On a class of integrals of Legendre polynomials with complicated arguments--with applications in electrostatics and biomolecular modeling.

PubMed

Yu, Yi-Kuo

2003-08-15

The exact analytical result for a class of integrals involving (associated) Legendre polynomials of complicated argument is presented. The method employed can in principle be generalized to integrals involving other special functions. This class of integrals also proves useful in the electrostatic problems in which dielectric spheres are involved, which is of importance in modeling the dynamics of biological macromolecules. In fact, with this solution, a more robust foundation is laid for the Generalized Born method in modeling the dynamics of biomolecules. c2003 Elsevier B.V. All rights reserved.

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

Fish biomarkers for environmental monitoring: An integrated model supporting enzyme activity and histopathological lesions

NASA Astrophysics Data System (ADS)

Neta, Raimunda Nonata Fortes Carvalho; Torres Junior, Audalio Rebelo

2014-10-01

We present a mathematical model describing the association between glutathione-S-transferase activity and brachial lesions in the catfish, Sciades herzbergii (Ariidae) from a polluted port. The catfish were sampled from a port known to be contaminated with heavy metals and organic compounds and from a natural reserve in São Marcos Bay, Brazil. Two biomarkers, hepatic glutathione S-transferase (GST) activity and histopathological lesions, in gills tissue were measured. The values for GST activity were modeled with the occurrence of branchial lesions by fitting a third order polynomial. Results from the mathematical model indicate that GST activity has a strong polynomial relationship with the occurrence of branchial lesions in both the wet and the dry seasons, but only at the polluted port site. The model developed in this study indicates that branchial and hepatic lesions are initiated when GST activity reaches 2.15 μmol min-1 mg protein-1. Beyond this limit, GST activity decreased to very low levels and irreversible histopathological lesions occurred. This mathematical model provides a realistic approach to analyze predictive biomarkers of environmental health status.

Extending Romanovski polynomials in quantum mechanics

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

Quesne, C.

2013-12-15

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties ofmore » second-order differential equations of Schrödinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.« less

A class of generalized Ginzburg-Landau equations with random switching

NASA Astrophysics Data System (ADS)

Wu, Zheng; Yin, George; Lei, Dongxia

2018-09-01

This paper focuses on a class of generalized Ginzburg-Landau equations with random switching. In our formulation, the nonlinear term is allowed to have higher polynomial growth rate than the usual cubic polynomials. The random switching is modeled by a continuous-time Markov chain with a finite state space. First, an explicit solution is obtained. Then properties such as stochastic-ultimate boundedness and permanence of the solution processes are investigated. Finally, two-time-scale models are examined leading to a reduction of complexity.

Equivalent Colorings with "Maple"

ERIC Educational Resources Information Center

Cecil, David R.; Wang, Rongdong

2005-01-01

Many counting problems can be modeled as "colorings" and solved by considering symmetries and Polya's cycle index polynomial. This paper presents a "Maple 7" program link http://users.tamuk.edu/kfdrc00/ that, given Polya's cycle index polynomial, determines all possible associated colorings and their partitioning into equivalence classes. These…

DIFFERENTIAL CROSS SECTION ANALYSIS IN KAON PHOTOPRODUCTION USING ASSOCIATED LEGENDRE POLYNOMIALS

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

P. T. P. HUTAURUK, D. G. IRELAND, G. ROSNER

2009-04-01

Angular distributions of differential cross sections from the latest CLAS data sets,6 for the reaction γ + p→K+ + Λ have been analyzed using associated Legendre polynomials. This analysis is based upon theoretical calculations in Ref. 1 where all sixteen observables in kaon photoproduction can be classified into four Legendre classes. Each observable can be described by an expansion of associated Legendre polynomial functions. One of the questions to be addressed is how many associated Legendre polynomials are required to describe the data. In this preliminary analysis, we used data models with different numbers of associated Legendre polynomials. We thenmore » compared these models by calculating posterior probabilities of the models. We found that the CLAS data set needs no more than four associated Legendre polynomials to describe the differential cross section data. In addition, we also show the extracted coefficients of the best model.« less

Interplanetary CubeSat for Technology Demonstration at Mars Artist Concept

NASA Image and Video Library

2015-06-12

NASA's two MarCO CubeSats will be flying past Mars in September 2016 just as NASA's next Mars lander, InSight, is descending through the Martian atmosphere and landing on the surface. MarCO, for Mars Cube One, will provide an experimental communications relay to inform Earth quickly about the landing. This illustration depicts a moment during the lander's descent when it is transmitting data in the UHF radio band, and the twin MarCO craft are receiving those transmissions while simultaneously relaying the data to Earth in a different radio band. Each of the MarCO twins carries two solar panels for power, and both UHF-band and X-band radio antennas. As a technology demonstration, MarCO could lead to other "bring-your-own-relay" mission designs and also to use of miniature spacecraft for a wide diversity of interplanetary missions. MarCO is the first interplanetary use of CubeSat technologies for small spacecraft. CubeSats are a class of spacecraft based on a standardized small size and modular use of off-the-shelf technologies to streamline development. Many have been made by university students, and dozens have been launched into Earth orbit using extra payload mass available on launches of larger spacecraft. The two briefcase-size MarCO CubeSats will ride along with InSight on an Atlas V launch vehicle lifting off in March 2016 from Vandenberg Air Force Base, California. MarCO is a technology demonstration aspect of the InSight mission and not needed for that mission's success. InSight, an acronym for Interior Exploration using Seismic Investigations, Geodesy and Heat Transport, will investigate the deep interior of Mars to advance understanding of how rocky planets, including Earth, formed and evolved. After launch, the MarCO twins and InSight will be navigated separately to Mars. Note: After thorough examination, NASA managers have decided to suspend the planned March 2016 launch of the Interior Exploration using Seismic Investigations Geodesy and Heat Transport (InSight) mission. The decision follows unsuccessful attempts to repair a leak in a section of the prime instrument in the science payload. http://photojournal.jpl.nasa.gov/catalog/PIA19388

Best uniform approximation to a class of rational functions

NASA Astrophysics Data System (ADS)

Zheng, Zhitong; Yong, Jun-Hai

2007-10-01

We explicitly determine the best uniform polynomial approximation to a class of rational functions of the form 1/(x-c)2+K(a,b,c,n)/(x-c) on [a,b] represented by their Chebyshev expansion, where a, b, and c are real numbers, n-1 denotes the degree of the best approximating polynomial, and K is a constant determined by a, b, c, and n. Our result is based on the explicit determination of a phase angle [eta] in the representation of the approximation error by a trigonometric function. Moreover, we formulate an ansatz which offers a heuristic strategies to determine the best approximating polynomial to a function represented by its Chebyshev expansion. Combined with the phase angle method, this ansatz can be used to find the best uniform approximation to some more functions.

Pluripotential theory and convex bodies

NASA Astrophysics Data System (ADS)

Bayraktar, T.; Bloom, T.; Levenberg, N.

2018-03-01

A seminal paper by Berman and Boucksom exploited ideas from complex geometry to analyze the asymptotics of spaces of holomorphic sections of tensor powers of certain line bundles L over compact, complex manifolds as the power grows. This yielded results on weighted polynomial spaces in weighted pluripotential theory in {C}^d. Here, motivated by a recent paper by the first author on random sparse polynomials, we work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body in ({R}^+)^d. These classes of polynomials need not occur as sections of tensor powers of a line bundle L over a compact, complex manifold. We follow the approach of Berman and Boucksom to obtain analogous results. Bibliography: 16 titles.

Random regression models using different functions to model milk flow in dairy cows.

PubMed

Laureano, M M M; Bignardi, A B; El Faro, L; Cardoso, V L; Tonhati, H; Albuquerque, L G

2014-09-12

We analyzed 75,555 test-day milk flow records from 2175 primiparous Holstein cows that calved between 1997 and 2005. Milk flow was obtained by dividing the mean milk yield (kg) of the 3 daily milking by the total milking time (min) and was expressed as kg/min. Milk flow was grouped into 43 weekly classes. The analyses were performed using a single-trait Random Regression Models that included direct additive genetic, permanent environmental, and residual random effects. In addition, the contemporary group and linear and quadratic effects of cow age at calving were included as fixed effects. Fourth-order orthogonal Legendre polynomial of days in milk was used to model the mean trend in milk flow. The additive genetic and permanent environmental covariance functions were estimated using random regression Legendre polynomials and B-spline functions of days in milk. The model using a third-order Legendre polynomial for additive genetic effects and a sixth-order polynomial for permanent environmental effects, which contained 7 residual classes, proved to be the most adequate to describe variations in milk flow, and was also the most parsimonious. The heritability in milk flow estimated by the most parsimonious model was of moderate to high magnitude.

Optimal control and Galois theory

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

Zelikin, M I; Kiselev, D D; Lokutsievskiy, L V

2013-11-30

An important role is played in the solution of a class of optimal control problems by a certain special polynomial of degree 2(n−1) with integer coefficients. The linear independence of a family of k roots of this polynomial over the field Q implies the existence of a solution of the original problem with optimal control in the form of an irrational winding of a k-dimensional Clifford torus, which is passed in finite time. In the paper, we prove that for n≤15 one can take an arbitrary positive integer not exceeding [n/2] for k. The apparatus developed in the paper is applied to the systems ofmore » Chebyshev-Hermite polynomials and generalized Chebyshev-Laguerre polynomials. It is proved that for such polynomials of degree 2m every subsystem of [(m+1)/2] roots with pairwise distinct squares is linearly independent over the field Q. Bibliography: 11 titles.« less

A recursive algorithm for Zernike polynomials

NASA Technical Reports Server (NTRS)

Davenport, J. W.

1982-01-01

The analysis of a function defined on a rotationally symmetric system, with either a circular or annular pupil is discussed. In order to numerically analyze such systems it is typical to expand the given function in terms of a class of orthogonal polynomials. Because of their particular properties, the Zernike polynomials are especially suited for numerical calculations. Developed is a recursive algorithm that can be used to generate the Zernike polynomials up to a given order. The algorithm is recursively defined over J where R(J,N) is the Zernike polynomial of degree N obtained by orthogonalizing the sequence R(J), R(J+2), ..., R(J+2N) over (epsilon, 1). The terms in the preceding row - the (J-1) row - up to the N+1 term is needed for generating the (J,N)th term. Thus, the algorith generates an upper left-triangular table. This algorithm was placed in the computer with the necessary support program also included.

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

On method of solving third-order ordinary differential equations directly using Bernstein polynomials

NASA Astrophysics Data System (ADS)

Khataybeh, S. N.; Hashim, I.

2018-04-01

In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials.

PubMed

Mota, L F M; Martins, P G M A; Littiere, T O; Abreu, L R A; Silva, M A; Bonafé, C M

2018-04-01

The objective was to estimate (co)variance functions using random regression models (RRM) with Legendre polynomials, B-spline function and multi-trait models aimed at evaluating genetic parameters of growth traits in meat-type quail. A database containing the complete pedigree information of 7000 meat-type quail was utilized. The models included the fixed effects of contemporary group and generation. Direct additive genetic and permanent environmental effects, considered as random, were modeled using B-spline functions considering quadratic and cubic polynomials for each individual segment, and Legendre polynomials for age. Residual variances were grouped in four age classes. Direct additive genetic and permanent environmental effects were modeled using 2 to 4 segments and were modeled by Legendre polynomial with orders of fit ranging from 2 to 4. The model with quadratic B-spline adjustment, using four segments for direct additive genetic and permanent environmental effects, was the most appropriate and parsimonious to describe the covariance structure of the data. The RRM using Legendre polynomials presented an underestimation of the residual variance. Lesser heritability estimates were observed for multi-trait models in comparison with RRM for the evaluated ages. In general, the genetic correlations between measures of BW from hatching to 35 days of age decreased as the range between the evaluated ages increased. Genetic trend for BW was positive and significant along the selection generations. The genetic response to selection for BW in the evaluated ages presented greater values for RRM compared with multi-trait models. In summary, RRM using B-spline functions with four residual variance classes and segments were the best fit for genetic evaluation of growth traits in meat-type quail. In conclusion, RRM should be considered in genetic evaluation of breeding programs.

Classifying quantum entanglement through topological links

NASA Astrophysics Data System (ADS)

Quinta, Gonçalo M.; André, Rui

2018-04-01

We propose an alternative classification scheme for quantum entanglement based on topological links. This is done by identifying a nonrigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the particle, and associating linked rings to entangled particles. This analogy naturally leads us to a classification of multipartite quantum entanglement based on all possible distinct links for a given number of rings. To determine all different possibilities, we develop a formalism that associates any link to a polynomial, with each polynomial thereby defining a distinct equivalence class. To demonstrate the use of this classification scheme, we choose qubit quantum states as our example of physical system. A possible procedure to obtain qubit states from the polynomials is also introduced, providing an example state for each link class. We apply the formalism for the quantum systems of three and four qubits and demonstrate the potential of these tools in a context of qubit networks.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models.

PubMed

Bignardi, A B; El Faro, L; Cardoso, V L; Machado, P F; Albuquerque, L G

2009-09-01

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Random regression models using Legendre orthogonal polynomials to evaluate the milk production of Alpine goats.

PubMed

Silva, F G; Torres, R A; Brito, L F; Euclydes, R F; Melo, A L P; Souza, N O; Ribeiro, J I; Rodrigues, M T

2013-12-11

The objective of this study was to identify the best random regression model using Legendre orthogonal polynomials to evaluate Alpine goats genetically and to estimate the parameters for test day milk yield. On the test day, we analyzed 20,710 records of milk yield of 667 goats from the Goat Sector of the Universidade Federal de Viçosa. The evaluated models had combinations of distinct fitting orders for polynomials (2-5), random genetic (1-7), and permanent environmental (1-7) fixed curves and a number of classes for residual variance (2, 4, 5, and 6). WOMBAT software was used for all genetic analyses. A random regression model using the best Legendre orthogonal polynomial for genetic evaluation of milk yield on the test day of Alpine goats considered a fixed curve of order 4, curve of genetic additive effects of order 2, curve of permanent environmental effects of order 7, and a minimum of 5 classes of residual variance because it was the most economical model among those that were equivalent to the complete model by the likelihood ratio test. Phenotypic variance and heritability were higher at the end of the lactation period, indicating that the length of lactation has more genetic components in relation to the production peak and persistence. It is very important that the evaluation utilizes the best combination of fixed, genetic additive and permanent environmental regressions, and number of classes of heterogeneous residual variance for genetic evaluation using random regression models, thereby enhancing the precision and accuracy of the estimates of parameters and prediction of genetic values.

