limit

NASA Astrophysics Data System (ADS)

Peng, Yan; Liu, Guohua

2017-09-01

We investigate the holographic superconductor model constructed in the (2+1)-dimensional AdS soliton background in the probe limit. With analytical methods, we obtain the formula of critical phase transition points with respect to the scalar mass. We also generalize this formula to higher-dimensional space-time. We mention that these formulas are precise compared to numerical results. In addition, we find a correspondence between the value of the charged scalar field at the tip and the scalar operator at infinity around the phase transition points.

Formal verification of automated teller machine systems using SPIN

NASA Astrophysics Data System (ADS)

Iqbal, Ikhwan Mohammad; Adzkiya, Dieky; Mukhlash, Imam

2017-08-01

Formal verification is a technique for ensuring the correctness of systems. This work focuses on verifying a model of the Automated Teller Machine (ATM) system against some specifications. We construct the model as a state transition diagram that is suitable for verification. The specifications are expressed as Linear Temporal Logic (LTL) formulas. We use Simple Promela Interpreter (SPIN) model checker to check whether the model satisfies the formula. This model checker accepts models written in Process Meta Language (PROMELA), and its specifications are specified in LTL formulas.

Hovering efficiency comparison of rotary and flapping flight for rigid rectangular wings via dimensionless multi-objective optimization.

PubMed

Bayiz, Yagiz; Ghanaatpishe, Mohammad; Fathy, Hosam; Cheng, Bo

2018-05-08

In this work, a multi-objective optimization framework is developed for optimizing low Reynolds number ([Formula: see text]) hovering flight. This framework is then applied to compare the efficiency of rigid revolving and flapping wings with rectangular shape under varying [Formula: see text] and Rossby number ([Formula: see text], or aspect ratio). The proposed framework is capable of generating sets of optimal solutions and Pareto fronts for maximizing the lift coefficient and minimizing the power coefficient in dimensionless space, explicitly revealing the trade-off between lift generation and power consumption. The results indicate that revolving wings are more efficient when the required average lift coefficient [Formula: see text] is low (<1 for [Formula: see text] and  <1.6 for [Formula: see text]), while flapping wings are more efficient in achieving higher [Formula: see text]. With the dimensionless power loading as the single-objective performance measure to be maximized, rotary flight is more efficient than flapping wings for [Formula: see text] regardless of the amount of energy storage assumed in the flapping wing actuation mechanism, while flapping flight is more efficient for [Formula: see text]. It is observed that wings with low [Formula: see text] perform better when higher [Formula: see text] is needed, whereas higher [Formula: see text] cases are more efficient at [Formula: see text] regions. However, for the selected geometry and [Formula: see text], the efficiency is weakly dependent on [Formula: see text] when the dimensionless power loading is maximized.

Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Felice, Antonio De; Tsujikawa, Shinji, E-mail: antoniod@nu.ac.th, E-mail: shinji@rs.kagu.tus.ac.jp

2012-02-01

In the Horndeski's most general scalar-tensor theories with second-order field equations, we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar, tensor, and vector perturbations in the presence of two perfect fluids on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) background. Our general results are useful for the construction of theoretically consistent models of dark energy. We apply our formulas to extended Galileon models in which a tracker solution with an equation of state smaller than -1 is present. We clarify the allowed parameter space in which the ghosts and Laplacian instabilities are absent and we numerically confirmmore » that such models are indeed cosmologically viable.« less

Space processing of electronic materials

NASA Technical Reports Server (NTRS)

Holland, L. R.

1982-01-01

The bulk growth of solid solution alloys of mercury telluride and cadmium telluride is discussed. These alloys are usually described by the formula Hg1-xCdxTe, and are useful for the construction of infrared detectors. The electronic energy band gap can be controlled between zero and 1.6 electron volts by adjusting the composition x. The most useful materials are at x approximately 20%, suitable for detection wavelengths of about 10 micrometers. The problems of growing large crystals are rooted in the wide phase diagram of the HgTe-CdTe pseudobinary system which leads to exaggerate segregation in freezing, constitutional supercooling, and other difficulties, and in the high vapor pressure of mercury at the growth temperatures, which leads to loss of stoichiometry and to the necessity of working in strong, pressure resistant sealed containers.

$$ \\mathcal{N} $$ = 2 supersymmetric Janus solutions and flows: From gauged supergravity to M theory

DOE PAGES

Pilch, Krzysztof; Tyukov, Alexander; Warner, Nicholas P.

2016-05-02

In this study, we investigate a family of SU(3)×U(1)×U(1)-invariant holographic flows and Janus solutions obtained from gaugedmore » $$ \\mathcal{N} $$ = 8 supergravity in four dimensions. We give complete details of how to use the uplift formulae to obtain the corresponding solutions in M theory. While the flow solutions appear to be singular from the four-dimensional perspective, we find that the eleven-dimensional solutions are much better behaved and give rise to interesting new classes of compactification geometries that are smooth, up to orbifolds, in the infra-red limit. Our solutions involve new phases in which M2 branes polarize partially or even completely into M5 branes. We derive the eleven-dimensional supersymmetries and show that the eleven-dimensional equations of motion and BPS equations are indeed satisfied as a consequence of their four-dimensional counterparts. Apart from elucidating a whole new class of eleven-dimensional Janus and flow solutions, our work provides extensive and highly non-trivial tests of the recently-derived uplift formulae.« less

Spatial derivatives of flow quantities behind curved shocks of all strengths

NASA Technical Reports Server (NTRS)

Darden, C. M.

1984-01-01

Explicit formulas in terms of shock curvature are developed for spatial derivatives of flow quantities behind a curved shock for two-dimensional inviscid steady flow. Factors which yield the equations indeterminate as the shock strength approaches 0 have been cancelled analytically so that formulas are valid for shocks of any strength. An application for the method is shown in the solution of shock coalescence when nonaxisymmetric effects are felt through derivatives in the circumferential direction. The solution of this problem requires flow derivatives behind the shock in both the axial and radial direction.

Simulation of solute transport through heterogeneous networks: analysis using the method of moments and the statistics of local transport characteristics.

PubMed

Li, Min; Qi, Tao; Bernabé, Yves; Zhao, Jinzhou; Wang, Ying; Wang, Dong; Wang, Zheming

2018-02-28

We used a time domain random walk approach to simulate passive solute transport in networks. In individual pores, solute transport was modeled as a combination of Poiseuille flow and Taylor dispersion. The solute plume data were interpreted via the method of moments. Analysis of the first and second moments showed that the longitudinal dispersivity increased with increasing coefficient of variation of the pore radii CV and decreasing pore coordination number Z. The third moment was negative and its magnitude grew linearly with time, meaning that the simulated dispersion was intrinsically non-Fickian. The statistics of the Eulerian mean fluid velocities [Formula: see text], the Taylor dispersion coefficients [Formula: see text] and the transit times [Formula: see text] were very complex and strongly affected by CV and Z. In particular, the probability of occurrence of negative velocities grew with increasing CV and decreasing Z. Hence, backward and forward transit times had to be distinguished. The high-τ branch of the transit-times probability curves had a power law form associated to non-Fickian behavior. However, the exponent was insensitive to pore connectivity, although variations of Z affected the third moment growth. Thus, we conclude that both the low- and high-τ branches played a role in generating the observed non-Fickian behavior.

Conformal Nets II: Conformal Blocks

NASA Astrophysics Data System (ADS)

Bartels, Arthur; Douglas, Christopher L.; Henriques, André

2017-08-01

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

NASA Technical Reports Server (NTRS)

King, H. F.; Komornicki, A.

1986-01-01

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

Brane - Anti-Brane Democracy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajaraman, Arvind

2003-06-02

We suggest a duality invariant formula for the entropy and temperature of nonextreme black holes in supersymmetric string theory. The entropy is given in terms of the duality invariant parameter of the deviation from extremality and 56 SU(8) covariant central charges. It interpolates between the entropies of Schwarzschild solution and extremal solutions with various amount of unbroken supersymmetries and therefore serves for classification of black holes in supersymmetric string theories. We introduce the second auxiliary 56 via E(7) symmetric constraint. The symmetric and antisymmetric combinations of these two multiplets are related via moduli to the corresponding two fundamental representations ofmore » E(7): brane and anti-brane ''numbers.'' Using the CPT as well as C symmetry of the entropy formula and duality one can explain the mysterious simplicity of the non-extreme black hole area formula in terms of branes and anti-branes.« less

Kinematics of velocity and vorticity correlations in turbulent flow

NASA Technical Reports Server (NTRS)

Bernard, P. S.

1983-01-01

The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.

Burst nucleation by hot injection for size controlled synthesis of ε-cobalt nanoparticles.

PubMed

Zacharaki, Eirini; Kalyva, Maria; Fjellvåg, Helmer; Sjåstad, Anja Olafsen

2016-01-01

Reproducible growth of narrow size distributed ε-Co nanoparticles with a specific size requires full understanding and identification of the role of essential synthesis parameters for the applied synthesis method. For the hot injection methodology, a significant discrepancy with respect to obtained sizes and applied reaction conditions is reported. Currently, a systematic investigation controlling key synthesis parameters as injection-temperature and time, metal to surfactant ratio and reaction holding time in terms of their impact on mean ([Formula: see text]mean) and median ([Formula: see text]median) particle diameter using dichlorobenzene (DCB), Co2(CO)8 and oleic acid (OA) as the reactant matrix is lacking. A series of solution-based ε-Co nanoparticles were synthesized using the hot injection method. Suspensions and obtained particles were analyzed by DLS, ICP-OES, (synchrotron)XRD and TEM. Rietveld refinements were used for structural analysis. Mean ([Formula: see text]mean) and median ([Formula: see text]median) particle diameters were calculated with basis in measurements of 250-500 particles for each synthesis. 95 % bias corrected confidence intervals using bootstrapping were calculated for syntheses with three or four replicas. ε-Co NPs in the size range ~4-10 nm with a narrow size distribution are obtained via the hot injection method, using OA as the sole surfactant. Typically the synthesis yield is ~75 %, and the particles form stable colloidal solutions when redispersed in hexane. Reproducibility of the adopted synthesis procedure on replicate syntheses was confirmed. We describe in detail the effects of essential synthesis parameters, such as injection-temperature and time, metal to surfactant ratio and reaction holding time in terms of their impact on mean ([Formula: see text]mean) and median ([Formula: see text]median) particle diameter. The described synthesis procedure towards ε-Co nanoparticles (NPs) is concluded to be robust when controlling key synthesis parameters, giving targeted particle diameters with a narrow size distribution. We have identified two major synthesis parameters which control particle size, i.e., the metal to surfactant molar ratio and the injection temperature of the hot OA-DCB solution into which the cobalt precursor is injected. By increasing the metal to surfactant molar ratio, the mean particle diameter of the ε-Co NPs has been found to increase. Furthermore, an increase in the injection temperature of the hot OA-DCB solution into which the cobalt precursor is injected, results in a decrease in the mean particle diameter of the ε-Co NPs, when the metal to surfactant molar ratio [Formula: see text] is fixed at ~12.9.

A Boundary Value Problem for Introductory Physics?

ERIC Educational Resources Information Center

Grundberg, Johan

2008-01-01

The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent…

Path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models

NASA Astrophysics Data System (ADS)

Lemmens, D.; Wouters, M.; Tempere, J.; Foulon, S.

2008-07-01

We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.

An analytic formula for the supercluster mass function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lim, Seunghwan; Lee, Jounghun, E-mail: slim@astro.umass.edu, E-mail: jounghun@astro.snu.ac.kr

2014-03-01

We present an analytic formula for the supercluster mass function, which is constructed by modifying the extended Zel'dovich model for the halo mass function. The formula has two characteristic parameters whose best-fit values are determined by fitting to the numerical results from N-body simulations for the standard ΛCDM cosmology. The parameters are found to be independent of redshifts and robust against variation of the key cosmological parameters. Under the assumption that the same formula for the supercluster mass function is valid for non-standard cosmological models, we show that the relative abundance of the rich superclusters should be a powerful indicatormore » of any deviation of the real universe from the prediction of the standard ΛCDM model.« less

Energy dependence of the transverse momentum distributions of charged particles in pp collisions measured by ALICE.

PubMed

Abelev, B; Adam, J; Adamová, D; Adare, A M; Aggarwal, M M; Aglieri Rinella, G; Agnello, M; Agocs, A G; Agostinelli, A; Ahammed, Z; Ahmad, N; Ahmad Masoodi, A; Ahmed, I; Ahn, S A; Ahn, S U; Aimo, I; Aiola, S; Ajaz, M; Akindinov, A; Aleksandrov, D; Alessandro, B; Alexandre, D; Alici, A; Alkin, A; Alme, J; Alt, T; Altini, V; Altinpinar, S; Altsybeev, I; Alves Garcia Prado, C; Andrei, C; Andronic, A; Anguelov, V; Anielski, J; Antičić, T; Antinori, F; Antonioli, P; Aphecetche, L; Appelshäuser, H; Arbor, N; Arcelli, S; Armesto, N; Arnaldi, R; Aronsson, T; Arsene, I C; Arslandok, M; Augustinus, A; Averbeck, R; Awes, T C; Äystö, J; Azmi, M D; Bach, M; Badalà, A; Baek, Y W; Bailhache, R; Bala, R; Baldisseri, A; Baltasar Dos Santos Pedrosa, F; Bán, J; Baral, R C; Barbera, R; Barile, F; Barnaföldi, G G; Barnby, L S; Barret, V; Bartke, J; Basile, M; Bastid, N; Basu, S; Bathen, B; Batigne, G; Batyunya, B; Batzing, P C; Baumann, C; Bearden, I G; Beck, H; Bedda, C; Behera, N K; Belikov, I; Bellini, F; Bellwied, R; Belmont-Moreno, E; Bencedi, G; Beole, S; Berceanu, I; Bercuci, A; Berdnikov, Y; Berenyi, D; Bergognon, A A E; Bertens, R A; Berzano, D; Betev, L; Bhasin, A; Bhati, A K; Bhom, J; Bianchi, L; Bianchi, N; Bianchin, C; Bielčík, J; Bielčíková, J; Bilandzic, A; Bjelogrlic, S; Blanco, F; Blanco, F; Blau, D; Blume, C; Bock, F; Bogdanov, A; Bøggild, H; Bogolyubsky, M; Boldizsár, L; Bombara, M; Book, J; Borel, H; Borissov, A; Bornschein, J; Botje, M; Botta, E; Böttger, S; Braidot, E; Braun-Munzinger, P; Bregant, M; Breitner, T; Broker, T A; Browning, T A; Broz, M; Brun, R; Bruna, E; Bruno, G E; Budnikov, D; Buesching, H; Bufalino, S; Buncic, P; Busch, O; Buthelezi, Z; Caffarri, D; Cai, X; Caines, H; Caliva, A; Calvo Villar, E; Camerini, P; Canoa Roman, V; Cara Romeo, G; Carena, F; Carena, W; Carminati, F; Casanova Díaz, A; Castillo Castellanos, J; Casula, E A R; Catanescu, V; Cavicchioli, C; Ceballos Sanchez, C; Cepila, J; Cerello, P; Chang, B; Chapeland, S; Charvet, J L; Chattopadhyay, S; Chattopadhyay, S; Cherney, M; Cheshkov, C; Cheynis, B; Chibante Barroso, V; Chinellato, D D; Chochula, P; Chojnacki, M; Choudhury, S; Christakoglou, P; Christensen, C H; Christiansen, P; Chujo, T; Chung, S U; Cicalo, C; Cifarelli, L; Cindolo, F; Cleymans, J; Colamaria, F; Colella, D; Collu, A; Colocci, M; Conesa Balbastre, G; Conesa Del Valle, Z; Connors, M E; Contin, G; Contreras, J G; Cormier, T M; Corrales Morales, Y; Cortese, P; Cortés Maldonado, I; Cosentino, M R; Costa, F; Crochet, P; Cruz Albino, R; Cuautle, E; Cunqueiro, L; Dainese, A; Dang, R; Danu, A; Das, K; Das, D; Das, I; Dash, A; Dash, S; De, S; Delagrange, H; Deloff, A; Dénes, E; Deppman, A; de Barros, G O V; De Caro, A; de Cataldo, G; de Cuveland, J; De Falco, A; De Gruttola, D; De Marco, N; De Pasquale, S; de Rooij, R; Diaz Corchero, M A; Dietel, T; Divià, R; Di Bari, D; Di Giglio, C; Di Liberto, S; Di Mauro, A; Di Nezza, P; Djuvsland, Ø; Dobrin, A; Dobrowolski, T; Dönigus, B; Dordic, O; Dubey, A K; Dubla, A; Ducroux, L; Dupieux, P; Dutta Majumdar, A K; D Erasmo, G; Elia, D; Emschermann, D; Engel, H; Erazmus, B; Erdal, H A; Eschweiler, D; Espagnon, B; Estienne, M; Esumi, S; Evans, D; Evdokimov, S; Eyyubova, G; Fabris, D; Faivre, J; Falchieri, D; Fantoni, A; Fasel, M; Fehlker, D; Feldkamp, L; Felea, D; Feliciello, A; Feofilov, G; Fernández Téllez, A; Ferreiro, E G; Ferretti, A; Festanti, A; Figiel, J; Figueredo, M A S; Filchagin, S; Finogeev, D; Fionda, F M; Fiore, E M; Floratos, E; Floris, M; Foertsch, S; Foka, P; Fokin, S; Fragiacomo, E; Francescon, A; Frankenfeld, U; Fuchs, U; Furget, C; Fusco Girard, M; Gaardhøje, J J; Gagliardi, M; Gago, A; Gallio, M; Gangadharan, D R; Ganoti, P; Garabatos, C; Garcia-Solis, E; Gargiulo, C; Garishvili, I; Gerhard, J; Germain, M; Gheata, A; Gheata, M; Ghidini, B; Ghosh, P; Gianotti, P; Giubellino, P; Gladysz-Dziadus, E; Glässel, P; Goerlich, L; Gomez, R; González-Zamora, P; Gorbunov, S; Gotovac, S; Graczykowski, L K; Grajcarek, R; Grelli, A; Grigoras, C; Grigoras, A; Grigoriev, V; Grigoryan, A; Grigoryan, S; Grinyov, B; Grion, N; Grosse-Oetringhaus, J F; Grossiord, J-Y; Grosso, R; Guber, F; Guernane, R; Guerzoni, B; Guilbaud, M; Gulbrandsen, K; Gulkanyan, H; Gunji, T; Gupta, A; Gupta, R; Khan, K H; Haake, R; Haaland, Ø; Hadjidakis, C; Haiduc, M; Hamagaki, H; Hamar, G; Hanratty, L D; Hansen, A; Harris, J W; Harton, A; Hatzifotiadou, D; Hayashi, S; Hayrapetyan, A; Heckel, S T; Heide, M; Helstrup, H; Herghelegiu, A; Herrera Corral, G; Herrmann, N; Hess, B A; Hetland, K F; Hicks, B; Hippolyte, B; Hori, Y; Hristov, P; Hřivnáčová, I; Huang, M; Humanic, T J; Hutter, D; Hwang, D S; Ichou, R; Ilkaev, R; Ilkiv, I; Inaba, M; Incani, E; Innocenti, G M; Ionita, C; Ippolitov, M; Irfan, M; Ivanov, V; Ivanov, M; Ivanytskyi, O; Jachołkowski, A; Jahnke, C; Jang, H J; Janik, M A; Jayarathna, P H S Y; Jena, S; Jimenez Bustamante, R T; Jones, P G; Jung, H; Jusko, A; Kalcher, S; Kaliňák, P; Kalliokoski, T; Kalweit, A; Kang, J H; Kaplin, V; Kar, S; Karasu Uysal, A; Karavichev, O; Karavicheva, T; Karpechev, E; Kazantsev, A; Kebschull, U; Keidel, R; Ketzer, B; Khan, S A; Khan, M M; Khan, P; Khanzadeev, A; Kharlov, Y; Kileng, B; Kim, S; Kim, D W; Kim, D J; Kim, B; Kim, T; Kim, M; Kim, M; Kim, J S; Kirsch, S; Kisel, I; Kiselev, S; Kisiel, A; Kiss, G; Klay, J L; Klein, J; Klein-Bösing, C; Kluge, A; Knichel, M L; Knospe, A G; Köhler, M K; Kollegger, T; Kolojvari, A; Kondratiev, V; Kondratyeva, N; Konevskikh, A; Kovalenko, V; Kowalski, M; Kox, S; Koyithatta Meethaleveedu, G; Kral, J; Králik, I; Kramer, F; Kravčáková, A; Krelina, M; Kretz, M; Krivda, M; Krizek, F; Krus, M; Kryshen, E; Krzewicki, M; Kucera, V; Kucheriaev, Y; Kugathasan, T; Kuhn, C; Kuijer, P G; Kulakov, I; Kumar, J; Kurashvili, P; Kurepin, A B; Kurepin, A; Kuryakin, A; Kushpil, S; Kushpil, V; Kweon, M J; Kwon, Y; Ladrón de Guevara, P; Lagana Fernandes, C; Lakomov, I; Langoy, R; Lara, C; Lardeux, A; La Pointe, S L; La Rocca, P; Lea, R; Lechman, M; Lee, S C; Lee, G R; Legrand, I; Lehnert, J; Lemmon, R C; Lenhardt, M; Lenti, V; León Monzón, I; Lévai, P; Li, S; Lien, J; Lietava, R; Lindal, S; Lindenstruth, V; Lippmann, C; Lisa, M A; Ljunggren, H M; Lodato, D F; Loenne, P I; Loggins, V R; Loginov, V; Lohner, D; Loizides, C; Loo, K K; Lopez, X; López Torres, E; Løvhøiden, G; Lu, X-G; Luettig, P; Lunardon, M; Luo, J; Luparello, G; Luzzi, C; Jacobs, P M; Ma, R; Maevskaya, A; Mager, M; Mahapatra, D P; Maire, A; Malaev, M; Maldonado Cervantes, I; Malinina, L; Mal'Kevich, D; Malzacher, P; Mamonov, A; Manceau, L; Manko, V; Manso, F; Manzari, V; Marchisone, M; Mareš, J; Margagliotti, G V; Margotti, A; Marín, A; Markert, C; Marquard, M; Martashvili, I; Martin, N A; Martinengo, P; Martínez, M I; Martínez García, G; Martin Blanco, J; Martynov, Y; Mas, A; Masciocchi, S; Masera, M; Masoni, A; Massacrier, L; Mastroserio, A; Matyja, A; Mazer, J; Mazumder, R; Mazzoni, M A; Meddi, F; Menchaca-Rocha, A; Mercado Pérez, J; Meres, M; Miake, Y; Mikhaylov, K; Milano, L; Milosevic, J; Mischke, A; Mishra, A N; Miśkowiec, D; Mitu, C; Mlynarz, J; Mohanty, B; Molnar, L; Montaño Zetina, L; Monteno, M; Montes, E; Moon, T; Morando, M; Moreira De Godoy, D A; Moretto, S; Morreale, A; Morsch, A; Muccifora, V; Mudnic, E; Muhuri, S; Mukherjee, M; Müller, H; Munhoz, M G; Murray, S; Musa, L; Nandi, B K; Nania, R; Nappi, E; Nattrass, C; Nayak, T K; Nazarenko, S; Nedosekin, A; Nicassio, M; Niculescu, M; Nielsen, B S; Nikolaev, S; Nikulin, S; Nikulin, V; Nilsen, B S; Nilsson, M S; Noferini, F; Nomokonov, P; Nooren, G; Nyanin, A; Nyatha, A; Nystrand, J; Oeschler, H; Oh, S K; Oh, S; Olah, L; Oleniacz, J; Oliveira Da Silva, A C; Onderwaater, J; Oppedisano, C; Ortiz Velasquez, A; Oskarsson, A; Otwinowski, J; Oyama, K; Pachmayer, Y; Pachr, M; Pagano, P; Paić, G; Painke, F; Pajares, C; Pal, S K; Palaha, A; Palmeri, A; Papikyan, V; Pappalardo, G S; Park, W J; Passfeld, A; Patalakha, D I; Paticchio, V; Paul, B; Pawlak, T; Peitzmann, T; Pereira Da Costa, H; Pereira De Oliveira Filho, E; Peresunko, D; Pérez Lara, C E; Perrino, D; Peryt, W; Pesci, A; Pestov, Y; Petráček, V; Petran, M; Petris, M; Petrov, P; Petrovici, M; Petta, C; Piano, S; Pikna, M; Pillot, P; Pinazza, O; Pinsky, L; Pitz, N; Piyarathna, D B; Planinic, M; Płoskoń, M; Pluta, J; Pochybova, S; Podesta-Lerma, P L M; Poghosyan, M G; Polichtchouk, B; Poljak, N; Pop, A; Porteboeuf-Houssais, S; Pospíšil, V; Potukuchi, B; Prasad, S K; Preghenella, R; Prino, F; Pruneau, C A; Pshenichnov, I; Puddu, G; Punin, V; Putschke, J; Qvigstad, H; Rachevski, A; Rademakers, A; Rak, J; Rakotozafindrabe, A; Ramello, L; Raniwala, S; Raniwala, R; Räsänen, S S; Rascanu, B T; Rathee, D; Rauch, W; Rauf, A W; Razazi, V; Read, K F; Real, J S; Redlich, K; Reed, R J; Rehman, A; Reichelt, P; Reicher, M; Reidt, F; Renfordt, R; Reolon, A R; Reshetin, A; Rettig, F; Revol, J-P; Reygers, K; Riccati, L; Ricci, R A; Richert, T; Richter, M; Riedler, P; Riegler, W; Riggi, F; Rivetti, A; Rodríguez Cahuantzi, M; Rodriguez Manso, A; Røed, K; Rogochaya, E; Rohni, S; Rohr, D; Röhrich, D; Romita, R; Ronchetti, F; Rosnet, P; Rossegger, S; Rossi, A; Roy, P; Roy, C; Rubio Montero, A J; Rui, R; Russo, R; Ryabinkin, E; Rybicki, A; Sadovsky, S; Šafařík, K; Sahoo, R; Sahu, P K; Saini, J; Sakaguchi, H; Sakai, S; Sakata, D; Salgado, C A; Salzwedel, J; Sambyal, S; Samsonov, V; Sanchez Castro, X; Šándor, L; Sandoval, A; Sano, M; Santagati, G; Santoro, R; Sarkar, D; Scapparone, E; Scarlassara, F; Scharenberg, R P; Schiaua, C; Schicker, R; Schmidt, C; Schmidt, H R; Schuchmann, S; Schukraft, J; Schulc, M; Schuster, T; Schutz, Y; Schwarz, K; Schweda, K; Scioli, G; Scomparin, E; Scott, R; Scott, P A; Segato, G; Selyuzhenkov, I; Seo, J; Serci, S; Serradilla, E; Sevcenco, A; Shabetai, A; Shabratova, G; Shahoyan, R; Sharma, S; Sharma, N; Shigaki, K; Shtejer, K; Sibiriak, Y; Siddhanta, S; Siemiarczuk, T; Silvermyr, D; Silvestre, C; Simatovic, G; Singaraju, R; Singh, R; Singha, S; Singhal, V; Sinha, B C; Sinha, T; Sitar, B; Sitta, M; Skaali, T B; Skjerdal, K; Smakal, R; Smirnov, N; Snellings, R J M; Søgaard, C; Soltz, R; Song, M; Song, J; Soos, C; Soramel, F; Spacek, M; Sputowska, I; Spyropoulou-Stassinaki, M; Srivastava, B K; Stachel, J; Stan, I; Stefanek, G; Steinpreis, M; Stenlund, E; Steyn, G; Stiller, J H; Stocco, D; Stolpovskiy, M; Strmen, P; Suaide, A A P; Subieta Vásquez, M A; Sugitate, T; Suire, C; Suleymanov, M; Sultanov, R; Šumbera, M; Susa, T; Symons, T J M; Szanto de Toledo, A; Szarka, I; Szczepankiewicz, A; Szymański, M; Takahashi, J; Tangaro, M A; Tapia Takaki, J D; Tarantola Peloni, A; Tarazona Martinez, A; Tauro, A; Tejeda Muñoz, G; Telesca, A; Terrevoli, C; Ter Minasyan, A; Thäder, J; Thomas, D; Tieulent, R; Timmins, A R; Toia, A; Torii, H; Trubnikov, V; Trzaska, W H; Tsuji, T; Tumkin, A; Turrisi, R; Tveter, T S; Ulery, J; Ullaland, K; Ulrich, J; Uras, A; Urciuoli, G M; Usai, G L; Vajzer, M; Vala, M; Valencia Palomo, L; Vande Vyvre, P; Vannucci, L; Van Hoorne, J W; van Leeuwen, M; Vargas, A; Varma, R; Vasileiou, M; Vasiliev, A; Vechernin, V; Veldhoen, M; Venaruzzo, M; Vercellin, E; Vergara, S; Vernet, R; Verweij, M; Vickovic, L; Viesti, G; Viinikainen, J; Vilakazi, Z; Villalobos Baillie, O; Vinogradov, A; Vinogradov, L; Vinogradov, Y; Virgili, T; Viyogi, Y P; Vodopyanov, A; Völkl, M A; Voloshin, S; Voloshin, K; Volpe, G; von Haller, B; Vorobyev, I; Vranic, D; Vrláková, J; Vulpescu, B; Vyushin, A; Wagner, B; Wagner, V; Wagner, J; Wang, Y; Wang, Y; Wang, M; Watanabe, D; Watanabe, K; Weber, M; Wessels, J P; Westerhoff, U; Wiechula, J; Wikne, J; Wilde, M; Wilk, G; Wilkinson, J; Williams, M C S; Windelband, B; Winn, M; Xiang, C; Yaldo, C G; Yamaguchi, Y; Yang, H; Yang, P; Yang, S; Yano, S; Yasnopolskiy, S; Yi, J; Yin, Z; Yoo, I-K; Yushmanov, I; Zaccolo, V; Zach, C; Zampolli, C; Zaporozhets, S; Zarochentsev, A; Závada, P; Zaviyalov, N; Zbroszczyk, H; Zelnicek, P; Zgura, I S; Zhalov, M; Zhang, F; Zhang, Y; Zhang, H; Zhang, X; Zhou, D; Zhou, Y; Zhou, F; Zhu, X; Zhu, J; Zhu, J; Zhu, H; Zichichi, A; Zimmermann, M B; Zimmermann, A; Zinovjev, G; Zoccarato, Y; Zynovyev, M; Zyzak, M

Differential cross sections of charged particles in inelastic pp collisions as a function of p T have been measured at [Formula: see text] at the LHC. The p T spectra are compared to NLO-pQCD calculations. Though the differential cross section for an individual [Formula: see text] cannot be described by NLO-pQCD, the relative increase of cross section with [Formula: see text] is in agreement with NLO-pQCD. Based on these measurements and observations, procedures are discussed to construct pp reference spectra at [Formula: see text] up to p T =50 GeV/ c as required for the calculation of the nuclear modification factor in nucleus-nucleus and proton-nucleus collisions.

Assessment of Simple Models for Molecular Simulation of Ethylene Carbonate and Propylene Carbonate as Solvents for Electrolyte Solutions.

PubMed

Chaudhari, Mangesh I; Muralidharan, Ajay; Pratt, Lawrence R; Rempe, Susan B

2018-02-12

Progress in understanding liquid ethylene carbonate (EC) and propylene carbonate (PC) on the basis of molecular simulation, emphasizing simple models of interatomic forces, is reviewed. Results on the bulk liquids are examined from the perspective of anticipated applications to materials for electrical energy storage devices. Preliminary results on electrochemical double-layer capacitors based on carbon nanotube forests and on model solid-electrolyte interphase (SEI) layers of lithium ion batteries are considered as examples. The basic results discussed suggest that an empirically parameterized, non-polarizable force field can reproduce experimental structural, thermodynamic, and dielectric properties of EC and PC liquids with acceptable accuracy. More sophisticated force fields might include molecular polarizability and Buckingham-model description of inter-atomic overlap repulsions as extensions to Lennard-Jones models of van der Waals interactions. Simple approaches should be similarly successful also for applications to organic molecular ions in EC/PC solutions, but the important case of Li[Formula: see text] deserves special attention because of the particularly strong interactions of that small ion with neighboring solvent molecules. To treat the Li[Formula: see text] ions in liquid EC/PC solutions, we identify interaction models defined by empirically scaled partial charges for ion-solvent interactions. The empirical adjustments use more basic inputs, electronic structure calculations and ab initio molecular dynamics simulations, and also experimental results on Li[Formula: see text] thermodynamics and transport in EC/PC solutions. Application of such models to the mechanism of Li[Formula: see text] transport in glassy SEI models emphasizes the advantage of long time-scale molecular dynamics studies of these non-equilibrium materials.

Covariant Uniform Acceleration

NASA Astrophysics Data System (ADS)

Friedman, Yaakov; Scarr, Tzvi

2013-04-01

We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation , where F is the 3D force and p = m0γv is the 3D relativistic momentum. The standard 4D equation is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. This solves a problem of Einstein and Planck. We compute explicit solutions for uniformly accelerated motion. The solutions are divided into four Lorentz-invariant types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We introduce the 4D velocity, an adaptation of Horwitz and Piron s notion of "off-shell." We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.

A novel approach based on preference-based index for interval bilevel linear programming problem.

PubMed

Ren, Aihong; Wang, Yuping; Xue, Xingsi

2017-01-01

This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficients in both objective functions only through normal variation of interval number and chance-constrained programming. With the consideration of different preferences of different decision makers, the concept of the preference level that the interval objective function is preferred to a target interval is defined based on the preference-based index. Then a preference-based deterministic bilevel programming problem is constructed in terms of the preference level and the order relation [Formula: see text]. Furthermore, the concept of a preference δ -optimal solution is given. Subsequently, the constructed deterministic nonlinear bilevel problem is solved with the help of estimation of distribution algorithm. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed approach.