Genetic parameters for test-day yield of milk, fat and protein in buffaloes estimated by random regression models.

PubMed

Aspilcueta-Borquis, Rúsbel R; Araujo Neto, Francisco R; Baldi, Fernando; Santos, Daniel J A; Albuquerque, Lucia G; Tonhati, Humberto

2012-08-01

The test-day yields of milk, fat and protein were analysed from 1433 first lactations of buffaloes of the Murrah breed, daughters of 113 sires from 12 herds in the state of São Paulo, Brazil, born between 1985 and 2007. For the test-day yields, 10 monthly classes of lactation days were considered. The contemporary groups were defined as the herd-year-month of the test day. Random additive genetic, permanent environmental and residual effects were included in the model. The fixed effects considered were the contemporary group, number of milkings (1 or 2 milkings), linear and quadratic effects of the covariable cow age at calving and the mean lactation curve of the population (modelled by third-order Legendre orthogonal polynomials). The random additive genetic and permanent environmental effects were estimated by means of regression on third- to sixth-order Legendre orthogonal polynomials. The residual variances were modelled with a homogenous structure and various heterogeneous classes. According to the likelihood-ratio test, the best model for milk and fat production was that with four residual variance classes, while a third-order Legendre polynomial was best for the additive genetic effect for milk and fat yield, a fourth-order polynomial was best for the permanent environmental effect for milk production and a fifth-order polynomial was best for fat production. For protein yield, the best model was that with three residual variance classes and third- and fourth-order Legendre polynomials were best for the additive genetic and permanent environmental effects, respectively. The heritability estimates for the characteristics analysed were moderate, varying from 0·16±0·05 to 0·29±0·05 for milk yield, 0·20±0·05 to 0·30±0·08 for fat yield and 0·18±0·06 to 0·27±0·08 for protein yield. The estimates of the genetic correlations between the tests varied from 0·18±0·120 to 0·99±0·002; from 0·44±0·080 to 0·99±0·004; and from 0·41±0·080 to 0·99±0·004, for milk, fat and protein production, respectively, indicating that whatever the selection criterion used, indirect genetic gains can be expected throughout the lactation curve.

Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials

NASA Astrophysics Data System (ADS)

Volkmer, Hans

2008-04-01

Sequences of polynomials, orthogonal with respect to signed measures, are associated with a class of differential equations including the Mathieu, Lame and Whittaker-Hill equation. It is shown that the zeros of pn form sequences which converge to the eigenvalues of the corresponding differential equations. Moreover, interlacing properties of the zeros of pn are found. Applications to the numerical treatment of eigenvalue problems are given.

Finding higher order Darboux polynomials for a family of rational first order ordinary differential equations

NASA Astrophysics Data System (ADS)

Avellar, J.; Claudino, A. L. G. C.; Duarte, L. G. S.; da Mota, L. A. C. P.

2015-10-01

For the Darbouxian methods we are studying here, in order to solve first order rational ordinary differential equations (1ODEs), the most costly (computationally) step is the finding of the needed Darboux polynomials. This can be so grave that it can render the whole approach unpractical. Hereby we introduce a simple heuristics to speed up this process for a class of 1ODEs.

Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

NASA Astrophysics Data System (ADS)

Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.

2017-03-01

Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.

Linear decomposition approach for a class of nonconvex programming problems.

PubMed

Shen, Peiping; Wang, Chunfeng

2017-01-01

This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

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

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

DOE PAGES

Jakeman, John D.; Narayan, Akil; Zhou, Tao

2017-06-22

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

A bispectral q-hypergeometric basis for a class of quantum integrable models

NASA Astrophysics Data System (ADS)

Baseilhac, Pascal; Martin, Xavier

2018-01-01

For the class of quantum integrable models generated from the q-Onsager algebra, a basis of bispectral multivariable q-orthogonal polynomials is exhibited. In the first part, it is shown that the multivariable Askey-Wilson polynomials with N variables and N + 3 parameters introduced by Gasper and Rahman [Dev. Math. 13, 209 (2005)] generate a family of infinite dimensional modules for the q-Onsager algebra, whose fundamental generators are realized in terms of the multivariable q-difference and difference operators proposed by Iliev [Trans. Am. Math. Soc. 363, 1577 (2011)]. Raising and lowering operators extending those of Sahi [SIGMA 3, 002 (2007)] are also constructed. In the second part, finite dimensional modules are constructed and studied for a certain class of parameters and if the N variables belong to a discrete support. In this case, the bispectral property finds a natural interpretation within the framework of tridiagonal pairs. In the third part, eigenfunctions of the q-Dolan-Grady hierarchy are considered in the polynomial basis. In particular, invariant subspaces are identified for certain conditions generalizing Nepomechie's relations. In the fourth part, the analysis is extended to the special case q = 1. This framework provides a q-hypergeometric formulation of quantum integrable models such as the open XXZ spin chain with generic integrable boundary conditions (q ≠ 1).

The symmetric = ω -semi-classical orthogonal polynomials of class one

NASA Astrophysics Data System (ADS)

Maroni, P.; Mejri, M.

2008-12-01

We give the system of Laguerre-Freud equations associated with the = ω -semi-classical functionals of class one, where = ω is the divided difference operator. This system is solved in the symmetric case. There are essentially two canonical cases. The corresponding integral representations are given.

Covariance functions for body weight from birth to maturity in Nellore cows.

PubMed

Boligon, A A; Mercadante, M E Z; Forni, S; Lôbo, R B; Albuquerque, L G

2010-03-01

The objective of this study was to estimate (co)variance functions using random regression models on Legendre polynomials for the analysis of repeated measures of BW from birth to adult age. A total of 82,064 records from 8,145 females were analyzed. Different models were compared. The models included additive direct and maternal effects, and animal and maternal permanent environmental effects as random terms. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of animal age (cubic regression) were considered as random covariables. Eight models with polynomials of third to sixth order were used to describe additive direct and maternal effects, and animal and maternal permanent environmental effects. Residual effects were modeled using 1 (i.e., assuming homogeneity of variances across all ages) or 5 age classes. The model with 5 classes was the best to describe the trajectory of residuals along the growth curve. The model including fourth- and sixth-order polynomials for additive direct and animal permanent environmental effects, respectively, and third-order polynomials for maternal genetic and maternal permanent environmental effects were the best. Estimates of (co)variance obtained with the multi-trait and random regression models were similar. Direct heritability estimates obtained with the random regression models followed a trend similar to that obtained with the multi-trait model. The largest estimates of maternal heritability were those of BW taken close to 240 d of age. In general, estimates of correlation between BW from birth to 8 yr of age decreased with increasing distance between ages.

Meixner Class of Non-commutative Generalized Stochastic Processes with Freely Independent Values II. The Generating Function

NASA Astrophysics Data System (ADS)

Bożejko, Marek; Lytvynov, Eugene

2011-03-01

Let T be an underlying space with a non-atomic measure σ on it. In [ Comm. Math. Phys. 292, 99-129 (2009)] the Meixner class of non-commutative generalized stochastic processes with freely independent values, {ω=(ω(t))_{tin T}} , was characterized through the continuity of the corresponding orthogonal polynomials. In this paper, we derive a generating function for these orthogonal polynomials. The first question we have to answer is: What should serve as a generating function for a system of polynomials of infinitely many non-commuting variables? We construct a class of operator-valued functions {Z=(Z(t))_{tin T}} such that Z( t) commutes with ω( s) for any {s,tin T}. Then a generating function can be understood as {G(Z,ω)=sum_{n=0}^infty int_{T^n}P^{(n)}(ω(t_1),dots,ω(t_n))Z(t_1)dots Z(t_n)} {σ(dt_1) dots σ(dt_n)} , where {P^{(n)}(ω(t_1),dots,ω(t_n))} is (the kernel of the) n th orthogonal polynomial. We derive an explicit form of G( Z, ω), which has a resolvent form and resembles the generating function in the classical case, albeit it involves integrals of non-commuting operators. We finally discuss a related problem of the action of the annihilation operators {partial_t,t in T} . In contrast to the classical case, we prove that the operators ∂ t related to the free Gaussian and Poisson processes have a property of globality. This result is genuinely infinite-dimensional, since in one dimension one loses the notion of globality.

Classes of exact Einstein Maxwell solutions

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Maharaj, S. D.

2007-12-01

We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

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.

Aula Verde: Art as Experience in Community-Based Environmental Education

ERIC Educational Resources Information Center

Abarca, Marco A.

2010-01-01

After winning a class-action lawsuit against unconstitutional prison conditions in Puerto Rico, Marco Abarca managed to direct part of the fine monies accumulated throughout years of litigation toward an investment that would improve the living conditions in one of the largest and poorest housing projects in Puerto Rico. With the participation of…

Computational complexity of ecological and evolutionary spatial dynamics

PubMed Central

Ibsen-Jensen, Rasmus; Chatterjee, Krishnendu; Nowak, Martin A.

2015-01-01

There are deep, yet largely unexplored, connections between computer science and biology. Both disciplines examine how information proliferates in time and space. Central results in computer science describe the complexity of algorithms that solve certain classes of problems. An algorithm is deemed efficient if it can solve a problem in polynomial time, which means the running time of the algorithm is a polynomial function of the length of the input. There are classes of harder problems for which the fastest possible algorithm requires exponential time. Another criterion is the space requirement of the algorithm. There is a crucial distinction between algorithms that can find a solution, verify a solution, or list several distinct solutions in given time and space. The complexity hierarchy that is generated in this way is the foundation of theoretical computer science. Precise complexity results can be notoriously difficult. The famous question whether polynomial time equals nondeterministic polynomial time (i.e., P = NP) is one of the hardest open problems in computer science and all of mathematics. Here, we consider simple processes of ecological and evolutionary spatial dynamics. The basic question is: What is the probability that a new invader (or a new mutant) will take over a resident population? We derive precise complexity results for a variety of scenarios. We therefore show that some fundamental questions in this area cannot be answered by simple equations (assuming that P is not equal to NP). PMID:26644569

Application of Vector Spherical Harmonics and Kernel Regression to the Computations of OMM Parameters

NASA Astrophysics Data System (ADS)

Marco, F. J.; Martínez, M. J.; López, J. A.

2015-04-01

The high quality of Hipparcos data in position, proper motion, and parallax has allowed for studies about stellar kinematics with the aim of achieving a better physical understanding of our galaxy, based on accurate calculus of the Ogorodnikov-Milne model (OMM) parameters. The use of discrete least squares is the most common adjustment method, but it may lead to errors mainly because of the inhomogeneous spatial distribution of the data. We present an example of the instability of this method using the case of a function given by a linear combination of Legendre polynomials. These polynomials are basic in the use of vector spherical harmonics, which have been used to compute the OMM parameters by several authors, such as Makarov & Murphy, Mignard & Klioner, and Vityazev & Tsvetkov. To overcome the former problem, we propose the use of a mixed method (see Marco et al.) that includes the extension of the functions of residuals to any point on the celestial sphere. The goal is to be able to work with continuous variables in the calculation of the coefficients of the vector spherical harmonic developments with stability and efficiency. We apply this mixed procedure to the study of the kinematics of the stars in our Galaxy, employing the Hipparcos velocity field data to obtain the OMM parameters. Previously, we tested the method by perturbing the Vectorial Spherical Harmonics model as well as the velocity vector field.

Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials

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

Olesov, A V

2014-10-31

New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles.

Enumerative Algebraic Geometry of Conics

DTIC Science & Technology

2008-10-01

polynomial defining the conic factors into a product of linear polynomials, then the conic is just the union of two lines. Such a conic is said to be...corresponds to the union of two varieties, so [H ] + [H ] will be the class representing the union of two hyperplanes. But the union of two...sets form a topology, the union S′ = S ∪ [(P5)5 × E] is also closed. Now one great fact about projective varieties is that if we have a projection

Supersymmetric Casimir energy and the anomaly polynomial

NASA Astrophysics Data System (ADS)

Bobev, Nikolay; Bullimore, Mathew; Kim, Hee-Cheol

2015-09-01

We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology S 1 × S D-1 is equal to an equivariant integral of the anomaly polynomial. The equivariant integration is defined with respect to the Cartan subalgebra of the global symmetry algebra that commutes with a given supercharge. We test our proposal extensively by computing the supersymmetric Casimir energy for large classes of superconformal field theories, with and without known Lagrangian descriptions, in two, four and six dimensions.

Homogenous polynomially parameter-dependent H∞ filter designs of discrete-time fuzzy systems.

PubMed

Zhang, Huaguang; Xie, Xiangpeng; Tong, Shaocheng

2011-10-01

This paper proposes a novel H(∞) filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H(∞) filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H(∞) performance of the filtering error system. Second, relaxed conditions for H(∞) performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H(∞) filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.

School Subtracts Math Texts to Add E-Lessons, Tests

ERIC Educational Resources Information Center

Trotter, Andrew

2007-01-01

This article discusses how math teachers at San Marcos High School turned to an online curriculum and in-class assessments to increase student achievement. Setting aside their 7-year-old textbooks, teachers filled the void largely with an online math curriculum, called Agile Mind, that comes equipped with an array of assessment tools. The idea was…

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle.

PubMed

Pereira, R J; Bignardi, A B; El Faro, L; Verneque, R S; Vercesi Filho, A E; Albuquerque, L G

2013-01-01

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

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

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

Maximal aggregation of polynomial dynamical systems

PubMed Central

Cardelli, Luca; Tschaikowski, Max

2017-01-01

Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory. PMID:28878023

Recognition of Arabic Sign Language Alphabet Using Polynomial Classifiers

NASA Astrophysics Data System (ADS)

Assaleh, Khaled; Al-Rousan, M.