The Torsion of Members Having Sections Common in Aircraft Construction

NASA Technical Reports Server (NTRS)

Trayer, George W; March, H W

1930-01-01

Within recent years a great variety of approximate torsion formulas and drafting-room processes have been advocated. In some of these, especially where mathematical considerations are involved, the results are extremely complex and are not generally intelligible to engineers. The principal object of this investigation was to determine by experiment and theoretical investigation how accurate the more common of these formulas are and on what assumptions they are founded and, if none of the proposed methods proved to be reasonable accurate in practice, to produce simple, practical formulas from reasonably correct assumptions, backed by experiment. A second object was to collect in readily accessible form the most useful of known results for the more common sections. Formulas for all the important solid sections that have yielded to mathematical treatment are listed. Then follows a discussion of the torsion of tubular rods with formulas both rigorous and approximate.

Fiscal Response of School Districts to District Fiscal Capacity and State Aid. Working Papers in Education Finance, Paper No. 15.

ERIC Educational Resources Information Center

Adams, E. Kathleen; Vincent, Phillip E.

Data on 174 Colorado school districts were used to measure districts' responses (as indicated by per-pupil expenditures) to their own fiscal capacity and to state aid that changes over time. Colorado's modified guaranteed tax base (GTB) formula was analyzed and a model constructed that took into account the formula's limits on district spending…

Higher order derivatives of R-Jacobi polynomials

NASA Astrophysics Data System (ADS)

Das, Sourav; Swaminathan, A.

2016-06-01

In this work, the R-Jacobi polynomials defined on the nonnegative real axis related to F-distribution are considered. Using their Sturm-Liouville system higher order derivatives are constructed. Orthogonality property of these higher ordered R-Jacobi polynomials are obtained besides their normal form, self-adjoint form and hypergeometric representation. Interesting results on the Interpolation formula and Gaussian quadrature formulae are obtained with numerical examples.

Time resolution of the plastic scintillator strips with matrix photomultiplier readout for J-PET tomograph.

PubMed

Moskal, P; Rundel, O; Alfs, D; Bednarski, T; Białas, P; Czerwiński, E; Gajos, A; Giergiel, K; Gorgol, M; Jasińska, B; Kamińska, D; Kapłon, Ł; Korcyl, G; Kowalski, P; Kozik, T; Krzemień, W; Kubicz, E; Niedźwiecki, Sz; Pałka, M; Raczyński, L; Rudy, Z; Sharma, N G; Słomski, A; Silarski, M; Strzelecki, A; Wieczorek, A; Wiślicki, W; Witkowski, P; Zieliński, M; Zoń, N

2016-03-07

Recent tests of a single module of the Jagiellonian Positron Emission Tomography system (J-PET) consisting of 30 cm long plastic scintillator strips have proven its applicability for the detection of annihilation quanta (0.511 MeV) with a coincidence resolving time (CRT) of 0.266 ns. The achieved resolution is almost by a factor of two better with respect to the current TOF-PET detectors and it can still be improved since, as it is shown in this article, the intrinsic limit of time resolution for the determination of time of the interaction of 0.511 MeV gamma quanta in plastic scintillators is much lower. As the major point of the article, a method allowing to record timestamps of several photons, at two ends of the scintillator strip, by means of matrix of silicon photomultipliers (SiPM) is introduced. As a result of simulations, conducted with the number of SiPM varying from 4 to 42, it is shown that the improvement of timing resolution saturates with the growing number of photomultipliers, and that the [Formula: see text] configuration at two ends allowing to read twenty timestamps, constitutes an optimal solution. The conducted simulations accounted for the emission time distribution, photon transport and absorption inside the scintillator, as well as quantum efficiency and transit time spread of photosensors, and were checked based on the experimental results. Application of the [Formula: see text] matrix of SiPM allows for achieving the coincidence resolving time in positron emission tomography of [Formula: see text]0.170 ns for 15 cm axial field-of-view (AFOV) and [Formula: see text]0.365 ns for 100 cm AFOV. The results open perspectives for construction of a cost-effective TOF-PET scanner with significantly better TOF resolution and larger AFOV with respect to the current TOF-PET modalities.

Conformally Invariant Powers of the Laplacian, Q-Curvature, and Tractor Calculus

NASA Astrophysics Data System (ADS)

Gover, A. Rod; Peterson, Lawrence J.

We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian. Conformal tractor calculus is the natural induced bundle calculus associated to the conformal Cartan connection. Applications discussed include standard formulae for these operators in terms of the Levi-Civita connection and its curvature and a direct definition and formula for T. Branson's so-called Q-curvature (which integrates to a global conformal invariant) as well as generalisations of the operators and the Q-curvature. Among examples, the operators of order 4, 6 and 8 and the related Q-curvatures are treated explicitly. The algorithm exploits the ambient metric construction of Fefferman and Graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions. This is partly based on [12], where the relationship of the normal standard tractor bundle to the ambient construction is described.

Spectral analysis of localized rotating waves in parabolic systems.

PubMed

Beyn, Wolf-Jürgen; Otten, Denny

2018-04-13

In this paper, we study the spectra and Fredholm properties of Ornstein-Uhlenbeck operators [Formula: see text]where [Formula: see text] is the profile of a rotating wave satisfying [Formula: see text] as [Formula: see text], the map [Formula: see text] is smooth and the matrix [Formula: see text] has eigenvalues with positive real parts and commutes with the limit matrix [Formula: see text] The matrix [Formula: see text] is assumed to be skew-symmetric with eigenvalues (λ 1 ,…,λ d )=(±i σ 1 ,…,±i σ k ,0,…,0). The spectra of these linearized operators are crucial for the nonlinear stability of rotating waves in reaction-diffusion systems. We prove under appropriate conditions that every [Formula: see text] satisfying the dispersion relation [Formula: see text]belongs to the essential spectrum [Formula: see text] in L p For values Re λ to the right of the spectral bound for [Formula: see text], we show that the operator [Formula: see text] is Fredholm of index 0, solve the identification problem for the adjoint operator [Formula: see text] and formulate the Fredholm alternative. Moreover, we show that the set [Formula: see text]belongs to the point spectrum [Formula: see text] in L p We determine the associated eigenfunctions and show that they decay exponentially in space. As an application, we analyse spinning soliton solutions which occur in the Ginzburg-Landau equation and compute their numerical spectra as well as associated eigenfunctions. Our results form the basis for investigating the nonlinear stability of rotating waves in higher space dimensions and truncations to bounded domains. This article is part of the themed issue 'Stability of nonlinear waves and patterns and related topics'. © 2018 The Author(s).

Markovian Anderson Model: Bounds for the Rate of Propagation

NASA Astrophysics Data System (ADS)

Tcheremchantsev, Serguei

We consider the Anderson model in with potentials whose values at any site of the lattice are Markovian independent random functions of time. For solutions to the time-dependent Schrödinger equation we show under some conditions that with probability 1 where for d=1,2 and for .

A "Paperclip" Approach to Curvature, Torsion, and the Frenet-Serret Formulas

ERIC Educational Resources Information Center

Hoensch, Ulrich A.

2009-01-01

We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…

Least-Squares Data Adjustment with Rank-Deficient Data Covariance Matrices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, J.G.

2011-07-01

A derivation of the linear least-squares adjustment formulae is required that avoids the assumption that the covariance matrix of prior parameters can be inverted. Possible proofs are of several kinds, including: (i) extension of standard results for the linear regression formulae, and (ii) minimization by differentiation of a quadratic form of the deviations in parameters and responses. In this paper, the least-squares adjustment equations are derived in both these ways, while explicitly assuming that the covariance matrix of prior parameters is singular. It will be proved that the solutions are unique and that, contrary to statements that have appeared inmore » the literature, the least-squares adjustment problem is not ill-posed. No modification is required to the adjustment formulae that have been used in the past in the case of a singular covariance matrix for the priors. In conclusion: The linear least-squares adjustment formula that has been used in the past is valid in the case of a singular covariance matrix for the covariance matrix of prior parameters. Furthermore, it provides a unique solution. Statements in the literature, to the effect that the problem is ill-posed are wrong. No regularization of the problem is required. This has been proved in the present paper by two methods, while explicitly assuming that the covariance matrix of prior parameters is singular: i) extension of standard results for the linear regression formulae, and (ii) minimization by differentiation of a quadratic form of the deviations in parameters and responses. No modification is needed to the adjustment formulae that have been used in the past. (author)« less

Algebraic function operator expectation value based quantum eigenstate determination: A case of twisted or bent Hamiltonian, or, a spatially univariate quantum system on a curved space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baykara, N. A.

Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraicmore » equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.« less

A numerical solution of a singular boundary value problem arising in boundary layer theory.

PubMed

Hu, Jiancheng

2016-01-01

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

27 CFR 21.41 - Formula No. 13-A.

Code of Federal Regulations, 2011 CFR

2011-04-01

... medicinal chemicals (including alkaloids). 345.Processing blood and blood products. 349.Miscellaneous drug... photographic chemicals. 358.Processing other chemicals. 359.Processing miscellaneous products. 430.Sterilizing and preserving solutions. 481.Photoengraving and rotogravure solutions and dyes. (2) As a raw material...

27 CFR 21.59 - Formula No. 32.

Code of Federal Regulations, 2011 CFR

2011-04-01

... vaccines. 344.Processing medicinal chemicals (including alkaloids). 430.Sterilizing and preserving solutions. 481.Photoengraving and rotogravure solutions and dyes. (2) As a raw material: 522.Ethyl chloride.... 575.Drugs and medicinal chemicals. 579.Other chemicals. 580.Synthetic rubber. (3) Miscellaneous uses...

27 CFR 21.37 - Formula No. 3-C.

Code of Federal Regulations, 2013 CFR

2013-04-01

... intermediates and industrial collodions. 035.Soldering flux. 036.Adhesives and binders. 043.Solvents, special... solutions. 440.Industrial detergents and soaps. 450.Cleaning solutions (including household detergents). 470...: 530.Ethylamines. 540.Dyes and intermediates. 575.Drugs and medicinal chemicals. 576.Organo-silicone...

27 CFR 21.37 - Formula No. 3-C.

Code of Federal Regulations, 2010 CFR

2010-04-01

... intermediates and industrial collodions. 035.Soldering flux. 036.Adhesives and binders. 043.Solvents, special... solutions. 440.Industrial detergents and soaps. 450.Cleaning solutions (including household detergents). 470...: 530.Ethylamines. 540.Dyes and intermediates. 575.Drugs and medicinal chemicals. 576.Organo-silicone...

27 CFR 21.37 - Formula No. 3-C.

Code of Federal Regulations, 2012 CFR

2012-04-01

... intermediates and industrial collodions. 035.Soldering flux. 036.Adhesives and binders. 043.Solvents, special... solutions. 440.Industrial detergents and soaps. 450.Cleaning solutions (including household detergents). 470...: 530.Ethylamines. 540.Dyes and intermediates. 575.Drugs and medicinal chemicals. 576.Organo-silicone...

27 CFR 21.35 - Formula No. 3-A.

Code of Federal Regulations, 2011 CFR

2011-04-01

... intermediates and industrial collodions. 035.Soldering flux. 036.Adhesives and binders. 041.Proprietary solvents... solutions. 440.Industrial detergents and soaps. 450.Cleaning solutions (including household detergents). 470...: 530.Ethylamines. 540.Dyes and intermediates. 575.Drugs and medicinal chemicals. 576.Organo-silicone...

27 CFR 21.35 - Formula No. 3-A.

Code of Federal Regulations, 2013 CFR

2013-04-01

... intermediates and industrial collodions. 035.Soldering flux. 036.Adhesives and binders. 041.Proprietary solvents... solutions. 440.Industrial detergents and soaps. 450.Cleaning solutions (including household detergents). 470...: 530.Ethylamines. 540.Dyes and intermediates. 575.Drugs and medicinal chemicals. 576.Organo-silicone...

27 CFR 21.37 - Formula No. 3-C.

Code of Federal Regulations, 2011 CFR

2011-04-01

... intermediates and industrial collodions. 035.Soldering flux. 036.Adhesives and binders. 043.Solvents, special... solutions. 440.Industrial detergents and soaps. 450.Cleaning solutions (including household detergents). 470...: 530.Ethylamines. 540.Dyes and intermediates. 575.Drugs and medicinal chemicals. 576.Organo-silicone...

27 CFR 21.37 - Formula No. 3-C.

Code of Federal Regulations, 2014 CFR

2014-04-01

... intermediates and industrial collodions. 035.Soldering flux. 036.Adhesives and binders. 043.Solvents, special... solutions. 440.Industrial detergents and soaps. 450.Cleaning solutions (including household detergents). 470...: 530.Ethylamines. 540.Dyes and intermediates. 575.Drugs and medicinal chemicals. 576.Organo-silicone...

27 CFR 21.35 - Formula No. 3-A.

Code of Federal Regulations, 2010 CFR

2010-04-01

... intermediates and industrial collodions. 035.Soldering flux. 036.Adhesives and binders. 041.Proprietary solvents... solutions. 440.Industrial detergents and soaps. 450.Cleaning solutions (including household detergents). 470...: 530.Ethylamines. 540.Dyes and intermediates. 575.Drugs and medicinal chemicals. 576.Organo-silicone...

27 CFR 21.35 - Formula No. 3-A.

Code of Federal Regulations, 2012 CFR

2012-04-01

... intermediates and industrial collodions. 035.Soldering flux. 036.Adhesives and binders. 041.Proprietary solvents... solutions. 440.Industrial detergents and soaps. 450.Cleaning solutions (including household detergents). 470...: 530.Ethylamines. 540.Dyes and intermediates. 575.Drugs and medicinal chemicals. 576.Organo-silicone...

27 CFR 21.35 - Formula No. 3-A.

Code of Federal Regulations, 2014 CFR

2014-04-01

... intermediates and industrial collodions. 035.Soldering flux. 036.Adhesives and binders. 041.Proprietary solvents... solutions. 440.Industrial detergents and soaps. 450.Cleaning solutions (including household detergents). 470...: 530.Ethylamines. 540.Dyes and intermediates. 575.Drugs and medicinal chemicals. 576.Organo-silicone...

Upon Generating Discrete Expanding Integrable Models of the Toda Lattice Systems and Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Zhang, Yufeng; Zhang, Xiangzhi; Wang, Yan; Liu, Jiangen

2017-01-01

With the help of R-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula by R-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional generalised Toda lattice system and a new (2+1)-dimensional lattice system are generated, respectively.

Quadrature imposition of compatibility conditions in Chebyshev methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Streett, C. L.

1990-01-01

Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.; Ahmed, H. M.

2004-08-01

A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed.

A new method to distinguish hadronically decaying boosted Z bosons from W bosons using the ATLAS detector.

PubMed

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Schioppa, M; Schlenker, S; Schmieden, K; Schmitt, C; Schmitt, S; Schmitt, S; Schneider, B; Schnellbach, Y J; Schnoor, U; Schoeffel, L; Schoening, A; Schoenrock, B D; Schopf, E; Schorlemmer, A L S; Schott, M; Schouten, D; Schovancova, J; Schramm, S; Schreyer, M; Schroeder, C; Schuh, N; Schultens, M J; Schultz-Coulon, H-C; Schulz, H; Schumacher, M; Schumm, B A; Schune, Ph; Schwanenberger, C; Schwartzman, A; Schwarz, T A; Schwegler, Ph; Schweiger, H; Schwemling, Ph; Schwienhorst, R; Schwindling, J; Schwindt, T; Sciacca, F G; Scifo, E; Sciolla, G; Scuri, F; Scutti, F; Searcy, J; Sedov, G; Sedykh, E; Seema, P; Seidel, S C; Seiden, A; Seifert, F; Seixas, J M; Sekhniaidze, G; Sekhon, K; Sekula, S J; Seliverstov, D M; Semprini-Cesari, N; Serfon, C; Serin, L; Serkin, L; Serre, T; Sessa, M; Seuster, R; Severini, H; Sfiligoj, T; Sforza, F; Sfyrla, A; Shabalina, E; Shamim, M; Shan, L Y; Shang, R; Shank, J T; Shapiro, M; Shatalov, P B; Shaw, K; Shaw, S M; Shcherbakova, A; Shehu, C Y; Sherwood, P; Shi, L; Shimizu, S; Shimmin, C O; Shimojima, M; Shiyakova, M; Shmeleva, A; Shoaleh Saadi, D; Shochet, M J; Shojaii, S; Shrestha, S; Shulga, E; Shupe, M A; Shushkevich, S; Sicho, P; Sidebo, P E; Sidiropoulou, O; Sidorov, D; Sidoti, A; Siegert, F; Sijacki, Dj; Silva, J; Silver, Y; Silverstein, S B; Simak, V; Simard, O; Simic, Lj; Simion, S; Simioni, E; Simmons, B; Simon, D; Sinervo, P; Sinev, N B; Sioli, M; Siragusa, G; Sisakyan, A N; Sivoklokov, S Yu; Sjölin, J; Sjursen, T B; Skinner, M B; Skottowe, H P; Skubic, P; Slater, M; Slavicek, T; Slawinska, M; Sliwa, K; Smakhtin, V; Smart, B H; Smestad, L; Smirnov, S Yu; Smirnov, Y; Smirnova, L N; Smirnova, O; Smith, M N K; Smith, R W; Smizanska, M; Smolek, K; Snesarev, A A; Snidero, G; Snyder, S; Sobie, R; Socher, F; Soffer, A; Soh, D A; Sokhrannyi, G; Solans, C A; Solar, M; Solc, J; Soldatov, E Yu; Soldevila, U; Solodkov, A A; Soloshenko, A; Solovyanov, O V; Solovyev, V; Sommer, P; Song, H Y; Soni, N; Sood, A; Sopczak, A; Sopko, B; Sopko, V; Sorin, V; Sosa, D; Sosebee, M; Sotiropoulou, C L; Soualah, R; Soukharev, A M; South, D; Sowden, B C; Spagnolo, S; Spalla, M; Spangenberg, M; Spanò, F; Spearman, W R; Sperlich, D; Spettel, F; Spighi, R; Spigo, G; Spiller, L A; Spousta, M; Spreitzer, T; St Denis, R D; Stabile, A; Staerz, S; Stahlman, J; Stamen, R; Stamm, S; Stanecka, E; Stanescu, C; Stanescu-Bellu, M; Stanitzki, M M; Stapnes, S; Starchenko, E A; Stark, J; Staroba, P; Starovoitov, P; Staszewski, R; Steinberg, P; Stelzer, B; Stelzer, H J; Stelzer-Chilton, O; Stenzel, H; Stewart, G A; Stillings, J A; Stockton, M C; Stoebe, M; Stoicea, G; Stolte, P; Stonjek, S; Stradling, A R; Straessner, A; Stramaglia, M E; Strandberg, J; Strandberg, S; Strandlie, A; Strauss, E; Strauss, M; Strizenec, P; Ströhmer, R; Strom, D M; Stroynowski, R; Strubig, A; Stucci, S A; Stugu, B; Styles, N A; Su, D; Su, J; Subramaniam, R; Succurro, A; Sugaya, Y; Suk, M; Sulin, V V; Sultansoy, S; Sumida, T; Sun, S; Sun, X; Sundermann, J E; Suruliz, K; Susinno, G; Sutton, M R; Suzuki, S; Svatos, M; Swiatlowski, M; Sykora, I; Sykora, T; Ta, D; Taccini, C; Tackmann, K; Taenzer, J; Taffard, A; Tafirout, R; Taiblum, N; Takai, H; Takashima, R; Takeda, H; Takeshita, T; Takubo, Y; Talby, M; Talyshev, A A; Tam, J Y C; Tan, K G; Tanaka, J; Tanaka, R; Tanaka, S; Tannenwald, B B; Tannoury, N; Tapprogge, S; Tarem, S; Tarrade, F; Tartarelli, G F; Tas, P; Tasevsky, M; Tashiro, T; Tassi, E; Tavares Delgado, A; Tayalati, Y; Taylor, F E; Taylor, G N; Taylor, P T E; Taylor, W; Teischinger, F A; Teixeira Dias Castanheira, M; Teixeira-Dias, P; Temming, K K; Temple, D; Ten Kate, H; Teng, P K; Teoh, J J; Tepel, F; Terada, S; Terashi, K; Terron, J; Terzo, S; Testa, M; Teuscher, R J; Theveneaux-Pelzer, T; Thomas, J P; Thomas-Wilsker, J; Thompson, E N; Thompson, P D; Thompson, R J; Thompson, A S; Thomsen, L A; Thomson, E; Thomson, M; Thun, R P; Tibbetts, M J; Ticse Torres, R E; Tikhomirov, V O; Tikhonov, Yu A; Timoshenko, S; Tiouchichine, E; Tipton, P; Tisserant, S; Todome, K; Todorov, T; Todorova-Nova, S; Tojo, J; Tokár, S; Tokushuku, K; Tollefson, K; Tolley, E; Tomlinson, L; Tomoto, M; Tompkins, L; Toms, K; Torrence, E; Torres, H; Torró Pastor, E; Toth, J; Touchard, F; Tovey, D R; Trefzger, T; Tremblet, L; Tricoli, A; Trigger, I M; Trincaz-Duvoid, S; Tripiana, M F; Trischuk, W; Trocmé, B; Troncon, C; Trottier-McDonald, M; Trovatelli, M; True, P; Truong, L; Trzebinski, M; Trzupek, A; Tsarouchas, C; Tseng, J C-L; Tsiareshka, P V; Tsionou, D; Tsipolitis, G; Tsirintanis, N; Tsiskaridze, S; Tsiskaridze, V; Tskhadadze, E G; Tsukerman, I I; Tsulaia, V; Tsuno, S; Tsybychev, D; Tudorache, A; Tudorache, V; Tuna, A N; Tupputi, S A; Turchikhin, S; Turecek, D; Turra, R; Turvey, A J; Tuts, P M; Tykhonov, A; Tylmad, M; Tyndel, M; Ueda, I; Ueno, R; Ughetto, M; Ugland, M; Ukegawa, F; Unal, G; Undrus, A; Unel, G; Ungaro, F C; Unno, Y; Unverdorben, C; Urban, J; Urquijo, P; Urrejola, P; Usai, G; Usanova, A; Vacavant, L; Vacek, V; Vachon, B; Valderanis, C; Valencic, N; Valentinetti, S; Valero, A; Valery, L; Valkar, S; Valladolid Gallego, E; Vallecorsa, S; Valls Ferrer, J A; Van Den Wollenberg, W; Van Der Deijl, P C; van der Geer, R; van der Graaf, H; van Eldik, N; van Gemmeren, P; Van Nieuwkoop, J; van Vulpen, I; van Woerden, M C; Vanadia, M; Vandelli, W; Vanguri, R; Vaniachine, A; Vannucci, F; Vardanyan, G; Vari, R; Varnes, E W; Varol, T; Varouchas, D; Vartapetian, A; Varvell, K E; Vazeille, F; Vazquez Schroeder, T; Veatch, J; Veloce, L M; Veloso, F; Velz, T; Veneziano, S; Ventura, A; Ventura, D; Venturi, M; Venturi, N; Venturini, A; Vercesi, V; Verducci, M; Verkerke, W; Vermeulen, J C; Vest, A; Vetterli, M C; Viazlo, O; Vichou, I; Vickey, T; Vickey Boeriu, O E; Viehhauser, G H A; Viel, S; Vigne, R; Villa, M; Villaplana Perez, M; Vilucchi, E; Vincter, M G; Vinogradov, V B; Vivarelli, I; Vives Vaque, F; Vlachos, S; Vladoiu, D; Vlasak, M; Vogel, M; Vokac, P; Volpi, G; Volpi, M; von der Schmitt, H; von Radziewski, H; von Toerne, E; Vorobel, V; Vorobev, K; Vos, M; Voss, R; Vossebeld, J H; Vranjes, N; Vranjes Milosavljevic, M; Vrba, V; Vreeswijk, M; Vuillermet, R; Vukotic, I; Vykydal, Z; Wagner, P; Wagner, W; Wahlberg, H; Wahrmund, S; Wakabayashi, J; Walder, J; Walker, R; Walkowiak, W; Wang, C; Wang, F; Wang, H; Wang, H; Wang, J; Wang, J; Wang, K; Wang, R; Wang, S M; Wang, T; Wang, T; Wang, X; Wanotayaroj, C; Warburton, A; Ward, C P; Wardrope, D R; Washbrook, A; Wasicki, C; Watkins, P M; Watson, A T; Watson, I J; Watson, M F; Watts, G; Watts, S; Waugh, B M; Webb, S; Weber, M S; Weber, S W; Webster, J S; Weidberg, A R; Weinert, B; Weingarten, J; Weiser, C; Weits, H; Wells, P S; Wenaus, T; Wengler, T; Wenig, S; Wermes, N; Werner, M; Werner, P; Wessels, M; Wetter, J; Whalen, K; Wharton, A M; White, A; White, M J; White, R; White, S; Whiteson, D; Wickens, F J; Wiedenmann, W; Wielers, M; Wienemann, P; Wiglesworth, C; Wiik-Fuchs, L A M; Wildauer, A; Wilkens, H G; Williams, H H; Williams, S; Willis, C; Willocq, S; Wilson, A; Wilson, J A; Wingerter-Seez, I; Winklmeier, F; Winter, B T; Wittgen, M; Wittkowski, J; Wollstadt, S J; Wolter, M W; Wolters, H; Wosiek, B K; Wotschack, J; Woudstra, M J; Wozniak, K W; Wu, M; Wu, M; Wu, S L; Wu, X; Wu, Y; Wyatt, T R; Wynne, B M; Xella, S; Xu, D; Xu, L; Yabsley, B; Yacoob, S; Yakabe, R; Yamada, M; Yamaguchi, D; Yamaguchi, Y; Yamamoto, A; Yamamoto, S; Yamanaka, T; Yamauchi, K; Yamazaki, Y; Yan, Z; Yang, H; Yang, H; Yang, Y; Yao, W-M; Yasu, Y; Yatsenko, E; Yau Wong, K H; Ye, J; Ye, S; Yeletskikh, I; Yen, A L; Yildirim, E; Yorita, K; Yoshida, R; Yoshihara, K; Young, C; Young, C J S; Youssef, S; Yu, D R; Yu, J; Yu, J M; Yu, J; Yuan, L; Yuen, S P Y; Yurkewicz, A; Yusuff, I; Zabinski, B; Zaidan, R; Zaitsev, A M; Zalieckas, J; Zaman, A; Zambito, S; Zanello, L; Zanzi, D; Zeitnitz, C; Zeman, M; Zemla, A; Zeng, Q; Zengel, K; Zenin, O; Ženiš, T; Zerwas, D; Zhang, D; Zhang, F; Zhang, H; Zhang, J; Zhang, L; Zhang, R; Zhang, X; Zhang, Z; Zhao, X; Zhao, Y; Zhao, Z; Zhemchugov, A; Zhong, J; Zhou, B; Zhou, C; Zhou, L; Zhou, L; Zhou, M; Zhou, N; Zhu, C G; Zhu, H; Zhu, J; Zhu, Y; Zhuang, X; Zhukov, K; Zibell, A; Zieminska, D; Zimine, N I; Zimmermann, C; Zimmermann, S; Zinonos, Z; Zinser, M; Ziolkowski, M; Živković, L; Zobernig, G; Zoccoli, A; Zur Nedden, M; Zurzolo, G; Zwalinski, L

2016-01-01

The distribution of particles inside hadronic jets produced in the decay of boosted W and Z bosons can be used to discriminate such jets from the continuum background. Given that a jet has been identified as likely resulting from the hadronic decay of a boosted W or Z boson, this paper presents a technique for further differentiating Z bosons from W bosons. The variables used are jet mass, jet charge, and a b -tagging discriminant. A likelihood tagger is constructed from these variables and tested in the simulation of [Formula: see text] for bosons in the transverse momentum range 200 GeV [Formula: see text] 400 GeV in [Formula: see text] TeV pp collisions with the ATLAS detector at the LHC. For Z -boson tagging efficiencies of [Formula: see text], 50, and [Formula: see text], one can achieve [Formula: see text]-boson tagging rejection factors ([Formula: see text]) of 1.7, 8.3 and 1000, respectively. It is not possible to measure these efficiencies in the data due to the lack of a pure sample of high [Formula: see text], hadronically decaying Z bosons. However, the modelling of the tagger inputs for boosted W bosons is studied in data using a [Formula: see text]-enriched sample of events in 20.3 fb[Formula: see text] of data at [Formula: see text] TeV. The inputs are well modelled within uncertainties, which builds confidence in the expected tagger performance.

Implementation of Rosenbrock methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shampine, L. F.

1980-11-01

Rosenbrock formulas have shown promise in research codes for the solution of initial-value problems for stiff systems of ordinary differential equations (ODEs). To help assess their practical value, the author wrote an item of mathematical software based on such a formula. This required a variety of algorithmic and software developments. Those of general interest are reported in this paper. Among them is a way to select automatically, at every step, an explicit Runge-Kutta formula or a Rosenbrock formula according to the stiffness of the problem. Solving linear systems is important to methods for stiff ODEs, and is rather special formore » Rosenbrock methods. A cheap, effective estimate of the condition of the linear systems is derived. Some numerical results are presented to illustrate the developments.« less

Constructing and validating readability models: the method of integrating multilevel linguistic features with machine learning.

PubMed

Sung, Yao-Ting; Chen, Ju-Ling; Cha, Ji-Her; Tseng, Hou-Chiang; Chang, Tao-Hsing; Chang, Kuo-En

2015-06-01

Multilevel linguistic features have been proposed for discourse analysis, but there have been few applications of multilevel linguistic features to readability models and also few validations of such models. Most traditional readability formulae are based on generalized linear models (GLMs; e.g., discriminant analysis and multiple regression), but these models have to comply with certain statistical assumptions about data properties and include all of the data in formulae construction without pruning the outliers in advance. The use of such readability formulae tends to produce a low text classification accuracy, while using a support vector machine (SVM) in machine learning can enhance the classification outcome. The present study constructed readability models by integrating multilevel linguistic features with SVM, which is more appropriate for text classification. Taking the Chinese language as an example, this study developed 31 linguistic features as the predicting variables at the word, semantic, syntax, and cohesion levels, with grade levels of texts as the criterion variable. The study compared four types of readability models by integrating unilevel and multilevel linguistic features with GLMs and an SVM. The results indicate that adopting a multilevel approach in readability analysis provides a better representation of the complexities of both texts and the reading comprehension process.

New verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints.

PubMed

Benko, Matúš; Gfrerer, Helmut

2018-01-01

In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Formula: see text]-stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-called [Formula: see text]-stationarity. We show how the property of [Formula: see text]-stationarity (and thus also of M-stationarity) can be efficiently verified for the considered problem class by computing [Formula: see text]-stationary solutions of a certain quadratic program. We consider further the situation that the point which is to be tested for [Formula: see text]-stationarity, is not known exactly, but is approximated by some convergent sequence, as it is usually the case when applying some numerical method.

Existence of anti-periodic (differentiable) mild solutions to semilinear differential equations with nondense domain.

PubMed

Liu, Jinghuai; Zhang, Litao

2016-01-01

In this paper, we investigate the existence of anti-periodic (or anti-periodic differentiable) mild solutions to the semilinear differential equation [Formula: see text] with nondense domain. Furthermore, an example is given to illustrate our results.

Formulas in First and Second Language Acquisition. Papers and Reports on Child Language Development, No. 18.

ERIC Educational Resources Information Center

Vihman, Marilyn May

The use of formulaic speech is seen as a learning strategy in children's first language (L1) acquisition to a limited extent, and to an even greater extent in their second language (L2) acquisition. While the first utterances of the child learning L1 are mostly one-word constructions, many of them are routine words or phrases that the child learns…

Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, T.-W, E-mail: attwl@asu.edu; An, Keju

2016-06-15

We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.

Agent-based model for the h-index - exact solution

NASA Astrophysics Data System (ADS)

Żogała-Siudem, Barbara; Siudem, Grzegorz; Cena, Anna; Gagolewski, Marek

2016-01-01

Hirsch's h-index is perhaps the most popular citation-based measure of scientific excellence. In 2013, Ionescu and Chopard proposed an agent-based model describing a process for generating publications and citations in an abstract scientific community [G. Ionescu, B. Chopard, Eur. Phys. J. B 86, 426 (2013)]. Within such a framework, one may simulate a scientist's activity, and - by extension - investigate the whole community of researchers. Even though the Ionescu and Chopard model predicts the h-index quite well, the authors provided a solution based solely on simulations. In this paper, we complete their results with exact, analytic formulas. What is more, by considering a simplified version of the Ionescu-Chopard model, we obtained a compact, easy to compute formula for the h-index. The derived approximate and exact solutions are investigated on a simulated and real-world data sets.

The Kirchhoff Formulas for Moving Surfaces in Aeroacoustics - The Subsonic and Supersonic Cases

NASA Technical Reports Server (NTRS)

Farassat, F.

1996-01-01

One of the active areas of computational aeroacoustics is the application of the Kirchhoff formulas to the problems of the rotating machinery noise predictions. The original Kirchhoff formula was derived for a stationary surface. In 1988, Farassat and Myers derived a Kirchhoff Formula obtained originally by Morgans using modem mathematics. These authors gave a formula particularly useful for applications in aeroacoustics. This formula is for a surface moving at subsonic speed. Later in 1995 these authors derived the Kirchhoff formula for a super-sonically moving surface. This technical memorandum presents the viewgraphs of a day long workshop by the author on the derivation of the Kirchhoff formulas. All necessary background mathematics such as differential geometry and multidimensional generalized function theory are discussed in these viewgraphs. Abstraction is kept at minimum level here. These viewgraphs are also suitable for understanding the derivation and obtaining the solutions of the Ffowcs Williams-Hawkings equation. In the first part of this memorandum, some introductory remarks are made on generalized functions, the derivation of the Kirchhoff formulas and the development and validation of Kirchhoff codes. Separate lists of references by Lyrintzis, Long, Strawn and their co-workers are given in this memorandum. This publication is aimed at graduate students, physicists and engineers who are in need of the understanding and applications of the Kirchhoff formulas in acoustics and electromagnetics.

Growth of wormlike micelles in nonionic surfactant solutions: Quantitative theory vs. experiment.

PubMed

Danov, Krassimir D; Kralchevsky, Peter A; Stoyanov, Simeon D; Cook, Joanne L; Stott, Ian P; Pelan, Eddie G

2018-06-01

Despite the considerable advances of molecular-thermodynamic theory of micelle growth, agreement between theory and experiment has been achieved only in isolated cases. A general theory that can provide self-consistent quantitative description of the growth of wormlike micelles in mixed surfactant solutions, including the experimentally observed high peaks in viscosity and aggregation number, is still missing. As a step toward the creation of such theory, here we consider the simplest system - nonionic wormlike surfactant micelles from polyoxyethylene alkyl ethers, C i E j . Our goal is to construct a molecular-thermodynamic model that is in agreement with the available experimental data. For this goal, we systematized data for the micelle mean mass aggregation number, from which the micelle growth parameter was determined at various temperatures. None of the available models can give a quantitative description of these data. We constructed a new model, which is based on theoretical expressions for the interfacial-tension, headgroup-steric and chain-conformation components of micelle free energy, along with appropriate expressions for the parameters of the model, including their temperature and curvature dependencies. Special attention was paid to the surfactant chain-conformation free energy, for which a new more general formula was derived. As a result, relatively simple theoretical expressions are obtained. All parameters that enter these expressions are known, which facilitates the theoretical modeling of micelle growth for various nonionic surfactants in excellent agreement with the experiment. The constructed model can serve as a basis that can be further upgraded to obtain quantitative description of micelle growth in more complicated systems, including binary and ternary mixtures of nonionic, ionic and zwitterionic surfactants, which determines the viscosity and stability of various formulations in personal-care and house-hold detergency. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

A Module Analysis Approach to Investigate Molecular Mechanism of TCM Formula: A Trial on Shu-feng-jie-du Formula

PubMed Central

Zhang, Fangbo; Tang, Shihuan; Liu, Xi; Gao, Yibo; Wang, Yanping

2013-01-01

At the molecular level, it is acknowledged that a TCM formula is often a complex system, which challenges researchers to fully understand its underlying pharmacological action. However, module detection technique developed from complex network provides new insight into systematic investigation of the mode of action of a TCM formula from the molecule perspective. We here proposed a computational approach integrating the module detection technique into a 2-class heterogeneous network (2-HN) which models the complex pharmacological system of a TCM formula. This approach takes three steps: construction of a 2-HN, identification of primary pharmacological units, and pathway analysis. We employed this approach to study Shu-feng-jie-du (SHU) formula, which aimed at discovering its molecular mechanism in defending against influenza infection. Actually, four primary pharmacological units were identified from the 2-HN for SHU formula and further analysis revealed numbers of biological pathways modulated by the four pharmacological units. 24 out of 40 enriched pathways that were ranked in top 10 corresponding to each of the four pharmacological units were found to be involved in the process of influenza infection. Therefore, this approach is capable of uncovering the mode of action underlying a TCM formula via module analysis. PMID:24376467

Piezoviscosity In Lubrication Of Nonconformal Contacts

NASA Technical Reports Server (NTRS)

Jeng, Yeau-Ren; Hamrock, Bernard J.; Brewe, David E.

1988-01-01

Developments in theory of lubrication. Analysis of piezoviscous-rigid regime of lubrication of two ellipsoidal contacts. Begins with Reynolds equation for point contact. Equation nondimensionalized using Roelands empirical formula and Dowson and Higginson formula. Equation solved numerically. Solutions obtained for full spectrum of conditions to find effects of dimensionless load, speed, parameters of lubricated and lubricating materials, and angle between direction of rolling and direction of entrainment of lubricant.

A possible pole problem in the formula for klystron gap fields

NASA Technical Reports Server (NTRS)

Kosmahl, H. G.

1977-01-01

In isolated cases a pole may be encountered in a previously published solution for the fields in a klystron gap. Formulas, permitting the critical combinations of parameters to be defined, are presented. It is noted that the region of inaccuracy surrounding the pole is sufficiently small and that a 0.1% change in the field changing parameter is enough to avoid it.

A Generalized Formula to Determine Pythagorean Triples

ERIC Educational Resources Information Center

Mohapatra, Amar Kumar; Prakash, Nupur

2010-01-01

This note proposes a unique solutions to find out the value of x, y and z which satisfies the equation x[superscript 2] + y[superscript 2] = z[superscript 2]. The uniqueness of the proposed formulae is to find the total number of y's and z's at a given value of x. The value of y and z can be calculated by factoring x[superscript 2] or…

Analytical Solutions for an Escape Problem in a Disc with an Arbitrary Distribution of Exit Holes Along Its Boundary

NASA Astrophysics Data System (ADS)

Marshall, J. S.

2016-12-01

We analytically construct solutions for the mean first-passage time and splitting probabilities for the escape problem of a particle moving with continuous Brownian motion in a confining planar disc with an arbitrary distribution (i.e., of any number, size and spacing) of exit holes/absorbing sections along its boundary. The governing equations for these quantities are Poisson's equation with a (non-zero) constant forcing term and Laplace's equation, respectively, and both are subject to a mixture of homogeneous Neumann and Dirichlet boundary conditions. Our solutions are expressed as explicit closed formulae written in terms of a parameterising variable via a conformal map, using special transcendental functions that are defined in terms of an associated Schottky group. They are derived by exploiting recent results for a related problem of fluid mechanics that describes a unidirectional flow over "no-slip/no-shear" surfaces, as well as results from potential theory, all of which were themselves derived using the same theory of Schottky groups. They are exact up to the determination of a finite set of mapping parameters, which is performed numerically. Their evaluation also requires the numerical inversion of the parameterising conformal map. Computations for a series of illustrative examples are also presented.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin

The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an examplemore » of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.« less

Non-aqueous electrolyte for lithium-ion battery

DOEpatents

Amine, Khalil; Zhang, Lu; Zhang, Zhengcheng

2016-01-26

A substantially non-aqueous electrolyte solution includes an alkali metal salt, a polar aprotic solvent, and an organophosphorus compound of Formula IA, IB, or IC: ##STR00001## where R.sup.1, R.sup.2, R.sup.3 and R.sup.4 are each independently hydrogen, halogen, alkyl, alkenyl, alkynyl, cycloalkyl, aryl, heterocyclyl, heteroaryl, alkoxy, alkenoxy, alkynoxy, cycloalkoxy, aryloxy, heterocyclyloxy, heteroaryloxy, siloxyl, silyl, or organophosphatyl; R.sup.5 and R.sup.6 are each independently alkyl, alkenyl, alkynyl, cycloalkyl, aryl, heterocyclyl, or heteroaryl; R.sup.7 is ##STR00002## and R.sup.8, R.sup.9 and R.sup.10 are each independently alkyl, cycloalkyl, aryl, heterocyclyl, or heteroaryl; provided that if the organophosphorus compound is of Formula IB, then at least one of R.sup.5, and R.sup.6 are other than hydrogen, alkyl, or alkenyl; and if the organophosphorus compound is of Formula IC, then the electrolyte solution does not include 4-methylene-1,3-dioxolan-2-one or 4,5-dimethylene-1,3-dioxolan-2-one.

Unified semiclassical theory for the two-state system: an analytical solution for general nonadiabatic tunneling.

PubMed

Zhu, Chaoyuan; Lin, Sheng Hsien

2006-07-28

Unified semiclasical solution for general nonadiabatic tunneling between two adiabatic potential energy surfaces is established by employing unified semiclassical solution for pure nonadiabatic transition [C. Zhu, J. Chem. Phys. 105, 4159 (1996)] with the certain symmetry transformation. This symmetry comes from a detailed analysis of the reduced scattering matrix for Landau-Zener type of crossing as a special case of nonadiabatic transition and nonadiabatic tunneling. Traditional classification of crossing and noncrossing types of nonadiabatic transition can be quantitatively defined by the rotation angle of adiabatic-to-diabatic transformation, and this rotational angle enters the analytical solution for general nonadiabatic tunneling. The certain two-state exponential potential models are employed for numerical tests, and the calculations from the present general nonadiabatic tunneling formula are demonstrated in very good agreement with the results from exact quantum mechanical calculations. The present general nonadiabatic tunneling formula can be incorporated with various mixed quantum-classical methods for modeling electronically nonadiabatic processes in photochemistry.

Asymptotics for Large Time of Global Solutions to the Generalized Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Hayashi, Nakao; Naumkin, Pavel I.; Saut, Jean-Claude

We study the large time asymptotic behavior of solutions to the generalized Kadomtsev-Petviashvili (KP) equations where σ= 1 or σ=- 1. When ρ= 2 and σ=- 1, (KP) is known as the KPI equation, while ρ= 2, σ=+ 1 corresponds to the KPII equation. The KP equation models the propagation along the x-axis of nonlinear dispersive long waves on the surface of a fluid, when the variation along the y-axis proceeds slowly [10]. The case ρ= 3, σ=- 1 has been found in the modeling of sound waves in antiferromagnetics [15]. We prove that if ρ>= 3 is an integer and the initial data are sufficiently small, then the solution u of (KP) satisfies the following estimates: for all t∈R, where κ= 1 if ρ= 3 and κ= 0 if ρ>= 4. We also find the large time asymptotics for the solution.

Comparison of soymilk, powdered milk, Hank's balanced salt solution and tap water on periodontal ligament cell survival.

PubMed

Moazami, Fariborz; Mirhadi, Hosein; Geramizadeh, Bita; Sahebi, Safoura

2012-04-01

The purpose of this study was to evaluate the ability of soymilk, powdered milk, and Hank's balanced salt solution (HBSS) to maintain human periodontal ligament (PDL) cell viability in vitro. PDL cells were obtained from extracted healthy third molars and cultured in Dulbecco's modified Eagles medium (DMEM). The cultures were exposed for 1, 2, 4, and 8 h to experimental solutions (tap water served as negative control and DMEM as positive control) at 37°C. The viable cells were then counted using the trypan blue exclusion technique. Data were analyzed by using one-way anova, post hoc Scheffe and two-way anova test. Statistical analysis showed that HBSS, powdered baby formula, and soymilk maintain cell viability equally well in different periods of times. Tap water cannot keep cells viable as well as other solutions. Soymilk and powdered baby formula can be recommended as suitable storage media for avulsed teeth for up to 8 h. © 2011 John Wiley & Sons A/S.

TemperSAT: A new efficient fair-sampling random k-SAT solver

NASA Astrophysics Data System (ADS)

Fang, Chao; Zhu, Zheng; Katzgraber, Helmut G.

The set membership problem is of great importance to many applications and, in particular, database searches for target groups. Recently, an approach to speed up set membership searches based on the NP-hard constraint-satisfaction problem (random k-SAT) has been developed. However, the bottleneck of the approach lies in finding the solution to a large SAT formula efficiently and, in particular, a large number of independent solutions is needed to reduce the probability of false positives. Unfortunately, traditional random k-SAT solvers such as WalkSAT are biased when seeking solutions to the Boolean formulas. By porting parallel tempering Monte Carlo to the sampling of binary optimization problems, we introduce a new algorithm (TemperSAT) whose performance is comparable to current state-of-the-art SAT solvers for large k with the added benefit that theoretically it can find many independent solutions quickly. We illustrate our results by comparing to the currently fastest implementation of WalkSAT, WalkSATlm.

Use of the refractometer as a tool to monitor dietary formula concentration in gastric juice.

PubMed

Chang, W-K; Chen, M-Z; Chao, Y-C

2002-12-01

Critically ill patients do not always tolerate nasogastric tube feeding. Gastric residual volumes are widely used to evaluate feeding tolerance, but controversy exists about what constitutes the residual volume (diet formula or digestive juice). In this paper, we describe the use of the refractometer as a tool to monitor dietary formula concentration in gastric juice and evaluate gastric juice refractometry as a possible clinical application. Brix value (an index of the total solutes in solution) readings for polymeric diet at pH 1, 4, 7 and 8, and at 4 degrees C, 25 degrees C and 37 degrees C, and in fasting gastric juice were determined with a refractometer. We found that distilled water, minerals, and vitamins had low Brix values of 0+/-0, 1.2+/-0.1, and 0.4+/-0.1, respectively. On the other hand, because carbohydrate (17 g/100 ml), protein (5.3 g/100 ml), fat (4.1 g/100 ml), and full-strength polymeric diet had high concentrations of dissolved nutrients, they also had high Brix values (12.1+/-0.6, 6.5+/-0.1, 6.0+/-0.1, and 23.5+/-0.1, respectively). The Brix values of polymeric diet had a linear additive relationship with the diet formula concentration at various pHs, temperatures, and in the gastric juice. Brix value measurement can be used to monitor stomach dietary formula concentration. Such information can be obtained at the bedside and used to evaluate feeding-intolerant patients receiving enteral feeding.

Design of cationic nanostructured heterolipid matrices for ocular delivery of methazolamide

PubMed Central

Youshia, John; Kamel, Amany O; El Shamy, Abdelhameed; Mansour, Samar

2012-01-01

Solid lipid nanoparticles (SLNs) formulated from one type of lipid (homolipid) suffer from low drug encapsulation and drug bursting due to crystallization of the lipid into the more ordered β modification, which leads to decreased drug entrapment and faster drug release. This study assessed the feasibility of using nanostructured lipid matrices (NLMs) for ocular delivery of methazolamide-(MZA) adopting heterolipids composed of novel mixtures of Compritol ® and cetostearyl alcohol (CSA), and stabilized by Tween 80®. The systems were prepared using the modified high shear homogenization followed by ultrasonication method, which avoids the use of organic solvents. A 32 full factorial design was constructed to study the influence of two independent variables, namely the ratio of CSA:Compritol and the concentration of Tween 80, each in three levels. The dependent variables were the entrapment efficiency percentages (EE%), mean particle size (PS), polydispersity index (PDI), and zeta potential (ZP). In vivo intraocular pressure (IOP) lowering activity for the selected formulae was compared to that of MZA solution. The results showed that increasing the ratio of CSA to Compritol increased the EE% and PS, while increasing the concentration of Tween 80, decreased PS with no significant effect on EE%. The ZP values of all formulae were positive, and greater than 30 mV. The best formula, composed of 4% CSA, 2% Compritol, 0.15% stearylamine, and 2% Tween 80, with EE% of 25.62%, PS of 207.1 nm, PDI of 0.243, and ZP of 41.50 mV, showed in vitro sustained release properties for 8 hours and lowered the intraocular pressure by 8.3 mmHg within 3 hours, with this drop in pressure lasting for 12 hours. PMID:22679362

Characterizing hydrophobicity of amino acid side chains in a protein environment via measuring contact angle of a water nanodroplet on planar peptide network.

PubMed

Zhu, Chongqin; Gao, Yurui; Li, Hui; Meng, Sheng; Li, Lei; Francisco, Joseph S; Zeng, Xiao Cheng

2016-11-15

Hydrophobicity of macroscopic planar surface is conventionally characterized by the contact angle of water droplets. However, this engineering measurement cannot be directly extended to surfaces of proteins, due to the nanometer scale of amino acids and inherent nonplanar structures. To measure the hydrophobicity of side chains of proteins quantitatively, numerous parameters were developed to characterize behavior of hydrophobic solvation. However, consistency among these parameters is not always apparent. Herein, we demonstrate an alternative way of characterizing hydrophobicity of amino acid side chains in a protein environment by constructing a monolayer of amino acids (i.e., artificial planar peptide network) according to the primary and the β-sheet secondary structures of protein so that the conventional engineering measurement of the contact angle of a water droplet can be brought to bear. Using molecular dynamics simulations, contact angles θ of a water nanodroplet on the planar peptide network, together with excess chemical potentials of purely repulsive methane-sized Weeks-Chandler-Andersen solute, are computed. All of the 20 types of amino acids and the corresponding planar peptide networks are studied. Expectedly, all of the planar peptide networks with nonpolar amino acids are hydrophobic due to θ [Formula: see text] 90°, whereas all of the planar peptide networks of the polar and charged amino acids are hydrophilic due to θ [Formula: see text] 90°. Planar peptide networks of the charged amino acids exhibit complete-wetting behavior due to θ [Formula: see text] 0°. This computational approach for characterization of hydrophobicity can be extended to artificial planar networks of other soft matter.

On the numerical treatment of selected oscillatory evolutionary problems

NASA Astrophysics Data System (ADS)

Cardone, Angelamaria; Conte, Dajana; D'Ambrosio, Raffaele; Paternoster, Beatrice

2017-07-01

We focus on evolutionary problems whose qualitative behaviour is known a-priori and exploited in order to provide efficient and accurate numerical schemes. For classical numerical methods, depending on constant coefficients, the required computational effort could be quite heavy, due to the necessary employ of very small stepsizes needed to accurately reproduce the qualitative behaviour of the solution. In these situations, it may be convenient to use special purpose formulae, i.e. non-polynomially fitted formulae on basis functions adapted to the problem (see [16, 17] and references therein). We show examples of special purpose strategies to solve two families of evolutionary problems exhibiting periodic solutions, i.e. partial differential equations and Volterra integral equations.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

NASA Astrophysics Data System (ADS)

Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

2017-11-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

Construction and temporal behaviour study of multi RLC intense light pulses for dermatological applications.

PubMed

Hamoudi, Walid K; Ismail, Raid A; Shakir, Hussein A

2017-10-01

Driving a flash lamp in an intense pulsed light system requires a high-voltage DC power supply, capacitive energy storage and a flash lamp triggering unit. Single, double, triple and quadruple-mesh discharge and triggering circuits were constructed to provide intense light pulses of variable energy and time durations. The system was treated as [Formula: see text] circuit in some cases and [Formula: see text] circuit in others with a light pulse profile following the temporal behaviour of the exciting current pulse. Distributing the energy delivered to one lamp onto a number of LC meshes permitted longer current pulses, and consequently increased the light pulse length. Positive results were obtained when using the system to treat skin wrinkles.

The Singular Set of Solutions to Non-Differentiable Elliptic Systems

NASA Astrophysics Data System (ADS)

Mingione, Giuseppe

We estimate the Hausdorff dimension of the singular set of solutions to elliptic systems of the type If the vector fields a and b are Hölder continuous with respect to the variable x with exponent α, then the Hausdorff dimension of the singular set of any weak solution is at most n-2α.

Transfer of Solutions to Conditional Probability Problems: Effects of Example Problem Format, Solution Format, and Problem Context

ERIC Educational Resources Information Center

Chow, Alan F.; Van Haneghan, James P.

2016-01-01

This study reports the results of a study examining how easily students are able to transfer frequency solutions to conditional probability problems to novel situations. University students studied either a problem solved using the traditional Bayes formula format or using a natural frequency (tree diagram) format. In addition, the example problem…

Polynomial functors and combinatorial Dyson-Schwinger equations

NASA Astrophysics Data System (ADS)

Kock, Joachim

2017-04-01

We present a general abstract framework for combinatorial Dyson-Schwinger equations, in which combinatorial identities are lifted to explicit bijections of sets, and more generally equivalences of groupoids. Key features of combinatorial Dyson-Schwinger equations are revealed to follow from general categorical constructions and universal properties. Rather than beginning with an equation inside a given Hopf algebra and referring to given Hochschild 1-cocycles, our starting point is an abstract fixpoint equation in groupoids, shown canonically to generate all the algebraic structures. Precisely, for any finitary polynomial endofunctor P defined over groupoids, the system of combinatorial Dyson-Schwinger equations X = 1 + P(X) has a universal solution, namely the groupoid of P-trees. The isoclasses of P-trees generate naturally a Connes-Kreimer-like bialgebra, in which the abstract Dyson-Schwinger equation can be internalised in terms of canonical B+-operators. The solution to this equation is a series (the Green function), which always enjoys a Faà di Bruno formula, and hence generates a sub-bialgebra isomorphic to the Faà di Bruno bialgebra. Varying P yields different bialgebras, and cartesian natural transformations between various P yield bialgebra homomorphisms and sub-bialgebras, corresponding for example to truncation of Dyson-Schwinger equations. Finally, all constructions can be pushed inside the classical Connes-Kreimer Hopf algebra of trees by the operation of taking core of P-trees. A byproduct of the theory is an interpretation of combinatorial Green functions as inductive data types in the sense of Martin-Löf type theory (expounded elsewhere).

Critical Compressive Stress for Flat Rectangular Plates Supported Along All Edges and Elastically Restrained Against Rotation along the Unloaded Edges

NASA Technical Reports Server (NTRS)

Lundquist, Eugene E; Stowell, Elbridge Z

1942-01-01

A chart is presented for the values of the coefficient in the formula for the critical compressive stress at which buckling may be expected to occur in flat rectangular plates supported along all edges and, in addition, elastically restrained against rotation along the unloaded edges. The mathematical derivations of the formulas required in the construction of the chart are given.

Vertical bending strength and torsional rigidity analysis of formula student car chassis

NASA Astrophysics Data System (ADS)

Hazimi, Hashfi; Ubaidillah, Setiyawan, Adi Eka Putra; Ramdhani, Hanief Cahya; Saputra, Murnanda Zaesy; Imaduddin, Fitrian

2018-02-01

Formula Society of Automotive Engineers (FSAE) is a competition for students to construct formula student car. One of an essential part of a formula student car is its chassis. Chassis is an internal vehicle frame which holds all another part of the vehicle and secures the driver. The team have to design their chassis and tests their design to achieve the best chassis that fulfill the regulation. This paper contains chassis design from Bengawan FSAE Team and some FEA tests to find out the Tensile Strength, Torsional Rigidity, and Von Misses Stress of Formula SAE car. Torsional rigidity was found by applying the static torsional test. The results from torsional rigidity test are a maximum deformation of 9.9512 mm with 1.7064 safety factor, and 35.935 MPa maximum Von Misses Stress. Moreover, then the result of the vertical bending strength test is 8.1214 mm max deformation with safety factor 4.2717, and 29.226 MPa maximum Von Misses Stress.

An embedded formula of the Chebyshev collocation method for stiff problems

NASA Astrophysics Data System (ADS)

Piao, Xiangfan; Bu, Sunyoung; Kim, Dojin; Kim, Philsu

2017-12-01

In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge-Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods.

Fourier Series and Elliptic Functions

ERIC Educational Resources Information Center

Fay, Temple H.

2003-01-01

Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…

Positive periodic solution for p-Laplacian neutral Rayleigh equation with singularity of attractive type.

PubMed

Xin, Yun; Liu, Hongmin; Cheng, Zhibo

2018-01-01

In this paper, we consider a kind of p -Laplacian neutral Rayleigh equation with singularity of attractive type, [Formula: see text] By applications of an extension of Mawhin's continuation theorem, sufficient conditions for the existence of periodic solution are established.

The concept of surgical operating list 'efficiency': a formula to describe the term.

PubMed

Pandit, J J; Westbury, S; Pandit, M

2007-09-01

While numerous reports have sought ways of improving the efficiency of surgical operating lists, none has defined 'efficiency'. We describe a formula that defines efficiency as incorporating three elements: maximising utilisation, minimising over-running and minimising cancellations on a list. We applied this formula to hypothetical (but realistic) scenarios, and our formula yielded plausible descriptions of these. We also applied the formula to 16 consecutive elective surgical lists from three gynaecology teams (two at a university hospital and one at a non-university hospital). Again, the formula gave useful insights into problems faced by the teams in improving their performance, and it also guided possible solutions. The formula confirmed that a team that schedules cases according to the predicted durations of the operations listed (i.e. the non-university hospital team) suffered fewer cancellations (median 5% vs 8% and 13%) and fewer list over-runs (6% vs 38% and 50%), and performed considerably more efficiently (90% vs 79% and 72%; p = 0.038) than teams that did not do so (i.e. those from the university hospital). We suggest that surgical list performance is more completely described by our formula for efficiency than it is by other conventional measures such as list utilisation or cancellation rate alone.

Calculation method for steady-state pollutant concentration in mixing zones considering variable lateral diffusion coefficient.

PubMed

Wu, Wen; Wu, Zhouhu; Song, Zhiwen

2017-07-01

Prediction of the pollutant mixing zone (PMZ) near the discharge outfall in Huangshaxi shows large error when using the methods based on the constant lateral diffusion assumption. The discrepancy is due to the lack of consideration of the diffusion coefficient variation. The variable lateral diffusion coefficient is proposed to be a function of the longitudinal distance from the outfall. Analytical solution of the two-dimensional advection-diffusion equation of a pollutant is derived and discussed. Formulas to characterize the geometry of the PMZ are derived based on this solution, and a standard curve describing the boundary of the PMZ is obtained by proper choices of the normalization scales. The change of PMZ topology due to the variable diffusion coefficient is then discussed using these formulas. The criterion of assuming the lateral diffusion coefficient to be constant without large error in PMZ geometry is found. It is also demonstrated how to use these analytical formulas in the inverse problems including estimating the lateral diffusion coefficient in rivers by convenient measurements, and determining the maximum allowable discharge load based on the limitations of the geometrical scales of the PMZ. Finally, applications of the obtained formulas to onsite PMZ measurements in Huangshaxi present excellent agreement.

α '-corrected black holes in String Theory

NASA Astrophysics Data System (ADS)

Cano, Pablo A.; Meessen, Patrick; Ortín, Tomás; Ramírez, Pedro F.

2018-05-01

We consider the well-known solution of the Heterotic Superstring effective action to zeroth order in α ' that describes the intersection of a fundamental string with momentum and a solitonic 5-brane and which gives a 3-charge, static, extremal, supersymmetric black hole in 5 dimensions upon dimensional reduction on T5. We compute explicitly the first-order in α ' corrections to this solution, including SU(2) Yang-Mills fields which can be used to cancel some of these corrections and we study the main properties of this α '-corrected solution: supersymmetry, values of the near-horizon and asymptotic charges, behavior under α '-corrected T-duality, value of the entropy (using Wald formula directly in 10 dimensions), existence of small black holes etc. The value obtained for the entropy agrees, within the limits of approximation, with that obtained by microscopic methods. The α ' corrections coming from Wald's formula prove crucial for this result.

Method and system for suppression of stimulated Raman scattering in laser materials

DOEpatents

Caird, John A; Bayramian, Andrew J; Ebbers, Christopher A

2013-11-19

A composition of matter is provided having the general chemical formula K(H,D).sub.2P(.sup.16O.sub.x,.sup.18O.sub.y).sub.4, where x<0.998 or y>0.002, and x+y.apprxeq.1. Additionally, a method of fabricating an optical material by growth from solution is provided. The method includes providing a solution including a predetermined percentage of (H,D).sub.2.sup.16O and a predetermined percentage of (H,D).sub.2.sup.18O, providing a seed crystal, and supporting the seed crystal on a platform. The method also includes immersing the seed crystal in the solution and forming the optical material. The optical material has the general chemical formula K(H,D).sub.2P(.sup.16O.sub.x,.sup.18O.sub.y).sub.4, where x<0.998 or y>0.002, and x+y.apprxeq.1.

Method and system for suppression of stimulated Raman scattering in laser materials

DOEpatents

Caird, John A.; Bayramian, Andrew J.; Ebbers, Christopher A.

2015-07-14

A composition of matter is provided having the general chemical formula K(H,D).sub.2P(.sup.16O.sub.x,.sup.18O.sub.y).sub.4, where x<0.998 or y>0.002, and x+y.apprxeq.1. Additionally, a method of fabricating an optical material by growth from solution is provided. The method includes providing a solution including a predetermined percentage of (H,D).sub.2.sup.16O and a predetermined percentage of (H,D).sub.2.sup.18O, providing a seed crystal, and supporting the seed crystal on a platform. The method also includes immersing the seed crystal in the solution and forming the optical material. The optical material has the general chemical formula K(H,D).sub.2P(.sup.16O.sub.x,.sup.18O.sub.y).sub.4, where x<0.998 or y>0.002, and x+y.apprxeq.1.

Optimal Mortgage Refinancing: A Closed Form Solution.

PubMed

Agarwal, Sumit; Driscoll, John C; Laibson, David I

2013-06-01

We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least [Formula: see text] In this formula W (.) is the Lambert W -function, [Formula: see text] ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of the tax-adjusted refinancing cost and the remaining mortgage value, and τ is the marginal tax rate. This expression is derived by solving a tractable class of refinancing problems. Our quantitative results closely match those reported by researchers using numerical methods.

27 CFR 21.63 - Formula No. 36.

Code of Federal Regulations, 2010 CFR

2010-04-01

... gallons of ammonia, aqueous, 27 to 30 percent by weight; 3 gallons of strong ammonia solution, N.F.: 17.5... N.F. 450.Cleaning solutions (including household detergents). (2) As a raw material: 530.Ethylamines. 540.Dyes and intermediates. 579.Other chemicals. (3) Miscellaneous uses: 812.Product development and...

27 CFR 21.63 - Formula No. 36.

Code of Federal Regulations, 2011 CFR

2011-04-01

... gallons of ammonia, aqueous, 27 to 30 percent by weight; 3 gallons of strong ammonia solution, N.F.: 17.5... N.F. 450.Cleaning solutions (including household detergents). (2) As a raw material: 530.Ethylamines. 540.Dyes and intermediates. 579.Other chemicals. (3) Miscellaneous uses: 812.Product development and...

The Equivalence of Three Statistical Packages for Performing Hierarchical Cluster Analysis

ERIC Educational Resources Information Center

Blashfield, Roger

1977-01-01

Three different software programs which contain hierarchical agglomerative cluster analysis procedures were shown to generate different solutions on the same data set using apparently the same options. The basis for the differences in the solutions was the formulae used to calculate Euclidean distance. (Author/JKS)

A fast indirect method to compute functions of genomic relationships concerning genotyped and ungenotyped individuals, for diversity management.

PubMed

Colleau, Jean-Jacques; Palhière, Isabelle; Rodríguez-Ramilo, Silvia T; Legarra, Andres

2017-12-01

Pedigree-based management of genetic diversity in populations, e.g., using optimal contributions, involves computation of the [Formula: see text] type yielding elements (relationships) or functions (usually averages) of relationship matrices. For pedigree-based relationships [Formula: see text], a very efficient method exists. When all the individuals of interest are genotyped, genomic management can be addressed using the genomic relationship matrix [Formula: see text]; however, to date, the computational problem of efficiently computing [Formula: see text] has not been well studied. When some individuals of interest are not genotyped, genomic management should consider the relationship matrix [Formula: see text] that combines genotyped and ungenotyped individuals; however, direct computation of [Formula: see text] is computationally very demanding, because construction of a possibly huge matrix is required. Our work presents efficient ways of computing [Formula: see text] and [Formula: see text], with applications on real data from dairy sheep and dairy goat breeding schemes. For genomic relationships, an efficient indirect computation with quadratic instead of cubic cost is [Formula: see text], where Z is a matrix relating animals to genotypes. For the relationship matrix [Formula: see text], we propose an indirect method based on the difference between vectors [Formula: see text], which involves computation of [Formula: see text] and of products such as [Formula: see text] and [Formula: see text], where [Formula: see text] is a working vector derived from [Formula: see text]. The latter computation is the most demanding but can be done using sparse Cholesky decompositions of matrix [Formula: see text], which allows handling very large genomic and pedigree data files. Studies based on simulations reported in the literature show that the trends of average relationships in [Formula: see text] and [Formula: see text] differ as genomic selection proceeds. When selection is based on genomic relationships but management is based on pedigree data, the true genetic diversity is overestimated. However, our tests on real data from sheep and goat obtained before genomic selection started do not show this. We present efficient methods to compute elements and statistics of the genomic relationships [Formula: see text] and of matrix [Formula: see text] that combines ungenotyped and genotyped individuals. These methods should be useful to monitor and handle genomic diversity.

Comparison of constructed wetland and stabilization pond for the treatment of digested effluent of swine wastewater.

PubMed

Liu, Gang-Jin; Zheng, Dan; Deng, Liang-Wei; Wen, Quan; Liu, Yi

2014-01-01

A laboratory-scale horizontal subsurface flow constructed wetland (HSFCW) and a stabilization pond (SP) were constructed to compare their performances on the treatment of digested effluent of swine wastewater. After 457 days of operation, the removal efficiencies of the HSFCW were as follows: chemical oxygen demand (COD), 17-54%; total phosphorus (TP), 32-45% and ammonia nitrogen [Formula: see text], 27-88%, while they were 25-55%, 31-56% and 56-98%, respectively, for the SP, with a hydraulic retention time of 54 days and hydraulic loading of 0.01 m³ m⁻² d⁻¹. The average removed loads for the HSFCW were as follows: COD, 0.25-4.33; TP, 0.01-0.11 and [Formula: see text], 0.34-2.54 g m⁻² d⁻¹, while they were 0.25-4.45, 0.02-0.13 and 0.72-2.87 g m⁻² d⁻¹, respectively, for the SP. The SP performed better than the HSFCW because the SP showed a 20% of higher removal efficiency for [Formula: see text] than the HSFCW. Especially, the COD removal rate of SP was 10% higher than the HSFCW when the influent concentration was at the lowest and highest stages. Meanwhile, given the lower costs, the SP is more suitable for the treatment of digested effluent of swine wastewater than the HSFCW.