2005-12-01

Building an accurate automatic sign language recognition system is of great importance in facilitating efficient communication with deaf people. In this paper, we propose the use of polynomial classifiers as a classification engine for the recognition of Arabic sign language (ArSL) alphabet. Polynomial classifiers have several advantages over other classifiers in that they do not require iterative training, and that they are highly computationally scalable with the number of classes. Based on polynomial classifiers, we have built an ArSL system and measured its performance using real ArSL data collected from deaf people. We show that the proposed system provides superior recognition results when compared with previously published results using ANFIS-based classification on the same dataset and feature extraction methodology. The comparison is shown in terms of the number of misclassified test patterns. The reduction in the rate of misclassified patterns was very significant. In particular, we have achieved a 36% reduction of misclassifications on the training data and 57% on the test data.

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

Sevast'yanov, E A; Sadekova, E Kh

The Bulgarian mathematicians Sendov, Popov, and Boyanov have well-known results on the asymptotic behaviour of the least deviations of 2{pi}-periodic functions in the classes H{sup {omega}} from trigonometric polynomials in the Hausdorff metric. However, the asymptotics they give are not adequate to detect a difference in, for example, the rate of approximation of functions f whose moduli of continuity {omega}(f;{delta}) differ by factors of the form (log(1/{delta})){sup {beta}}. Furthermore, a more detailed determination of the asymptotic behaviour by traditional methods becomes very difficult. This paper develops an approach based on using trigonometric snakes as approximating polynomials. The snakes of ordermore » n inscribed in the Minkowski {delta}-neighbourhood of the graph of the approximated function f provide, in a number of cases, the best approximation for f (for the appropriate choice of {delta}). The choice of {delta} depends on n and f and is based on constructing polynomial kernels adjusted to the Hausdorff metric and polynomials with special oscillatory properties. Bibliography: 19 titles.« less

Algebraic solutions of shape-invariant position-dependent effective mass systems

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

Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@seecs.edu.pk; Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk

2016-06-15

Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with position-dependent effective mass is discussed. We quantize the Hamiltonian of the pertaining system by using symmetric ordering of the operators concerning momentum and the spatially varying mass, initially proposed by von Roos and Lévy-Leblond. The algebraic method, used to obtain the solutions, is based on the concepts of supersymmetric quantum mechanics and shape invariance. In order to exemplify the general formalism a class ofmore » non-linear oscillators has been considered. This class includes the particular example of a one-dimensional oscillator with different position-dependent effective mass profiles. Explicit expressions for the eigenenergies and eigenfunctions in terms of generalized Hermite polynomials are presented. Moreover, properties of these modified Hermite polynomials, like existence of generating function and recurrence relations among the polynomials have also been studied. Furthermore, it has been shown that in the harmonic limit, all the results for the linear harmonic oscillator are recovered.« less

Using polynomials to simplify fixed pattern noise and photometric correction of logarithmic CMOS image sensors.

PubMed

Li, Jing; Mahmoodi, Alireza; Joseph, Dileepan

2015-10-16

An important class of complementary metal-oxide-semiconductor (CMOS) image sensors are those where pixel responses are monotonic nonlinear functions of light stimuli. This class includes various logarithmic architectures, which are easily capable of wide dynamic range imaging, at video rates, but which are vulnerable to image quality issues. To minimize fixed pattern noise (FPN) and maximize photometric accuracy, pixel responses must be calibrated and corrected due to mismatch and process variation during fabrication. Unlike literature approaches, which employ circuit-based models of varying complexity, this paper introduces a novel approach based on low-degree polynomials. Although each pixel may have a highly nonlinear response, an approximately-linear FPN calibration is possible by exploiting the monotonic nature of imaging. Moreover, FPN correction requires only arithmetic, and an optimal fixed-point implementation is readily derived, subject to a user-specified number of bits per pixel. Using a monotonic spline, involving cubic polynomials, photometric calibration is also possible without a circuit-based model, and fixed-point photometric correction requires only a look-up table. The approach is experimentally validated with a logarithmic CMOS image sensor and is compared to a leading approach from the literature. The novel approach proves effective and efficient.

Explicit bounds for the positive root of classes of polynomials with applications

NASA Astrophysics Data System (ADS)

Herzberger, Jürgen

2003-03-01

We consider a certain type of polynomial equations for which there exists--according to Descartes' rule of signs--only one simple positive root. These equations are occurring in Numerical Analysis when calculating or estimating the R-order or Q-order of convergence of certain iterative processes with an error-recursion of special form. On the other hand, these polynomial equations are very common as defining equations for the effective rate of return for certain cashflows like bonds or annuities in finance. The effective rate of interest i* for those cashflows is i*=q*-1, where q* is the unique positive root of such polynomial. We construct bounds for i* for a special problem concerning an ordinary simple annuity which is obtained by changing the conditions of such an annuity with given data applying the German rule (Preisangabeverordnung or short PAngV). Moreover, we consider a number of results for such polynomial roots in Numerical Analysis showing that by a simple variable transformation we can derive several formulas out of earlier results by applying this transformation. The same is possible in finance in order to generalize results to more complicated cashflows.

The leading term of the Plancherel-Rotach asymptotic formula for solutions of recurrence relations

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

Aptekarev, A I; Tulyakov, D N

Recurrence relations generating Padé and Hermite-Padé polynomials are considered. Their coefficients increase with the index of the relation, but after dividing by an appropriate power of the scaling function they tend to a finite limit. As a result, after scaling the polynomials 'stabilize' for large indices; this type of asymptotic behaviour is called Plancherel-Rotach asymptotics. An explicit expression for the leading term of the asymptotic formula, which is valid outside sets containing the zeros of the polynomials, is obtained for wide classes of three- and four-term relations. For three-term recurrence relations this result generalizes a theorem Van Assche obtained for recurrence relations withmore » 'regularly' growing coefficients. Bibliography: 19 titles.« less

Ricci polynomial gravity

NASA Astrophysics Data System (ADS)

Hao, Xin; Zhao, Liu

2017-12-01

We study a novel class of higher-curvature gravity models in n spacetime dimensions which we call Ricci polynomial gravity. The action consists purely of a polynomial in Ricci curvature of order N . In the absence of the second-order terms in the action, the models are ghost free around the Minkowski vacuum. By appropriately choosing the coupling coefficients in front of each term in the action, it is shown that the models can have multiple vacua with different effective cosmological constants, and can be made free of ghost and scalar degrees of freedom around at least one of the maximally symmetric vacua for any n >2 and any N ≥4 . We also discuss some of the physical implications of the existence of multiple vacua in the contexts of black hole physics and cosmology.

The Oral Histories of Six African American Males in Their Ecology of Advanced Placement Biology

ERIC Educational Resources Information Center

Halasa, Katrina Bassam

2012-01-01

The major purpose of this qualitative study was to examine the past in order to understand the complex phenomenon of students engaging in science (Newman, Ridenour, Newman, & DeMarco, 2003) specifically through the oral histories of six self-identified African American males enrolled in a high school Advanced Placement Biology class and the…

Parameterization of the shape of intracranial saccular aneurysms using Legendre polynomials.

PubMed

Banatwala, M; Farley, C; Feinberg, D; Humphrey, J D

2005-04-01

Our recent studies of the nonlinear mechanics of saccular aneurysms suggest that it is unlikely that these lesions enlarge or rupture via material (limit point) or dynamic (resonance) instabilities. Rather, there is a growing body of evidence from both vascular biology and biomechanical analyses that implicate mechanosensitive growth and remodeling processes. There is, therefore, a pressing need to quantify regional multiaxial wall stresses which, because of the membrane-like behavior of many aneurysms, necessitates better information on the applied loads and regional surface curvatures. Herein, we present and illustrate a method whereby regional curvatures can be estimated easily for sub-classes of human aneurysms based on clinically available data from magnetic resonance angiography (MRA). Whereas Legendre polynomials are used to illustrate this approach, different functions may prove useful for different sub-classes of lesions.

A class of reduced-order models in the theory of waves and stability.

PubMed

Chapman, C J; Sorokin, S V

2016-02-01

This paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental. The approximations have two defining characteristics: (i) they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the (frequency, wavenumber) plane and (ii) the approximate dispersion relations are polynomials that pass exactly through points on this grid. Thus, the method is interpolatory in nature, but the interpolation takes place in (frequency, wavenumber) space, rather than in physical space. Full details are presented for a non-trivial example, that of antisymmetric elastic waves in a layer. The method is related to partial fraction expansions and barycentric representations of functions. An asymptotic analysis is presented, involving Stirling's approximation to the psi function, and a logarithmic correction to the polynomial dispersion relation.

Grover Search and the No-Signaling Principle

NASA Astrophysics Data System (ADS)

Bao, Ning; Bouland, Adam; Jordan, Stephen P.

2016-09-01

Two of the key properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Here, we investigate the degree to which these two properties are connected. We examine four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox. We show that in these models, the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover's algorithm. Hence the no-signaling principle is equivalent to the inability to solve NP-hard problems efficiently by brute force within the classes of theories analyzed.

Killings, duality and characteristic polynomials

NASA Astrophysics Data System (ADS)

Álvarez, Enrique; Borlaf, Javier; León, José H.

1998-03-01

In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and T-duality invariant, relevant result that top forms are zero when there is an isometry without fixed points is easily proved. © 1998

The algorithmic details of polynomials application in the problems of heat and mass transfer control on the hypersonic aircraft permeable surfaces

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2018-03-01

The hypersonic aircraft permeable surfaces heat and mass transfer effective control mathematical modeling problems are considered. The analysis of the control (the blowing) constructive and gasdynamical restrictions is carried out for the porous and perforated surfaces. The functions classes allowing realize the controls taking into account the arising types of restrictions are suggested. Estimates of the computational complexity of the W. G. Horner scheme application in the case of using the C. Hermite interpolation polynomial are given.

Exploring the potential energy landscape over a large parameter-space

NASA Astrophysics Data System (ADS)

He, Yang-Hui; Mehta, Dhagash; Niemerg, Matthew; Rummel, Markus; Valeanu, Alexandru

2013-07-01

Solving large polynomial systems with coefficient parameters are ubiquitous and constitute an important class of problems. We demonstrate the computational power of two methods — a symbolic one called the Comprehensive Gröbner basis and a numerical one called coefficient-parameter polynomial continuation — applied to studying both potential energy landscapes and a variety of questions arising from geometry and phenomenology. Particular attention is paid to an example in flux compactification where important physical quantities such as the gravitino and moduli masses and the string coupling can be efficiently extracted.

Building dynamical models from data and prior knowledge: the case of the first period-doubling bifurcation.

PubMed

Aguirre, Luis Antonio; Furtado, Edgar Campos

2007-10-01

This paper reviews some aspects of nonlinear model building from data with (gray box) and without (black box) prior knowledge. The model class is very important because it determines two aspects of the final model, namely (i) the type of nonlinearity that can be accurately approximated and (ii) the type of prior knowledge that can be taken into account. Such features are usually in conflict when it comes to choosing the model class. The problem of model structure selection is also reviewed. It is argued that such a problem is philosophically different depending on the model class and it is suggested that the choice of model class should be performed based on the type of a priori available. A procedure is proposed to build polynomial models from data on a Poincaré section and prior knowledge about the first period-doubling bifurcation, for which the normal form is also polynomial. The final models approximate dynamical data in a least-squares sense and, by design, present the first period-doubling bifurcation at a specified value of parameters. The procedure is illustrated by means of simulated examples.

The exaptive excellence of spandrels as a term and prototype

PubMed Central

Gould, Stephen Jay

1997-01-01

In 1979, Lewontin and I borrowed the architectural term “spandrel” (using the pendentives of San Marco in Venice as an example) to designate the class of forms and spaces that arise as necessary byproducts of another decision in design, and not as adaptations for direct utility in themselves. This proposal has generated a large literature featuring two critiques: (i) the terminological claim that the spandrels of San Marco are not true spandrels at all and (ii) the conceptual claim that they are adaptations and not byproducts. The features of the San Marco pendentives that we explicitly defined as spandrel-properties—their necessary number (four) and shape (roughly triangular)—are inevitable architectural byproducts, whatever the structural attributes of the pendentives themselves. The term spandrel may be extended from its particular architectural use for two-dimensional byproducts to the generality of “spaces left over,” a definition that properly includes the San Marco pendentives. Evolutionary biology needs such an explicit term for features arising as byproducts, rather than adaptations, whatever their subsequent exaptive utility. The concept of biological spandrels—including the examples here given of masculinized genitalia in female hyenas, exaptive use of an umbilicus as a brooding chamber by snails, the shoulder hump of the giant Irish deer, and several key features of human mentality—anchors the critique of overreliance upon adaptive scenarios in evolutionary explanation. Causes of historical origin must always be separated from current utilities; their conflation has seriously hampered the evolutionary analysis of form in the history of life. PMID:11038582

33 CFR 110.74 - Marco Island, Marco River, Fla.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 33 Navigation and Navigable Waters 1 2012-07-01 2012-07-01 false Marco Island, Marco River, Fla. 110.74 Section 110.74 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY ANCHORAGES ANCHORAGE REGULATIONS Special Anchorage Areas § 110.74 Marco Island, Marco River, Fla. Beginning...

33 CFR 110.74 - Marco Island, Marco River, Fla.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 33 Navigation and Navigable Waters 1 2011-07-01 2011-07-01 false Marco Island, Marco River, Fla. 110.74 Section 110.74 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY ANCHORAGES ANCHORAGE REGULATIONS Special Anchorage Areas § 110.74 Marco Island, Marco River, Fla. Beginning...

33 CFR 110.74 - Marco Island, Marco River, Fla.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Marco Island, Marco River, Fla. 110.74 Section 110.74 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY ANCHORAGES ANCHORAGE REGULATIONS Special Anchorage Areas § 110.74 Marco Island, Marco River, Fla. Beginning...

33 CFR 110.74 - Marco Island, Marco River, Fla.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 33 Navigation and Navigable Waters 1 2013-07-01 2013-07-01 false Marco Island, Marco River, Fla. 110.74 Section 110.74 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY ANCHORAGES ANCHORAGE REGULATIONS Special Anchorage Areas § 110.74 Marco Island, Marco River, Fla. Beginning...

33 CFR 110.74 - Marco Island, Marco River, Fla.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 33 Navigation and Navigable Waters 1 2014-07-01 2014-07-01 false Marco Island, Marco River, Fla. 110.74 Section 110.74 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY ANCHORAGES ANCHORAGE REGULATIONS Special Anchorage Areas § 110.74 Marco Island, Marco River, Fla. Beginning...