Principal-Centric Reasoning in Constructive Authorization Logic

DTIC Science & Technology

2009-04-14

formulas of DTL0 to formulas of CS4m as 19 follows. pPq = P pA ∧ Bq = pAq ∧ pBq pA ∨ Bq = pAq ∨ pBq pA ⊃ Bq = pAq ⊃ pBq p>q = > p⊥q = ⊥ pK says Aq...K(K ⊃ pAq ) The important part of the translation is the mapping of K says A to K(K ⊃ pAq ). The formula K on the left of the implication acts as a...guard” on pAq , and recovers the effect of the context associated with hypothetical judgments in DTL0: pAq can be obtained from K ⊃ pAq only if K is

Solution of linear systems by a singular perturbation technique

NASA Technical Reports Server (NTRS)

Ardema, M. D.

1976-01-01

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

Rational Solutions to the ABS List: Transformation Approach

NASA Astrophysics Data System (ADS)

Zhang, Danda; Zhang, Da-Jun

2017-10-01

In the paper we derive rational solutions for the lattice potential modified Korteweg-de Vries equation, and Q2, Q1(δ), H3(δ), H2 and H1 in the Adler-Bobenko-Suris list. Bäcklund transformations between these lattice equations are used. All these rational solutions are related to a unified τ function in Casoratian form which obeys a bilinear superposition formula.

Grazing-incidence X-ray diffraction from a crystal with subsurface defects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaevskii, A. Yu., E-mail: transilv@mail.ru; Golentus, I. E.

2015-03-15

The diffraction of X rays incident on a crystal surface under grazing angles under conditions of total external reflection has been investigated. An approach is proposed in which exact solutions to the dynamic problem of grazing-incidence diffraction in an ideal crystal are used as initial functions to calculate the diffuse component of diffraction in a crystal with defects. The diffuse component of diffraction is calculated for a crystal with surface defects of a dilatation-center type. Exact formulas of the continuum theory which take into account the mirror-image forces are used for defect-induced atomic displacements. Scattering intensity maps near Bragg peaksmore » are constructed for different scan modes, and the conditions for detecting primarily the diffuse component are determined. The results of dynamic calculations of grazing-incidence diffraction in defect-containing crystals are compared with calculations in the kinematic approximation.« less

Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach

NASA Astrophysics Data System (ADS)

Camassa, R.; Falqui, G.; Ortenzi, G.

2017-02-01

The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite two-dimensional channel. The Hamiltonian structure of the averaged equations is obtained directly from that of the Euler equations through the process of Hamiltonian reduction. Long-wave asymptotics together with the Boussinesq approximation of neglecting the fluids’ inertia is then applied to reduce the leading order vertically averaged equations to the shallow-water Airy system, albeit in a non-trivial way. The full non-Boussinesq system for the dispersionless limit can then be viewed as a deformation of this well known equation. In a perturbative study of this deformation, a family of approximate constants of the motion are explicitly constructed and used to find local solutions of the evolution equations by means of hodograph-like formulae.

Geometrically derived difference formulae for the numerical integration of trajectory problems

NASA Technical Reports Server (NTRS)

Mcleod, R. J. Y.; Sanz-Serna, J. M.

1982-01-01

An initial value problem for the autonomous system of ordinary differential equations dy/dt = f(y), where y is a vector, is considered. In a number of practical applications the interest lies in obtaining the curve traced by the solution y. These applications include the computation of trajectories in mechanical problems. The term 'trajectory problem' is employed to refer to these cases. Lambert and McLeod (1979) have introduced a method involving local rotation of the axes in the y-plane for the two-dimensional case. The present investigation continues the study of difference schemes specifically derived for trajectory problems. A simple geometrical way of constructing such methods is presented, and the local accuracy of the schemes is investigated. A circularly exact, fixed-step predictor-corrector algorithm is defined, and a variable-step version of a circularly exact algorithm is presented.

Simplified analysis about horizontal displacement of deep soil under tunnel excavation

NASA Astrophysics Data System (ADS)

Tian, Xiaoyan; Gu, Shuancheng; Huang, Rongbin

2017-11-01

Most of the domestic scholars focus on the study about the law of the soil settlement caused by subway tunnel excavation, however, studies on the law of horizontal displacement are lacking. And it is difficult to obtain the horizontal displacement data of any depth in the project. At present, there are many formulas for calculating the settlement of soil layers. In terms of integral solutions of Mindlin classic elastic theory, stochastic medium theory, source-sink theory, the Peck empirical formula is relatively simple, and also has a strong applicability at home. Considering the incompressibility of rock and soil mass, based on the principle of plane strain, the calculation formula of the horizontal displacement of the soil along the cross section of the tunnel was derived by using the Peck settlement formula. The applicability of the formula is verified by comparing with the existing engineering cases, a simple and rapid analytical method for predicting the horizontal displacement is presented.

A strategy for reducing gross errors in the generalized Born models of implicit solvation

PubMed Central

Onufriev, Alexey V.; Sigalov, Grigori

2011-01-01

The “canonical” generalized Born (GB) formula [C. Still, A. Tempczyk, R. C. Hawley, and T. Hendrickson, J. Am. Chem. Soc. 112, 6127 (1990)] is known to provide accurate estimates for total electrostatic solvation energies ΔGel of biomolecules if the corresponding effective Born radii are accurate. Here we show that even if the effective Born radii are perfectly accurate, the canonical formula still exhibits significant number of gross errors (errors larger than 2kBT relative to numerical Poisson equation reference) in pairwise interactions between individual atomic charges. Analysis of exact analytical solutions of the Poisson equation (PE) for several idealized nonspherical geometries reveals two distinct spatial modes of the PE solution; these modes are also found in realistic biomolecular shapes. The canonical GB Green function misses one of two modes seen in the exact PE solution, which explains the observed gross errors. To address the problem and reduce gross errors of the GB formalism, we have used exact PE solutions for idealized nonspherical geometries to suggest an alternative analytical Green function to replace the canonical GB formula. The proposed functional form is mathematically nearly as simple as the original, but depends not only on the effective Born radii but also on their gradients, which allows for better representation of details of nonspherical molecular shapes. In particular, the proposed functional form captures both modes of the PE solution seen in nonspherical geometries. Tests on realistic biomolecular structures ranging from small peptides to medium size proteins show that the proposed functional form reduces gross pairwise errors in all cases, with the amount of reduction varying from more than an order of magnitude for small structures to a factor of 2 for the largest ones. PMID:21528947

Stress Intensity Formulas for Three Dimensional Crack in the Vicinity of an Interface

NASA Astrophysics Data System (ADS)

Noda, Nao-Aki; Liang, Bin; Xu, Chunhui

2008-02-01

In this study, stress intensity factors are considered by using exact solutions available for cracks near an interface. The effect of crack shape on the stress intensity factors is studied with varying the aspect ratio of the cracks. Then, the stress intensity factors are expressed as formulas useful for engineering applications. The stress intensity factors for interface cracks and a crack in a functionally graded material are also discussed.

An Astronomical Test of CCD Photometric Precision

NASA Technical Reports Server (NTRS)

Koch, David; Dunham, Edward; Borucki, William; Jenkins, Jon; DeVingenzi, D. (Technical Monitor)

1998-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Realization of Rectangular Artificial Spin Ice and Direct Observation of High Energy Topology.

PubMed

Ribeiro, I R B; Nascimento, F S; Ferreira, S O; Moura-Melo, W A; Costa, C A R; Borme, J; Freitas, P P; Wysin, G M; de Araujo, C I L; Pereira, A R

2017-10-25

In this work, we have constructed and experimentally investigated frustrated arrays of dipoles forming two-dimensional artificial spin ices with different lattice parameters (rectangular arrays with horizontal and vertical lattice spacings denoted by a and b respectively). Arrays with three different aspect ratios γ = a/b = [Formula: see text], [Formula: see text] and [Formula: see text] are studied. Theoretical calculations of low-energy demagnetized configurations for these same parameters are also presented. Experimental data for demagnetized samples confirm most of the theoretical results. However, the highest energy topology (doubly-charged monopoles) does not emerge in our theoretical model, while they are seen in experiments for large enough γ. Our results also insinuate that the string tension connecting two magnetic monopoles in a pair vanishes in rectangular lattices with a critical ratio γ = γ c  = [Formula: see text], supporting previous theoretical predictions.

Validity and Reliability Testing of an e-learning Questionnaire for Chemistry Instruction

NASA Astrophysics Data System (ADS)

Guspatni, G.; Kurniawati, Y.

2018-04-01

The aim of this paper is to examine validity and reliability of a questionnaire used to evaluate e-learning implementation in chemistry instruction. 48 questionnaires were filled in by students who had studied chemistry through e-learning system. The questionnaire consisted of 20 indicators evaluating students’ perception on using e-learning. Parametric testing was done as data were assumed to follow normal distribution. Item validity of the questionnaire was examined through item-total correlation using Pearson’s formula while its reliability was assessed with Cronbach’s alpha formula. Moreover, convergent validity was assessed to see whether indicators building a factor had theoretically the same underlying construct. The result of validity testing revealed 19 valid indicators while the result of reliability testing revealed Cronbach’s alpha value of .886. The result of factor analysis showed that questionnaire consisted of five factors, and each of them had indicators building the same construct. This article shows the importance of factor analysis to get a construct valid questionnaire before it is used as research instrument.

The "Don't Know" Option in Progress Testing

ERIC Educational Resources Information Center

Ravesloot, C. J.; Van der Schaaf, M. F.; Muijtjens, A. M. M.; Haaring, C.; Kruitwagen, C. L. J. J.; Beek, F. J. A.; Bakker, J.; Van Schaik, J.P.J.; Ten Cate, Th. J.

2015-01-01

Formula scoring (FS) is the use of a don't know option (DKO) with subtraction of points for wrong answers. Its effect on construct validity and reliability of progress test scores, is subject of discussion. Choosing a DKO may not only be affected by knowledge level, but also by risk taking tendency, and may thus introduce construct-irrelevant…

The mean and variance of phylogenetic diversity under rarefaction

PubMed Central

Matsen, Frederick A.

2013-01-01

Summary Phylogenetic diversity (PD) depends on sampling depth, which complicates the comparison of PD between samples of different depth. One approach to dealing with differing sample depth for a given diversity statistic is to rarefy, which means to take a random subset of a given size of the original sample. Exact analytical formulae for the mean and variance of species richness under rarefaction have existed for some time but no such solution exists for PD.We have derived exact formulae for the mean and variance of PD under rarefaction. We confirm that these formulae are correct by comparing exact solution mean and variance to that calculated by repeated random (Monte Carlo) subsampling of a dataset of stem counts of woody shrubs of Toohey Forest, Queensland, Australia. We also demonstrate the application of the method using two examples: identifying hotspots of mammalian diversity in Australasian ecoregions, and characterising the human vaginal microbiome.There is a very high degree of correspondence between the analytical and random subsampling methods for calculating mean and variance of PD under rarefaction, although the Monte Carlo method requires a large number of random draws to converge on the exact solution for the variance.Rarefaction of mammalian PD of ecoregions in Australasia to a common standard of 25 species reveals very different rank orderings of ecoregions, indicating quite different hotspots of diversity than those obtained for unrarefied PD. The application of these methods to the vaginal microbiome shows that a classical score used to quantify bacterial vaginosis is correlated with the shape of the rarefaction curve.The analytical formulae for the mean and variance of PD under rarefaction are both exact and more efficient than repeated subsampling. Rarefaction of PD allows for many applications where comparisons of samples of different depth is required. PMID:23833701

The mean and variance of phylogenetic diversity under rarefaction.

PubMed

Nipperess, David A; Matsen, Frederick A

2013-06-01

Phylogenetic diversity (PD) depends on sampling depth, which complicates the comparison of PD between samples of different depth. One approach to dealing with differing sample depth for a given diversity statistic is to rarefy, which means to take a random subset of a given size of the original sample. Exact analytical formulae for the mean and variance of species richness under rarefaction have existed for some time but no such solution exists for PD.We have derived exact formulae for the mean and variance of PD under rarefaction. We confirm that these formulae are correct by comparing exact solution mean and variance to that calculated by repeated random (Monte Carlo) subsampling of a dataset of stem counts of woody shrubs of Toohey Forest, Queensland, Australia. We also demonstrate the application of the method using two examples: identifying hotspots of mammalian diversity in Australasian ecoregions, and characterising the human vaginal microbiome.There is a very high degree of correspondence between the analytical and random subsampling methods for calculating mean and variance of PD under rarefaction, although the Monte Carlo method requires a large number of random draws to converge on the exact solution for the variance.Rarefaction of mammalian PD of ecoregions in Australasia to a common standard of 25 species reveals very different rank orderings of ecoregions, indicating quite different hotspots of diversity than those obtained for unrarefied PD. The application of these methods to the vaginal microbiome shows that a classical score used to quantify bacterial vaginosis is correlated with the shape of the rarefaction curve.The analytical formulae for the mean and variance of PD under rarefaction are both exact and more efficient than repeated subsampling. Rarefaction of PD allows for many applications where comparisons of samples of different depth is required.

Effects of American Ginseng on Preimplantation Development and Pregnancy in Mice.

PubMed

Belanger, Danyka; Calder, Michele D; Gianetto-Berruti, Alessandra; Lui, Edmund M; Watson, Andrew J; Feyles, Valter

2016-01-01

In North America, a high proportion of pregnant women use herbal medications including North American ginseng. This medicinal plant contains high amounts of triterpene saponins (ginsenosides), which are the main bioactive compounds. It is important to assess ginseng's impact on all reproductive functions to ensure the safety of pregnant women and fetuses. In this study, we defined the concentration-responsive effects of North American alcoholic and aqueous ginseng extracts on preimplantation development in vitro and on pregnancy and post-partum development in the mouse. Two-cell mouse embryos were cultured with 5 different concentrations of whole ginseng root extracts, or ginsenosides Rb1, Rg1 and Re alone, a combinatorial ginsenoside solution and a crude polysaccharide fraction solution. Embryonic development and recovery from each treatment was assessed. To investigate the in vivo effects of ginseng extracts, female mice were gavaged with 50[Formula: see text]mg/kg/day, 500[Formula: see text]mg/kg/day or 2000[Formula: see text]mg/kg/day of either extract (treatment) or water (sham) for 2 weeks prior to mating and throughout gestation. Gestation period, litter size, pup growth and pup sex ratio were evaluated. Oral ginseng consumption did not significantly affect fertility or pregnancy in the mouse. High doses of ginseng (2000[Formula: see text]mg/kg/day) decreased maternal weight gain. Direct treatment of preimplantation embryos in vitro demonstrated that ALC and AQ extract treatment reduced development in a concentration responsive manner, while only ALC extract effects were largely reversible. Treatments with individual or combinatorial ginsenosides, or the polysaccharide fraction solution alone did not impair preimplantation development, in vitro. In conclusion, maternal oral consumption of ginseng has little negative impact on pregnancy in the mouse, however, direct exposure to ginseng extract during mouse preimplantation development in vitro is detrimental.

Mathematical Problems in Synthetic Aperture Radar

NASA Astrophysics Data System (ADS)

Klein, Jens

2010-10-01

This thesis is concerned with problems related to Synthetic Aperture Radar (SAR). The thesis is structured as follows: The first chapter explains what SAR is, and the physical and mathematical background is illuminated. The following chapter points out a problem with a divergent integral in a common approach and proposes an improvement. Numerical comparisons are shown that indicate that the improvements allow for a superior image quality. Thereafter the problem of limited data is analyzed. In a realistic SAR-measurement the data gathered from the electromagnetic waves reflected from the surface can only be collected from a limited area. However the reconstruction formula requires data from an infinite distance. The chapter gives an analysis of the artifacts which can obscure the reconstructed images due to this problem. Additionally, some numerical examples are shown that point to the severity of the problem. In chapter 4 the fact that data is available only from a limited area is used to propose a new inversion formula. This inversion formula has the potential to make it easier to suppress artifacts due to limited data and, depending on the application, can be refined to a fast reconstruction formula. In the penultimate chapter a solution to the problem of left-right ambiguity is presented. This problem exists since the invention of SAR and is caused by the geometry of the measurements. This leads to the fact that only symmetric images can be obtained. With the solution from this chapter it is possible to reconstruct not only the even part of the reflectivity function, but also the odd part, thus making it possible to reconstruct asymmetric images. Numerical simulations are shown to demonstrate that this solution is not affected by stability problems as other approaches have been. The final chapter develops some continuative ideas that could be pursued in the future.

Thermodynamics of feldspathoid solutions

NASA Astrophysics Data System (ADS)

Sack, Richard O.; Ghiorso, Mark S.

We have developed models for the thermody-namic properties of nephelines, kalsilites, and leucites in the simple system NaAlSiO4-KAlSiO4-Ca0.5AlSiO4-SiO2-H2O that are consistent with all known constraints on subsolidus equilibria and thermodynamic properties, and have integrated them into the existing MELTS software package. The model for nepheline is formulated for the simplifying assumptions that (1) a molecular mixing-type approximation describes changes in the configurational entropy associated with the coupled exchange substitutions □Si?NaAl and □Ca? Na2 and that (2) Na+ and K+ display long-range non-convergent ordering between a large cation and the three small cation sites in the Na4Al4Si4O16 formula unit. Notable features of the model include the prediction that the mineral tetrakalsilite (``panunzite'', sensu stricto) results from anti-ordering of Na and K between the large cation and the three small cation sites in the nepheline structure at high temperatures, an average dT/dP slope of about 55°/kbar for the reaction over the temperature and pressure ranges 800-1050 °C and 500-5000 bars, roughly symmetric (i.e. quadratic) solution behavior of the K-Na substitution along joins between fully ordered components in nepheline, and large positive Gibbs energies for the nepheline reciprocal reactions and and for the leucite reciprocal reaction

Hydrodynamics with conserved current via AdS/CFT correspondence in the Maxwell-Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu Yapeng; Sun Peng; Zhang Jianhui

2011-06-15

Using the AdS/CFT correspondence, we study the hydrodynamics with conserved current from the dual Maxwell-Gauss-Bonnet gravity. After constructing the perturbative solution to the first order based on the boosted black brane solution in the bulk Maxwell-Gauss-Bonnet gravity, we extract the stress tensor and conserved current of the dual conformal fluid on its boundary, and also find the effect of the Gauss-Bonnet term on the dual conformal fluid. Our results show that the Gauss-Bonnet term can affect the parameters such as the shear viscosity {eta}, entropy density s, thermal conductivity {kappa} and electrical conductivity {sigma}. However, it does not affect themore » so-called Wiedemann-Franz law which relates {kappa} to {sigma}, while it affects the ratio {eta}/s. In addition, another interesting result is that {eta}/s can also be affected by the bulk Maxwell field in our case, which is consistent with some previous results predicted through the Kubo formula. Moreover, the anomalous magnetic and vortical effects by adding the Chern-Simons term are also considered in our case in the Maxwell-Gauss-Bonnet gravity.« less

A model for interprovincial air pollution control based on futures prices.

PubMed

Zhao, Laijun; Xue, Jian; Gao, Huaizhu Oliver; Li, Changmin; Huang, Rongbing

2014-05-01

Based on the current status of research on tradable emission rights futures, this paper introduces basic market-related assumptions for China's interprovincial air pollution control problem. The authors construct an interprovincial air pollution control model based on futures prices: the model calculated the spot price of emission rights using a classic futures pricing formula, and determined the identities of buyers and sellers for various provinces according to a partitioning criterion, thereby revealing five trading markets. To ensure interprovincial cooperation, a rational allocation result for the benefits from this model was achieved using the Shapley value method to construct an optimal reduction program and to determine the optimal annual decisions for each province. Finally, the Beijing-Tianjin-Hebei region was used as a case study, as this region has recently experienced serious pollution. It was found that the model reduced the overall cost of reducing SO2 pollution. Moreover, each province can lower its cost for air pollution reduction, resulting in a win-win solution. Adopting the model would therefore enhance regional cooperation and promote the control of China's air pollution. The authors construct an interprovincial air pollution control model based on futures prices. The Shapley value method is used to rationally allocate the cooperation benefit. Interprovincial pollution control reduces the overall reduction cost of SO2. Each province can lower its cost for air pollution reduction by cooperation.

Topological sources of soliton mass and supersymmetry breaking

NASA Astrophysics Data System (ADS)

Haas, Patrick A.

2018-06-01

We derive the Smarr formulae for two five-dimensional solutions of supergravity, which are asymptotically ; in particular, one has a magnetic ‘bolt’ in its center, and one is a two-center solution. We show for both spacetimes that supersymmetry—and so the BPS-bound—is broken by the holonomy and how each topological feature of a space-like hypersurface enters Smarr’s mass formula, with emphasis on the ones that give rise to the stated violation of the BPS-bound. In this light, we question if any violating extra-mass term in a spacetime with such asymptotics is only evident in the ADM mass while the Komar mass per se ‘tries’ to preserve BPS. Finally, we derive the cohomological fluxes for each situation and examine in a more general fashion how the breaking of supersymmetry—and so the BPS-bound violation—is associated with their topologies. In the second (and more complicated) scenario, we especially focus on the compact cycle linking the centers, and the contribution of non-vanishing bulk terms in the mass formula to the breaking of supersymmetry.

CASMI 2013: Identification of Small Molecules by Tandem Mass Spectrometry Combined with Database and Literature Mining

PubMed Central

Newsome, Andrew G.; Nikolic, Dejan

2014-01-01

The Critical Assessment of Small Molecule Identification (CASMI) contest was initiated in 2012 to evaluate manual and automated strategies for the identification of small molecules from raw mass spectrometric data. The authors participated in both category 1 (molecular formula determination) and category 2 (molecular structure determination) of the second annual CASMI contest (CASMI 2013) using slow but effective manual methods. The provided high resolution mass spectrometric data were interpreted manually using a combination of molecular formula calculators, fragment and neutral loss analysis, literature consultation, manual database searches, deductive logic, and experience. The authors submitted correct formulas as lead candidates for 16 of 16 challenges and submitted correct structure solutions as lead candidates for 14 of 16 challenges. One structure submission (Challenge 3) was very close but not exact (N2-acetylglutaminylisoleucinamide instead of the correct N2-acetylglutaminylleucinamide). A solution for one (Challenge 13) was not submitted due to an inability to reconcile the provided fragmentation pattern with any known structures with the provided molecular composition. PMID:26819877

Exact solutions in oscillating airfoil theory

NASA Technical Reports Server (NTRS)

Williams, M. H.

1977-01-01

A result obtained by Williams (1977) for two-dimensional airfoils oscillating in an arbitrary subsonic parallel flowfield is reformulated to show that the pressure distribution induced by any deformation can be construed from the particular solutions for heaving and pitching motions. Specific formulas are presented for an oscillating control surface with a sealed gap.

Laser interferometry of the hydrolytic changes in protein solutions: the refractive index and hydration shells.

PubMed

Sarimov, R M; Matveyeva, T A; Binhi, V N

2018-05-11

Using an original laser interferometer of enhanced sensitivity, an increase in the refractive index of a protein solution was observed during the reaction of proteolysis catalyzed by pepsin. The increase in the refractive index of the protein solution at a concentration of 4 mg/ml was [Formula: see text] for bovine serum albumin and [Formula: see text] for lysozyme. The observed effect disproves the existing idea that the refractive index of protein solutions is determined only by their amino acid composition and concentration. It is shown that the refractive index also depends on the state of protein fragmentation. A mathematical model of proteolysis and a real-time method for estimating the state of protein hydration based on the measurement of refractive index during the reaction are proposed. A good agreement between the experimental and calculated time dependences of the refractive index shows that the growth of the surface of protein fragments and the change in the number of hydration cavities during proteolysis can be responsible for the observed effect.

An experimental study of the Rayleigh-Taylor instability critical wave length

NASA Astrophysics Data System (ADS)

Kong, Xujing; Wang, Youchun; Zhang, Shufei; Xu, Hongkun

1992-06-01

A physical model has been constructed to represent the condensate film pattern on a horizontal downward-facing surface with fins, which is based on visual observation in experiment. The results of analysis using this model confirms the validity of the critical wave length formula obtained from Rayleigh-Taylor stability analysis. This formula may be used as a criterion to design horizontal downward-facing surfaces with fins that can best destabilize the condensate film, thus enhancing condensation heat transfer.

Bivariate tensor product [Formula: see text]-analogue of Kantorovich-type Bernstein-Stancu-Schurer operators.

PubMed

Cai, Qing-Bo; Xu, Xiao-Wei; Zhou, Guorong

2017-01-01

In this paper, we construct a bivariate tensor product generalization of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of [Formula: see text]-integers. We obtain moments and central moments of these operators, give the rate of convergence by using the complete modulus of continuity for the bivariate case and estimate a convergence theorem for the Lipschitz continuous functions. We also give some graphs and numerical examples to illustrate the convergence properties of these operators to certain functions.

Singular vectors for the WN algebras

NASA Astrophysics Data System (ADS)

Ridout, David; Siu, Steve; Wood, Simon

2018-03-01

In this paper, we use free field realisations of the A-type principal, or Casimir, WN algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogues. The resulting formulae depend on sequences of pairs of integers that completely determine the Fock module as well as the Jack symmetric functions.

Infinite tension limit of the pure spinor superstring

NASA Astrophysics Data System (ADS)

Berkovits, Nathan

2014-03-01

Mason and Skinner recently constructed a chiral infinite tension limit of the Ramond-Neveu-Schwarz superstring which was shown to compute the Cachazo-He-Yuan formulae for tree-level d = 10 Yang-Mills amplitudes and the NS-NS sector of tree-level d = 10 supergravity amplitudes. In this letter, their chiral infinite tension limit is generalized to the pure spinor superstring which computes a d = 10 superspace version of the Cachazo-He-Yuan formulae for tree-level d = 10 super-Yang-Mills and supergravity amplitudes.

INTERNATIONAL CONFERENCE ON SEMICONDUCTOR INJECTION LASERS SELCO-87: Simple formula for the thermal conductivity of a quaternary solid solution

NASA Astrophysics Data System (ADS)

Nakwaski, W.

1988-11-01

An analysis is made of the thermal conductivity of quaternary solid solutions (alloys) allowing for their disordered structure on the basis of a phenomenological analysis proposed by Abeles. This method is applied to a quaternary solid solution In1 - xGaxAsyP1 - y. A simple analytic expression is derived for the thermal conductivity of this material.

Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization

NASA Astrophysics Data System (ADS)

Dütsch, Michael; Fredenhagen, Klaus; Keller, Kai Johannes; Rejzner, Katarzyna

2014-12-01

We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. This closed expression, which we call the Epstein-Glaser Forest Formula, is analogous to Zimmermann's Forest Formula for BPH renormalization. For scalar fields, the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.

Compositions for, solutions for, and methods of use of siloxane based aromatic trisureas as viscosifiers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doherty, Mark Daniel; O'Brien, Michael Joseph; Lee, Jason

A compound represented by the following formula is provided: ##STR00001## Also provided is a solution including a compound disclosed herein, a volume of dense carbon dioxide (CO.sub.2), and a co-solvent, where the solution has an increased viscosity greater than the viscosity of dense CO.sub.2. Methods of increasing the viscosity of dense CO.sub.2 and natural gas liquids (NGLs) by, for example, dissolving a compound disclosed herein to form a solution, are also provided.

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Larson, Mats G.; Barth, Timothy J.

1999-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Estimation of distribution overlap of urn models.

PubMed

Hampton, Jerrad; Lladser, Manuel E

2012-01-01

A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to random samples of two discrete distributions. Specifically, we estimate what we call the dissimilarity probability of a sample, i.e., the probability of a draw from one distribution not being observed in [Formula: see text] draws from another distribution. We show our estimator of dissimilarity to be a [Formula: see text]-statistic and a uniformly minimum variance unbiased estimator of dissimilarity over the largest appropriate range of [Formula: see text]. Furthermore, despite the non-Markovian nature of our estimator when applied sequentially over [Formula: see text], we show it converges uniformly in probability to the dissimilarity parameter, and we present criteria when it is approximately normally distributed and admits a consistent jackknife estimator of its variance. As proof of concept, we analyze V35 16S rRNA data to discern between various microbial environments. Other potential applications concern any situation where dissimilarity of two discrete distributions may be of interest. For instance, in SELEX experiments, each urn could represent a random RNA pool and each draw a possible solution to a particular binding site problem over that pool. The dissimilarity of these pools is then related to the probability of finding binding site solutions in one pool that are absent in the other.

Preventing Ice Before it Forms

NASA Technical Reports Server (NTRS)

2006-01-01

In the late 1990s, a team of engineers at Ames Research Center invented an anti-icing fluid to keep ice from building up on airplane wings. Ice on wings can be a serious safety hazard, especially during takeoff, when a sheet of ice the thickness of a compact disc can reduce lift by 25 percent or more. The typical approach to clearing off the ice is to use a deicing solution once the ice has built up. The fluid created by the Ames team, though, when applied to a dry surface, prevents the ice from even forming a surface bond, which saves deicing time and money, while also preventing excessive use of chemical solvents. If, however, the solution is not applied before ice forms, it also serves as a traditional deicing formula. The formula contains propylene glycol, which has a very low freezing point, and a thickener, which helps the fluid adhere to the surface. Ice gathers on top of the formula, and then it can be wiped off with little effort. This thickening agent, a pseudo-plastic, sprays on as a liquid, like lemonade, gels like a lemon sherbet, turns back to a liquid when wiped, and then gels again into its sherbet consistency when left to solidify. The sherbet-gel stage is especially important when the formula is sprayed onto a vertical or steeped surface, as it clings better than a liquid would.

Solitonic properties for a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Qu, Qi-Xing; Zhen, Hui-Ling; Chai, Han-Peng

2018-07-01

In this paper, investigation is given to a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon. Based on the Lax pair, under certain variable-coefficient-dependent constraints, we present an infinite sequence of the conservation laws. Through the Riccati equations obtained from the Lax pair, a Wahlquist-Estabrook-type Bäcklund transformation (BT) is derived, based on which the nonlinear superposition formula as well as one- and two-soliton-like solutions are obtained. Via the truncated Painlevé expansion, we give a Painlevé BT, along with the one-soliton-like solutions. With the Painlevé BT, bilinear forms are constructed, and we get a bilinear BT as well as the corresponding one-soliton-like solutions. Bell-type bright and dark soliton-like waves and kink-type soliton-like waves are observed, respectively. Graphic analysis shows that (1) the velocities of the soliton-like waves are related to h(t), d(t), f(t) and R(t), while the soliton-like wave amplitudes just depend on f(t), and (2) with the nonzero f(t) and R(t), soliton-like waves propagate on the varying backgrounds, where h(t), d(t) and f(t) are the dispersive, dissipative and line-damping coefficients, respectively, R(t) is the external-force term, and t is the scaled time coordinate.

A Procedure for Deriving Formulas to Convert Transition Rates to Probabilities for Multistate Markov Models.

PubMed

Jones, Edmund; Epstein, David; García-Mochón, Leticia

2017-10-01

For health-economic analyses that use multistate Markov models, it is often necessary to convert from transition rates to transition probabilities, and for probabilistic sensitivity analysis and other purposes it is useful to have explicit algebraic formulas for these conversions, to avoid having to resort to numerical methods. However, if there are four or more states then the formulas can be extremely complicated. These calculations can be made using packages such as R, but many analysts and other stakeholders still prefer to use spreadsheets for these decision models. We describe a procedure for deriving formulas that use intermediate variables so that each individual formula is reasonably simple. Once the formulas have been derived, the calculations can be performed in Excel or similar software. The procedure is illustrated by several examples and we discuss how to use a computer algebra system to assist with it. The procedure works in a wide variety of scenarios but cannot be employed when there are several backward transitions and the characteristic equation has no algebraic solution, or when the eigenvalues of the transition rate matrix are very close to each other.

How Crossover Speeds up Building Block Assembly in Genetic Algorithms.

PubMed

Sudholt, Dirk

2017-01-01

We reinvestigate a fundamental question: How effective is crossover in genetic algorithms in combining building blocks of good solutions? Although this has been discussed controversially for decades, we are still lacking a rigorous and intuitive answer. We provide such answers for royal road functions and OneMax, where every bit is a building block. For the latter, we show that using crossover makes every ([Formula: see text]+[Formula: see text]) genetic algorithm at least twice as fast as the fastest evolutionary algorithm using only standard bit mutation, up to small-order terms and for moderate [Formula: see text] and [Formula: see text]. Crossover is beneficial because it can capitalize on mutations that have both beneficial and disruptive effects on building blocks: crossover is able to repair the disruptive effects of mutation in later generations. Compared to mutation-based evolutionary algorithms, this makes multibit mutations more useful. Introducing crossover changes the optimal mutation rate on OneMax from [Formula: see text] to [Formula: see text]. This holds both for uniform crossover and k-point crossover. Experiments and statistical tests confirm that our findings apply to a broad class of building block functions.

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

Underscreening in ionic liquids: a first principles analysis.

PubMed

Rotenberg, Benjamin; Bernard, Olivier; Hansen, Jean-Pierre

2018-02-07

An attempt is made to understand the underscreening effect, observed in concentrated electrolyte solutions or melts, on the basis of simple, admittedly crude models involving charged (for the ions) and neutral (for the solvent molecules) hard spheres. The thermodynamic and structural properties of these 'primitive' and 'semi-primitive' models are calculated within mean spherical approximation, which provides the basic input required to determine the partial density response functions. The screening length [Formula: see text], which is unambiguously defined in terms of the wave-number-dependent response functions, exhibits a cross-over from a low density, Debye-like regime, to a regime where [Formula: see text] increases with density beyond a critical density at which the Debye length [Formula: see text] becomes comparable to the ion diameter. In this high density regime the ratio [Formula: see text] increases according to a power law, in qualitative agreement with experimental measurements, albeit at a much slower rate.

Reaching to a featured formula to deduce the energy of the heaviest particles producing from the controlled thermonuclear fusion reactions

NASA Astrophysics Data System (ADS)

Majeed, Raad H.; Oudah, Osamah N.

2018-05-01

Thermonuclear fusion reaction plays an important role in developing and construction any power plant system. Studying the physical behavior for the possible mechanism governed energies released by the fusion products to precise understanding the related kinematics. In this work a theoretical formula controlled the general applied thermonuclear fusion reactions is achieved to calculating the fusion products energy depending upon the reactants physical properties and therefore, one can calculate other parameters governed a given reaction. By using this formula, the energy spectrum of 4He produced from T-3He fusion reaction has been sketched with respect to reaction angle and incident energy ranged from (0.08-0.6) MeV.

Nuclear mass formula with the shell energies obtained by a new method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koura, H.; Tachibana, T.; Yamada, M.

1998-12-21

Nuclear shapes and masses are estimated by a new method. The main feature of this method lies in estimating shell energies of deformed nuclei from spherical shell energies by mixing them with appropriate weights. The spherical shell energies are calculated from single-particle potentials, and, till now, two mass formulas have been constructed from two different sets of potential parameters. The standard deviation of the calculated masses from all the experimental masses of the 1995 Mass Evaluation is about 760 keV. Contrary to the mass formula by Tachibana, Uno, Yamada and Yamada in the 1987-1988 Atomic Mass Predictions, the present formulasmore » can give nuclear shapes and predict on super-heavy elements.« less

Risk assessment of nitrate transport through subsurface layers and groundwater using experimental and modeling approach.

PubMed

Alslaibi, Tamer M; Abunada, Ziyad; Abu Amr, Salem S; Abustan, Ismail

2017-09-22

Landfills are one of the main point sources of groundwater pollution. This research mainly aims to assess the risk of nitrate [Formula: see text] transport from the unlined landfill to subsurface layers and groundwater using experimental results and the SESOIL model. Samples from 12 groundwater wells downstream of the landfill were collected and analyzed in 2008, 21 years after the landfill construction. The average [Formula: see text] concentration in the wells was 54 mg/L, slightly higher than the World Health Organization ([Formula: see text] 50 mg/L) standards. SESOIL model was used to predict the [Formula: see text] concentration at the bottom of the unsaturated zone. Results indicated that the current mean [Formula: see text] concentration at the bottom of the unsaturated zone is 75 mg/L. the model predicted that the level of NO 3 will increased up to 325 mg/L within 30 years. Accordingly, the [Formula: see text] concentration in groundwater wells near the landfill area is expected to gradually increase with time. Although the current risk associated with the [Formula: see text] level might not be harm to adults, however, it might pose severe risks to both adults and infants in the near future due to [Formula: see text] leaching. Urgent mitigation measures such as final cell cover (cap), lining system and vertical expansion should be considered at the landfill to protect the public health in the area.

Iteration with Spreadsheets.

ERIC Educational Resources Information Center

Smith, Michael

1990-01-01

Presents several examples of the iteration method using computer spreadsheets. Examples included are simple iterative sequences and the solution of equations using the Newton-Raphson formula, linear interpolation, and interval bisection. (YP)

Rail-highway crossing hazard prediction : research results

DOT National Transportation Integrated Search

1979-12-01

This document presents techniques for constructing and evaluating railroad grade : crossing hazard indexes. Hazard indexes are objective formulas for comparing or ranking : crossings according to relative hazard or for calculating absolute hazard (co...

Cooperative answers in database systems

NASA Technical Reports Server (NTRS)

Gaasterland, Terry; Godfrey, Parke; Minker, Jack; Novik, Lev

1993-01-01

A major concern of researchers who seek to improve human-computer communication involves how to move beyond literal interpretations of queries to a level of responsiveness that takes the user's misconceptions, expectations, desires, and interests into consideration. At Maryland, we are investigating how to better meet a user's needs within the framework of the cooperative answering system of Gal and Minker. We have been exploring how to use semantic information about the database to formulate coherent and informative answers. The work has two main thrusts: (1) the construction of a logic formula which embodies the content of a cooperative answer; and (2) the presentation of the logic formula to the user in a natural language form. The information that is available in a deductive database system for building cooperative answers includes integrity constraints, user constraints, the search tree for answers to the query, and false presuppositions that are present in the query. The basic cooperative answering theory of Gal and Minker forms the foundation of a cooperative answering system that integrates the new construction and presentation methods. This paper provides an overview of the cooperative answering strategies used in the CARMIN cooperative answering system, an ongoing research effort at Maryland. Section 2 gives some useful background definitions. Section 3 describes techniques for collecting cooperative logical formulae. Section 4 discusses which natural language generation techniques are useful for presenting the logic formula in natural language text. Section 5 presents a diagram of the system.

A Study of Supersonic Surface Sources: The Ffowcs Williams-Hawkings Equation and the Kirchhoff Formula

NASA Technical Reports Server (NTRS)

Farassat, F.; Brentner, Kenneth S.; Dunn, M. H.

2004-01-01

In this paper we address the mathematical problem of noise generation from high speed moving surfaces. The problem we are solving is the linear wave equation with sources on a moving surface. The Ffowcs Williams-Hawkings (FW-H) equation as well as the govern- ing equation for deriving the Kirchhoff formula for moving surfaces are both this type of partial differential equation. We give a new exact solution of this problem here in closed form which is valid for subsonic and supersonic motion of the surface but it is particularly suitable for supersonically moving surfaces. This new solution is the simplest of all high speed formulations of Langley and is denoted formulation 4 following the tradition of numbering of our major results for the prediction of the noise of rotating blades. We show that for a smooth surface moving at supersonic speed, our solution has only removable singularities. Thus it can be used for numerical work.

Geometric scaling behavior of the scattering amplitude for DIS with nuclei

NASA Astrophysics Data System (ADS)

Kormilitzin, Andrey; Levin, Eugene; Tapia, Sebastian

2011-12-01

The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky-Kovchegov equation in the form which is useful for treating the interaction with nuclei. Using the simplified BFKL kernel, we find the analytical solution to this equation with the initial condition given by the McLerran-Venugopalan formula. This solution does not show the geometric scaling behavior of the amplitude deeply in the saturation region. On the other hand, the BFKL Pomeron calculus with the initial condition at x=1/mR given by the solution to Balitsky-Kovchegov equation, leads to the geometric scaling behavior. The McLerran-Venugopalan formula is the natural initial condition for the Color Glass Condensate (CGC) approach. Therefore, our result gives a possibility to check experimentally which approach: CGC or BFKL Pomeron calculus, is more satisfactory.

Entire solutions of nonlinear differential-difference equations.

PubMed

Li, Cuiping; Lü, Feng; Xu, Junfeng

2016-01-01

In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result of Liu.

9 CFR 325.13 - Denaturing procedures.

Code of Federal Regulations, 2011 CFR

2011-01-01

...) Tripe may be denatured by dipping it in a 6 percent solution of tannic acid for 1 minute followed by... coloring; (4) Meat may be denatured by dipping it in a solution of 0.0625 percent tannic acid, followed by... carbolic acid; cresylic disinfectant; a formula consisting of 1 part FD&C green No. 3 coloring, 40 parts...

9 CFR 325.13 - Denaturing procedures.

Code of Federal Regulations, 2010 CFR

2010-01-01

...) Tripe may be denatured by dipping it in a 6 percent solution of tannic acid for 1 minute followed by... coloring; (4) Meat may be denatured by dipping it in a solution of 0.0625 percent tannic acid, followed by... carbolic acid; cresylic disinfectant; a formula consisting of 1 part FD&C green No. 3 coloring, 40 parts...

Choosing the Right Solution Approach: The Crucial Role of Situational Knowledge in Electricity and Magnetism

ERIC Educational Resources Information Center

Savelsbergh, Elwin R.; de Jong, Ton; Ferguson-Hessler, Monica G. M.

2011-01-01

Novice problem solvers are rather sensitive to surface problem features, and they often resort to trial and error formula matching rather than identifying an appropriate solution approach. These observations have been interpreted to imply that novices structure their knowledge according to surface features rather than according to problem type…

Spatial correlations and exact solution of the problem of the boson peak profile in amorphous media

NASA Astrophysics Data System (ADS)

Kirillov, Sviatoslav A.; A. Voyiatzis, George; Kolomiyets, Tatiana M.; H. Anastasiadis, Spiros

1999-11-01

Based on a model correlation function which covers spatial correlations from Gaussian to exponential, we have arrived at an exact analytic solution of the problem of the Boson peak profile in amorphous media. Probe fits made for polyisoprene and triacetin prove the working ability of the formulae obtained.

The S-curve for forecasting waste generation in construction projects.

PubMed

Lu, Weisheng; Peng, Yi; Chen, Xi; Skitmore, Martin; Zhang, Xiaoling

2016-10-01

Forecasting construction waste generation is the yardstick of any effort by policy-makers, researchers, practitioners and the like to manage construction and demolition (C&D) waste. This paper develops and tests an S-curve model to indicate accumulative waste generation as a project progresses. Using 37,148 disposal records generated from 138 building projects in Hong Kong in four consecutive years from January 2011 to June 2015, a wide range of potential S-curve models are examined, and as a result, the formula that best fits the historical data set is found. The S-curve model is then further linked to project characteristics using artificial neural networks (ANNs) so that it can be used to forecast waste generation in future construction projects. It was found that, among the S-curve models, cumulative logistic distribution is the best formula to fit the historical data. Meanwhile, contract sum, location, public-private nature, and duration can be used to forecast construction waste generation. The study provides contractors with not only an S-curve model to forecast overall waste generation before a project commences, but also with a detailed baseline to benchmark and manage waste during the course of construction. The major contribution of this paper is to the body of knowledge in the field of construction waste generation forecasting. By examining it with an S-curve model, the study elevates construction waste management to a level equivalent to project cost management where the model has already been readily accepted as a standard tool. Copyright © 2016 Elsevier Ltd. All rights reserved.

A tale of two Bethe ansätze

NASA Astrophysics Data System (ADS)

Lima-Santos, Antonio; Nepomechie, Rafael I.; Pimenta, Rodrigo A.

2018-04-01

We revisit the construction of the eigenvectors of the single and double-row transfer matrices associated with the Zamolodchikov–Fateev model, within the algebraic Bethe ansatz method. The left and right eigenvectors are constructed using two different methods: the fusion technique and Tarasov’s construction. A simple explicit relation between the eigenvectors from the two Bethe ansätze is obtained. As a consequence, we obtain the Slavnov formula for the scalar product between on-shell and off-shell Tarasov–Bethe vectors.

Understanding women's interpretations of infant formula advertising.

PubMed

Parry, Kathleen; Taylor, Emily; Hall-Dardess, Pam; Walker, Marsha; Labbok, Miriam

2013-06-01

Exclusive breastfeeding for 6 months and continued breastfeeding for at least 1 year is recommended by all major health organizations. Whereas 74.6 percent of mothers initiate breastfeeding at birth, exclusivity and duration remain significantly lower than national goals. Empirical evidence suggests that exposure to infant formula marketing contributes to supplementation and premature cessation. The objective of this study was to explore how women interpret infant formula advertising to aid in an understanding of this association. Four focus groups were structured to include women with similar childbearing experience divided according to reproductive status: preconceptional, pregnant, exclusive breastfeeders, and formula feeders. Facilitators used a prepared protocol to guide discussion of infant formula advertisements. Authors conducted a thematic content analysis with special attention to women's statements about what they believed the advertisements said about how the products related to human milk (superior, inferior, similar) and how they reported reacting to these interpretations. Participants reported that the advertisements conveyed an expectation of failure with breastfeeding, and that formula is a solution to fussiness, spitting up, and other normal infant behaviors. Participants reported that the advertisements were confusing in terms of how formula-feeding is superior, inferior or the same as breastfeeding. This confusion was exacerbated by an awareness of distribution by health care practitioners and institutions, suggesting provider endorsement of infant formula. Formula marketing appears to decrease mothers' confidence in their ability to breastfeed, especially when provided by health care practitioners and institutions. Therefore, to be supportive of breastfeeding, perinatal educators and practitioners could be more effective if they did not offer infant formula advertising to mothers. © 2013, Copyright the Authors, Journal compilation © 2013, Wiley Periodicals, Inc.

Thermal Network Modelling Handbook

NASA Technical Reports Server (NTRS)

1972-01-01

Thermal mathematical modelling is discussed in detail. A three-fold purpose was established: (1) to acquaint the new user with the terminology and concepts used in thermal mathematical modelling, (2) to present the more experienced and occasional user with quick formulas and methods for solving everyday problems, coupled with study cases which lend insight into the relationships that exist among the various solution techniques and parameters, and (3) to begin to catalog in an orderly fashion the common formulas which may be applied to automated conversational language techniques.

9.9 Sales Grid Style Produces Results

ERIC Educational Resources Information Center

Blake, Robert R.; Mouton, Jane Srygley

1970-01-01

Selling effectiveness experiments have provided evidence that solution selling (problem solving) produces far better results than formula selling (sales technique oriented), hard sell, people-oriented selling, or order taking. (PT)

An Analysis of Chemical Ingredients Network of Chinese Herbal Formulae for the Treatment of Coronary Heart Disease

PubMed Central

Ding, Fan; Zhang, Qianru; Ung, Carolina Oi Lam; Wang, Yitao; Han, Yifan; Hu, Yuanjia; Qi, Jin

2015-01-01

As a complex system, the complicated interactions between chemical ingredients, as well as the potential rules of interactive associations among chemical ingredients of traditional Chinese herbal formulae are not yet fully understood by modern science. On the other hand, network analysis is emerging as a powerful approach focusing on processing complex interactive data. By employing network approach in selected Chinese herbal formulae for the treatment of coronary heart disease (CHD), this article aims to construct and analyze chemical ingredients network of herbal formulae, and provide candidate herbs, chemical constituents, and ingredient groups for further investigation. As a result, chemical ingredients network composed of 1588 ingredients from 36 herbs used in 8 core formulae for the treatment of CHD was produced based on combination associations in herbal formulae. In this network, 9 communities with relative dense internal connections are significantly associated with 14 kinds of chemical structures with P<0.001. Moreover, chemical structural fingerprints of network communities were detected, while specific centralities of chemical ingredients indicating different levels of importance in the network were also measured. Finally, several distinct herbs, chemical ingredients, and ingredient groups with essential position in the network or high centrality value are recommended for further pharmacology study in the context of new drug development. PMID:25658855

Effects of the inclusion of a mixed Psychrotrophic bacteria strain for sewage treatment in constructed wetland in winter seasons.

PubMed

Tang, Meizhen; Li, Zhengtao; Yang, Yuewei; Chen, Junfeng; Jiang, Jie

2018-04-01

Constructed wetlands (CWs) have been used globally in wastewater treatment for years. CWs represent an efficient ecological system which is both energy-saving and low in investment for construction and operational cost. In addition, CWs also have the advantage of being easy to operate and maintain. However, the operation of CWs at northern latitudes (both mid and high) is sometimes quite demanding, due to the inhibitory effect of low temperatures that often occur in winter. To evaluate the wastewater treatment performance of a culture of mixed Psychrotrophic bacteria strains in an integrated vertical-flow CW, the removal rates of ammonia nitrogen (NH 3 -N), chemical oxygen demand (COD), nitrite nitrogen [Formula: see text], nitrate nitrogen [Formula: see text] and total phosphorus (TP) were quantified at different bacterial dosages to determine the best bacterial dosage and establish kinetic degradation models of the mixed strains. The bacterial culture was made up of Psychrobacter TM-1, Sphingobacterium TM-2 and Pseudomonas TM-3, mixed together at a volume/volume ratio of 1 : 1 : 1 (at bacterial suspension concentrations of 4.4 × 10 9  ml -1 ). Results showed that the organic pollutants (nitrogen and phosphorus) in the sewage could be efficiently removed by the culture of mixed Psychrotrophic bacteria. The optimal dosage of this mixed bacteria strain was 2.5%, and the treatment efficiency of COD, NH 3 -N, [Formula: see text], [Formula: see text], total nitrogen and TP were stable at 91.8%, 91.1%, 88.0%, 93.8%, 94.8% and 95.2%, respectively, which were 1.5, 2.0, 2.1, 1.5, 2.2 and 1.3 times those of the control group. In addition, a pseudo-first-order degradation model was a good fit for the degradation pattern observed for each of these pollutants.

A Mathematical Model Supports a Key Role for Ae4 (Slc4a9) in Salivary Gland Secretion.

PubMed

Vera-Sigüenza, Elías; Catalán, Marcelo A; Peña-Münzenmayer, Gaspar; Melvin, James E; Sneyd, James

2018-02-01

We develop a mathematical model of a salivary gland acinar cell with the objective of investigating the role of two [Formula: see text] exchangers from the solute carrier family 4 (Slc4), Ae2 (Slc4a2) and Ae4 (Slc4a9), in fluid secretion. Water transport in this type of cell is predominantly driven by [Formula: see text] movement. Here, a basolateral [Formula: see text] adenosine triphosphatase pump (NaK-ATPase) and a [Formula: see text]-[Formula: see text]-[Formula: see text] cotransporter (Nkcc1) are primarily responsible for concentrating the intracellular space with [Formula: see text] well above its equilibrium potential. Gustatory and olfactory stimuli induce the release of [Formula: see text] ions from the internal stores of acinar cells, which triggers saliva secretion. [Formula: see text]-dependent [Formula: see text] and [Formula: see text] channels promote ion secretion into the luminal space, thus creating an osmotic gradient that promotes water movement in the secretory direction. The current model for saliva secretion proposes that [Formula: see text] anion exchangers (Ae), coupled with a basolateral [Formula: see text] ([Formula: see text]) (Nhe1) antiporter, regulate intracellular pH and act as a secondary [Formula: see text] uptake mechanism (Nauntofte in Am J Physiol Gastrointest Liver Physiol 263(6):G823-G837, 1992; Melvin et al. in Annu Rev Physiol 67:445-469, 2005. https://doi.org/10.1146/annurev.physiol.67.041703.084745 ). Recent studies demonstrated that Ae4 deficient mice exhibit an approximate [Formula: see text] decrease in gland salivation (Peña-Münzenmayer et al. in J Biol Chem 290(17):10677-10688, 2015). Surprisingly, the same study revealed that absence of Ae2 does not impair salivation, as previously suggested. These results seem to indicate that the Ae4 may be responsible for the majority of the secondary [Formula: see text] uptake and thus a key mechanism for saliva secretion. Here, by using 'in-silico' Ae2 and Ae4 knockout simulations, we produced mathematical support for such controversial findings. Our results suggest that the exchanger's cotransport of monovalent cations is likely to be important in establishing the osmotic gradient necessary for optimal transepithelial fluid movement.

Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci

NASA Astrophysics Data System (ADS)

Kirk, Toby L.

2018-03-01

This paper presents new analytical formulae for flow in a channel with one or both walls patterned with a longitudinal array of ridges and arbitrarily protruding menisci. Derived from a matched asymptotic expansion, they extend results by Crowdy (J. Fluid Mech., vol. 791, 2016, R7) for shear flow, and thus make no restriction on the protrusion into or out of the liquid. The slip length formula is compared against full numerical solutions and, despite the assumption of small ridge period in its derivation, is found to have a very large range of validity; relative errors are small even for periods large enough for the protruding menisci to degrade the flow and touch the opposing wall.

CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roldan, Omar, E-mail: oaroldan@if.ufrj.br

2017-08-01

We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instance, facilitate the search for primordial non-Gaussianity in future works. It also disentangles the non-linear ISW from other effects. Finally, we provide a method which canmore » iteratively be used to obtain the lensing solution at the desired order.« less

Exotic superconducting states in the extended attractive Hubbard model.

PubMed

Nayak, Swagatam; Kumar, Sanjeev

2018-04-04

We show that the extended attractive Hubbard model on a square lattice allows for a variety of superconducting phases, including exotic mixed-symmetry phases with [Formula: see text] and [Formula: see text] symmetries, and a novel [Formula: see text] state. The calculations are performed within the Hartree-Fock Bardeen-Cooper-Schrieffer framework. The ground states of the mean-field Hamiltonian are obtained via a minimization scheme that relaxes the symmetry constraints on the superconducting solutions, hence allowing for a mixing of s-, p- and d-wave order parameters. The results are obtained within the assumption of uniform-density states. Our results show that extended attractive Hubbard model can serve as an effective model for investigating properties of exotic superconductors.

27 CFR 21.77 - Formula No. 40-C.

Code of Federal Regulations, 2010 CFR

2010-04-01

....Bay rum. 113.Lotions and creams (hand, face, and body). 114.Deodorants (body). 121.Perfumes and... deodorants. 485.Miscellaneous solutions. (2) Miscellaneous uses. 812.Product development and pilot plant uses...

27 CFR 21.77 - Formula No. 40-C.

Code of Federal Regulations, 2013 CFR

2013-04-01

....Bay rum. 113.Lotions and creams (hand, face, and body). 114.Deodorants (body). 121.Perfumes and... deodorants. 485.Miscellaneous solutions. (2) Miscellaneous uses. 812.Product development and pilot plant uses...

27 CFR 21.77 - Formula No. 40-C.

Code of Federal Regulations, 2011 CFR

2011-04-01

....Bay rum. 113.Lotions and creams (hand, face, and body). 114.Deodorants (body). 121.Perfumes and... deodorants. 485.Miscellaneous solutions. (2) Miscellaneous uses. 812.Product development and pilot plant uses...

27 CFR 21.77 - Formula No. 40-C.

Code of Federal Regulations, 2014 CFR

2014-04-01

....Bay rum. 113.Lotions and creams (hand, face, and body). 114.Deodorants (body). 121.Perfumes and... deodorants. 485.Miscellaneous solutions. (2) Miscellaneous uses. 812.Product development and pilot plant uses...

27 CFR 21.77 - Formula No. 40-C.

Code of Federal Regulations, 2012 CFR

2012-04-01

....Bay rum. 113.Lotions and creams (hand, face, and body). 114.Deodorants (body). 121.Perfumes and... deodorants. 485.Miscellaneous solutions. (2) Miscellaneous uses. 812.Product development and pilot plant uses...

Chinese Biogas Digester. A Potential Model for Small-Scale, Rural Applications. (A Manual for Construction and Operation). Reprint No. R-51.

ERIC Educational Resources Information Center

Nakagawa, Charles H.; Honquilada, Q. L.

This book provides the basic knowledge and guides for the construction and operation of a small-scale, family-size biogas unit. The first chapter discusses the benefits of biogas production and the Chinese biogas model. The second chapter shows the components, design formulas, and sizing units of the biogas model. Chapter 3 describes actual…

Delay decomposition approach to [Formula: see text] filtering analysis of genetic oscillator networks with time-varying delays.

PubMed

Revathi, V M; Balasubramaniam, P

2016-04-01

In this paper, the [Formula: see text] filtering problem is treated for N coupled genetic oscillator networks with time-varying delays and extrinsic molecular noises. Each individual genetic oscillator is a complex dynamical network that represents the genetic oscillations in terms of complicated biological functions with inner or outer couplings denote the biochemical interactions of mRNAs, proteins and other small molecules. Throughout the paper, first, by constructing appropriate delay decomposition dependent Lyapunov-Krasovskii functional combined with reciprocal convex approach, improved delay-dependent sufficient conditions are obtained to ensure the asymptotic stability of the filtering error system with a prescribed [Formula: see text] performance. Second, based on the above analysis, the existence of the designed [Formula: see text] filters are established in terms of linear matrix inequalities with Kronecker product. Finally, numerical examples including a coupled Goodwin oscillator model are inferred to illustrate the effectiveness and less conservatism of the proposed techniques.

Atmospheric guidance law for planar skip trajectories

NASA Technical Reports Server (NTRS)

Mease, K. D.; Mccreary, F. A.

1985-01-01

The applicability of an approximate, closed-form, analytical solution to the equations of motion, as a basis for a deterministic guidance law for controlling the in-plane motion during a skip trajectory, is investigated. The derivation of the solution by the method of matched asymptotic expansions is discussed. Specific issues that arise in the application of the solution to skip trajectories are addressed. Based on the solution, an explicit formula for the approximate energy loss due to an atmospheric pass is derived. A guidance strategy is proposed that illustrates the use of the approximate solution. A numerical example shows encouraging performance.

Stress distributions caused by three types of loading on a circular semimonocoque cylinder with flexible rings

NASA Technical Reports Server (NTRS)

Mccomb, Harvey G , Jr

1954-01-01

Equations are derived for the stress distributions caused by three types of loading on infinitely long circular, semimonocoque cylinders with flexible rings. The results are given as formula for the stringer loads and shear flows in the shell due to each type of loading. For each loading case these formulas can be used to construct tables of influence coefficients giving stringer loads and shear flows in the neighborhood of the load due to a unit magnitude of the load. (author)

Effects of horizontal refractivity gradients on the accuracy of laser ranging to satellites

NASA Technical Reports Server (NTRS)

Gardner, C. S.

1976-01-01

Numerous formulas have been developed to partially correct laser ranging data for the effects of atmospheric refraction. All the formulas assume the atmospheric refractivity profile is spherically symmetric. The effects of horizontal refractivity gradients are investigated by ray tracing through spherically symmetric and three-dimensional refractivity profiles. The profiles are constructed from radiosonde data. The results indicate that the horizontal gradients introduce an rms error of approximately 3 cm when the satellite is near 10 deg elevation. The error decreases to a few millimeters near zenith.

Methods of mathematical modeling using polynomials of algebra of sets

NASA Astrophysics Data System (ADS)

Kazanskiy, Alexandr; Kochetkov, Ivan

2018-03-01

The article deals with the construction of discrete mathematical models for solving applied problems arising from the operation of building structures. Security issues in modern high-rise buildings are extremely serious and relevant, and there is no doubt that interest in them will only increase. The territory of the building is divided into zones for which it is necessary to observe. Zones can overlap and have different priorities. Such situations can be described using formulas algebra of sets. Formulas can be programmed, which makes it possible to work with them using computer models.

Estimated Glomerular Filtration Rate Is a Poor Predictor of Concentration for a Broad Range of Uremic Toxins

PubMed Central

Schepers, Eva; Barreto, Daniela V.; Barreto, Fellype C.; Liabeuf, Sophie; Van Biesen, Wim; Verbeke, Francis; Glorieux, Griet; Choukroun, Gabriel; Massy, Ziad; Vanholder, Raymond

2011-01-01

Summary Background and objectives The degree of chronic kidney disease (CKD) is currently expressed in terms of GFR, which can be determined directly or estimated according to different formulas on the basis of serum creatinine and/or cystatin C measurements (estimated GFR [eGFR]). The purpose of this study was to investigate whether eGFR values are representative for uremic toxin concentrations in patients with different degrees of CKD. Design, setting, participants, & measurements Associations between eGFR based on serum cystatin C and different uremic solutes (mol wt range 113 to 240 D; determined by colorimetry, HPLC, or ELISA) were evaluated in 95 CKD patients not on dialysis (CKD stage 2 to 5). The same analysis was also applied for six other eGFR formulas. Results There was a substantial disparity in fits among solutes. In linear regression, explained variance of eGFR was extremely low for most solutes, with eGFR > 0.4 only for creatinine. The other eGFR formulations gave comparably disappointing results with regard to their association to uremic solutes. Relative similarity in R2 values per solute for the different eGFR values and the strong disparity in values between solutes suggest that the differences in R2 are mainly due to discrepancies in solute handling apart from GFR. Conclusions eGFR is poorly associated with concentrations of all studied uremic toxins in patients with different degrees of CKD, correlates differently with each individual solute, and can thus not be considered representative for evaluating the accumulation of solutes in the course of CKD. PMID:21617084

Warped AdS3 black holes

NASA Astrophysics Data System (ADS)

Song, Wei; Anninos, Dionysios; Li, Wei; Padi, Megha; Strominger, Andrew

2009-03-01

Three dimensional topologically massive gravity (TMG) with a negative cosmological constant -ell-2 and positive Newton constant G admits an AdS3 vacuum solution for any value of the graviton mass μ. These are all known to be perturbatively unstable except at the recently explored chiral point μell = 1. However we show herein that for every value of μell ≠ 3 there are two other (potentially stable) vacuum solutions given by SL(2,Bbb R) × U(1)-invariant warped AdS3 geometries, with a timelike or spacelike U(1) isometry. Critical behavior occurs at μell = 3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For μell > 3, there are known warped black hole solutions which are asymptotic to warped AdS3. We show that these black holes are discrete quotients of warped AdS3 just as BTZ black holes are discrete quotients of ordinary AdS3. Moreover new solutions of this type, relevant to any theory with warped AdS3 solutions, are exhibited. Finally we note that the black hole thermodynamics is consistent with the hypothesis that, for μell > 3, the warped AdS3 ground state of TMG is holographically dual to a 2D boundary CFT with central charges c_R-formula and c_L-formula.

Warped AdS3 black holes

NASA Astrophysics Data System (ADS)

Anninos, Dionysios; Li, Wei; Padi, Megha; Song, Wei; Strominger, Andrew

2009-03-01

Three dimensional topologically massive gravity (TMG) with a negative cosmological constant -l-2 and positive Newton constant G admits an AdS3 vacuum solution for any value of the graviton mass μ. These are all known to be perturbatively unstable except at the recently explored chiral point μl = 1. However we show herein that for every value of μl ≠ 3 there are two other (potentially stable) vacuum solutions given by SL(2,Bbb R) × U(1)-invariant warped AdS3 geometries, with a timelike or spacelike U(1) isometry. Critical behavior occurs at μl = 3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For μl > 3, there are known warped black hole solutions which are asymptotic to warped AdS3. We show that these black holes are discrete quotients of warped AdS3 just as BTZ black holes are discrete quotients of ordinary AdS3. Moreover new solutions of this type, relevant to any theory with warped AdS3 solutions, are exhibited. Finally we note that the black hole thermodynamics is consistent with the hypothesis that, for μl > 3, the warped AdS3 ground state of TMG is holographically dual to a 2D boundary CFT with central charges c_R-formula and c_L-formula.

Chebyshev collocation spectral method for one-dimensional radiative heat transfer in linearly anisotropic-scattering cylindrical medium

NASA Astrophysics Data System (ADS)

Zhou, Rui-Rui; Li, Ben-Wen

2017-03-01

In this study, the Chebyshev collocation spectral method (CCSM) is developed to solve the radiative integro-differential transfer equation (RIDTE) for one-dimensional absorbing, emitting and linearly anisotropic-scattering cylindrical medium. The general form of quadrature formulas for Chebyshev collocation points is deduced. These formulas are proved to have the same accuracy as the Gauss-Legendre quadrature formula (GLQF) for the F-function (geometric function) in the RIDTE. The explicit expressions of the Lagrange basis polynomials and the differentiation matrices for Chebyshev collocation points are also given. These expressions are necessary for solving an integro-differential equation by the CCSM. Since the integrand in the RIDTE is continuous but non-smooth, it is treated by the segments integration method (SIM). The derivative terms in the RIDTE are carried out to improve the accuracy near the origin. In this way, a fourth order accuracy is achieved by the CCSM for the RIDTE, whereas it's only a second order one by the finite difference method (FDM). Several benchmark problems (BPs) with various combinations of optical thickness, medium temperature distribution, degree of anisotropy, and scattering albedo are solved. The results show that present CCSM is efficient to obtain high accurate results, especially for the optically thin medium. The solutions rounded to seven significant digits are given in tabular form, and show excellent agreement with the published data. Finally, the solutions of RIDTE are used as benchmarks for the solution of radiative integral transfer equations (RITEs) presented by Sutton and Chen (JQSRT 84 (2004) 65-103). A non-uniform grid refined near the wall is advised to improve the accuracy of RITEs solutions.

Understanding the Cu-Zn brass alloys using a short-range-order cluster model: significance of specific compositions of industrial alloys

PubMed Central

Hong, H. L.; Wang, Q.; Dong, C.; Liaw, Peter K.

2014-01-01

Metallic alloys show complex chemistries that are not yet understood so far. It has been widely accepted that behind the composition selection lies a short-range-order mechanism for solid solutions. The present paper addresses this fundamental question by examining the face-centered-cubic Cu-Zn α-brasses. A new structural approach, the cluster-plus-glue-atom model, is introduced, which suits specifically for the description of short-range-order structures in disordered systems. Two types of formulas are pointed out, [Zn-Cu12]Zn1~6 and [Zn-Cu12](Zn,Cu)6, which explain the α-brasses listed in the American Society for Testing and Materials (ASTM) specifications. In these formulas, the bracketed parts represent the 1st-neighbor cluster, and each cluster is matched with one to six 2nd-neighbor Zn atoms or with six mixed (Zn,Cu) atoms. Such a cluster-based formulism describes the 1st- and 2nd-neighbor local atomic units where the solute and solvent interactions are ideally satisfied. The Cu-Ni industrial alloys are also explained, thus proving the universality of the cluster-formula approach in understanding the alloy selections. The revelation of the composition formulas for the Cu-(Zn,Ni) industrial alloys points to the common existence of simple composition rules behind seemingly complex chemistries of industrial alloys, thus offering a fundamental and practical method towards composition interpretations of all kinds of alloys. PMID:25399835

Understanding the Cu-Zn brass alloys using a short-range-order cluster model: Significance of specific compositions of industrial alloys

DOE PAGES

Hong, H. L.; Wang, Q.; Dong, C.; ...