On the derivatives of unimodular polynomials

NASA Astrophysics Data System (ADS)

Nevai, P.; Erdélyi, T.

2016-04-01

Let D be the open unit disk of the complex plane; its boundary, the unit circle of the complex plane, is denoted by \\partial D. Let \\mathscr P_n^c denote the set of all algebraic polynomials of degree at most n with complex coefficients. For λ ≥ 0, let {\\mathscr K}_n^λ \\stackrel{{def}}{=} \\biggl\\{P_n: P_n(z) = \\sumk=0^n{ak k^λ z^k}, ak \\in { C}, |a_k| = 1 \\biggr\\} \\subset {\\mathscr P}_n^c.The class \\mathscr K_n^0 is often called the collection of all (complex) unimodular polynomials of degree n. Given a sequence (\\varepsilon_n) of positive numbers tending to 0, we say that a sequence (P_n) of polynomials P_n\\in\\mathscr K_n^λ is \\{λ, (\\varepsilon_n)\\}-ultraflat if \\displaystyle (1-\\varepsilon_n)\\frac{nλ+1/2}{\\sqrt{2λ+1}}≤\\ve......a +1/2}}{\\sqrt{2λ +1}},\\qquad z \\in \\partial D,\\quad n\\in N_0.Although we do not know, in general, whether or not \\{λ, (\\varepsilon_n)\\}-ultraflat sequences of polynomials P_n\\in\\mathscr K_n^λ exist for each fixed λ>0, we make an effort to prove various interesting properties of them. These allow us to conclude that there are no sequences (P_n) of either conjugate, or plain, or skew reciprocal unimodular polynomials P_n\\in\\mathscr K_n^0 such that (Q_n) with Q_n(z)\\stackrel{{def}}{=} zP_n'(z)+1 is a \\{1,(\\varepsilon_n)\\}-ultraflat sequence of polynomials.Bibliography: 18 titles.

Gabor-based kernel PCA with fractional power polynomial models for face recognition.

PubMed

Liu, Chengjun

2004-05-01

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.

Limit cycles via higher order perturbations for some piecewise differential systems

NASA Astrophysics Data System (ADS)

Buzzi, Claudio A.; Lima, Maurício Firmino Silva; Torregrosa, Joan

2018-05-01

A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x‧ ,y‧) =(- y + εf(x , y , ε) , x + εg(x , y , ε)) . In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. We prove that, for polynomial perturbations of degree n , no more than Nn - 1 limit cycles appear up to a study of order N. We also show that this upper bound is reached for orders one and two. Moreover, we study this problem in some classes of piecewise Liénard differential systems providing better upper bounds for higher order perturbation in ε, showing also when they are reached. The Poincaré-Pontryagin-Melnikov theory is the main technique used to prove all the results.

Symbolic integration of a class of algebraic functions. [by an algorithmic approach

NASA Technical Reports Server (NTRS)

Ng, E. W.

1974-01-01

An algorithm is presented for the symbolic integration of a class of algebraic functions. This class consists of functions made up of rational expressions of an integration variable x and square roots of polynomials, trigonometric and hyperbolic functions of x. The algorithm is shown to consist of the following components:(1) the reduction of input integrands to conical form; (2) intermediate internal representations of integrals; (3) classification of outputs; and (4) reduction and simplification of outputs to well-known functions.

Immunomodulators targeting MARCO expression improve resistance to postinfluenza bacterial pneumonia.

PubMed

Wu, Muzo; Gibbons, John G; DeLoid, Glen M; Bedugnis, Alice S; Thimmulappa, Rajesh K; Biswal, Shyam; Kobzik, Lester

2017-07-01

Downregulation of the alveolar macrophage (AM) receptor with collagenous structure (MARCO) leads to susceptibility to postinfluenza bacterial pneumonia, a major cause of morbidity and mortality. We sought to determine whether immunomodulation of MARCO could improve host defense and resistance to secondary bacterial pneumonia. RNAseq analysis identified a striking increase in MARCO expression between days 9 and 11 after influenza infection and indicated important roles for Akt and Nrf2 in MARCO recovery. In vitro, primary human AM-like monocyte-derived macrophages (AM-MDMs) and THP-1 macrophages were treated with IFNγ to model influenza effects. Activators of Nrf2 (sulforaphane) or Akt (SC79) caused increased MARCO expression and a MARCO-dependent improvement in phagocytosis in IFNγ-treated cells and improved survival in mice with postinfluenza pneumococcal pneumonia. Transcription factor analysis also indicated a role for transcription factor E-box (TFEB) in MARCO recovery. Overexpression of TFEB in THP-1 cells led to marked increases in MARCO. The ability of Akt activation to increase MARCO expression in IFNγ-treated AM-MDMs was abrogated in TFEB-knockdown cells, indicating Akt increases MARCO expression through TFEB. Increasing MARCO expression by targeting Nrf2 signaling or the Akt-TFEB-MARCO pathway are promising strategies to improve bacterial clearance and survival in postinfluenza bacterial pneumonia. Copyright © 2017 the American Physiological Society.

Using Polynomials to Simplify Fixed Pattern Noise and Photometric Correction of Logarithmic CMOS Image Sensors

PubMed Central

Li, Jing; Mahmoodi, Alireza; Joseph, Dileepan

2015-01-01

An important class of complementary metal-oxide-semiconductor (CMOS) image sensors are those where pixel responses are monotonic nonlinear functions of light stimuli. This class includes various logarithmic architectures, which are easily capable of wide dynamic range imaging, at video rates, but which are vulnerable to image quality issues. To minimize fixed pattern noise (FPN) and maximize photometric accuracy, pixel responses must be calibrated and corrected due to mismatch and process variation during fabrication. Unlike literature approaches, which employ circuit-based models of varying complexity, this paper introduces a novel approach based on low-degree polynomials. Although each pixel may have a highly nonlinear response, an approximately-linear FPN calibration is possible by exploiting the monotonic nature of imaging. Moreover, FPN correction requires only arithmetic, and an optimal fixed-point implementation is readily derived, subject to a user-specified number of bits per pixel. Using a monotonic spline, involving cubic polynomials, photometric calibration is also possible without a circuit-based model, and fixed-point photometric correction requires only a look-up table. The approach is experimentally validated with a logarithmic CMOS image sensor and is compared to a leading approach from the literature. The novel approach proves effective and efficient. PMID:26501287

A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models

NASA Technical Reports Server (NTRS)

Giunta, Anthony A.; Watson, Layne T.

1998-01-01

Two methods of creating approximation models are compared through the calculation of the modeling accuracy on test problems involving one, five, and ten independent variables. Here, the test problems are representative of the modeling challenges typically encountered in realistic engineering optimization problems. The first approximation model is a quadratic polynomial created using the method of least squares. This type of polynomial model has seen considerable use in recent engineering optimization studies due to its computational simplicity and ease of use. However, quadratic polynomial models may be of limited accuracy when the response data to be modeled have multiple local extrema. The second approximation model employs an interpolation scheme known as kriging developed in the fields of spatial statistics and geostatistics. This class of interpolating model has the flexibility to model response data with multiple local extrema. However, this flexibility is obtained at an increase in computational expense and a decrease in ease of use. The intent of this study is to provide an initial exploration of the accuracy and modeling capabilities of these two approximation methods.

Beyond the Reference Desk: A Study on the Effectiveness of Low-Cost Distance Library Services at California State University San Marcos

ERIC Educational Resources Information Center

Olivas, Antonia P.; Chan, Ian

2013-01-01

Many of our reference interactions are face-to-face at a desk or in our offices. Unfortunately, not all of our students are on campus. Whether a non-traditional student or a traditional undergraduate, more of our patrons are attending online classes or attending satellite campuses with no librarians on site. It's difficult to reach these students,…

Control Synthesis of Discrete-Time T-S Fuzzy Systems via a Multi-Instant Homogenous Polynomial Approach.

PubMed

Xie, Xiangpeng; Yue, Dong; Zhang, Huaguang; Xue, Yusheng

2016-03-01

This paper deals with the problem of control synthesis of discrete-time Takagi-Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper.

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Polynomial-time solution of prime factorization and NP-complete problems with digital memcomputing machines

NASA Astrophysics Data System (ADS)

Traversa, Fabio L.; Di Ventra, Massimiliano

2017-02-01

We introduce a class of digital machines, we name Digital Memcomputing Machines, (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space, and energy). An abstract DMM with this power must satisfy a set of compatible mathematical constraints underlying its practical realization. We prove this by making a connection with the dynamical systems theory. This leads us to a set of physical constraints for poly-resource resolvability. Once the mathematical requirements have been assessed, we propose a practical scheme to solve the above class of problems based on the novel concept of self-organizing logic gates and circuits (SOLCs). These are logic gates and circuits able to accept input signals from any terminal, without distinction between conventional input and output terminals. They can solve boolean problems by self-organizing into their solution. They can be fabricated either with circuit elements with memory (such as memristors) and/or standard MOS technology. Using tools of functional analysis, we prove mathematically the following constraints for the poly-resource resolvability: (i) SOLCs possess a global attractor; (ii) their only equilibrium points are the solutions of the problems to solve; (iii) the system converges exponentially fast to the solutions; (iv) the equilibrium convergence rate scales at most polynomially with input size. We finally provide arguments that periodic orbits and strange attractors cannot coexist with equilibria. As examples, we show how to solve the prime factorization and the search version of the NP-complete subset-sum problem. Since DMMs map integers into integers, they are robust against noise and hence scalable. We finally discuss the implications of the DMM realization through SOLCs to the NP = P question related to constraints of poly-resources resolvability.

Supersymmetric quantum mechanics: Engineered hierarchies of integrable potentials and related orthogonal polynomials

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

Balondo Iyela, Daddy; Centre for Cosmology, Particle Physics and Phenomenology; Département de Physique, Université de Kinshasa

2013-09-15

Within the context of supersymmetric quantum mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy which should allow for its resolution. Specific classes of orthogonal polynomials characteristicmore » of such periodic hierarchies are thereby generated, while the methods of supersymmetric quantum mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper, these ideas are presented and solved explicitly for the cases N= 1 and N= 2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. In the context of dressing chains and deformed polynomial Heisenberg algebras, some partial results for N⩾ 3 also exist in the literature, which should be relevant to a complete study of the N⩾ 3 general periodic hierarchies.« less

Rogers-Schur-Ramanujan Type Identities for the M(p,p') Minimal Models of Conformal Field Theory

NASA Astrophysics Data System (ADS)

Berkovich, Alexander; McCoy, Barry M.; Schilling, Anne

We present and prove Rogers-Schur-Ramanujan (Bose/Fermi) type identities for the Virasoro characters of the minimal model M(p,p'). The proof uses the continued fraction decomposition of p'/p introduced by Takahashi and Suzuki for the study of the Bethe's Ansatz equations of the XXZ model and gives a general method to construct polynomial generalizations of the fermionic form of the characters which satisfy the same recursion relations as the bosonic polynomials of Forrester and Baxter. We use this method to get fermionic representations of the characters for many classes of r and s.

Sandia Higher Order Elements (SHOE) v 0.5 alpha

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

2013-09-24

SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likelymore » exist.« less

A new order-theoretic characterisation of the polytime computable functions☆

PubMed Central

Avanzini, Martin; Eguchi, Naohi; Moser, Georg

2015-01-01

We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the small polynomial path order (sPOP⁎ for short). This termination order entails a new syntactic method to analyse the innermost runtime complexity of term rewrite systems fully automatically: for any rewrite system compatible with sPOP⁎ that employs recursion up to depth d, the (innermost) runtime complexity is polynomially bounded of degree d. This bound is tight. Thus we obtain a direct correspondence between a syntactic (and easily verifiable) condition of a program and the asymptotic worst-case complexity of the program. PMID:26412933

Classical verification of quantum circuits containing few basis changes

NASA Astrophysics Data System (ADS)

Demarie, Tommaso F.; Ouyang, Yingkai; Fitzsimons, Joseph F.

2018-04-01

We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. This contains circuits giving rise to the second level of the Fourier hierarchy, the lowest level for which there is an established quantum advantage. We show that when the circuit has an outcome with probability at least the inverse of some polynomial in the circuit size, the outcome can be checked in polynomial time with bounded error by a completely classical verifier. This verification procedure is based on random sampling of computational paths and is only possible given knowledge of the likely outcome.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

76 FR 72369 - Safety Zone; Marco Island Marriott Charity Fireworks Display, Gulf of Mexico, Marco Island, FL

Federal Register 2010, 2011, 2012, 2013, 2014

2011-11-23

...-AA00 Safety Zone; Marco Island Marriott Charity Fireworks Display, Gulf of Mexico, Marco Island, FL... establish a temporary safety zone on the waters of the Gulf of Mexico in the vicinity of Marco Island... reached the Facility, please enclose a stamped, self-addressed postcard or envelope. We will consider all...

On the modular structure of the genus-one Type II superstring low energy expansion

NASA Astrophysics Data System (ADS)

D'Hoker, Eric; Green, Michael B.; Vanhove, Pierre

2015-08-01

The analytic contribution to the low energy expansion of Type II string amplitudes at genus-one is a power series in space-time derivatives with coefficients that are determined by integrals of modular functions over the complex structure modulus of the world-sheet torus. These modular functions are associated with world-sheet vacuum Feynman diagrams and given by multiple sums over the discrete momenta on the torus. In this paper we exhibit exact differential and algebraic relations for a certain infinite class of such modular functions by showing that they satisfy Laplace eigenvalue equations with inhomogeneous terms that are polynomial in non-holomorphic Eisenstein series. Furthermore, we argue that the set of modular functions that contribute to the coefficients of interactions up to order are linear sums of functions in this class and quadratic polynomials in Eisenstein series and odd Riemann zeta values. Integration over the complex structure results in coefficients of the low energy expansion that are rational numbers multiplying monomials in odd Riemann zeta values.

Qualitative-Modeling-Based Silicon Neurons and Their Networks

PubMed Central

Kohno, Takashi; Sekikawa, Munehisa; Li, Jing; Nanami, Takuya; Aihara, Kazuyuki

2016-01-01

The ionic conductance models of neuronal cells can finely reproduce a wide variety of complex neuronal activities. However, the complexity of these models has prompted the development of qualitative neuron models. They are described by differential equations with a reduced number of variables and their low-dimensional polynomials, which retain the core mathematical structures. Such simple models form the foundation of a bottom-up approach in computational and theoretical neuroscience. We proposed a qualitative-modeling-based approach for designing silicon neuron circuits, in which the mathematical structures in the polynomial-based qualitative models are reproduced by differential equations with silicon-native expressions. This approach can realize low-power-consuming circuits that can be configured to realize various classes of neuronal cells. In this article, our qualitative-modeling-based silicon neuron circuits for analog and digital implementations are quickly reviewed. One of our CMOS analog silicon neuron circuits can realize a variety of neuronal activities with a power consumption less than 72 nW. The square-wave bursting mode of this circuit is explained. Another circuit can realize Class I and II neuronal activities with about 3 nW. Our digital silicon neuron circuit can also realize these classes. An auto-associative memory realized on an all-to-all connected network of these silicon neurons is also reviewed, in which the neuron class plays important roles in its performance. PMID:27378842

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

NASA Technical Reports Server (NTRS)

Coutsias, Evangelos A.; Torres, David; Hagstrom, Thomas

1994-01-01

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Analogue of the Kelley condition for optimal systems with retarded control

NASA Astrophysics Data System (ADS)

Mardanov, Misir J.; Melikov, Telman K.

2017-07-01

In this paper, we consider an optimal control problem with retarded control and study a larger class of singular (in the classical sense) controls. The Kelley and equality type optimality conditions are obtained. To prove our main results, we use the Legendre polynomials as variations of control.

Analysis of spectral operators in one-dimensional domains

NASA Technical Reports Server (NTRS)

Maday, Y.

1985-01-01

Results are proven concerning certain projection operators on the space of all polynomials of degree less than or equal to N with respect to a class of one-dimensional weighted Sobolev spaces. The results are useful in the theory of the approximation of partial differential equations with spectral methods.

Graph characterization via Ihara coefficients.

PubMed

Ren, Peng; Wilson, Richard C; Hancock, Edwin R

2011-02-01

The novel contributions of this paper are twofold. First, we demonstrate how to characterize unweighted graphs in a permutation-invariant manner using the polynomial coefficients from the Ihara zeta function, i.e., the Ihara coefficients. Second, we generalize the definition of the Ihara coefficients to edge-weighted graphs. For an unweighted graph, the Ihara zeta function is the reciprocal of a quasi characteristic polynomial of the adjacency matrix of the associated oriented line graph. Since the Ihara zeta function has poles that give rise to infinities, the most convenient numerically stable representation is to work with the coefficients of the quasi characteristic polynomial. Moreover, the polynomial coefficients are invariant to vertex order permutations and also convey information concerning the cycle structure of the graph. To generalize the representation to edge-weighted graphs, we make use of the reduced Bartholdi zeta function. We prove that the computation of the Ihara coefficients for unweighted graphs is a special case of our proposed method for unit edge weights. We also present a spectral analysis of the Ihara coefficients and indicate their advantages over other graph spectral methods. We apply the proposed graph characterization method to capturing graph-class structure and clustering graphs. Experimental results reveal that the Ihara coefficients are more effective than methods based on Laplacian spectra.

Is the scavenger receptor MARCO a new immune checkpoint?

PubMed

Arredouani, Mohamed S

2014-11-01

Whereas macrophages use the scavenger receptor MARCO primarily in antimicrobial immunity by interacting with both exogenous and endogenous environments, in dendritic cells (DCs) MARCO is believed to pleiotropically link innate to adaptive immunity. MARCO exerts a significant modulatory effect on TLR-induced DC activation, thus offering novel avenues in cancer immunotherapy.

San Marco D/L Explorer

NASA Technical Reports Server (NTRS)

1988-01-01

ti March 26, 1964, Centro Ricerche Aerospaziali (CRA) successfully launched a two-stage Nike sounding rocket from the Santa Rita launch platform off the Kenya coast, concluding Phase I. It carried basic elements of the San Marco science instrumentation and served further to flight qualify these canponents as well as provide a means of check-out of range instrumentation and equipment. The second phase culminated in the launch of the San Marco-I Spacecraft fran Wallops Island on a Scout vehicle on December 15, 1964. This launch derronstrated the readiness of the CRA launch crews for Phase III operations and qualified the basic spacecraft design. In addition it confirmed the usefulness and reliability of the drag balance device for accurate determinations of air density values and satellite attitude. phase III was completed with the launching of San Marco-11 frcm the San Marco platform off the coast of Kenya on April 26, 1967. ?he San Marco-II carried the same instrunentation as the San Marco-I, but the equatorial orbit permitted a more detailed study to be made of density variations versus altitude in the equatorial region. Ihe successful launch also served to qualify the San Marco Range as a reliable facility for future satellite launches. The successful culmination of the first San Marco endeavor paved the way for still closer collaboration in future space explorations.

Key Role of the Scavenger Receptor MARCO in Mediating Adenovirus Infection and Subsequent Innate Responses of Macrophages.

PubMed

Maler, Mareike D; Nielsen, Peter J; Stichling, Nicole; Cohen, Idan; Ruzsics, Zsolt; Wood, Connor; Engelhard, Peggy; Suomalainen, Maarit; Gyory, Ildiko; Huber, Michael; Müller-Quernheim, Joachim; Schamel, Wolfgang W A; Gordon, Siamon; Jakob, Thilo; Martin, Stefan F; Jahnen-Dechent, Willi; Greber, Urs F; Freudenberg, Marina A; Fejer, György

2017-08-01

The scavenger receptor MARCO is expressed in several subsets of naive tissue-resident macrophages and has been shown to participate in the recognition of various bacterial pathogens. However, the role of MARCO in antiviral defense is largely unexplored. Here, we investigated whether MARCO might be involved in the innate sensing of infection with adenovirus and recombinant adenoviral vectors by macrophages, which elicit vigorous immune responses in vivo Using cells derived from mice, we show that adenovirus infection is significantly more efficient in MARCO-positive alveolar macrophages (AMs) and in AM-like primary macrophage lines (Max Planck Institute cells) than in MARCO-negative bone marrow-derived macrophages. Using antibodies blocking ligand binding to MARCO, as well as gene-deficient and MARCO-transfected cells, we show that MARCO mediates the rapid adenovirus transduction of macrophages. By enhancing adenovirus infection, MARCO contributes to efficient innate virus recognition through the cytoplasmic DNA sensor cGAS. This leads to strong proinflammatory responses, including the production of interleukin-6 (IL-6), alpha/beta interferon, and mature IL-1α. These findings contribute to the understanding of viral pathogenesis in macrophages and may open new possibilities for the development of tools to influence the outcome of infection with adenovirus or adenovirus vectors. IMPORTANCE Macrophages play crucial roles in inflammation and defense against infection. Several macrophage subtypes have been identified with differing abilities to respond to infection with both natural adenoviruses and recombinant adenoviral vectors. Adenoviruses are important respiratory pathogens that elicit vigorous innate responses in vitro and in vivo The cell surface receptors mediating macrophage type-specific adenovirus sensing are largely unknown. The scavenger receptor MARCO is expressed on some subsets of naive tissue-resident macrophages, including lung alveolar macrophages. Its role in antiviral macrophage responses is largely unexplored. Here, we studied whether the differential expression of MARCO might contribute to the various susceptibilities of macrophage subtypes to adenovirus. We demonstrate that MARCO significantly enhances adenovirus infection and innate responses in macrophages. These results help to understand adenoviral pathogenesis and may open new possibilities to influence the outcome of infection with adenoviruses or adenovirus vectors. Copyright © 2017 Maler et al.

Genome-wide association study on legendre random regression coefficients for the growth and feed intake trajectory on Duroc Boars.

PubMed

Howard, Jeremy T; Jiao, Shihui; Tiezzi, Francesco; Huang, Yijian; Gray, Kent A; Maltecca, Christian

2015-05-30

Feed intake and growth are economically important traits in swine production. Previous genome wide association studies (GWAS) have utilized average daily gain or daily feed intake to identify regions that impact growth and feed intake across time. The use of longitudinal models in GWAS studies, such as random regression, allows for SNPs having a heterogeneous effect across the trajectory to be characterized. The objective of this study is therefore to conduct a single step GWAS (ssGWAS) on the animal polynomial coefficients for feed intake and growth. Corrected daily feed intake (DFI Adj) and average daily weight measurements (DBW Avg) on 8981 (n=525,240 observations) and 5643 (n=283,607 observations) animals were utilized in a random regression model using Legendre polynomials (order=2) and a relationship matrix that included genotyped and un-genotyped animals. A ssGWAS was conducted on the animal polynomials coefficients (intercept, linear and quadratic) for animals with genotypes (DFIAdj: n=855; DBWAvg: n=590). Regions were characterized based on the variance of 10-SNP sliding windows GEBV (WGEBV). A bootstrap analysis (n=1000) was conducted to declare significance. Heritability estimates for the traits trajectory ranged from 0.34-0.52 to 0.07-0.23 for DBWAvg and DFIAdj, respectively. Genetic correlations across age classes were large and positive for both DBWAvg and DFIAdj, albeit age classes at the beginning had a small to moderate genetic correlation with age classes towards the end of the trajectory for both traits. The WGEBV variance explained by significant regions (P<0.001) for each polynomial coefficient ranged from 0.2-0.9 to 0.3-1.01% for DBWAvg and DFIAdj, respectively. The WGEBV variance explained by significant regions for the trajectory was 1.54 and 1.95% for DBWAvg and DFIAdj. Both traits identified candidate genes with functions related to metabolite and energy homeostasis, glucose and insulin signaling and behavior. We have identified regions of the genome that have an impact on the intercept, linear and quadratic terms for DBWAvg and DFIAdj. These results provide preliminary evidence that individual growth and feed intake trajectories are impacted by different regions of the genome at different times.

Efficient algorithms for a class of partitioning problems

NASA Technical Reports Server (NTRS)

Iqbal, M. Ashraf; Bokhari, Shahid H.

1990-01-01

The problem of optimally partitioning the modules of chain- or tree-like tasks over chain-structured or host-satellite multiple computer systems is addressed. This important class of problems includes many signal processing and industrial control applications. Prior research has resulted in a succession of faster exact and approximate algorithms for these problems. Polynomial exact and approximate algorithms are described for this class that are better than any of the previously reported algorithms. The approach is based on a preprocessing step that condenses the given chain or tree structured task into a monotonic chain or tree. The partitioning of this monotonic take can then be carried out using fast search techniques.

Nonlinear Structured Growth Mixture Models in M"plus" and OpenMx

ERIC Educational Resources Information Center

Grimm, Kevin J.; Ram, Nilam; Estabrook, Ryne

2010-01-01

Growth mixture models (GMMs; B. O. Muthen & Muthen, 2000; B. O. Muthen & Shedden, 1999) are a combination of latent curve models (LCMs) and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. GMMs are often fit with linear, latent basis, multiphase, or polynomial change models…

Oscillatory singular integrals and harmonic analysis on nilpotent groups

PubMed Central

Ricci, F.; Stein, E. M.

1986-01-01

Several related classes of operators on nilpotent Lie groups are considered. These operators involve the following features: (i) oscillatory factors that are exponentials of imaginary polynomials, (ii) convolutions with singular kernels supported on lower-dimensional submanifolds, (iii) validity in the general context not requiring the existence of dilations that are automorphisms. PMID:16593640

Von Bertalanffy's dynamics under a polynomial correction: Allee effect and big bang bifurcation

NASA Astrophysics Data System (ADS)

Leonel Rocha, J.; Taha, A. K.; Fournier-Prunaret, D.

2016-02-01

In this work we consider new one-dimensional populational discrete dynamical systems in which the growth of the population is described by a family of von Bertalanffy's functions, as a dynamical approach to von Bertalanffy's growth equation. The purpose of introducing Allee effect in those models is satisfied under a correction factor of polynomial type. We study classes of von Bertalanffy's functions with different types of Allee effect: strong and weak Allee's functions. Dependent on the variation of four parameters, von Bertalanffy's functions also includes another class of important functions: functions with no Allee effect. The complex bifurcation structures of these von Bertalanffy's functions is investigated in detail. We verified that this family of functions has particular bifurcation structures: the big bang bifurcation of the so-called “box-within-a-box” type. The big bang bifurcation is associated to the asymptotic weight or carrying capacity. This work is a contribution to the study of the big bang bifurcation analysis for continuous maps and their relationship with explosion birth and extinction phenomena.

Towards syntactic characterizations of approximation schemes via predicate and graph decompositions

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

Hunt, H.B. III; Stearns, R.E.; Jacob, R.

1998-12-01

The authors present a simple extensible theoretical framework for devising polynomial time approximation schemes for problems represented using natural syntactic (algebraic) specifications endowed with natural graph theoretic restrictions on input instances. Direct application of the technique yields polynomial time approximation schemes for all the problems studied in [LT80, NC88, KM96, Ba83, DTS93, HM+94a, HM+94] as well as the first known approximation schemes for a number of additional combinatorial problems. One notable aspect of the work is that it provides insights into the structure of the syntactic specifications and the corresponding algorithms considered in [KM96, HM+94]. The understanding allows them tomore » extend the class of syntactic specifications for which generic approximation schemes can be developed. The results can be shown to be tight in many cases, i.e. natural extensions of the specifications can be shown to yield non-approximable problems. The results provide a non-trivial characterization of a class of problems having a PTAS and extend the earlier work on this topic by [KM96, HM+94].« less

Backwater Flooding in San Marcos, TX from the Blanco River

NASA Technical Reports Server (NTRS)

Earl, Richard; Gaenzle, Kyle G.; Hollier, Andi B.

2016-01-01

Large sections of San Marcos, TX were flooded in Oct. 1998, May 2015, and Oct. 2015. Much of the flooding in Oct. 1998 and Oct. 2015 was produced by overbank flooding of San Marcos River and its tributaries by spills from upstream dams. The May 2015 flooding was almost entirely produced by backwater flooding from the Blanco River whose confluence is approximately 2.2 miles southeast of downtown. We use the stage height of the Blanco River to generate maps of the areas of San Marcos that are lower than the flood peaks and compare those results with data for the observed extent of flooding in San Marcos. Our preliminary results suggest that the flooding occurred at locations more than 20 feet lower than the maximum stage height of the Blanco River at San Marcos gage (08171350). This suggest that the datum for either gage 08171350 or 08170500 (San Marcos River at San Marcos) or both are incorrect. There are plans for the U.S. Army Corps of Engineers to construct a Blanco River bypass that will divert Blanco River floodwaters approximately 2 miles farther downstream, but the $60 million price makes its implementation problematic.