2014-11-17

Metallic alloys show complex chemistries that are not yet understood so far. It has been widely accepted that behind the composition selection lies a short-range-order mechanism for solid solutions. The present paper addresses this fundamental question by examining the face-centered-cubic Cu-Zn α-brasses. A new structural approach, the cluster-plus-glue-atom model, is introduced, which suits specifically for the description of short-range-order structures in disordered systems. Two types of formulas are pointed out, [Zn-Cu 12]Zn 1~6 and [Zn-Cu 12](Zn,Cu) 6, which explain the α-brasses listed in the American Society for Testing and Materials (ASTM) specifications. In these formulas, the bracketed parts represent themore » 1 st-neighbor cluster, and each cluster is matched with one to six 2 nd-neighbor Zn atoms or with six mixed (Zn,Cu) atoms. Such a cluster-based formulism describes the 1 st- and 2 nd-neighbor local atomic units where the solute and solvent interactions are ideally satisfied. The Cu-Ni industrial alloys are also explained, thus proving the universality of the cluster-formula approach in understanding the alloy selections. As a result, the revelation of the composition formulas for the Cu-(Zn,Ni) industrial alloys points to the common existence of simple composition rules behind seemingly complex chemistries of industrial alloys, thus offering a fundamental and practical method towards composition interpretations of all kinds of alloys.« less

Rigorous theoretical constraint on constant negative EoS parameter [Formula: see text] and its effect for the late Universe.

PubMed

Burgazli, Alvina; Eingorn, Maxim; Zhuk, Alexander

In this paper, we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Supposing that the Universe contains also the cosmological constant and a perfect fluid with a negative constant equation of state (EoS) parameter [Formula: see text] (e.g., quintessence, phantom or frustrated network of topological defects), we investigate scalar perturbations of the Friedmann-Robertson-Walker metrics due to inhomogeneities. Our analysis shows that, to be compatible with the theory of scalar perturbations, this perfect fluid, first, should be clustered and, second, should have the EoS parameter [Formula: see text]. In particular, this value corresponds to the frustrated network of cosmic strings. Therefore, the frustrated network of domain walls with [Formula: see text] is ruled out. A perfect fluid with [Formula: see text] neither accelerates nor decelerates the Universe. We also obtain the equation for the nonrelativistic gravitational potential created by a system of inhomogeneities. Due to the perfect fluid with [Formula: see text], the physically reasonable solutions take place for flat, open and closed Universes. This perfect fluid is concentrated around the inhomogeneities and results in screening of the gravitational potential.

The construction of combinatorial manifolds with prescribed sets of links of vertices

NASA Astrophysics Data System (ADS)

Gaifullin, A. A.

2008-10-01

To every oriented closed combinatorial manifold we assign the set (with repetitions) of isomorphism classes of links of its vertices. The resulting transformation \\mathcal{L} is the main object of study in this paper. We pose an inversion problem for \\mathcal{L} and show that this problem is closely related to Steenrod's problem on the realization of cycles and to the Rokhlin-Schwartz-Thom construction of combinatorial Pontryagin classes. We obtain a necessary condition for a set of isomorphism classes of combinatorial spheres to belong to the image of \\mathcal{L}. (Sets satisfying this condition are said to be balanced.) We give an explicit construction showing that every balanced set of isomorphism classes of combinatorial spheres falls into the image of \\mathcal{L} after passing to a multiple set and adding several pairs of the form (Z,-Z), where -Z is the sphere Z with the orientation reversed. Given any singular simplicial cycle \\xi of a space X, this construction enables us to find explicitly a combinatorial manifold M and a map \\varphi\\colon M\\to X such that \\varphi_* \\lbrack M \\rbrack =r[\\xi] for some positive integer r. The construction is based on resolving singularities of \\xi. We give applications of the main construction to cobordisms of manifolds with singularities and cobordisms of simple cells. In particular, we prove that every rational additive invariant of cobordisms of manifolds with singularities admits a local formula. Another application is the construction of explicit (though inefficient) local combinatorial formulae for polynomials in the rational Pontryagin classes of combinatorial manifolds.

26 CFR 1.6038A-2 - Requirement of return.

Code of Federal Regulations, 2010 CFR

2010-04-01

..., formulas, inventions, models, patents, processes, trademarks, and other similar intangible property rights; (v) Consideration paid and received for technical, managerial, engineering, construction, scientific... of all property (including monetary consideration), rights, or obligations transferred from the...

Chemistry Notes

ERIC Educational Resources Information Center

School Science Review, 1972

1972-01-01

Short articles describing the construction of a self-testing device for learning ionic formulae, problems with standard'' experiments in crystallizing sulfur, preparative details for a cold-setting adhesive and vermillion dye, and providing data related to the industrial manufacture of sulphuric acid. (AL)

New constraints for holographic entropy from maximin: A no-go theorem

NASA Astrophysics Data System (ADS)

Rota, Massimiliano; Weinberg, Sean J.

2018-04-01

The Ryu-Takayanagi (RT) formula for static spacetimes arising in the AdS/CFT correspondence satisfies inequalities that are not yet proven in the case of the Rangamani-Hubeny-Takayanagi (HRT) formula, which applies to general dynamical spacetimes. Wall's maximin construction is the only known technique for extending inequalities of holographic entanglement entropy from the static to dynamical case. We show that this method currently has no further utility when dealing with inequalities for five or fewer regions. Despite this negative result, we propose the validity of one new inequality for covariant holographic entanglement entropy for five regions. This inequality, while not maximin provable, is much weaker than many of the inequalities satisfied by the RT formula and should therefore be easier to prove. If it is valid, then there is strong evidence that holographic entanglement entropy plays a role in general spacetimes including those that arise in cosmology. Our new inequality is obtained by the assumption that the HRT formula satisfies every known balanced inequality obeyed by the Shannon entropies of classical probability distributions. This is a property that the RT formula has been shown to possess and which has been previously conjectured to hold for quantum mechanics in general.

Sirolimus formulation with improved pharmacokinetic properties produced by a continuous flow method.

PubMed

Solymosi, Tamás; Angi, Réka; Basa-Dénes, Orsolya; Ránky, Soma; Ötvös, Zsolt; Glavinas, Hristos; Filipcsei, Genovéva; Heltovics, Gábor

2015-08-01

The oral bioavailability of Sirolimus is limited by poor dissolution of the compound in the gastrointestinal tract resulting in a low bioavailability and large inter-individual differences in blood levels. Several different formulation approaches were applied to overcome these disadvantageous pharmacokinetic properties including the marketed oral solution and a tablet form containing wet milled nanocrystals. These approaches deliver improved pharmacokinetics, yet, they share the characteristics of complex production method and composition. We have developed a nanostructured Sirolimus formulation prepared by the controlled continuous flow precipitation of the compound from its solution in the presence of stabilizers. We have shown that contrary to the batch production the process could be easily intensified and scaled up; apparently the uniformity of the precipitation is heavily dependent on the production parameters, most likely the mixing of the solvent and antisolvent. We compared the physicochemical and pharmacokinetic properties of the nanostructured formula with the marketed nanoformula. We found that our method produces particles in the size range of less than 100nm. The solid form redispersed instantaneously in water and in biorelevant media. Both the solid form and the redispersed colloid solution showed excellent stability even in accelerated test conditions. The oral administration of the nanostructured formula resulted in faster absorption, higher exposure and higher trough concentrations when compared to the marked form. These advantageous properties could allow the development of solid oral Sirolimus formulae with lower strength and gel based topical delivery systems. Copyright © 2015 Elsevier B.V. All rights reserved.

Higher-Loop Amplitude Monodromy Relations in String and Gauge Theory.

PubMed

Tourkine, Piotr; Vanhove, Pierre

2016-11-18

The monodromy relations in string theory provide a powerful and elegant formalism to understand some of the deepest properties of tree-level field theory amplitudes, like the color-kinematics duality. This duality has been instrumental in tremendous progress on the computations of loop amplitudes in quantum field theory, but a higher-loop generalization of the monodromy construction was lacking. In this Letter, we extend the monodromy relations to higher loops in open string theory. Our construction, based on a contour deformation argument of the open string diagram integrands, leads to new identities that relate planar and nonplanar topologies in string theory. We write one and two-loop monodromy formulas explicitly at any multiplicity. In the field theory limit, at one-loop we obtain identities that reproduce known results. At two loops, we check our formulas by unitarity in the case of the four-point N=4 super-Yang-Mills amplitude.

GoPhast: a graphical user interface for PHAST

USGS Publications Warehouse

Winston, Richard B.

2006-01-01

GoPhast is a graphical user interface (GUI) for the USGS model PHAST. PHAST simulates multicomponent, reactive solute transport in three-dimensional, saturated, ground-water flow systems. PHAST can model both equilibrium and kinetic geochemical reactions. PHAST is derived from HST3D (flow and transport) and PHREEQC (geochemical calculations). The flow and transport calculations are restricted to constant fluid density and constant temperature. The complexity of the input required by PHAST makes manual construction of its input files tedious and error-prone. GoPhast streamlines the creation of the input file and helps reduce errors. GoPhast allows the user to define the spatial input for the PHAST flow and transport data file by drawing points, lines, or polygons on top, front, and side views of the model domain. These objects can have up to two associated formulas that define their extent perpendicular to the view plane, allowing the objects to be three-dimensional. Formulas are also used to specify the values of spatial data (data sets) both globally and for individual objects. Objects can be used to specify the values of data sets independent of the spatial and temporal discretization of the model. Thus, the grid and simulation periods for the model can be changed without respecifying spatial data pertaining to the hydrogeologic framework and boundary conditions. This report describes the operation of GoPhast and demonstrates its use with examples. GoPhast runs on Windows 2000, Windows XP, and Linux operating systems.

First Born amplitude for transitions from a circular state to a state of large (l, m)

NASA Astrophysics Data System (ADS)

Dewangan, D. P.

2005-01-01

The use of cylindrical polar coordinates instead of the conventional spherical polar coordinates enables us to derive compact expressions of the first Born amplitude for some selected sets of transitions from an arbitrary initial circular \\big|\\psi_{n_i,n_i-1,n_i-1}\\big\\rangle state to a final \\big|\\psi_{n_f,l_f,m_f}\\big\\rangle state of large (lf, mf). The formulae for \\big|\\psi_{n_i,n_i-1,n_i-1}\\big\\rangle \\longrightarrow \\big|\\psi_{n_f,n_f-1,n_f-2}\\big\\rangle and \\big|\\psi_{n_i,n_i-1,n_i-1}\\big\\rangle \\longrightarrow \\big|\\psi_{n_f,n_f-1,n_f-3}\\big\\rangle transitions are expressed in terms of the Jacobi polynomials which serve as suitable starting points for constructing complete solutions over the bound energy levels of hydrogen-like atoms. The formulae for \\big|\\psi_{n_i,n_i-1,n_i-1}\\big\\rangle \\longrightarrow \\big|\\psi_{n_f,n_f-1,-(n_f-2)}\\big\\rangle and \\big|\\psi_{n_i,n_i-1,n_i-1}\\big\\rangle \\longrightarrow \\big|\\psi_{n_f,n_f-1,-(n_f-3)}\\big\\rangle transitions are in simple algebraic forms and are directly applicable to all possible values of ni and nf. It emerges that the method can be extended to evaluate the first Born amplitude for many other transitions involving states of large (l, m).

An Effective Solution to Discover Synergistic Drugs for Anti-Cerebral Ischemia from Traditional Chinese Medicinal Formulae

PubMed Central

Lu, Peng; Chen, Chang; Fu, Meihong; Fang, Jing; Gao, Jian; Zhu, Li; Liang, Rixin; Shen, Xin; Yang, Hongjun

2013-01-01

Recently, the pharmaceutical industry has shifted to pursuing combination therapies that comprise more than one active ingredient. Interestingly, combination therapies have been used for more than 2500 years in traditional Chinese medicine (TCM). Understanding optimal proportions and synergistic mechanisms of multi-component drugs are critical for developing novel strategies to combat complex diseases. A new multi-objective optimization algorithm based on least angle regression-partial least squares was proposed to construct the predictive model to evaluate the synergistic effect of the three components of a novel combination drug Yi-qi-jie-du formula (YJ), which came from clinical TCM prescription for the treatment of encephalopathy. Optimal proportion of the three components, ginsenosides (G), berberine (B) and jasminoidin (J) was determined via particle swarm optimum. Furthermore, the combination mechanisms were interpreted using PLS VIP and principal components analysis. The results showed that YJ had optimal proportion 3(G): 2(B): 0.5(J), and it yielded synergy in the treatment of rats impaired by middle cerebral artery occlusion induced focal cerebral ischemia. YJ with optimal proportion had good pharmacological effects on acute ischemic stroke. The mechanisms study demonstrated that the combination of G, B and J could exhibit the strongest synergistic effect. J might play an indispensable role in the formula, especially when combined with B for the acute stage of stroke. All these data in this study suggested that in the treatment of acute ischemic stroke, besides restoring blood supply and protecting easily damaged cells in the area of the ischemic penumbra as early as possible, we should pay more attention to the removal of the toxic metabolites at the same time. Mathematical system modeling may be an essential tool for the analysis of the complex pharmacological effects of multi-component drug. The powerful mathematical analysis method could greatly improve the efficiency in finding new combination drug from TCM. PMID:24236065

Abductive Equivalential Translation and its application to Natural Language Database Interfacing

NASA Astrophysics Data System (ADS)

Rayner, Manny

1994-05-01

The thesis describes a logical formalization of natural-language database interfacing. We assume the existence of a ``natural language engine'' capable of mediating between surface linguistic string and their representations as ``literal'' logical forms: the focus of interest will be the question of relating ``literal'' logical forms to representations in terms of primitives meaningful to the underlying database engine. We begin by describing the nature of the problem, and show how a variety of interface functionalities can be considered as instances of a type of formal inference task which we call ``Abductive Equivalential Translation'' (AET); functionalities which can be reduced to this form include answering questions, responding to commands, reasoning about the completeness of answers, answering meta-questions of type ``Do you know...'', and generating assertions and questions. In each case, a ``linguistic domain theory'' (LDT) Γ and an input formula F are given, and the goal is to construct a formula with certain properties which is equivalent to F, given Γ and a set of permitted assumptions. If the LDT is of a certain specified type, whose formulas are either conditional equivalences or Horn-clauses, we show that the AET problem can be reduced to a goal-directed inference method. We present an abstract description of this method, and sketch its realization in Prolog. The relationship between AET and several problems previously discussed in the literature is discussed. In particular, we show how AET can provide a simple and elegant solution to the so-called ``Doctor on Board'' problem, and in effect allows a ``relativization'' of the Closed World Assumption. The ideas in the thesis have all been implemented concretely within the SRI CLARE project, using a real projects and payments database. The LDT for the example database is described in detail, and examples of the types of functionality that can be achieved within the example domain are presented.

A Study to Ascertain the Feasibility of Joint Efforts to Establish a Comprehensive Health Care Delivery System Utilizing Hill-Burton Constructed Hospital,

DTIC Science & Technology

1978-12-15

Utilization Review Procedures ................ 22 Reduced Philanthropy ......................... 22 Lack of Incentives ........................... 23 Reductions...challenges are made on hospitals in the form of status of technology, elite physician compliments, and increased specialization of labor which ccnstantly...construction are now marginally subsidized by philanthropy . Third party reimbursement is now the dominant source of hospital revenue with cost based formula

A reaction-diffusion within-host HIV model with cell-to-cell transmission.

PubMed

Ren, Xinzhi; Tian, Yanni; Liu, Lili; Liu, Xianning

2018-06-01

In this paper, a reaction-diffusion within-host HIV model is proposed. It incorporates cell mobility, spatial heterogeneity and cell-to-cell transmission, which depends on the diffusion ability of the infected cells. In the case of a bounded domain, the basic reproduction number [Formula: see text] is established and shown as a threshold: the virus-free steady state is globally asymptotically stable if [Formula: see text] and the virus is uniformly persistent if [Formula: see text]. The explicit formula for [Formula: see text] and the global asymptotic stability of the constant positive steady state are obtained for the case of homogeneous space. In the case of an unbounded domain and [Formula: see text], the existence of the traveling wave solutions is proved and the minimum wave speed [Formula: see text] is obtained, providing the mobility of infected cells does not exceed that of the virus. These results are obtained by using Schauder fixed point theorem, limiting argument, LaSalle's invariance principle and one-side Laplace transform. It is found that the asymptotic spreading speed may be larger than the minimum wave speed via numerical simulations. However, our simulations show that it is possible either to underestimate or overestimate the spread risk [Formula: see text] if the spatial averaged system is used rather than one that is spatially explicit. The spread risk may also be overestimated if we ignore the mobility of the cells. It turns out that the minimum wave speed could be either underestimated or overestimated as long as the mobility of infected cells is ignored.

Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group with motivations from string theory and QFT

NASA Astrophysics Data System (ADS)

Bibak, Khodakhast; Kapron, Bruce M.; Srinivasan, Venkatesh

2016-09-01

Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT). Recently, Koch et al. (2013) [12] gave a refined formula for counting ribbon graphs and discussed its applications to several physics problems. An important factor in this formula is the number of surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group. The aim of this paper is to give an explicit and practical formula for the number of such epimorphisms. As a consequence, we obtain an 'equivalent' form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.

Optical Activity of Benzil Crystal

NASA Astrophysics Data System (ADS)

Říha, Jan; Vyšín, Ivo

2003-09-01

Optical activity of benzil as an example of optically active matter in the crystalline state only, not in solution, is studied for the wavelengths ranging from 0.320 m to 0.585 m. Previously measured experimental data are approximated by the theoretical set of formulas, which were derived by the use of the three coupled oscillators model. The earlier published formula consisting of six terms differed from the experimental data particularly in the wavelength region (0.380-0.510) m. This formula is replaced by the twelve-term formula which was computed by our specially worked computer program for the interpretation of the experimental data of optical activity based on the Marquardt-Levenberg method of the sum of least squares minimization. The possibility of molecular contribution to the resulting optical activity of benzil is mentioned. The use of Kramers-Kronig transforms for the determination of the circular dichroism curve based on the optical rotatory dispersion result is shown. The theoretically computed circular dichroism is compared with the available experimental data.

Method for extracting lanthanides and actinides from acid solutions

DOEpatents

Horwitz, E. Philip; Kalina, Dale G.; Kaplan, Louis; Mason, George W.

1985-01-01

A process for the recovery of actinide and lanthanide values from aqueous acidic solutions with an organic extractant having the formula: ##STR1## where .phi. is phenyl, R.sup.1 is a straight or branched alkyl or alkoxyalkyl containing from 6 to 12 carbon atoms and R.sup.2 is an alkyl containing from 3 to 6 carbon atoms. The process is suitable for the separation of actinide and lanthanide values from fission product values found together in high level nuclear reprocessing waste solutions.

On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order.

PubMed

Tunç, Cemil; Tunç, Osman

2016-01-01

In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

NASA Astrophysics Data System (ADS)

Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

2018-05-01

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

Water soluble laser dyes

DOEpatents

Hammond, P.R.; Feeman, J.F.; Field, G.F.

1998-08-11

Novel water soluble dyes of the formula 1 are provided by the formula described in the paper wherein R{sup 1} and R{sup 4} are alkyl of 1 to 4 carbon atoms or hydrogen; or R{sup 1}--R{sup 2} or R{sup 2}--R{sup 4} form part of aliphatic heterocyclic rings; R{sup 2} is hydrogen or joined with R{sup 1} or R{sup 4} as described above; R{sup 3} is --(CH{sub 2}){sub m}--SO{sub 3}{sup {minus}}, where m is 1 to 6; X is N, CH or formula 2 given in paper where Y is 2 --SO{sub 3}{sup {minus}} ; Z is 3, 4, 5 or 6 --SO{sub 3}{sup {minus}}. The novel dyes are particularly useful as the active media in water solution dye lasers.

Tops as building blocks for G 2 manifolds

NASA Astrophysics Data System (ADS)

Braun, Andreas P.

2017-10-01

A large number of examples of compact G 2 manifolds, relevant to supersymmetric compactifications of M-Theory to four dimensions, can be constructed by forming a twisted connected sum of two building blocks times a circle. These building blocks, which are appropriate K3-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes. In particular, this enables us to prove combinatorial formulas for the Hodge numbers and other relevant topological data.

The methodic of calculation for the need of basic construction machines on construction site when developing organizational and technological documentation

NASA Astrophysics Data System (ADS)

Zhadanovsky, Boris; Sinenko, Sergey

2018-03-01

Economic indicators of construction work, particularly in high-rise construction, are directly related to the choice of optimal number of machines. The shortage of machinery makes it impossible to complete the construction & installation work on scheduled time. Rates of performance of construction & installation works and labor productivity during high-rise construction largely depend on the degree of provision of construction project with machines (level of work mechanization). During calculation of the need for machines in construction projects, it is necessary to ensure that work is completed on scheduled time, increased level of complex mechanization, increased productivity and reduction of manual work, and improved usage and maintenance of machine fleet. The selection of machines and determination of their numbers should be carried out by using formulas presented in this work.

Colorful Chemistry.

ERIC Educational Resources Information Center

Williams, Suzanne

1991-01-01

Described is an color-making activity where students use food coloring, eyedroppers, and water to make various colored solutions. Included are the needed materials and procedures. Students are asked to write up the formulas for making their favorite color. (KR)

A Question of Interest

ERIC Educational Resources Information Center

Holley, Ann D.

1978-01-01

Formulas are developed which answer installment-buying questions without the use of amortization, sinking funds, or annuity tables. Applications for geometric progressions, proof by induction, solution of exponential equations, and the notion of recursive functions are displayed. (MN)

Dynamics of column stability with partial end restraints

NASA Technical Reports Server (NTRS)

Gregory, Peyton B.

1990-01-01

The dynamic behavior of columns with partial end restraints and loads consisting of a dead load and a pulsating load are investigated. The differential equation is solved using a lumped impulse recurrence formula relative to time coupled with a finite difference discretization along the member length. A computer program is written from which the first critical frequencies are found as a function of end stiffness. The case of a pinned ended column compares very well with the exact solution. Also, the natural frequency and buckling load formulas are derived for equal and unequal end restraints.

The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations

NASA Technical Reports Server (NTRS)

Bardi, Martino; Osher, Stanley

1991-01-01

Simple inequalities are presented for the viscosity solution of a Hamilton-Jacobi equation in N space dimensions when neither the initial data nor the Hamiltonian need be convex (or concave). The initial data are uniformly Lipschitz and can be written as the sum of a convex function in a group of variables and a concave function in the remaining variables, therefore including the nonconvex Riemann problem. The inequalities become equalities wherever a 'maxmin' equals a 'minmax', and thus a representation formula for this problem is obtained, generalizing the classical Hopi formulas.

Solving periodic block tridiagonal systems using the Sherman-Morrison-Woodbury formula

NASA Technical Reports Server (NTRS)

Yarrow, Maurice

1989-01-01

Many algorithms for solving the Navier-Stokes equations require the solution of periodic block tridiagonal systems of equations. By applying a splitting to the matrix representing this system of equations, it may first be reduced to a block tridiagonal matrix plus an outer product of two block vectors. The Sherman-Morrison-Woodbury formula is then applied. The algorithm thus reduces a periodic banded system to a non-periodic banded system with additional right-hand sides and is of higher efficiency than standard Thomas algorithm/LU decompositions.

Extraction and Liquid Chromatography-Tandem Mass Spectrometry Detection of 3-Monochloropropanediol Esters and Glycidyl Esters in Infant Formula.

PubMed

Leigh, Jessica K; MacMahon, Shaun

2016-12-14

A method was developed for the extraction of fatty acid esters of 3-chloro-1,2-propanediol (3-MCPD) and glycidol from infant formula, followed by quantitative analysis of the extracts using liquid chromatography-tandem mass spectrometry (LC-MS/MS). These process-induced chemical contaminants are found in refined vegetable oils, and studies have shown that they are potentially carcinogenic and/or genotoxic, making their presence in edible oils (and processed foods containing these oils) a potential health risk. The extraction procedure involves a liquid-liquid extraction, where powdered infant formula is dissolved in water and extracted with ethyl acetate. Following shaking, centrifugation, and drying of the organic phase, the resulting fat extract is cleaned-up using solid-phase extraction and analyzed by LC-MS/MS. Method performance was confirmed by verifying the percent recovery of each 3-MCPD and glycidyl ester in a homemade powdered infant formula reference material. Average ester recoveries in the reference material ranged from 84.9 to 109.0% (0.6-9.5% RSD). The method was also validated by fortifying three varieties of commercial infant formulas with a 3-MCPD and glycidyl ester solution. Average recoveries of the esters across all concentrations and varieties of infant formula ranged from 88.7 to 107.5% (1.0-9.5% RSD). Based on the validation results, this method is suitable for producing 3-MCPD and glycidyl ester occurrence data in all commercially available varieties of infant formula.

Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Chai, Han-Peng; Yuan, Yu-Qiang

2017-03-01

Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.

Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber.

PubMed

Liu, Lei; Tian, Bo; Chai, Han-Peng; Yuan, Yu-Qiang

2017-03-01

Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.

Recent results on output feedback problems

NASA Technical Reports Server (NTRS)

Byrnes, C. I.

1980-01-01

Given a real linear system sigma = (A, B, C) with m inputs, p outputs and degree n, the problem of generic pole placement by output feedback is studied, which is to compute the constant C(m,p) such that the inequality C(m,p) not less than n is necessary and sufficient for generically positioning the poles of the generic linear system by constant output feedback. A constant C prime (m,p) is determined, which gives a sufficient condition for generic pole placement and which, to the best of the author's knowledge, is at least as good an estimate of C(m,p) as any in the literature. Some results on the construction of solutions in case mp = n are announced, based on the degree formula of Brockett and Byrnes and the Galois theory. In particular, a question raised by Anderson, Bose, and Jury, on the existence of a rational procedure for computing the feedback law from the desired characteristic polynomial is answered.

N=2 supersymmetric a=4-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hussin, V.; Kiselev, A. V.; Krutov, A. O.

2010-08-15

We consider the problem of constructing Gardner's deformations for the N=2 supersymmetric a=4-Korteweg-de Vries (SKdV) equation; such deformations yield recurrence relations between the super-Hamiltonians of the hierarchy. We prove the nonexistence of supersymmetry-invariant deformations that retract to Gardner's formulas for the Korteweg-de Vries (KdV) with equation under the component reduction. At the same time, we propose a two-step scheme for the recursive production of the integrals of motion for the N=2, a=4-SKdV. First, we find a new Gardner's deformation of the Kaup-Boussinesq equation, which is contained in the bosonic limit of the superhierarchy. This yields the recurrence relation between themore » Hamiltonians of the limit, whence we determine the bosonic super-Hamiltonians of the full N=2, a=4-SKdV hierarchy. Our method is applicable toward the solution of Gardner's deformation problems for other supersymmetric KdV-type systems.« less

Rapid Equipping Force (REF) Analytical Support

DTIC Science & Technology

2007-06-01

document contains color images. 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER OF PAGES 44...interface and performs actions via Excel formulae, ActiveX controls, and VBA code. – Plan to provide both simple and complex weighting and scoring methods...Requirements Quad Chart. –Solution Set Information Worksheet: A spreadsheet containing detailed information concerning every potential solution considered

An Approximate Solution to the Equation of Motion for Large-Angle Oscillations of the Simple Pendulum with Initial Velocity

ERIC Educational Resources Information Center

Johannessen, Kim

2010-01-01

An analytic approximation of the solution to the differential equation describing the oscillations of a simple pendulum at large angles and with initial velocity is discussed. In the derivation, a sinusoidal approximation has been applied, and an analytic formula for the large-angle period of the simple pendulum is obtained, which also includes…

Calculation of flexoelectric deformations of finite-size bodies

NASA Astrophysics Data System (ADS)

Yurkov, A. S.

2015-03-01

The previously developed approximate theory of flexoelectric deformations of finite-size bodies has been considered as applied to three special cases: a uniformly polarized ball, a uniformly polarized circular rod, and a uniformly polarized thin circular plate of an isotropic material. For these cases simple algebraic formulas have been derived. In the case of the ball, the solution is compared with the previously obtained exact solution.

Isolation of Enterobacter sakazakii from ass' milk in Sicily: case report, safety and legal issues.

PubMed

Conte, F; Passantino, A

2008-07-01

Enterobacter sakazakii (Es) infections are likely to involve newborns and infants, causing meningitis and necrotizing enterocolitis and sepsis. Contamination of infant formulae milk during factory production or bottle preparation is implicated. Es has been isolated from environmental sources and from food other than infant formula and milk powder, but why it is associated only with the consumption of infant formulae, is unclear. According to Regulation (EC) No. 2073/2005 on the microbiological criteria for foodstuffs, Es is considered a microorganisms of greatest concern in infant formulae and follow-on formulae. Es is included between "safety criteria". The isolation of two strains of Es from 50 samples of ass' milk in Sicily is described. The antibiotic resistance profile of the isolates revealed a multiple resistance profile, including fluoroquinolones, commonly used to treat the infections. The authors underline the importance of survey because in Italy ass' milk is considered one of the solutions for infants suffering from hypersensitivity to milk protein of some animal species. There is scarce information about the ecology and the uncertainty concerning the source of infection in the children and adults; the authors are concerned that ass' milk could become a high-risk food.

Empirical mass formula with proton-neutron interaction

NASA Astrophysics Data System (ADS)

Tachibana, Takahiro; Uno, Masahiro; Yamada, So; Yamada, Masami

1987-12-01

An atomic mass formula consisting of a gross part, and averge even-odd part and an empirical shell part is studied. The gross part is, apart from a small atomic term, taken to be the sum of nucleon rest masses. Coulomb energies and a polynomial in A1/3 and ‖N-Z‖/A. The shell part includes, in addition to proton and neutron support of nuclear magicities and the cooperative deformation effect. After the first construction of such a formula, refinements have been made in two respects. One is a separate treatment of Z=N odd-odd nuclei suggested by a quartet model, and the other is an improvement of the proton neutron interaction term. By these refinements the root-mean-square deviation of calculated masses from the 1986 Audi-Wapstra masses has been reduced from 538 keV to 460 keV.

Elastic Instability of Members Having Sections Common in Aircraft Construction

NASA Technical Reports Server (NTRS)

Trayer, George W; March, H W

1932-01-01

Two fundamental problems of elastic stability are discussed in this report. In part one formulas are given for calculating the critical stress at which a thin, outstanding flange of a compression member will either wrinkle into several waves or form into a single half wave and twist the member about its longitudinal axis. A mathematical study of the problem, which together with experimental work has led to these formulas, is given in an appendix. Results of test substantiating the recommended formulas are also presented. In part two the lateral buckling of beams is discussed. The results of a number of mathematical studies of this phenomenon have been published prior to this writing, but very little experimentally determined information relating to the problem has been available heretofore. Experimental verification of the mathematical deductions is supplied.

Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Butko, Yana A., E-mail: yanabutko@yandex.ru, E-mail: kinderknecht@math.uni-sb.de; Grothaus, Martin, E-mail: grothaus@mathematik.uni-kl.de; Smolyanov, Oleg G., E-mail: Smolyanov@yandex.ru

2016-02-15

Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure ofmore » quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.« less

Radially separated classical lumps in non-Abelian gauge models

NASA Astrophysics Data System (ADS)

Burzlaff, Jürgen

1985-04-01

We search for smooth and time-independent finite-energy solutions to Yang-Mills-Higgs theory with an arbitrary compact gauge group. Excluding the monopole solutions which have been studied before, we concentrate on configurations with no long-range fields, which include the saddle points corresponding to noncontractible (hyper-) loops. It is shown that if the radial dependence of the fields is factorized, only one solution satisfies all these conditions. This solution is the one which has been studied before by Dashen, Hasslacher, and Neveu and by Boguta, and whose existence has recently been proved rigorously. Formulas for the asymptotic behavior of this solution are given.

The application of waste fly ash and construction-waste in cement filling material in goaf

NASA Astrophysics Data System (ADS)

Chen, W. X.; Xiao, F. K.; Guan, X. H.; Cheng, Y.; Shi, X. P.; Liu, S. M.; Wang, W. W.

2018-01-01

As the process of urbanization accelerated, resulting in a large number of abandoned fly ash and construction waste, which have occupied the farmland and polluted the environment. In this paper, a large number of construction waste and abandoned fly ash are mixed into the filling material in goaf, the best formula of the filling material which containing a large amount of abandoned fly ash and construction waste is obtained, and the performance of the filling material is analyzed. The experimental results show that the cost of filling material is very low while the performance is very good, which have a good prospect in goaf.

New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

NASA Astrophysics Data System (ADS)

Csörgő, Tamás; Kasza, Gábor; Csanád, Máté; Jiang, Zefang

2018-06-01

We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision data at RHIC and LHC. In the longitudinally boost-invariant limit, these new solutions approach the Hwa-Bjorken solution and the corresponding rapidity distributions approach a rapidity plateaux.

Exponential asymptotics of homoclinic snaking

NASA Astrophysics Data System (ADS)

Dean, A. D.; Matthews, P. C.; Cox, S. M.; King, J. R.

2011-12-01

We study homoclinic snaking in the cubic-quintic Swift-Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319-54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement.

Asymptotic formulae for likelihood-based tests of new physics

NASA Astrophysics Data System (ADS)

Cowan, Glen; Cranmer, Kyle; Gross, Eilam; Vitells, Ofer

2011-02-01

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the "Asimov data set", which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation.

Evaluation/modification of IDOT foundation piling design and construction policy.

DOT National Transportation Integrated Search

2009-03-01

The Illinois Department of Transportation (IDOT) estimates pile lengths based on a static analysis method; : however, the final length of the pile is determined with a dynamic formula based on the pile driving resistance : exhibited in the field. Bec...

21 CFR 10.20 - Submission of documents to Division of Dockets Management; computation of time; availability for...

Code of Federal Regulations, 2010 CFR

2010-04-01

...) Under § 20.63 (a) and (b), the names and other information that would identify patients or research... information. (e) Quantitative or semiquantitative formulas. (f) Information on product design or construction...

21 CFR 10.20 - Submission of documents to Division of Dockets Management; computation of time; availability for...

Code of Federal Regulations, 2014 CFR

2014-04-01

...) Under § 20.63 (a) and (b), the names and other information that would identify patients or research... information. (e) Quantitative or semiquantitative formulas. (f) Information on product design or construction...