MarCO CubeSat Engineers 2

NASA Image and Video Library

2016-01-20

Engineers for NASA's MarCO (Mars Cube One) technology demonstration inspect one of the two MarCO CubeSats. Cody Colley, MarCO integration and test deputy, left, and Andy Klesh, MarCO chief engineer, are on the team at NASA's Jet Propulsion Laboratory, Pasadena, California, preparing twin MarCO CubeSats. The briefcase-size MarCO twins were designed to ride along with NASA's next Mars lander, InSight. Its planned March 2016 launch was suspended. InSight -- an acronym for Interior Exploration using Seismic Investigations, Geodesy and Heat Transport -- will study the interior of Mars to improve understanding of the processes that formed and shaped rocky planets, including Earth. Note: After thorough examination, NASA managers have decided to suspend the planned March 2016 launch of the Interior Exploration using Seismic Investigations Geodesy and Heat Transport (InSight) mission. The decision follows unsuccessful attempts to repair a leak in a section of the prime instrument in the science payload. http://photojournal.jpl.nasa.gov/catalog/PIA20342

MarCO CubeSat Engineers 3

NASA Image and Video Library

2016-01-20

Engineers for NASA's MarCO (Mars Cube One) technology demonstration inspect one of the two MarCO CubeSats. Joel Steinkraus, MarCO lead mechanical engineer, left, and Andy Klesh, MarCO chief engineer, are on the team at NASA's Jet Propulsion Laboratory, Pasadena, California, preparing twin MarCO CubeSats. The briefcase-size MarCO twins were designed to ride along with NASA's next Mars lander, InSight. Its planned March 2016 launch was suspended. InSight -- an acronym for Interior Exploration using Seismic Investigations, Geodesy and Heat Transport -- will study the interior of Mars to improve understanding of the processes that formed and shaped rocky planets, including Earth. Note: After thorough examination, NASA managers have decided to suspend the planned March 2016 launch of the Interior Exploration using Seismic Investigations Geodesy and Heat Transport (InSight) mission. The decision follows unsuccessful attempts to repair a leak in a section of the prime instrument in the science payload. http://photojournal.jpl.nasa.gov/catalog/PIA20343

Differential geometric treewidth estimation in adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Wang, Chi; Jonckheere, Edmond; Brun, Todd

2016-10-01

The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular "Chimera" physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the D-Wave architecture. The latter problem is itself NP-hard. In this paper, we propose a novel polynomial-time approximation to the closely related treewidth based on the differential geometric concept of Ollivier-Ricci curvature. The latter runs in polynomial time and thus could significantly reduce the overall complexity of determining whether a QUBO problem is minor embeddable, and thus solvable on the D-Wave architecture.

Combinatorics of γ-structures.

PubMed

Han, Hillary S W; Li, Thomas J X; Reidys, Christian M

2014-08-01

In this article we study canonical γ-structures, a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A γ-structure is composed of specific building blocks that have topological genus less than or equal to γ, where composition means concatenation and nesting of such blocks. Our main result is the derivation of the generating function of γ-structures via symbolic enumeration using so called irreducible shadows. We furthermore recursively compute the generating polynomials of irreducible shadows of genus ≤ γ. The γ-structures are constructed via γ-matchings. For 1 ≤ γ ≤ 10, we compute Puiseux expansions at the unique, dominant singularities, allowing us to derive simple asymptotic formulas for the number of γ-structures.

San Marco-C Explorer

NASA Technical Reports Server (NTRS)

1971-01-01

On or about 24 April 1971, the San Marco-C spacecraft will be launched from the San Marco Range located off the coast of Kenya, Africa, by a Scout launch vehicle. The launch will be conducted by an Italian crew. The San Marco-C is the third cooperative satellite project between Italy and the United States. The first such cooperative project resulted in the San Marco-1 satellite which was launched into orbit from the Wallops Island Range with a Scout vehicle on 15 December 1964. The successful launch demonstrated the readiness of the Italian Centro Ricerche Aerospaziuli (CRA) launch crews to launch the Scout vehicle and qualified the basic spacecraft design. The second in the series of cooperative satellite launches was the San Marco-II which was successfully launched into orbit from the San Marco Range on 26 April 1967. This was the first Scout launch from the San Marco Range. The San Marco-II carried the same accelerometer as San Marco-1, but the orbit permitted the air drag to be studied in detail in the equatorial region. The successful launch also served to qualify the San Marco Range as a reliable facility for future satellite launches, and has since been used for the successful launch of SAS-A (Explorer 42). This cooperative project has been implemented jointly by the Italian Space Commission and NASA. The CRA provided the spacecraft, its subsystems, and an air drag balance; Goddard Space Flight Center (GSFC) provided an omegatron and a neutral mass spectrometer, technical consultation and support. In addition, NASA provided the Scout launch vehicle. The primary scientific objective of the San Marco-C is to obtain, by measurement, a description of the equatorial neutral-particle atmosphere in terms of its density, com- position, and temperature at altitudes of 200 km and above, and to obtain a description of variations that result from solar and geomagnetic activities. The secondary scientific objective is to investigate the interdependence of three neutral-density-measurement techniques from one spacecraft: direct particle detection, direct drag, and integrated drag.

Noncommutative Differential Geometry of Generalized Weyl Algebras

NASA Astrophysics Data System (ADS)

Brzeziński, Tomasz

2016-06-01

Elements of noncommutative differential geometry of Z-graded generalized Weyl algebras A(p;q) over the ring of polynomials in two variables and their zero-degree subalgebras B(p;q), which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed. In particular, three classes of skew derivations of A(p;q) are constructed, and three-dimensional first-order differential calculi induced by these derivations are described. The associated integrals are computed and it is shown that the dimension of the integral space coincides with the order of the defining polynomial p(z). It is proven that the restriction of these first-order differential calculi to the calculi on B(p;q) is isomorphic to the direct sum of degree 2 and degree -2 components of A(p;q). A Dirac operator for B(p;q) is constructed from a (strong) connection with respect to this differential calculus on the (free) spinor bimodule defined as the direct sum of degree 1 and degree -1 components of A(p;q). The real structure of KO-dimension two for this Dirac operator is also described.

Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

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

Marquette, Ian, E-mail: i.marquette@uq.edu.au; Quesne, Christiane, E-mail: cquesne@ulb.ac.be

2015-06-15

We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformedmore » oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.« less

Rational trigonometric approximations using Fourier series partial sums

NASA Technical Reports Server (NTRS)

Geer, James F.

1993-01-01

A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented.

An efficient higher order family of root finders

NASA Astrophysics Data System (ADS)

Petkovic, Ljiljana D.; Rancic, Lidija; Petkovic, Miodrag S.

2008-06-01

A one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial, based on a cubically convergent Hansen-Patrick's family, is studied. We show that the convergence of the basic family of the fourth order can be increased to five and six using Newton's and Halley's corrections, respectively. Since these corrections use the already calculated values, the computational efficiency of the accelerated methods is significantly increased. Further acceleration is achieved by applying the Gauss-Seidel approach (single-step mode). One of the most important problems in solving nonlinear equations, the construction of initial conditions which provide both the guaranteed and fast convergence, is considered for the proposed accelerated family. These conditions are computationally verifiable; they depend only on the polynomial coefficients, its degree and initial approximations, which is of practical importance. Some modifications of the considered family, providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions, are also studied. Numerical examples demonstrate the convergence properties of the presented family of root-finding methods.

Stability properties of a general class of nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Gléria, I. M.; Figueiredo, A.; Rocha Filho, T. M.

2001-05-01

We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

Random regression models on Legendre polynomials to estimate genetic parameters for weights from birth to adult age in Canchim cattle.

PubMed

Baldi, F; Albuquerque, L G; Alencar, M M

2010-08-01

The objective of this work was to estimate covariance functions for direct and maternal genetic effects, animal and maternal permanent environmental effects, and subsequently, to derive relevant genetic parameters for growth traits in Canchim cattle. Data comprised 49,011 weight records on 2435 females from birth to adult age. The model of analysis included fixed effects of contemporary groups (year and month of birth and at weighing) and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were allowed to vary and were modelled by a step function with 1, 4 or 11 classes based on animal's age. The model fitting four classes of residual variances was the best. A total of 12 random regression models from second to seventh order were used to model direct and maternal genetic effects, animal and maternal permanent environmental effects. The model with direct and maternal genetic effects, animal and maternal permanent environmental effects fitted by quadric, cubic, quintic and linear Legendre polynomials, respectively, was the most adequate to describe the covariance structure of the data. Estimates of direct and maternal heritability obtained by multi-trait (seven traits) and random regression models were very similar. Selection for higher weight at any age, especially after weaning, will produce an increase in mature cow weight. The possibility to modify the growth curve in Canchim cattle to obtain animals with rapid growth at early ages and moderate to low mature cow weight is limited.

On the robustness of bucket brigade quantum RAM

NASA Astrophysics Data System (ADS)

Arunachalam, Srinivasan; Gheorghiu, Vlad; Jochym-O'Connor, Tomas; Mosca, Michele; Varshinee Srinivasan, Priyaa

2015-12-01

We study the robustness of the bucket brigade quantum random access memory model introduced by Giovannetti et al (2008 Phys. Rev. Lett.100 160501). Due to a result of Regev and Schiff (ICALP ’08 733), we show that for a class of error models the error rate per gate in the bucket brigade quantum memory has to be of order o({2}-n/2) (where N={2}n is the size of the memory) whenever the memory is used as an oracle for the quantum searching problem. We conjecture that this is the case for any realistic error model that will be encountered in practice, and that for algorithms with super-polynomially many oracle queries the error rate must be super-polynomially small, which further motivates the need for quantum error correction. By contrast, for algorithms such as matrix inversion Harrow et al (2009 Phys. Rev. Lett.103 150502) or quantum machine learning Rebentrost et al (2014 Phys. Rev. Lett.113 130503) that only require a polynomial number of queries, the error rate only needs to be polynomially small and quantum error correction may not be required. We introduce a circuit model for the quantum bucket brigade architecture and argue that quantum error correction for the circuit causes the quantum bucket brigade architecture to lose its primary advantage of a small number of ‘active’ gates, since all components have to be actively error corrected.

MarCO CubeSat Engineers 1

NASA Image and Video Library

2016-01-20

Engineers for NASA's MarCO (Mars Cube One) technology demonstration inspect the MarCO test bed, which contains components that are identical to those built for a flight to Mars. Cody Colley, left, MarCO integration and test deputy, and Shannon Statham, MarCO integration and test lead, are on the team at NASA's Jet Propulsion Laboratory, Pasadena, California, preparing twin MarCO CubeSats. The briefcase-size MarCO twins were designed to ride along with NASA's next Mars lander, InSight. Its planned March 2016 launch was suspended. InSight -- an acronym for Interior Exploration using Seismic Investigations, Geodesy and Heat Transport -- will study the interior of Mars to improve understanding of the processes that formed and shaped rocky planets, including Earth. Note: After thorough examination, NASA managers have decided to suspend the planned March 2016 launch of the Interior Exploration using Seismic Investigations Geodesy and Heat Transport (InSight) mission. The decision follows unsuccessful attempts to repair a leak in a section of the prime instrument in the science payload. http://photojournal.jpl.nasa.gov/catalog/PIA20341

Schroedinger operators with the q-ladder symmetry algebras

NASA Technical Reports Server (NTRS)

Skorik, Sergei; Spiridonov, Vyacheslav

1994-01-01

A class of the one-dimensional Schroedinger operators L with the symmetry algebra LB(+/-) = q(+/-2)B(+/-)L, (B(+),B(-)) = P(sub N)(L), is described. Here B(+/-) are the 'q-ladder' operators and P(sub N)(L) is a polynomial of the order N. Peculiarities of the coherent states of this algebra are briefly discussed.

Archiving Student Solutions with Tablet PCs in a Discussion-based Introductory Physics Class

NASA Astrophysics Data System (ADS)

Price, Edward; De Leone, Charles

2008-10-01

Many active learning based physics courses use whiteboards as a space for groups to respond to prompts based on short lab activities, problem solving, or inquiry-oriented activities. Whiteboards are volatile; once erased, the material is lost. Tablet PCs and software such as Ubiquitous Presenter can be used as digital whiteboards in active learning classes. This enables automatic capture and archiving of student work for online review by students, instructors, and researchers. We studied the use of digital whiteboards in an active-learning introductory physics course at California State University, San Marcos. In this paper we examine the archival features of digital whiteboards', and characterize the use of these features by students and instructors, and explore possible uses for researchers and curriculum developers.

Fast optimization algorithms and the cosmological constant

NASA Astrophysics Data System (ADS)

Bao, Ning; Bousso, Raphael; Jordan, Stephen; Lackey, Brad

2017-11-01

Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of a problem that is hard for the complexity class NP (Nondeterministic Polynomial-time). The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable Universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10-120 in a randomly generated 1 09-dimensional Arkani-Hamed-Dimopoulos-Kachru landscape.

San Marco C-2 (San Marco-4) Post Launch Report No. 1

NASA Technical Reports Server (NTRS)

1974-01-01

The San Marco C-2 spacecraft, now designated San Marco-4, was successfully launched by a Scout vehicle from the San Marco Platform on 18 February 1974 at 6:05 a.m. EDT. The launch occurred 2 hours 50 minutes into the 3-hour window due co low cloud cover at the launch site. All spacecraft subsystems have been checked and are functioning normally. The protective caps for the two U.S. experiments were ejected and the Omegatron experiment activated on 19 February. The neutral mass spectrometer was activated as scheduled on 22 February after sufficient time to allow for spacecraft outgassing and to avoid the possibility of corona occurring. Both instruments are performing properly and worthwhile scientific data is being acquired.