21 CFR 10.20 - Submission of documents to Division of Dockets Management; computation of time; availability for...

Code of Federal Regulations, 2011 CFR

2011-04-01

...) Under § 20.63 (a) and (b), the names and other information that would identify patients or research... information. (e) Quantitative or semiquantitative formulas. (f) Information on product design or construction...

21 CFR 10.20 - Submission of documents to Division of Dockets Management; computation of time; availability for...

Code of Federal Regulations, 2013 CFR

2013-04-01

...) Under § 20.63 (a) and (b), the names and other information that would identify patients or research... information. (e) Quantitative or semiquantitative formulas. (f) Information on product design or construction...

21 CFR 10.20 - Submission of documents to Division of Dockets Management; computation of time; availability for...

Code of Federal Regulations, 2012 CFR

2012-04-01

...) Under § 20.63 (a) and (b), the names and other information that would identify patients or research... information. (e) Quantitative or semiquantitative formulas. (f) Information on product design or construction...

Effective quadrature formula in solving linear integro-differential equations of order two

NASA Astrophysics Data System (ADS)

Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

2017-08-01

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

Elastohydrodynamic lubrication of point contacts. Ph.D. Thesis - Leeds Univ.

NASA Technical Reports Server (NTRS)

Hamrock, B. J.

1976-01-01

A procedure for the numerical solution of the complete, isothermal, elastohydrodynamic lubrication problem for point contacts is given. This procedure calls for the simultaneous solution of the elasticity and Reynolds equations. By using this theory the influence of the ellipticity parameter and the dimensionless speed, load, and material parameters on the minimum and central film thicknesses was investigated. Thirty-four different cases were used in obtaining the fully flooded minimum- and central-film-thickness formulas. Lubricant starvation was also studied. From the results it was possible to express the minimum film thickness for a starved condition in terms of the minimum film thickness for a fully flooded condition, the speed parameter, and the inlet distance. Fifteen additional cases plus three fully flooded cases were used in obtaining this formula. Contour plots of pressure and film thickness in and around the contact have been presented for both fully flooded and starved lubrication conditions.

Cutting solid figures by plane - analytical solution and spreadsheet implementation

NASA Astrophysics Data System (ADS)

Benacka, Jan

2012-07-01

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and cosine rules. The basic problem is to find the section of the figure by a plane that is defined by three points related to the figure. In this article, a formula is derived that gives the positions of the intersection points of such a plane and the figure edges, that is, the vertices of the section polygon. Spreadsheet implementations of the formula for cuboid and right rectangular pyramids are presented. The user can check his/her graphical solution, or proceed if he/she is not able to complete the section.

A method of determining the refractive index of a prismatic lens.

PubMed

Buckley, John G

2010-01-01

A new method of measuring lens refractive index requiring immersion in solution and measuring lens power in air and in solution is extended. Prompted by a clinical need, the new method using lens power can be extended by applying it to prismatic power as well. This article provides a theoretical basis explaining why this can be done. The prismatic power of a prism is derived from first principles. Snell's Law and geometrical optics provide the framework for demonstrating the validity of the resulting formula. The sameness in formula derived using lens power or prism is shown, both from a paraxial and non-paraxial optics perspective. The effect of varying lens material and amount of prism is considered. The prismatic method described provides a useful alternative method of determining the refractive index of any lens. In some cases, it may be the only method available. Practitioners should consider when each method will provide optimal results.

Optimising concentrations of antimicrobial agents in pharmaceutical preparations: Case of an oral solution of glycerol and an ophthalmic solution containing cysteamine.

PubMed

Chan Hew Wai, A; Becasse, P; Tworski, S; Pradeau, D; Planas, V

2014-11-01

In the context of current distrust of antimicrobial preservatives, the quantities of these substances in two pharmaceutical formulas were studied: an ophthalmic solution of cysteamine preserved benzalkonium chloride at 1mg/5mL and Glycerotone(®) preserved with sorbic acid at 0.1g/100g. The purpose of this work was to verify that a reduction of the quantities of preservative continues to fulfil the requirements for antimicrobial preservation. The Test of efficacy of antimicrobial preservation, section 5.1.3 of the 8th edition of the European Pharmacopoeia, was carried out on each formulation prepared with decreasing quantities of preservative. The results show that formulations whose preservative concentration was reduced by a factor of four remained compliant with standards. It is to be noted that in formulas without preservative, fungal growth was observed in both the solution of Glycerotone(®) and the ophthalmic solution containing cysteamine. Although there is no question that an antimicrobial preservative is necessary, the quantity of preservative can be reduced without deteriorating the quality of the pharmaceutical product but the minimal effective concentration remains to be determined. The formulations of many pharmaceutical products should therefore be examined in order to limit the quantities of preservative while continuing to guarantee patient's safety. Copyright © 2014 Elsevier Masson SAS. All rights reserved.

Efficient transformation of DDT by peroxymonosulfate activated with cobalt in aqueous systems: Kinetics, products, and reactive species identification.

PubMed

Qin, Wenxiu; Fang, Guodong; Wang, Yujun; Wu, Tongliang; Zhu, Changyin; Zhou, Dongmei

2016-04-01

Recently, sulfate radical ( [Formula: see text] ) based-advanced oxidation technologies (AOTs) have been attracted great attention in the remediation of contaminated soil and groundwater. In the present study, Co(2+) ions activated peroxymonosulfate (PMS) system was used to degrade 1, 1, 1-trichloro-2, 2'bis(p-chlorophenyl) ethane (DDT) in aqueous solutions. It was found that DDT was efficiently degraded in the PMS/Co(II) solutions within several hours, and the degradation efficiency of DDT was dependent on the concentrations of PMS and Co(II), and the optimum molar ratio of PMS and Co(II) was 50:1. The degradation kinetics of DDT were well described with pseudo-first-order equations over a range of temperature (10-40 °C), and the activation energy that was calculated with Arrhenius equation was 72.3 ± 2.6 kJ/mol. Electron paramagnetic resonance (EPR) and GC-MS techniques were applied to identify the intermediates and reactive species for DDT degradation. The results indicated that [Formula: see text] and OH were the main reactive species accounting for DDT degradation. Dichlorobenzophenone, 4-chlorobenzoic acid and benzylalcohol were the dominant intermediates for DDT degradation, and the likely degradation pathway of DDT was proposed on the basis of these identified products. Increasing pH inhibited the formation of [Formula: see text] and OH, and thus decreased the catalytic degradation of DDT. Cl(-) ion was found to significantly inhibit, while [Formula: see text] and dissolved oxygen had limited effects on DDT degradation. Copyright © 2016 Elsevier Ltd. All rights reserved.

Rock Slope Stability Evaluation in a Steep-Walled Canyon: Application to Elevator Construction in the Yunlong River Valley, Enshi, China

NASA Astrophysics Data System (ADS)

Xiao, Lili; Chai, Bo; Yin, Kunlong

2015-09-01

A passenger elevator is to be built on a nearly vertical slope in the National Geological Park in Enshi, Hubei province, China. Three steps comprise the construction: excavating the slope toe for the elevator platform, building the elevator on the platform, and affixing the elevator to the slope using anchors. To evaluate the rock slope stability in the elevator area and the safety of the elevator construction, we applied three techniques: qualitative analysis, formula calculation, and numerical simulation methods, based on field investigation and parameter selection, and considering both wet and dry conditions, pre- and post-construction. Qualitative stability factors for sliding and falling were calculated using the limit equilibrium method; the results show that the slope as a whole is stable, with a few unstable blocks, notably block BT1. Formula-based stability factors were calculated for four sections on block BT1, revealing the following: anchors will decrease the stability of certain rock pieces; the lowest average stability factor after anchoring will be K f = 1.36 in wet conditions; block BT1 should be reinforced during elevator construction, up to a first-class slope stability factor of K f = 1.40; and the slope as a whole is stable. Numerical simulation using FLAC3D indicated that the stress distribution will reach equilibrium for all steps before and after construction, and that the factor of safety (FOS) is within the general slope safety range (FOS > 1.05). We suggest that unstable pieces in block BT1 be reinforced during construction to a first-class slope safety range (FOS > 1.3), and that deformation monitoring on the slope surface be implemented.

Solvent-free mechanochemical preparation of phosphonium salts, phosphorus ylides, and olefins

DOEpatents

Pecharsky, Vitalij K.; Balema, Viktor P.; Wiench, Jerzy W.; Pruski, Marek

2004-05-04

The present invention provides a method of preparing a phosphonium salt of the formula [R.sup.1 R.sup.2 R.sup.3 P--CR.sup.4 R.sup.5 R.sup.6 ]X, comprising ball-milling a phosphine of the formula R.sup.1 R.sup.2 R.sup.3 P with a compound of the formula XCR.sup.4 R.sup.5 R.sup.6 ; a method of preparing a phosphorus ylide of the formula R.sup.1 R.sup.2 R.sup.3 P.dbd.CR.sup.4 R.sup.5, comprising ball-milling a phosphonium salt of the formula [R.sup.1 R.sup.2 R.sup.3 P--HCR.sup.4 R.sup.5 ]X in the presence of a base; and a method of preparing an olefin of the formula R.sup.4 R.sup.5 C.dbd.CR.sup.7 H or R.sup.4 R.sup.5 C.dbd.CR.sup.7 R.sup.8, comprising ball-milling a phosphorus ylide of the formula R.sup.1 R.sup.2 R.sup.3 P.dbd.CR.sup.4 R.sup.5 with a compound of the formula R.sup.7 C(O)H or R.sup.7 C(O)R.sup.8. The inventive method produces phosphonium salts and phosphorus ylides by mechanical processing solid reagents under solvent-free conditions. The advantages of the present invention over conventional solution methods, include: (1) extremely high selectivity; (2) high yields; (3) low processing temperatures; (4) simple and scalable reactions using commercially available equipment; and (5) the complete elimination of solvents from the reaction.

Measurement of water-soluble B vitamins in infant formula by liquid chromatography/tandem mass spectrometry.

PubMed

Huang, Min; Winters, Doug; Crowley, Richard; Sullivan, Darryl

2009-01-01

A method has been developed for the simultaneous measurement of multiple B vitamins (i.e., B1, B2, B3, B5, and B6) in infant formulas by LC-MSIMS. The vitamins were extracted with acidic solvent, followed by protein precipitation at a pH range of 4.5 to 5.5, and filtered. This simplified procedure eliminates many of the potential sources of laboratory error and facilitates rapid and efficient analysis. As is common in most cases, isotope internal standards were added to account for variations in sample preparation, as well as changes in MS measurement. In this method, isotope-labeled internal standards of B1, B3, B5, and B6 were used. The factors affecting analytical performance were investigated and optimized. In addition, the stability of these vitamins in the extraction solution was investigated. An acidic condition (5 mM HCl) was applied to successfully stabilize B1, which had shown a decrease in signal when other solvents were used. The quantitative extraction and good stability allowed isotope standards to be added to the filtered sample solution, instead of to the extraction solvent. The addition of the isotope to the small portion of the filtered sample solution significantly reduces cost. A comprehensive evaluation of the analysis of the standard reference material and good spike recovery of the vitamins (100 +/- 6%) demonstrates the accuracy of the method. The results for commercially available infant formula samples were also compared with those obtained using the current microbiological method.

A novel method to produce nonlinear empirical physical formulas for experimental nonlinear electro-optical responses of doped nematic liquid crystals: Feedforward neural network approach

NASA Astrophysics Data System (ADS)

Yildiz, Nihat; San, Sait Eren; Okutan, Mustafa; Kaya, Hüseyin

2010-04-01

Among other significant obstacles, inherent nonlinearity in experimental physical response data poses severe difficulty in empirical physical formula (EPF) construction. In this paper, we applied a novel method (namely layered feedforward neural network (LFNN) approach) to produce explicit nonlinear EPFs for experimental nonlinear electro-optical responses of doped nematic liquid crystals (NLCs). Our motivation was that, as we showed in a previous theoretical work, an appropriate LFNN, due to its exceptional nonlinear function approximation capabilities, is highly relevant to EPF construction. Therefore, in this paper, we obtained excellently produced LFNN approximation functions as our desired EPFs for above-mentioned highly nonlinear response data of NLCs. In other words, by using suitable LFNNs, we successfully fitted the experimentally measured response and predicted the new (yet-to-be measured) response data. The experimental data (response versus input) were diffraction and dielectric properties versus bias voltage; and they were all taken from our previous experimental work. We conclude that in general, LFNN can be applied to construct various types of EPFs for the corresponding various nonlinear physical perturbation (thermal, electronic, molecular, electric, optical, etc.) data of doped NLCs.

Classification of commutator algebras leading to the new type of closed Baker-Campbell-Hausdorff formulas

NASA Astrophysics Data System (ADS)

Matone, Marco

2015-11-01

We show that there are {\\it 13 types} of commutator algebras leading to the new closed forms of the Baker-Campbell-Hausdorff (BCH) formula $$\\exp(X)\\exp(Y)\\exp(Z)=\\exp({AX+BZ+CY+DI}) \\ , $$ derived in arXiv:1502.06589, JHEP {\\bf 1505} (2015) 113. This includes, as a particular case, $\\exp(X) \\exp(Z)$, with $[X,Z]$ containing other elements in addition to $X$ and $Z$. The algorithm exploits the associativity of the BCH formula and is based on the decomposition $\\exp(X)\\exp(Y)\\exp(Z)=\\exp(X)\\exp({\\alpha Y}) \\exp({(1-\\alpha) Y}) \\exp(Z)$, with $\\alpha$ fixed in such a way that it reduces to $\\exp({\\tilde X})\\exp({\\tilde Y})$, with $\\tilde X$ and $\\tilde Y$ satisfying the Van-Brunt and Visser condition $[\\tilde X,\\tilde Y]=\\tilde u\\tilde X+\\tilde v\\tilde Y+\\tilde cI$. It turns out that $e^\\alpha$ satisfies, in the generic case, an algebraic equation whose exponents depend on the parameters defining the commutator algebra. In nine {\\it types} of commutator algebras, such an equation leads to rational solutions for $\\alpha$. We find all the equations that characterize the solution of the above decomposition problem by combining it with the Jacobi identity.

Predicting body fat percentage based on gender, age and BMI by using artificial neural networks.

PubMed

Kupusinac, Aleksandar; Stokić, Edita; Doroslovački, Rade

2014-02-01

In the human body, the relation between fat and fat-free mass (muscles, bones etc.) is necessary for the diagnosis of obesity and prediction of its comorbidities. Numerous formulas, such as Deurenberg et al., Gallagher et al., Jackson and Pollock, Jackson et al. etc., are available to predict body fat percentage (BF%) from gender (GEN), age (AGE) and body mass index (BMI). These formulas are all fairly similar and widely applicable, since they provide an easy, low-cost and non-invasive prediction of BF%. This paper presents a program solution for predicting BF% based on artificial neural network (ANN). ANN training, validation and testing are done by randomly divided dataset that includes 2755 subjects: 1332 women (GEN = 0) and 1423 men (GEN = 1), with AGE from 18 to 88 y and BMI from 16.60 to 64.60 kg/m(2). BF% was estimated by using Tanita bioelectrical impedance measurements (Tanita Corporation, Tokyo, Japan). ANN inputs are: GEN, AGE and BMI, and output is BF%. The predictive accuracy of our solution is 80.43%. The main goal of this paper is to promote a new approach to predicting BF% that has same complexity and costs but higher predictive accuracy than above-mentioned formulas. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

On the Tracy-Widomβ Distribution for β=6

NASA Astrophysics Data System (ADS)

Grava, Tamara; Its, Alexander; Kapaev, Andrei; Mezzadri, Francesco

2016-11-01

We study the Tracy-Widom distribution function for Dyson's β-ensemble with β = 6. The starting point of our analysis is the recent work of I. Rumanov where he produces a Lax-pair representation for the Bloemendal-Virág equation. The latter is a linear PDE which describes the Tracy-Widom functions corresponding to general values of β. Using his Lax pair, Rumanov derives an explicit formula for the Tracy-Widom β=6 function in terms of the second Painlevé transcendent and the solution of an auxiliary ODE. Rumanov also shows that this formula allows him to derive formally the asymptotic expansion of the Tracy-Widom function. Our goal is to make Rumanov's approach and hence the asymptotic analysis it provides rigorous. In this paper, the first one in a sequel, we show that Rumanov's Lax-pair can be interpreted as a certain gauge transformation of the standard Lax pair for the second Painlevé equation. This gauge transformation though contains functional parameters which are defined via some auxiliary nonlinear ODE which is equivalent to the auxiliary ODE of Rumanov's formula. The gauge-interpretation of Rumanov's Lax-pair allows us to highlight the steps of the original Rumanov's method which needs rigorous justifications in order to make the method complete. We provide a rigorous justification of one of these steps. Namely, we prove that the Painlevé function involved in Rumanov's formula is indeed, as it has been suggested by Rumanov, the Hastings-McLeod solution of the second Painlevé equation. The key issue which we also discuss and which is still open is the question of integrability of the auxiliary ODE in Rumanov's formula. We note that this question is crucial for the rigorous asymptotic analysis of the Tracy-Widom function. We also notice that our work is a partial answer to one of the problems related to the β-ensembles formulated by Percy Deift during the June 2015 Montreal Conference on integrable systems.

Inflation of the screening length induced by Bjerrum pairs.

PubMed

Zwanikken, Jos; van Roij, René

2009-10-21

Within a modified Poisson-Boltzmann theory we study the effect of Bjerrum pairs on the typical length scale [Formula: see text] over which electric fields are screened in electrolyte solutions, taking into account a simple association-dissociation equilibrium between free ions and Bjerrum pairs. At low densities of Bjerrum pairs, this length scale is well approximated by the Debye length [Formula: see text], with ρ(s) the free-ion density. At high densities of Bjerrum pairs, however, we find [Formula: see text], which is significantly larger than 1/κ due to the enhanced effective permittivity of the electrolyte, caused by the polarization of Bjerrum pairs. We argue that this mechanism may explain the recently observed anomalously large colloid-free zones between an oil-dispersed colloidal crystal and a colloidal monolayer at the oil-water interface.

"Cariogenic potential of homemade weaning diet v/s commercial formula feeds" an in-vitro study.

PubMed

Bhat, S; Madan, I

2002-12-01

The universal phenomenon of introducing weaning diet to the growing child sets its onset by the age of 4-6 months. This preliminary diet of the child governs his or her dental health in the long run. The main objective of this study is to investigate the histopathological and clinical invasion of deciduous teeth exposed to both the homemade weaning diet and commercial formula feeds. The study also aims at motivating the consumption of the most appropriate diet for the weaning baby. Extracted deciduous teeth were incubated with the test solutions of homemade diet and commercial formula feeds for the period of 6 weeks. Fewer carious invasion both clinically and histopathologically were seen in homemade feeds. Thus, homemade diet can be a strong candidate for the status of 'THE IDEAL WEANING FOOD'.

The Multiple Realities of Curriculum Policy Making.

ERIC Educational Resources Information Center

Hopmann, Stefan

Concerning curriculum making, it is impossible to integrate the different meanings of "curriculum" into a single formula. Read as social constructions, different conceptions reflect varying educational, social-political, and historical contexts. This paper explores how these contexts, or multiple realities, evolved historically and how…

Chemistry Illustrated.

ERIC Educational Resources Information Center

Acquistapace, Victoria Lazio

1997-01-01

Describes an approach that challenges students to construct illustrations of chemical reactions by using colorful Bingo card paint markers. Enables them to visually demonstrate their understanding of chemical notations and the law of conservation of mass. Also discusses teaching chemical formulas, a modeling lab, illustrating chemical reactions,…

An assessment of alternatives to the Eichleay formula for unabsorbed overhead in delay claims : final report.

DOT National Transportation Integrated Search

1988-01-01

This report presents an assessment of the accuracy of alternatives available to calculate unabsorbed overhead in construction delay claims submitted by contractors. It reviews the alternatives available, concludes that the Eichleay method, used by ma...

Oxazine laser dyes

DOEpatents

Hammond, Peter R.; Field, George F.

1992-01-01

New oxazine compounds useful as dye laser media in solution, are superiior to prior art materials. The oxazine dyes useful when pumped by the 578.2 nm copper line to operate in the 700-800 nm range are described by formula I ##STR1##

The role of sand, marble chips and Typha latifolia in domestic wastewater treatment - a column study on constructed wetlands.

PubMed

Kadaverugu, Rakesh; Shingare, Rita P; Raghunathan, Karthik; Juwarkar, Asha A; Thawale, Prashant R; Singh, Sanjeev K

2016-10-01

The relative importance of sand, marble chips and wetland plant Typha latifolia is evaluated in constructed wetlands (CWs) for the treatment of domestic wastewater intended for reuse in agriculture. The prototype CWs for the experiments are realized in polyvinyl chloride columns, which are grouped into four treatments, viz. sand (<2 mm) + Typha latifolia (cattail), sand, marble chips (5-20 mm) + cattail and marble chips. The removal percentage of organic and nutritional pollutants from the wastewater is measured at varying hydraulic retention time in the columns. The statistical analysis suggests that the main effects of sand and cattail are found to be significant (p < .05) for the removal of biological oxygen demand and chemical oxygen demand from the wastewater. The presence of cattail significantly (p < .01) contributes to the conversion of total nitrogen in wastewater into [Formula: see text] by fostering the growth of favorable microbes for the nitrification. The removal of [Formula: see text] and turbidity from the wastewater is significantly (p < .01) influenced by sand than the presence of cattail. The maximum [Formula: see text] adsorption capacity of the sand is estimated to be 2.5 mg/g. Marble chips have significantly (p < .01) influenced the removal of [Formula: see text]and its maximum removal capacity is estimated to be 9.3 mg/g. The negative correlation between the filter media biofilm and column hydraulic conductivity is also reported for all the treatments. Thus, the findings of this study elucidate the role of low-cost and easily available filter media and it will guide the environmental practitioners in designing cost-effective CWs for wastewater treatment.

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs.

PubMed

Yoon, Nara; Vander Velde, Robert; Marusyk, Andriy; Scott, Jacob G

2018-05-07

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, [Formula: see text] and [Formula: see text], each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for [Formula: see text] and [Formula: see text], we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., [Formula: see text]-long for DrugA and [Formula: see text]-long for DrugB with [Formula: see text] and [Formula: see text]). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, [Formula: see text], and the effect of each drug. We determine a critical ratio, which we term [Formula: see text], at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, [Formula: see text] changes monotonically to [Formula: see text] and then, during the second stage, remains at [Formula: see text] thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.

Empirical mass formula with proton-neutron interaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tachibana, T.; Uno, M.; Yamada, S.

An atomic mass formula consisting of a gross part, and averge even-odd part and an empirical shell part is studied. The gross part is, apart from a small atomic term, taken to be the sum of nucleon rest masses. Coulomb energies and a polynomial in A/sup 1/3/ and chemically bondN-Zchemically bond/A. The shell part includes, in addition to proton and neutron support of nuclear magicities and the cooperative deformation effect. After the first construction of such a formula, refinements have been made in two respects. One is a separate treatment of Z = N odd-odd nuclei suggested by a quartetmore » model, and the other is an improvement of the proton neutron interaction term. By these refinements the root-mean-square deviation of calculated masses from the 1986 Audi-Wapstra masses has been reduced from 538 keV to 460 keV.« less

Cross-section and rate formulas for electron-impact ionization, excitation, deexcitation, and total depopulation of excited atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vriens, L.; Smeets, A.H.M.

1980-09-01

For electron-induced ionization, excitation, and de-excitation, mainly from excited atomic states, a detailed analysis is presented of the dependence of the cross sections and rate coefficients on electron energy and temperature, and on atomic parameters. A wide energy range is covered, including sudden as well as adiabatic collisions. By combining the available experimental and theoretical information, a set of simple analytical formulas is constructed for the cross sections and rate coefficients of the processes mentioned, for the total depopulation, and for three-body recombination. The formulas account for large deviations from classical and semiclassical scaling, as found for excitation. They agreemore » with experimental data and with the theories in their respective ranges of validity, but have a wider range of validity than the separate theories. The simple analytical form further facilitates the application in plasma modeling.« less

Nonlocal nonlinear Schrödinger equations and their soliton solutions

NASA Astrophysics Data System (ADS)

Gürses, Metin; Pekcan, Aslı

2018-05-01

We study standard and nonlocal nonlinear Schrödinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standard and nonlocal reductions, respectively. By using the Hirota bilinear method, we first find soliton solutions of the coupled NLS system of equations; then using the reduction formulas, we find the soliton solutions of the standard and nonlocal NLS equations. We give examples for particular values of the parameters and plot the function |q(t, x)|2 for the standard and nonlocal NLS equations.

Radiation-driven winds of hot stars. VI - Analytical solutions for wind models including the finite cone angle effect

NASA Technical Reports Server (NTRS)

Kudritzki, R. P.; Pauldrach, A.; Puls, J.; Abbott, D. C.

1989-01-01

Analytical solutions for radiation-driven winds of hot stars including the important finite cone angle effect (see Pauldrach et al., 1986; Friend and Abbott, 1986) are derived which approximate the detailed numerical solutions of the exact wind equation of motion very well. They allow a detailed discussion of the finite cone angle effect and provide for given line force parameters k, alpha, delta definite formulas for mass-loss rate M and terminal velocity v-alpha as function of stellar parameters.

Yangian of the Queer Lie Superalgebra

NASA Astrophysics Data System (ADS)

Nazarov, Maxim

Consider the complex matrix Lie superalgebra with the standard generators , where . Define an involutory automorphism η of by . The twisted polynomial current Lie superalgebra has a natural Lie co-superalgebra structure. We quantise the universal enveloping algebra as a co-Poisson Hopf superalgebra. For the quantised algebra we give a description of the centre, and construct the double in the sense of Drinfeld. We also construct a wide class of irreducible representations of the quantised algebra.

De Rham-Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space

NASA Astrophysics Data System (ADS)

Privault, Nicolas

2016-05-01

We construct differential forms of all orders and a covariant derivative together with its adjoint on the probability space of a standard Poisson process, using derivation operators. In this framewok we derive a de Rham-Hodge-Kodaira decomposition as well as Weitzenböck and Clark-Ocone formulas for random differential forms. As in the Wiener space setting, this construction provides two distinct approaches to the vanishing of harmonic differential forms.

General Linewidth Formula for Steady-State Multimode Lasing in Arbitrary Cavities

NASA Astrophysics Data System (ADS)

Chong, Y. D.; Stone, A. Douglas

2012-08-01

A formula for the laser linewidth of arbitrary cavities in the multimode nonlinear regime is derived from a scattering analysis of the solutions to semiclassical laser theory. The theory generalizes previous treatments of the effects of gain and openness described by the Petermann factor. The linewidth is expressed using quantities based on the nonlinear scattering matrix, which can be computed from steady-state ab initio laser theory; unlike previous treatments, no passive cavity or phenomenological parameters are involved. We find that low cavity quality factor, combined with significant dielectric dispersion, can cause substantial deviations from the Shawlow-Townes-Petermann theory.

Slip Boundary Conditions for the Compressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Baranger, Céline; Hattori, Masanari; Kosuge, Shingo; Martalò, Giorgio; Mathiaud, Julien; Mieussens, Luc

2017-11-01

The slip boundary conditions for the compressible Navier-Stokes equations are derived systematically from the Boltzmann equation on the basis of the Chapman-Enskog solution of the Boltzmann equation and the analysis of the Knudsen layer adjacent to the boundary. The resulting formulas of the slip boundary conditions are summarized with explicit values of the slip coefficients for hard-sphere molecules as well as the Bhatnagar-Gross-Krook model. These formulas, which can be applied to specific problems immediately, help to prevent the use of often used slip boundary conditions that are either incorrect or without theoretical basis.

Asymptotic (h tending to infinity) absolute stability for BDFs applied to stiff differential equations. [Backward Differentiation Formulas

NASA Technical Reports Server (NTRS)

Krogh, F. T.; Stewart, K.

1984-01-01

Methods based on backward differentiation formulas (BDFs) for solving stiff differential equations require iterating to approximate the solution of the corrector equation on each step. One hope for reducing the cost of this is to make do with iteration matrices that are known to have errors and to do no more iterations than are necessary to maintain the stability of the method. This paper, following work by Klopfenstein, examines the effect of errors in the iteration matrix on the stability of the method. Application of the results to an algorithm is discussed briefly.

Theory and Circuit Model for Lossy Coaxial Transmission Line

DOE Office of Scientific and Technical Information (OSTI.GOV)

Genoni, T. C.; Anderson, C. N.; Clark, R. E.

2017-04-01

The theory of signal propagation in lossy coaxial transmission lines is revisited and new approximate analytic formulas for the line impedance and attenuation are derived. The accuracy of these formulas from DC to 100 GHz is demonstrated by comparison to numerical solutions of the exact field equations. Based on this analysis, a new circuit model is described which accurately reproduces the line response over the entire frequency range. Circuit model calculations are in excellent agreement with the numerical and analytic results, and with finite-difference-time-domain simulations which resolve the skindepths of the conducting walls.

Quaternion-Based Conversion Formulas for Kinematic Attitude of Floating Offshore Wind Turbines (FOWT)

NASA Astrophysics Data System (ADS)

Li, Yugang; Fu, Gaoyong

2018-01-01

A floater allowing large-angle motion supporting a large payload (wind turbine and nacelle) with large aerodynamic loads high above the water surface is a great challenge because of the raised center of gravity and large overturning moment. In this paper, the conversion formulas between Euler angles and quaternions were derived, the research offered an efficient methodology without singularity to compute large-angle rigid body rotations of a FOWT, which laid the foundation for quaternion-based attitude kinematic model introduced to describe the dynamic response of the FOWT system and further solution.

Phylogenetics beyond biology.

PubMed

Retzlaff, Nancy; Stadler, Peter F

2018-06-21

Evolutionary processes have been described not only in biology but also for a wide range of human cultural activities including languages and law. In contrast to the evolution of DNA or protein sequences, the detailed mechanisms giving rise to the observed evolution-like processes are not or only partially known. The absence of a mechanistic model of evolution implies that it remains unknown how the distances between different taxa have to be quantified. Considering distortions of metric distances, we first show that poor choices of the distance measure can lead to incorrect phylogenetic trees. Based on the well-known fact that phylogenetic inference requires additive metrics, we then show that the correct phylogeny can be computed from a distance matrix [Formula: see text] if there is a monotonic, subadditive function [Formula: see text] such that [Formula: see text] is additive. The required metric-preserving transformation [Formula: see text] can be computed as the solution of an optimization problem. This result shows that the problem of phylogeny reconstruction is well defined even if a detailed mechanistic model of the evolutionary process remains elusive.

Feynman formulas for semigroups generated by an iterated Laplace operator

NASA Astrophysics Data System (ADS)

Buzinov, M. S.

2017-04-01

In the present paper, we find representations of a one-parameter semigroup generated by a finite sum of iterated Laplace operators and an additive perturbation (the potential). Such semigroups and the evolution equations corresponding to them find applications in the field of physics, chemistry, biology, and pattern recognition. The representations mentioned above are obtained in the form of Feynman formulas, i.e., in the form of a limit of multiple integrals as the multiplicity tends to infinity. The term "Feynman formula" was proposed by Smolyanov. Smolyanov's approach uses Chernoff's theorems. A simple form of representations thus obtained enables one to use them for numerical modeling the dynamics of the evolution system as a method for the approximation of solutions of equations. The problems considered in this note can be treated using the approach suggested by Remizov (see also the monograph of Smolyanov and Shavgulidze on path integrals). The representations (of semigroups) obtained in this way are more complicated than those given by the Feynman formulas; however, it is possible to bypass some analytical difficulties.

Determination of the expansion of the potential of the earth's normal gravitational field

NASA Astrophysics Data System (ADS)

Kochiev, A. A.

The potential of the generalized problem of 2N fixed centers is expanded in a polynomial and Legendre function series. Formulas are derived for the expansion coefficients, and the disturbing function of the problem is constructed in an explicit form.

Delving Deeper: Transforming Shapes Physically and Analytically

ERIC Educational Resources Information Center

Rathouz, Margaret; Novak, Christopher; Clifford, John

2013-01-01

Constructing formulas "from scratch" for calculating geometric measurements of shapes--for example, the area of a triangle--involves reasoning deductively and drawing connections between different methods (Usnick, Lamphere, and Bright 1992). Visual and manipulative models also play a role in helping students understand the underlying…

An Improved Method for Real-Time 3D Construction of DTM

NASA Astrophysics Data System (ADS)

Wei, Yi

This paper discusses the real-time optimal construction of DTM by two measures. One is to improve coordinate transformation of discrete points acquired from lidar, after processing a total number of 10000 data points, the formula calculation for transformation costs 0.810s, while the table look-up method for transformation costs 0.188s, indicating that the latter is superior to the former. The other one is to adjust the density of the point cloud acquired from lidar, the certain amount of the data points are used for 3D construction in proper proportion in order to meet different needs for 3D imaging, and ultimately increase efficiency of DTM construction while saving system resources.

A low-cost tracked C-arm (TC-arm) upgrade system for versatile quantitative intraoperative imaging.