Kleinberg Complex Networks

DTIC Science & Technology

2014-10-21

linear combinations of paths. This project featured research on two classes of routing problems , namely traveling salesman problems and multicommodity...flows. One highlight of this research was our discovery of a polynomial-time algorithm for the metric traveling salesman s-t path problem whose...metric TSP would resolve one of the most venerable open problems in the theory of approximation algorithms. Our research on traveling salesman

Quintic quasi-topological gravity

NASA Astrophysics Data System (ADS)

Cisterna, Adolfo; Guajardo, Luis; Hassaïne, Mokhtar; Oliva, Julio

2017-04-01

We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing {\\mathcal{R}}^5 terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff's Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler's polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in arXiv:1003.4773, the general geometric structure of these Lagrangians remains an open problem.

Kinematics and design of a class of parallel manipulators

NASA Astrophysics Data System (ADS)

Hertz, Roger Barry

1998-12-01

This dissertation is concerned with the kinematic analysis and design of a class of three degree-of-freedom, spatial parallel manipulators. The class of manipulators is characterized by two platforms, between which are three legs, each possessing a succession of revolute, spherical, and revolute joints. The class is termed the "revolute-spherical-revolute" class of parallel manipulators. Two members of this class are examined. The first mechanism is a double-octahedral variable-geometry truss, and the second is termed a double tripod. The history the mechanisms is explored---the variable-geometry truss dates back to 1984, while predecessors of the double tripod mechanism date back to 1869. This work centers on the displacement analysis of these three-degree-of-freedom mechanisms. Two types of problem are solved: the forward displacement analysis (forward kinematics) and the inverse displacement analysis (inverse kinematics). The kinematic model of the class of mechanism is general in nature. A classification scheme for the revolute-spherical-revolute class of mechanism is introduced, which uses dominant geometric features to group designs into 8 different sub-classes. The forward kinematics problem is discussed: given a set of independently controllable input variables, solve for the relative position and orientation between the two platforms. For the variable-geometry truss, the controllable input variables are assumed to be the linear (prismatic) joints. For the double tripod, the controllable input variables are the three revolute joints adjacent to the base (proximal) platform. Multiple solutions are presented to the forward kinematics problem, indicating that there are many different positions (assemblies) that the manipulator can assume with equivalent inputs. For the double tripod these solutions can be expressed as a 16th degree polynomial in one unknown, while for the variable-geometry truss there exist two 16th degree polynomials, giving rise to 256 solutions. For special cases of the double tripod, the forward kinematics problem is shown to have a closed-form solution. Numerical examples are presented for the solution to the forward kinematics. A double tripod is presented that admits 16 unique and real forward kinematics solutions. Another example for a variable geometry truss is given that possesses 64 real solutions: 8 for each 16th order polynomial. The inverse kinematics problem is also discussed: given the relative position of the hand (end-effector), which is rigidly attached to one platform, solve for the independently controlled joint variables. Iterative solutions are proposed for both the variable-geometry truss and the double tripod. For special cases of both mechanisms, closed-form solutions are given. The practical problems of designing, building, and controlling a double-tripod manipulator are addressed. The resulting manipulator is a first-of-its kind prototype of a tapered (asymmetric) double-tripod manipulator. Real-time forward and inverse kinematics algorithms on an industrial robot controller is presented. The resulting performance of the prototype is impressive, since it was to achieve a maximum tool-tip speed of 4064 mm/s, maximum acceleration of 5 g, and a cycle time of 1.2 seconds for a typical pick-and-place pattern.

Slice regular functions of several Clifford variables

NASA Astrophysics Data System (ADS)

Ghiloni, R.; Perotti, A.

2012-11-01

We introduce a class of slice regular functions of several Clifford variables. Our approach to the definition of slice functions is based on the concept of stem functions of several variables and on the introduction on real Clifford algebras of a family of commuting complex structures. The class of slice regular functions include, in particular, the family of (ordered) polynomials in several Clifford variables. We prove some basic properties of slice and slice regular functions and give examples to illustrate this function theory. In particular, we give integral representation formulas for slice regular functions and a Hartogs type extension result.

On the functional optimization of a certain class of nonstationary spatial functions

USGS Publications Warehouse

Christakos, G.; Paraskevopoulos, P.N.

1987-01-01

Procedures are developed in order to obtain optimal estimates of linear functionals for a wide class of nonstationary spatial functions. These procedures rely on well-established constrained minimum-norm criteria, and are applicable to multidimensional phenomena which are characterized by the so-called hypothesis of inherentity. The latter requires elimination of the polynomial, trend-related components of the spatial function leading to stationary quantities, and also it generates some interesting mathematics within the context of modelling and optimization in several dimensions. The arguments are illustrated using various examples, and a case study computed in detail. ?? 1987 Plenum Publishing Corporation.

Estimation of genetic parameters for milk yield in Murrah buffaloes by Bayesian inference.

PubMed

Breda, F C; Albuquerque, L G; Euclydes, R F; Bignardi, A B; Baldi, F; Torres, R A; Barbosa, L; Tonhati, H

2010-02-01

Random regression models were used to estimate genetic parameters for test-day milk yield in Murrah buffaloes using Bayesian inference. Data comprised 17,935 test-day milk records from 1,433 buffaloes. Twelve models were tested using different combinations of third-, fourth-, fifth-, sixth-, and seventh-order orthogonal polynomials of weeks of lactation for additive genetic and permanent environmental effects. All models included the fixed effects of contemporary group, number of daily milkings and age of cow at calving as covariate (linear and quadratic effect). In addition, residual variances were considered to be heterogeneous with 6 classes of variance. Models were selected based on the residual mean square error, weighted average of residual variance estimates, and estimates of variance components, heritabilities, correlations, eigenvalues, and eigenfunctions. Results indicated that changes in the order of fit for additive genetic and permanent environmental random effects influenced the estimation of genetic parameters. Heritability estimates ranged from 0.19 to 0.31. Genetic correlation estimates were close to unity between adjacent test-day records, but decreased gradually as the interval between test-days increased. Results from mean squared error and weighted averages of residual variance estimates suggested that a model considering sixth- and seventh-order Legendre polynomials for additive and permanent environmental effects, respectively, and 6 classes for residual variances, provided the best fit. Nevertheless, this model presented the largest degree of complexity. A more parsimonious model, with fourth- and sixth-order polynomials, respectively, for these same effects, yielded very similar genetic parameter estimates. Therefore, this last model is recommended for routine applications. Copyright 2010 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Rigorous RG Algorithms and Area Laws for Low Energy Eigenstates in 1D

NASA Astrophysics Data System (ADS)

Arad, Itai; Landau, Zeph; Vazirani, Umesh; Vidick, Thomas

2017-11-01

One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. A recent advance (Landau et al. in Nat Phys, 2015) gave a polynomial time algorithm to compute a succinct classical description for unique ground states of gapped 1D quantum systems. Despite this progress many questions remained unsolved, including whether there exist efficient algorithms when the ground space is degenerate (and of polynomial dimension in the system size), or for the polynomially many lowest energy states, or even whether such states admit succinct classical descriptions or area laws. In this paper we give a new algorithm, based on a rigorously justified RG type transformation, for finding low energy states for 1D Hamiltonians acting on a chain of n particles. In the process we resolve some of the aforementioned open questions, including giving a polynomial time algorithm for poly( n) degenerate ground spaces and an n O(log n) algorithm for the poly( n) lowest energy states (under a mild density condition). For these classes of systems the existence of a succinct classical description and area laws were not rigorously proved before this work. The algorithms are natural and efficient, and for the case of finding unique ground states for frustration-free Hamiltonians the running time is {\\tilde{O}(nM(n))} , where M( n) is the time required to multiply two n × n matrices.

Optimal Sharpening of Compensated Comb Decimation Filters: Analysis and Design

PubMed Central

Troncoso Romero, David Ernesto

2014-01-01

Comb filters are a class of low-complexity filters especially useful for multistage decimation processes. However, the magnitude response of comb filters presents a droop in the passband region and low stopband attenuation, which is undesirable in many applications. In this work, it is shown that, for stringent magnitude specifications, sharpening compensated comb filters requires a lower-degree sharpening polynomial compared to sharpening comb filters without compensation, resulting in a solution with lower computational complexity. Using a simple three-addition compensator and an optimization-based derivation of sharpening polynomials, we introduce an effective low-complexity filtering scheme. Design examples are presented in order to show the performance improvement in terms of passband distortion and selectivity compared to other methods based on the traditional Kaiser-Hamming sharpening and the Chebyshev sharpening techniques recently introduced in the literature. PMID:24578674

Optimal sharpening of compensated comb decimation filters: analysis and design.

PubMed

Troncoso Romero, David Ernesto; Laddomada, Massimiliano; Jovanovic Dolecek, Gordana

2014-01-01

Comb filters are a class of low-complexity filters especially useful for multistage decimation processes. However, the magnitude response of comb filters presents a droop in the passband region and low stopband attenuation, which is undesirable in many applications. In this work, it is shown that, for stringent magnitude specifications, sharpening compensated comb filters requires a lower-degree sharpening polynomial compared to sharpening comb filters without compensation, resulting in a solution with lower computational complexity. Using a simple three-addition compensator and an optimization-based derivation of sharpening polynomials, we introduce an effective low-complexity filtering scheme. Design examples are presented in order to show the performance improvement in terms of passband distortion and selectivity compared to other methods based on the traditional Kaiser-Hamming sharpening and the Chebyshev sharpening techniques recently introduced in the literature.

Model of Mars-Bound MarCO CubeSat

NASA Image and Video Library

2015-06-12

Engineers for NASA's MarCO technology demonstration display a full-scale mechanical mock-up of the small craft in development as part of NASA's next mission to Mars. Mechanical engineer Joel Steinkraus and systems engineer Farah Alibay are on the team at NASA's Jet Propulsion Laboratory, Pasadena, California, preparing twin MarCO (Mars Cube One) CubeSats for a March 2016 launch. MarCO is the first interplanetary mission using CubeSat technologies for small spacecraft. The briefcase-size MarCO twins will ride along on an Atlas V launch vehicle lifting off from Vandenberg Air Force Base, California, with NASA's next Mars lander, InSight. The mock-up in the photo is in a configuration to show the deployed position of components that correspond to MarCO's two solar panels and two antennas. During launch, those components will be stowed for a total vehicle size of about 14.4 inches (36.6 centimeters) by 9.5 inches (24.3 centimeters) by 4.6 inches (11.8 centimeters). After launch, the two MarCO CubeSats and InSight will be navigated separately to Mars. The MarCO twins will fly past the planet in September 2016 just as InSight is descending through the atmosphere and landing on the surface. MarCO is a technology demonstration mission to relay communications from InSight to Earth during InSight's descent and landing. InSight communications during that critical period will also be recorded by NASA's Mars Reconnaissance Orbiter for delayed transmission to Earth. InSight -- an acronym for Interior Exploration using Seismic Investigations, Geodesy and Heat Transport -- will study the interior of Mars to improve understanding of the processes that formed and shaped rocky planets, including Earth. After launch, the MarCO twins and InSight will be navigated separately to Mars. Note: After thorough examination, NASA managers have decided to suspend the planned March 2016 launch of the Interior Exploration using Seismic Investigations Geodesy and Heat Transport (InSight) mission. The decision follows unsuccessful attempts to repair a leak in a section of the prime instrument in the science payload. http://photojournal.jpl.nasa.gov/catalog/PIA19389

Chiral zero energy modes in two-dimensional disordered Dirac semimetals

NASA Astrophysics Data System (ADS)

Liu, Lei; Yu, Yan; Wu, Hai-Bin; Zhang, Yan-Yang; Liu, Jian-Jun; Li, Shu-Shen

2018-04-01

The vacancy-induced chiral zero energy modes (CZEMs) of chiral-unitary-class (AIII) and chiral-symplectic-class (CII) two-dimensional (2 D ) disordered Dirac semimetals realized on a square bipartite lattice are investigated numerically by using the Kubo-Greenwood formula with the kernel polynomial method. The results show that, for both systems, the CZEMs exhibit the critical delocalization. The CZEM conductivity remains a robust constant (i.e., σ CZEM≈1.05 e2/h ), which is insensitive to the sample sizes, the vacancy concentrations, and the numbers of moments of Chebyshev polynomials, i.e., the dephasing strength. For both kinds of chiral systems, the CZEM conductivities are almost identical. However, they are not equal to that of graphene (i.e., 4 e2/π h ), which belongs to the chiral orthogonal class (BDI) semimetal on a 2 D hexagonal bipartite lattice. In addition, for the case that the vacancy concentrations are different in the two sublattices, the CZEM conductivity vanishes, and thus both systems exhibit localization at the Dirac point. Moreover, a band gap and a mobility gap open around zero energy. The widths of the energy gaps and mobility gaps are increasing with larger vacancy concentration difference. The width of the mobility gap is greater than that of the band gap, and a δ -function-like peak of density of states emerges at the Dirac point within the band gap, implying the existence of numerous localized states.

Origin and characteristics of discharge at San Marcos Springs, south-central Texas

USGS Publications Warehouse

Musgrove, MaryLynn; Crow, Cassi L.

2013-01-01

The Edwards aquifer in south-central Texas is one of the most productive aquifers in the Nation and is the primary source of water for the rapidly growing San Antonio area. Springs issuing from the Edwards aquifer provide habitat for several threatened and endangered species, serve as locations for recreational activities, and supply downstream users. Comal Springs and San Marcos Springs are major discharge points for the Edwards aquifer, and their discharges are used as thresholds in groundwater management strategies. Regional flow paths originating in the western part of the aquifer are generally understood to supply discharge at Comal Springs. In contrast, the hydrologic connection of San Marcos Springs with the regional Edwards aquifer flow system is less understood. During November 2008–December 2010, the U.S. Geological Survey, in cooperation with the San Antonio Water System, collected and analyzed hydrologic and geochemical data from springs, groundwater wells, and streams to gain a better understanding of the origin and characteristics of discharge at San Marcos Springs. During the study, climatic and hydrologic conditions transitioned from exceptional drought to wetter than normal. The wide range of hydrologic conditions that occurred during this study—and corresponding changes in surface-water, groundwater and spring discharge, and in physicochemical properties and geochemistry—provides insight into the origin of the water discharging from San Marcos Springs. Three orifices at San Marcos Springs (Deep, Diversion, and Weissmuller Springs) were selected to be representative of larger springs at the spring complex. Key findings include that discharge at San Marcos Springs was dominated by regional recharge sources and groundwater flow paths and that different orifices of San Marcos Springs respond differently to changes in hydrologic conditions; Deep Spring was less responsive to changes in hydrologic conditions than were Diversion Spring and Weissmuller Spring. Also, San Marcos Springs discharge is influenced by mixing with a component of saline groundwater.