PubMed

Amiri, Shahram; Wilson, David R; Masri, Bassam A; Anglin, Carolyn

2014-07-01

C-arm fluoroscopy is frequently used in clinical applications as a low-cost and mobile real-time qualitative assessment tool. C-arms, however, are not widely accepted for applications involving quantitative assessments, mainly due to the lack of reliable and low-cost position tracking methods, as well as adequate calibration and registration techniques. The solution suggested in this work is a tracked C-arm (TC-arm) which employs a low-cost sensor tracking module that can be retrofitted to any conventional C-arm for tracking the individual joints of the device. Registration and offline calibration methods were developed that allow accurate tracking of the gantry and determination of the exact intrinsic and extrinsic parameters of the imaging system for any acquired fluoroscopic image. The performance of the system was evaluated in comparison to an Optotrak[Formula: see text] motion tracking system and by a series of experiments on accurately built ball-bearing phantoms. Accuracies of the system were determined for 2D-3D registration, three-dimensional landmark localization, and for generating panoramic stitched views in simulated intraoperative applications. The system was able to track the center point of the gantry with an accuracy of [Formula: see text] mm or better. Accuracies of 2D-3D registrations were [Formula: see text] mm and [Formula: see text]. Three-dimensional landmark localization had an accuracy of [Formula: see text] of the length (or [Formula: see text] mm) on average, depending on whether the landmarks were located along, above, or across the table. The overall accuracies of the two-dimensional measurements conducted on stitched panoramic images of the femur and lumbar spine were 2.5 [Formula: see text] 2.0 % [Formula: see text] and [Formula: see text], respectively. The TC-arm system has the potential to achieve sophisticated quantitative fluoroscopy assessment capabilities using an existing C-arm imaging system. This technology may be useful to improve the quality of orthopedic surgery and interventional radiology.

27 CFR 21.40 - Formula No. 12-A.

Code of Federal Regulations, 2010 CFR

2010-04-01

... chemicals. 359.Processing miscellaneous products. 430.Sterilizing and preserving solutions. (2) As a raw... chemicals (including alkaloids). 345.Processing blood and blood products. 351.Processing dyes and... medicinal chemicals. 579.Other chemicals. (3) Miscellaneous uses: 812.Product development and pilot plant...

27 CFR 21.40 - Formula No. 12-A.

Code of Federal Regulations, 2011 CFR

2011-04-01

... chemicals. 359.Processing miscellaneous products. 430.Sterilizing and preserving solutions. (2) As a raw... chemicals (including alkaloids). 345.Processing blood and blood products. 351.Processing dyes and... medicinal chemicals. 579.Other chemicals. (3) Miscellaneous uses: 812.Product development and pilot plant...

27 CFR 21.51 - Formula No. 25-A.

Code of Federal Regulations, 2010 CFR

2010-04-01

... solution composed of 20 pounds of iodine, U.S.P.; 15 pounds of either potassium iodide, U.S.P., or sodium iodide, U.S.P.; and 15 pounds of water. (b) Authorized uses. (1) As a solvent: 230.Tinctures of iodine...

A CMOS Front-End With Integrated Magnetoresistive Sensors for Biomolecular Recognition Detection Applications.

PubMed

Costa, Tiago; Cardoso, Filipe A; Germano, Jose; Freitas, Paulo P; Piedade, Moises S

2017-10-01

The development of giant magnetoresistive (GMR) sensors has demonstrated significant advantages in nanomedicine, particularly for ultrasensitive point-of-care diagnostics. To this end, the detection system is required to be compact, portable, and low power consuming at the same time that a maximum signal to noise ratio is maintained. This paper reports a CMOS front-end with integrated magnetoresistive sensors for biomolecular recognition detection applications. Based on the characterization of the GMR sensor's signal and noise, CMOS building blocks (i.e., current source, multiplexers, and preamplifier) were designed targeting a negligible noise when compared with the GMR sensor's noise and a low power consumption. The CMOS front-end was fabricated using AMS [Formula: see text] technology and the magnetoresistive sensors were post-fabricated on top of the CMOS chip with high yield ( [Formula: see text]). Due to its low circuit noise (16 [Formula: see text]) and overall equivalent magnetic noise ([Formula: see text]), the full system was able to detect 250 nm magnetic nanoparticles with a circuit imposed signal-to-noise ratio degradation of only -1.4 dB. Furthermore, the low power consumption (6.5 mW) and small dimensions ([Formula: see text] ) of the presented solution guarantees the portability of the detection system allowing its usage at the point-of-care.

[Correlation of HPLC Characteristic Spectra of Vinegar Corydalis Rhizoma Decoction Pieces, Water Decoction and Formula Granules].

PubMed

Wei, Mei; Du, Lan-zhe; Li, Hui; Zhang, Guang-da; Chen, Xiang-dong

2015-05-01

To study the correlation of characteristic spectra of Vinegar Corydalis Rhizoma decoction pieces, water decoction and formula granules by HPLC, and to investigate the transfer of the main chemical constituents between three different forms. The analysis was carried out by a Phenomenex Gemini C18 column (250 mm x 4.6 mm,5 μm) with acetonitrile-1% acetic acid and ammonium acetate buffer solution (pH 6.0) as the mobile phase in a gradient elution mode. The detection wavelength was 280 nm with a flow rate of 0.8 mL /min. The column temperature was 30 degrees C. The characteristic spectra from 11 batches of Vinegar Corydalis Rhizoma decoction pieces, 11 batches of water decoction and 11 batches of formula granules were established respectively. Ten peaks in the HPLC characteristic spectra from 11 batches of formula granules could be tracked in the water decoction, nine peaks in the HPLC characteristic spectra could be tracked in the decoction pieces. In the ten common peaks, four components such as protopine, palnatine chloride, berberine hydrochloride and tetrahydropalmatine were verified. The main chemical components of Vinegar Corydalis Rhizoma decoction pieces, water decoction and formula granules are basically the same, the common component contents have similar proportion.

The Darboux transformation of the derivative nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Xu, Shuwei; He, Jingsong; Wang, Lihong

2011-07-01

The n-fold Darboux transformation (DT) is a 2 × 2 matrix for the Kaup-Newell (KN) system. In this paper, each element of this matrix is expressed by a ratio of the (n + 1) × (n + 1) determinant and n × n determinant of eigenfunctions. Using these formulae, the expressions of the q[n] and r[n] in the KN system are generated by the n-fold DT. Further, under the reduction condition, the rogue wave, rational traveling solution, dark soliton, bright soliton, breather solution and periodic solution of the derivative nonlinear Schrödinger equation are given explicitly by different seed solutions. In particular, the rogue wave and rational traveling solution are two kinds of new solutions. The complete classification of these solutions generated by one-fold DT is given.

Wheeled Pro(p)file of Batalin-Vilkovisky Formalism

NASA Astrophysics Data System (ADS)

Merkulov, S. A.

2010-05-01

Using a technique of wheeled props we establish a correspondence between the homotopy theory of unimodular Lie 1-bialgebras and the famous Batalin-Vilkovisky formalism. Solutions of the so-called quantum master equation satisfying certain boundary conditions are proven to be in 1-1 correspondence with representations of a wheeled dg prop which, on the one hand, is isomorphic to the cobar construction of the prop of unimodular Lie 1-bialgebras and, on the other hand, is quasi-isomorphic to the dg wheeled prop of unimodular Poisson structures. These results allow us to apply properadic methods for computing formulae for a homotopy transfer of a unimodular Lie 1-bialgebra structure on an arbitrary complex to the associated quantum master function on its cohomology. It is proven that in the category of quantum BV manifolds associated with the homotopy theory of unimodular Lie 1-bialgebras quasi-isomorphisms are equivalence relations. It is shown that Losev-Mnev’s BF theory for unimodular Lie algebras can be naturally extended to the case of unimodular Lie 1-bialgebras (and, eventually, to the case of unimodular Poisson structures). Using a finite-dimensional version of the Batalin-Vilkovisky quantization formalism it is rigorously proven that the Feynman integrals computing the effective action of this new BF theory describe precisely homotopy transfer formulae obtained within the wheeled properadic approach to the quantum master equation. Quantum corrections (which are present in our BF model to all orders of the Planck constant) correspond precisely to what are often called “higher Massey products” in the homological algebra.

Geochemical studies of clay minerals III. The determination of free silica and free alumina in montmorillonites

USGS Publications Warehouse

Foster, M.D.

1953-01-01

Determination of free silica by the method proposed made possible the derivation of logical formulas for several specimens of montmorillonites for which the formulas could not be derived from the analyses alone. Other montmorillonites, for which logical formulas could be derived from their analyses, were found to contain small amounts of free silica or free alumina. Others were found to contain neither free silica nor free alumina. The method consists of the following steps: (1) digestion of 1 g of the specimen with 0.5 N NaOH solution in a covered platinum crucible or dish on a steam bath for 4 hrs, stirring the mixture at 30-min intervals, (2) filtration of the undissolved material, followed by washing several times with 1% NaOH solution, (3) neutralization of the filtrate with HCl, addition of 5 ml HCl in excess and determination of SiO and Al2O3 in the usual way and (4) calculation of the amount of free SiO2 or free Al2O3 if any and the amount of attack of the clay structure by the treatment from the ratio of SiO2 to Al2O3 dissolved and the ratio of SiO2 to Al2O3 obtained on analysis. Tests with 5% Na2CO3 solution, the reagent formerly used for the solution of free SiO2 in rocks and minerals, showed that solution of opal by this reagent is always fractional, never complete, no matter how small the amount present or how long the period of treatment. Re-treatment of the sample results in 90-95% solution if 10 mg or less of opal is present, but for larger amounts of opal the percentage dissolved decreases as the amount present increases. On the other hand, 75 ml of 0.5 N NaOH completely dissolves as much as 400 mg of opal in 4 hrs digestion in a covered platinum crucible or dish, on a steam bath. However, a weaker solution or a shorter period of digestion does not effect complete solution. The same amount (75 ml) of 0.5 N NaOH also dissolves 90 mg of cristobalite and 57 mg of quartz having a grain size of less than 2 microns. Use of NaOH also permits determination of the amount of alumina dissolved, and estimation of the extent to which the clay structure was attacked by the treatment. ?? 1953.

Representation of solution for fully nonlocal diffusion equations with deviation time variable

NASA Astrophysics Data System (ADS)

Drin, I. I.; Drin, S. S.; Drin, Ya. M.

2018-01-01

We prove the solvability of the Cauchy problem for a nonlocal heat equation which is of fractional order both in space and time. The representation formula for classical solutions for time- and space- fractional partial differential operator Dat + a2 (-Δ) γ/2 (0 <= α <= 1, γ ɛ (0, 2]) and deviation time variable is given in terms of the Fox H-function, using the step by step method.

An approximate analysis of the diffusing flow in a self-controlled heat pipe.

NASA Technical Reports Server (NTRS)

Somogyi, D.; Yen, H. H.

1973-01-01

Constant-density two-dimensional axisymmetric equations are presented for the diffusing flow of a class of self-controlled heat pipes. The analysis is restricted to the vapor space. Condensation of the vapor is related to its mass fraction at the wall by the gas kinetic formula. The Karman-Pohlhausen integral method is applied to obtain approximate solutions. Solutions are presented for a water heat pipe with neon control gas.

Improved multidimensional semiclassical tunneling theory.

PubMed

Wagner, Albert F

2013-12-12

We show that the analytic multidimensional semiclassical tunneling formula of Miller et al. [Miller, W. H.; Hernandez, R.; Handy, N. C.; Jayatilaka, D.; Willets, A. Chem. Phys. Lett. 1990, 172, 62] is qualitatively incorrect for deep tunneling at energies well below the top of the barrier. The origin of this deficiency is that the formula uses an effective barrier weakly related to the true energetics but correctly adjusted to reproduce the harmonic description and anharmonic corrections of the reaction path at the saddle point as determined by second order vibrational perturbation theory. We present an analytic improved semiclassical formula that correctly includes energetic information and allows a qualitatively correct representation of deep tunneling. This is done by constructing a three segment composite Eckart potential that is continuous everywhere in both value and derivative. This composite potential has an analytic barrier penetration integral from which the semiclassical action can be derived and then used to define the semiclassical tunneling probability. The middle segment of the composite potential by itself is superior to the original formula of Miller et al. because it incorporates the asymmetry of the reaction barrier produced by the known reaction exoergicity. Comparison of the semiclassical and exact quantum tunneling probability for the pure Eckart potential suggests a simple threshold multiplicative factor to the improved formula to account for quantum effects very near threshold not represented by semiclassical theory. The deep tunneling limitations of the original formula are echoed in semiclassical high-energy descriptions of bound vibrational states perpendicular to the reaction path at the saddle point. However, typically ab initio energetic information is not available to correct it. The Supporting Information contains a Fortran code, test input, and test output that implements the improved semiclassical tunneling formula.

a Global Registration Algorithm of the Single-Closed Ring Multi-Stations Point Cloud

NASA Astrophysics Data System (ADS)

Yang, R.; Pan, L.; Xiang, Z.; Zeng, H.

2018-04-01

Aimed at the global registration problem of the single-closed ring multi-stations point cloud, a formula in order to calculate the error of rotation matrix was constructed according to the definition of error. The global registration algorithm of multi-station point cloud was derived to minimize the error of rotation matrix. And fast-computing formulas of transformation matrix with whose implementation steps and simulation experiment scheme was given. Compared three different processing schemes of multi-station point cloud, the experimental results showed that the effectiveness of the new global registration method was verified, and it could effectively complete the global registration of point cloud.

Alternative profit rate shariah-compliant for islamic banking

NASA Astrophysics Data System (ADS)

Gazali, Nadhirah; Halim, Nurfadhlina Abdul; Ghazali, Puspa Liza

2017-09-01

Profit is the aims for Islamic banking and conventional banking. Determination of profit in Islamic banking in Malaysia depends on the profit rate, whereas profit rate is essentially from reference rate which is known as the base rate (BR). However, the determination of the components contained in the BR such as benchmark cost of funds and the statutory reserve requirement (SRR) is non-compliance with the Shariah because its directly proportional to the overnight policy rate (OPR). Therefore, an alternative formula for the profit rate are proposed which is known as the base profit rate (BPR). Construction of BPR formula is based on the principle that are more Shariah-compliant.

Non-steady peristaltic propulsion with exponential variable viscosity: a study of transport through the digestive system.

PubMed

Tripathi, Dharmendra; Pandey, S K; Siddiqui, Abdul; Bég, O Anwar

2014-01-01

A theoretical study is presented for transient peristaltic flow of an incompressible fluid with variable viscosity in a finite length cylindrical tube as a simulation of transport in physiological vessels and biomimetic peristaltic pumps. The current axisymmetric analysis is qualitatively similar to two-dimensional analysis but exhibits quantitative variations. The current analysis is motivated towards further elucidating the physiological migration of gastric suspensions (food bolus) in the human digestive system. It also applies to variable viscosity industrial fluid (waste) peristaltic pumping systems. First, an axisymmetric model is analysed in the limit of large wavelength ([Formula: see text]) and low Reynolds number ([Formula: see text]) for axial velocity, radial velocity, pressure, hydromechanical efficiency and stream function in terms of radial vibration of the wall ([Formula: see text]), amplitude of the wave ([Formula: see text]), averaged flow rate ([Formula: see text]) and variable viscosity ([Formula: see text]). Subsequently, the peristaltic flow of a fluid with an exponential viscosity model is examined, which is based on the analytical solutions for pressure, wall shear stress, hydromechanical efficiency and streamline patterns in the finite length tube. The results are found to correlate well with earlier studies using a constant viscosity formulation. This study reveals some important features in the flow characteristics including the observation that pressure as well as both number and size of lower trapped bolus increases. Furthermore, the study indicates that hydromechanical efficiency reduces with increasing magnitude of viscosity parameter.

Ambitwistor Strings in Four Dimensions

NASA Astrophysics Data System (ADS)

Geyer, Yvonne; Lipstein, Arthur E.; Mason, Lionel

2014-08-01

We develop ambitwistor string theories for four dimensions to obtain new formulas for tree-level gauge and gravity amplitudes with arbitrary amounts of supersymmetry. Ambitwistor space is the space of complex null geodesics in complexified Minkowski space, and in contrast to earlier ambitwistor strings, we use twistors rather than vectors to represent this space. Although superficially similar to the original twistor string theories of Witten, Berkovits, and Skinner, these theories differ in the assignment of world sheet spins of the fields, rely on both twistor and dual twistor representatives for the vertex operators, and use the ambitwistor procedure for calculating correlation functions. Our models are much more flexible, no longer requiring maximal supersymmetry, and the resulting formulas for amplitudes are simpler, having substantially reduced moduli. These are supported on the solutions to the scattering equations refined according to helicity and can be checked by comparison with corresponding formulas of Witten and of Cachazo and Skinner.

On a quadrature formula of Gori and Micchelli

NASA Astrophysics Data System (ADS)

Yang, Shijun

2005-04-01

Sparked by Bojanov (J. Comput. Appl. Math. 70 (1996) 349), we provide an alternate approach to quadrature formulas based on the zeros of the Chebyshev polynomial of the first kind for any weight function w introduced and studied in Gori and Micchelli (Math. Comp. 65 (1996) 1567), thereby improving on their observations. Upon expansion of the divided differences, we obtain explicit expressions for the corresponding Cotes coefficients in Gauss-Turan quadrature formulas for and I(fTn;w) for a Gori-Micchelli weight function. It is also interesting to mention what has been neglected for about 30 years by the literature is that, as a consequence of expansion of the divided differences in the special case when , the solution of the famous Turan's Problem 26 raised in 1980 was in fact implied by a result of Micchelli and Rivlin (IBM J. Res. Develop. 16 (1972) 372) in 1972. Some concluding comments are made in the final section.

Asymptotic solutions for flow in microchannels with ridged walls and arbitrary meniscus protrusion

NASA Astrophysics Data System (ADS)

Kirk, Toby

2017-11-01

Flow over structured surfaces exhibiting apparent slip, such as parallel ridges, have received much attention experimentally and numerically, but analytical and asymptotic solutions that account for the microstructure have so far been limited to unbounded geometries such as shear-driven flows. Analysis for channel flows has been limited to (close to) flat interfaces spanning the grooves between ridges, but in applications the interfaces (menisci) can highly protrude and have a significant impact on the apparent slip. In this presentation, we consider pressure-driven flow through a microchannel with longitudinal ridges patterning one or both walls. With no restriction on the meniscus protrusion, we develop explicit formulae for the slip length using a formal matched asymptotic expansion. Assuming the ratio of channel height to ridge period is large, the periodicity is confined to an inner layer close to the ridges, and the expansion is found to all algebraic orders. As a result, the error is exponentially small and, under a further ``diluteness'' assumption, the explicit formulae are compared to finite element solutions. They are found to have a very wide range of validity in channel height (even when the menisci can touch the opposing wall) and so are useful for practitioners.

The Planning, Implementation, and Movement of an Academic Library Collection.

ERIC Educational Resources Information Center

Kurkul, Donna Lee

1983-01-01

Discusses methodology, logistics, and time/cost study of planning, implementation, and relocation of 682,810 volume Smith College Library collection into its newly constructed and renovated facility. Call number sequence location, collection movement phasing and formulas for sequence distribution, and personnel requirements are noted. Elementary…

Quadrilaterals: Diagonals and Area

ERIC Educational Resources Information Center

McGraw, Rebecca

2017-01-01

The task shared in this article provides geometry students with opportunities to recall and use basic geometry vocabulary, extend their knowledge of area relationships, and create area formulas. It is characterized by reasoning and sense making (NCTM 2009) and the "Construct viable arguments and critique the reasoning of others"…

27 CFR 21.57 - Formula No. 30.

Code of Federal Regulations, 2013 CFR

2013-04-01

... than proprietary solvents or special industrial solvents). 051.Polishes. 052.Inks (not including meat..., fungicides, and other biocides. 430.Sterilizing and preserving solutions. 440.Industrial detergents and soaps... a raw material: 575.Drugs and medicinal chemicals. 576.Organo-silicone products. 579.Other chemicals...

27 CFR 21.57 - Formula No. 30.

Code of Federal Regulations, 2014 CFR

2014-04-01

... than proprietary solvents or special industrial solvents). 051.Polishes. 052.Inks (not including meat..., fungicides, and other biocides. 430.Sterilizing and preserving solutions. 440.Industrial detergents and soaps... a raw material: 575.Drugs and medicinal chemicals. 576.Organo-silicone products. 579.Other chemicals...

27 CFR 21.57 - Formula No. 30.

Code of Federal Regulations, 2011 CFR

2011-04-01

... than proprietary solvents or special industrial solvents). 051.Polishes. 052.Inks (not including meat..., fungicides, and other biocides. 430.Sterilizing and preserving solutions. 440.Industrial detergents and soaps... a raw material: 575.Drugs and medicinal chemicals. 576.Organo-silicone products. 579.Other chemicals...

27 CFR 21.57 - Formula No. 30.

Code of Federal Regulations, 2012 CFR

2012-04-01

... than proprietary solvents or special industrial solvents). 051.Polishes. 052.Inks (not including meat..., fungicides, and other biocides. 430.Sterilizing and preserving solutions. 440.Industrial detergents and soaps... a raw material: 575.Drugs and medicinal chemicals. 576.Organo-silicone products. 579.Other chemicals...

27 CFR 21.57 - Formula No. 30.

Code of Federal Regulations, 2010 CFR

2010-04-01

... than proprietary solvents or special industrial solvents). 051.Polishes. 052.Inks (not including meat..., fungicides, and other biocides. 430.Sterilizing and preserving solutions. 440.Industrial detergents and soaps... a raw material: 575.Drugs and medicinal chemicals. 576.Organo-silicone products. 579.Other chemicals...

Macro Learning on a Micro Scale. Link Biology and Chemistry.

ERIC Educational Resources Information Center

Falk, Peter M.

1990-01-01

Described are several laboratory investigations that may be used to introduce biochemistry. Topics covered include carbohydrates, lipids, proteins, and metabolism. Reactions, stock solution formulas, and procedures are listed. Emphasized are individualizing work, designing alternative investigations, solving problems, and drawing conclusions. (KR)

On proper linearization, construction and analysis of the Boyle-van't Hoff plots and correct calculation of the osmotically inactive volume.

PubMed

Katkov, Igor I

2011-06-01

The Boyle-van't Hoff (BVH) law of physics has been widely used in cryobiology for calculation of the key osmotic parameters of cells and optimization of cryo-protocols. The proper use of linearization of the Boyle-vant'Hoff relationship for the osmotically inactive volume (v(b)) has been discussed in a rigorous way in (Katkov, Cryobiology, 2008, 57:142-149). Nevertheless, scientists in the field have been continuing to use inappropriate methods of linearization (and curve fitting) of the BVH data, plotting the BVH line and calculation of v(b). Here, we discuss the sources of incorrect linearization of the BVH relationship using concrete examples of recent publications, analyze the properties of the correct BVH line (which is unique for a given v(b)), provide appropriate statistical formulas for calculation of v(b) from the experimental data, and propose simplistic instructions (standard operation procedure, SOP) for proper normalization of the data, appropriate linearization and construction of the BVH plots, and correct calculation of v(b). The possible sources of non-linear behavior or poor fit of the data to the proper BVH line such as active water and/or solute transports, which can result in large discrepancy between the hyperosmotic and hypoosmotic parts of the BVH plot, are also discussed. Copyright © 2011 Elsevier Inc. All rights reserved.

The PMHT: solutions for some of its problems

NASA Astrophysics Data System (ADS)

Wieneke, Monika; Koch, Wolfgang

2007-09-01

Tracking multiple targets in a cluttered environment is a challenging task. Probabilistic Multiple Hypothesis Tracking (PMHT) is an efficient approach for dealing with it. Essentially PMHT is based on the method of Expectation-Maximization for handling with association conflicts. Linearity in the number of targets and measurements is the main motivation for a further development and extension of this methodology. Unfortunately, compared with the Probabilistic Data Association Filter (PDAF), PMHT has not yet shown its superiority in terms of track-lost statistics. Furthermore, the problem of track extraction and deletion is apparently not yet satisfactorily solved within this framework. Four properties of PMHT are responsible for its problems in track maintenance: Non-Adaptivity, Hospitality, Narcissism and Local Maxima. 1, 2 In this work we present a solution for each of them and derive an improved PMHT by integrating the solutions into the PMHT formalism. The new PMHT is evaluated by Monte-Carlo simulations. A sequential Likelihood-Ratio (LR) test for track extraction has been developed and already integrated into the framework of traditional Bayesian Multiple Hypothesis Tracking. 3 As a multi-scan approach, also the PMHT methodology has the potential for track extraction. In this paper an analogous integration of a sequential LR test into the PMHT framework is proposed. We present an LR formula for track extraction and deletion using the PMHT update formulae. As PMHT provides all required ingredients for a sequential LR calculation, the LR is thus a by-product of the PMHT iteration process. Therefore the resulting update formula for the sequential LR test affords the development of Track-Before-Detect algorithms for PMHT. The approach is illustrated by a simple example.

Connections between Kac-Moody algebras and M-theory

NASA Astrophysics Data System (ADS)

Cook, Paul P.

2007-11-01

We investigate some of the motivations and consequences of the conjecture that the Kac-Moody algebra E11 is the symmetry algebra of M-theory, and we develop methods to aid the further investigation of this idea. The definitions required to work with abstract root systems of Lie algebras are given in review leading up to the definition of a Kac-Moody algebra. The motivations for the E11 conjecture are presented and the nonlinear realisation of gravity relevant to the conjecture is described. We give a beginner's guide to producing the algebras of E11, relevant to M-theory, and K27, relevant to the bosonic string theory, along with their l1 representations are constructed. Reference tables of low level roots are produced for both the adjoint and l1 representations of these algebras. In addition a particular group element, having a generic form for all G+++ algebras, is shown to encode all the half-BPS brane solutions of the maximally oxidised supergravities. Special analysis is given to the role of space-time signature in the context of this group element and subsequent to this analysis spacelike brane solutions are derived from the same solution generating group element. Finally the appearance of U-duality charge multiplets from E11 is reviewed. General formulae for finding the content of arbitrary brane charge multiplets are given and the content of the particle and string multiplets in dimensions 4,5,6,7 and 8 is shown to be contained in the l1 representation of E11.

Finite-g Strings

NASA Astrophysics Data System (ADS)

Vicedo, Benoit

2008-10-01

In view of one day proving the AdS/CFT correspondence, a deeper understanding of string theory on certain curved backgrounds such as AdS_5xS^5 is required. In this dissertation we make a step in this direction by focusing on RxS^3. It was discovered in recent years that string theory on AdS_5xS^5 admits a Lax formulation. However, the complete statement of integrability requires not only the existence of a Lax formulation, but also that the resulting integrals of motion are in pairwise involution. This idea is central to the first part of this thesis. Exploiting this integrability we apply algebro-geometric methods to string theory on RxS^3 and obtain the general finite-gap solution. The construction is based on an invariant algebraic curve previously found in the AdS_5xS^5 case. However, encoding the dynamics of the solution requires specification of additional marked points. By restricting the symplectic structure of the string to this algebro-geometric data we derive the action-angle variables of the system. We then perform a first-principle semiclassical quantisation of string theory on RxS^3 as a toy model for strings on AdS_5xS^5. The result is exactly what one expects from the dual gauge theory perspective, namely the underlying algebraic curve discretises in a natural way. We also derive a general formula for the fluctuation energies around the generic finite-gap solution. The ideas used can be generalised to AdS_5xS^5.

3D surface voxel tracing corrector for accurate bone segmentation.

PubMed

Guo, Haoyan; Song, Sicong; Wang, Jinke; Guo, Maozu; Cheng, Yuanzhi; Wang, Yadong; Tamura, Shinichi

2018-06-18

For extremely close bones, their boundaries are weak and diffused due to strong interaction between adjacent surfaces. These factors prevent the accurate segmentation of bone structure. To alleviate these difficulties, we propose an automatic method for accurate bone segmentation. The method is based on a consideration of the 3D surface normal direction, which is used to detect the bone boundary in 3D CT images. Our segmentation method is divided into three main stages. Firstly, we consider a surface tracing corrector combined with Gaussian standard deviation [Formula: see text] to improve the estimation of normal direction. Secondly, we determine an optimal value of [Formula: see text] for each surface point during this normal direction correction. Thirdly, we construct the 1D signal and refining the rough boundary along the corrected normal direction. The value of [Formula: see text] is used in the first directional derivative of the Gaussian to refine the location of the edge point along accurate normal direction. Because the normal direction is corrected and the value of [Formula: see text] is optimized, our method is robust to noise images and narrow joint space caused by joint degeneration. We applied our method to 15 wrists and 50 hip joints for evaluation. In the wrist segmentation, Dice overlap coefficient (DOC) of [Formula: see text]% was obtained by our method. In the hip segmentation, fivefold cross-validations were performed for two state-of-the-art methods. Forty hip joints were used for training in two state-of-the-art methods, 10 hip joints were used for testing and performing comparisons. The DOCs of [Formula: see text], [Formula: see text]%, and [Formula: see text]% were achieved by our method for the pelvis, the left femoral head and the right femoral head, respectively. Our method was shown to improve segmentation accuracy for several specific challenging cases. The results demonstrate that our approach achieved a superior accuracy over two state-of-the-art methods.

The reliability and validity of fatigue measures during short-duration maximal-intensity intermittent cycling.

PubMed

Glaister, Mark; Stone, Michael H; Stewart, Andrew M; Hughes, Michael; Moir, Gavin L

2004-08-01

The purpose of the present study was to assess the reliability and validity of fatigue measures, as derived from 4 separate formulae, during tests of repeat sprint ability. On separate days over a 3-week period, 2 groups of 7 recreationally active men completed 6 trials of 1 of 2 maximal (20 x 5 seconds) intermittent cycling tests with contrasting recovery periods (10 or 30 seconds). All trials were conducted on a friction-braked cycle ergometer, and fatigue scores were derived from measures of mean power output for each sprint. Apart from formula 1, which calculated fatigue from the percentage difference in mean power output between the first and last sprint, all remaining formulae produced fatigue scores that showed a reasonably good level of test-retest reliability in both intermittent test protocols (intraclass correlation range: 0.78-0.86; 95% likely range of true values: 0.54-0.97). Although between-protocol differences in the magnitude of the fatigue scores suggested good construct validity, within-protocol differences highlighted limitations with each formula. Overall, the results support the use of the percentage decrement score as the most valid and reliable measure of fatigue during brief maximal intermittent work.

A Variant of the Mukai Pairing via Deformation Quantization

NASA Astrophysics Data System (ADS)

Ramadoss, Ajay C.

2012-06-01

Let X be a smooth projective complex variety. The Hochschild homology HH•( X) of X is an important invariant of X, which is isomorphic to the Hodge cohomology of X via the Hochschild-Kostant-Rosenberg isomorphism. On HH•( X), one has the Mukai pairing constructed by Caldararu. An explicit formula for the Mukai pairing at the level of Hodge cohomology was proven by the author in an earlier work (following ideas of Markarian). This formula implies a similar explicit formula for a closely related variant of the Mukai pairing on HH•( X). The latter pairing on HH•( X) is intimately linked to the study of Fourier-Mukai transforms of complex projective varieties. We give a new method to prove a formula computing the aforementioned variant of Caldararu's Mukai pairing. Our method is based on some important results in the area of deformation quantization. In particular, we use part of the work of Kashiwara and Schapira on Deformation Quantization modules together with an algebraic index theorem of Bressler, Nest and Tsygan. Our new method explicitly shows that the "Noncommutative Riemann-Roch" implies the classical Riemann-Roch. Further, it is hoped that our method would be useful for generalization to settings involving certain singular varieties.

Travelling Fronts and Entire Solutionsof the Fisher-KPP Equation in N

NASA Astrophysics Data System (ADS)

Hamel, François; Nadirashvili, Nikolaï

This paper is devoted to time-global solutions of the Fisher-KPP equation in N: where f is a C2 concave function on [0,1] such that f(0)=f(1)=0 and f>0 on (0,1). It is well known that this equation admits a finite-dimensional manifold of planar travelling-fronts solutions. By considering the mixing of any density of travelling fronts, we prove the existence of an infinite-dimensional manifold of solutions. In particular, there are infinite-dimensional manifolds of (nonplanar) travelling fronts and radial solutions. Furthermore, up to an additional assumption, a given solution u can be represented in terms of such a mixing of travelling fronts.

The Fundamental Solution of the Linearized Navier Stokes Equations for Spinning Bodies in Three Spatial Dimensions Time Dependent Case

NASA Astrophysics Data System (ADS)

Thomann, Enrique A.; Guenther, Ronald B.

2006-02-01

Explicit formulae for the fundamental solution of the linearized time dependent Navier Stokes equations in three spatial dimensions are obtained. The linear equations considered in this paper include those used to model rigid bodies that are translating and rotating at a constant velocity. Estimates extending those obtained by Solonnikov in [23] for the fundamental solution of the time dependent Stokes equations, corresponding to zero translational and angular velocity, are established. Existence and uniqueness of solutions of these linearized problems is obtained for a class of functions that includes the classical Lebesgue spaces L p (R 3), 1 < p < ∞. Finally, the asymptotic behavior and semigroup properties of the fundamental solution are established.

Interval Predictor Models with a Formal Characterization of Uncertainty and Reliability

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Giesy, Daniel P.; Kenny, Sean P.

2014-01-01

This paper develops techniques for constructing empirical predictor models based on observations. By contrast to standard models, which yield a single predicted output at each value of the model's inputs, Interval Predictors Models (IPM) yield an interval into which the unobserved output is predicted to fall. The IPMs proposed prescribe the output as an interval valued function of the model's inputs, render a formal description of both the uncertainty in the model's parameters and of the spread in the predicted output. Uncertainty is prescribed as a hyper-rectangular set in the space of model's parameters. The propagation of this set through the empirical model yields a range of outputs of minimal spread containing all (or, depending on the formulation, most) of the observations. Optimization-based strategies for calculating IPMs and eliminating the effects of outliers are proposed. Outliers are identified by evaluating the extent by which they degrade the tightness of the prediction. This evaluation can be carried out while the IPM is calculated. When the data satisfies mild stochastic assumptions, and the optimization program used for calculating the IPM is convex (or, when its solution coincides with the solution to an auxiliary convex program), the model's reliability (that is, the probability that a future observation would be within the predicted range of outputs) can be bounded rigorously by a non-asymptotic formula.