Alternative activation of macrophages and pulmonary fibrosis are modulated by scavenger receptor, macrophage receptor with collagenous structure.

PubMed

Murthy, Shubha; Larson-Casey, Jennifer L; Ryan, Alan J; He, Chao; Kobzik, Lester; Carter, A Brent

2015-08-01

Alternative activation of alveolar macrophages is linked to fibrosis following exposure to asbestos. The scavenger receptor, macrophage receptor with collagenous structure (MARCO), provides innate immune defense against inhaled particles and pathogens; however, a receptor for asbestos has not been identified. We hypothesized that MARCO acts as an initial signaling receptor for asbestos, polarizes macrophages to a profibrotic M2 phenotype, and is required for the development of asbestos-induced fibrosis. Compared with normal subjects, alveolar macrophages isolated from patients with asbestosis express higher amounts of MARCO and have greater profibrotic polarization. Arginase 1 (40-fold) and IL-10 (265-fold) were higher in patients. In vivo, the genetic deletion of MARCO attenuated the profibrotic environment and pulmonary fibrosis in mice exposed to chrysotile. Moreover, alveolar macrophages from MARCO(-/-) mice polarize to an M1 phenotype, whereas wild-type mice have higher Ym1 (>3.0-fold) and nearly 7-fold more active TGF-β1 in bronchoalveolar lavage (BAL) fluid (BALF). Arg(432) and Arg(434) in domain V of MARCO are required for the polarization of macrophages to a profibrotic phenotype as mutation of these residues reduced FIZZ1 expression (17-fold) compared with cells expressing MARCO. These observations demonstrate that a macrophage membrane protein regulates the fibrotic response to lung injury and suggest a novel target for therapeutic intervention. © FASEB.

History of the Italian San Marco equatorial mobile range

NASA Technical Reports Server (NTRS)

Nesbitt, H. N.

1971-01-01

Events leading to the development of the San Marco Equatorial Range are presented. Included are background information leading to the cooperative space program between the United States and Italy, conceptual planning, training activities, equipment design and fabrication, and range utilization. The technical support provided the San Marco Program by Scout Project Office, and other NASA installations is described.

The midnight density maximum in the S. Marco V and the S. Marco III equatorial density data sets

NASA Astrophysics Data System (ADS)

Arduini, C.; Laneve, G.; Ponzi, U.

In a previous paper we showed some systematic deviations of the S. Marco V drag balance equatorial density data with respect to the MSIS86 model. We interpreted these deviations as due, at least in part, to the presence of a variable ``Midnight Density Maximum'' (MDM). In the data, there was in fact evidence of some altitude and seasonal variation of this pattern. In the present paper we consider, besides the S. Marco V data base (density measured during 1988), the S. Marco III data base, collected in 1971 almost in the same seasonal period and altitude range, with an instrument very similar to that of the S. Marco V. The use of both data sets is allowing a rather detailed description of the phenomenon as seen by the DBI instrument, for what concerns both the ``seasonal'' and altitude variations. In addition also some longitude effects are evidenced, for instance, by the MITS and QUITO data subsets of S. Marco III, taken respectively around 40 deg and 280 deg East longitude. Notice in addition that S. M. III data refer to the year 1971 (descending part of solar cycle 20) while SMV was launched in 1988 (ascending part of solar cycle 22); the comparison is thus allowing to evidence the persistence of the phenomenon and of its main characteristics. The observed data are consistent ``at large'' for both S. Marco III and V, while the differences in the details are providing hints on the mechanisms of the thermospheric dynamics (tidal theory and neutral-charged interactions). The paper presents the above said features together with a discussion on the characteristics of the two data bases and on their possible relevance for modeling the considered MDM feature.

Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function

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

Linton, C. M., E-mail: C.M.Linton@lboro.ac.uk

2015-01-15

A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green’s function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of θ-functions which are significant generalisations of known results.

MarCOs, Mars and Earth

NASA Image and Video Library

2018-03-29

An artist's rendering of the twin Mars Cube One (MarCO) spacecraft flying over Mars with Earth in the distance. The MarCOs will be the first CubeSats -- a kind of modular, mini-satellite -- flown in deep space. They're designed to fly along behind NASA's InSight lander on its cruise to Mars. If they make the journey, they will test a relay of data about InSight's entry, descent and landing back to Earth. Though InSight's mission will not depend on the success of the MarCOs, they will be a test of how CubeSats can be used in deep space. https://photojournal.jpl.nasa.gov/catalog/PIA22316

Some properties for integro-differential operator defined by a fractional formal.

PubMed

Abdulnaby, Zainab E; Ibrahim, Rabha W; Kılıçman, Adem

2016-01-01

Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.

A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras

NASA Astrophysics Data System (ADS)

Alshammari, Fahad; Isaac, Phillip S.; Marquette, Ian

2018-02-01

We introduce a search algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. To demonstrate the algorithm, we look at two classes of examples: (1) the model filiform Lie algebras and (2) the Schrödinger Lie algebras. We find that an abstract form of dimensional analysis assists us in our algorithm, and greatly reduces the complexity of the problem.

Algorithms, complexity, and the sciences

PubMed Central

Papadimitriou, Christos

2014-01-01

Algorithms, perhaps together with Moore’s law, compose the engine of the information technology revolution, whereas complexity—the antithesis of algorithms—is one of the deepest realms of mathematical investigation. After introducing the basic concepts of algorithms and complexity, and the fundamental complexity classes P (polynomial time) and NP (nondeterministic polynomial time, or search problems), we discuss briefly the P vs. NP problem. We then focus on certain classes between P and NP which capture important phenomena in the social and life sciences, namely the Nash equlibrium and other equilibria in economics and game theory, and certain processes in population genetics and evolution. Finally, an algorithm known as multiplicative weights update (MWU) provides an algorithmic interpretation of the evolution of allele frequencies in a population under sex and weak selection. All three of these equivalences are rife with domain-specific implications: The concept of Nash equilibrium may be less universal—and therefore less compelling—than has been presumed; selection on gene interactions may entail the maintenance of genetic variation for longer periods than selection on single alleles predicts; whereas MWU can be shown to maximize, for each gene, a convex combination of the gene’s cumulative fitness in the population and the entropy of the allele distribution, an insight that may be pertinent to the maintenance of variation in evolution. PMID:25349382

Geometric properties of commutative subalgebras of partial differential operators

NASA Astrophysics Data System (ADS)

Zheglov, A. B.; Kurke, H.

2015-05-01

We investigate further algebro-geometric properties of commutative rings of partial differential operators, continuing our research started in previous articles. In particular, we start to explore the simplest and also certain known examples of quantum algebraically completely integrable systems from the point of view of a recent generalization of Sato's theory, developed by the first author. We give a complete characterization of the spectral data for a class of 'trivial' commutative algebras and strengthen geometric properties known earlier for a class of known examples. We also define a kind of restriction map from the moduli space of coherent sheaves with fixed Hilbert polynomial on a surface to an analogous moduli space on a divisor (both the surface and the divisor are part of the spectral data). We give several explicit examples of spectral data and corresponding algebras of commuting (completed) operators, producing as a by-product interesting examples of surfaces that are not isomorphic to spectral surfaces of any (maximal) commutative ring of partial differential operators of rank one. Finally, we prove that any commutative ring of partial differential operators whose normalization is isomorphic to the ring of polynomials k \\lbrack u,t \\rbrack is a Darboux transformation of a ring of operators with constant coefficients. Bibliography: 39 titles.

Global stabilisation of a class of generalised cascaded systems by homogeneous method

NASA Astrophysics Data System (ADS)

Ding, Shihong; Zheng, Wei Xing

2016-04-01

This paper considers the problem of global stabilisation of a class of generalised cascaded systems. By using the extended adding a power integrator technique, a global controller is first constructed for the driving subsystem. Then based on the homogeneous properties and polynomial assumption, it is shown that the stabilisation of the driving subsystem implies the stabilisation of the overall cascaded system. Meanwhile, by properly choosing some control parameters, the global finite-time stability of the closed-loop cascaded system is also established. The proposed control method has several new features. First, the nonlinear cascaded systems considered in the paper are more general than the conventional ones, since the powers in the nominal part of the driving subsystem are not required to be restricted to ratios of positive odd numbers. Second, the proposed method has some flexible parameters which provide the possibility for designing continuously differentiable controllers for cascaded systems, while the existing designed controllers for such kind of cascaded systems are only continuous. Third, the homogenous and polynomial conditions adopted for the driven subsystem are easier to verify when compared with the matching conditions that are widely used previously. Furthermore, the efficiency of the proposed control method is validated by its application to finite-time tracking control of non-holonomic wheeled mobile robot.

An Analytical Framework for Runtime of a Class of Continuous Evolutionary Algorithms.

PubMed

Zhang, Yushan; Hu, Guiwu

2015-01-01

Although there have been many studies on the runtime of evolutionary algorithms in discrete optimization, relatively few theoretical results have been proposed on continuous optimization, such as evolutionary programming (EP). This paper proposes an analysis of the runtime of two EP algorithms based on Gaussian and Cauchy mutations, using an absorbing Markov chain. Given a constant variation, we calculate the runtime upper bound of special Gaussian mutation EP and Cauchy mutation EP. Our analysis reveals that the upper bounds are impacted by individual number, problem dimension number n, searching range, and the Lebesgue measure of the optimal neighborhood. Furthermore, we provide conditions whereby the average runtime of the considered EP can be no more than a polynomial of n. The condition is that the Lebesgue measure of the optimal neighborhood is larger than a combinatorial calculation of an exponential and the given polynomial of n.

Quadrature rules with multiple nodes for evaluating integrals with strong singularities

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2006-05-01

We present a method based on the Chakalov-Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turan quadrature rules, Numer. Algorithms 10 (1995), 27-39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhauser, Basel, 1999, pp. 109-119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.

An Approach to Stable Gradient-Descent Adaptation of Higher Order Neural Units.

PubMed

Bukovsky, Ivo; Homma, Noriyasu

2017-09-01

Stability evaluation of a weight-update system of higher order neural units (HONUs) with polynomial aggregation of neural inputs (also known as classes of polynomial neural networks) for adaptation of both feedforward and recurrent HONUs by a gradient descent method is introduced. An essential core of the approach is based on the spectral radius of a weight-update system, and it allows stability monitoring and its maintenance at every adaptation step individually. Assuring the stability of the weight-update system (at every single adaptation step) naturally results in the adaptation stability of the whole neural architecture that adapts to the target data. As an aside, the used approach highlights the fact that the weight optimization of HONU is a linear problem, so the proposed approach can be generally extended to any neural architecture that is linear in its adaptable parameters.

Comments on Samal and Henderson: Parallel consistent labeling algorithms

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

Swain, M.J.

Samal and Henderson claim that any parallel algorithm for enforcing arc consistency in the worst case must have {Omega}(na) sequential steps, where n is the number of nodes, and a is the number of labels per node. The authors argue that Samal and Henderon's argument makes assumptions about how processors are used and give a counterexample that enforces arc consistency in a constant number of steps using O(n{sup 2}a{sup 2}2{sup na}) processors. It is possible that the lower bound holds for a polynomial number of processors; if such a lower bound were to be proven it would answer an importantmore » open question in theoretical computer science concerning the relation between the complexity classes P and NC. The strongest existing lower bound for the arc consistency problem states that it cannot be solved in polynomial log time unless P = NC.« less

Georeferencing CAMS data: Polynomial rectification and beyond

NASA Astrophysics Data System (ADS)

Yang, Xinghe

The Calibrated Airborne Multispectral Scanner (CAMS) is a sensor used in the commercial remote sensing program at NASA Stennis Space Center. In geographic applications of the CAMS data, accurate geometric rectification is essential for the analysis of the remotely sensed data and for the integration of the data into Geographic Information Systems (GIS). The commonly used rectification techniques such as the polynomial transformation and ortho rectification have been very successful in the field of remote sensing and GIS for most remote sensing data such as Landsat imagery, SPOT imagery and aerial photos. However, due to the geometric nature of the airborne line scanner which has high spatial frequency distortions, the polynomial model and the ortho rectification technique in current commercial software packages such as Erdas Imagine are not adequate for obtaining sufficient geometric accuracy. In this research, the geometric nature, especially the major distortions, of the CAMS data has been described. An analytical step-by-step geometric preprocessing has been utilized to deal with the potential high frequency distortions of the CAMS data. A generic sensor-independent photogrammetric model has been developed for the ortho-rectification of the CAMS data. Three generalized kernel classes and directional elliptical basis have been formulated into a rectification model of summation of multisurface functions, which is a significant extension to the traditional radial basis functions. The preprocessing mechanism has been fully incorporated into the polynomial, the triangle-based finite element analysis as well as the summation of multisurface functions. While the multisurface functions and the finite element analysis have the characteristics of localization, piecewise logic has been applied to the polynomial and photogrammetric methods, which can produce significant accuracy improvement over the global approach. A software module has been implemented with full integration of data preprocessing and rectification techniques under Erdas Imagine development environment. The final root mean square (RMS) errors for the test CAMS data are about two pixels which are compatible with the random RMS errors existed in the reference map coordinates.

In the Footsteps of Roger Revelle: Seagoing Oceanography for Middle School Science

NASA Astrophysics Data System (ADS)

Brice, D.; Foley, S.; Knox, R. A.; Mauricio, P.

2007-12-01

Now in its fourth year, "In the Footsteps of Roger Revelle" (IFRR) is a middle school science education program that draws student interest, scientific content and coherence with National Science Standards from real-time research at sea in fields of physical science. As a successful collaboration involving Scripps Institution of Oceanography (SIO), Woods Hole Oceanographic Institution (WHOI), National Oceanic and Atmospheric Administration (NOAA), Office of Naval Research (ONR), National Science Foundation (NSF), San Diego County Office of Education (SDCOE), and San Marcos Middle School (SMMS), IFRR brings physical oceanography and related sciences to students at the San Marcos Middle School in real-time from research vessels at sea using SIO's HiSeasNet satellite communication system. With their science teacher on the ship as an education outreach specialist or ashore guiding students in their interactions with selected scientists at sea, students observe shipboard research being carried out live via videoconference, daily e-mails, interviews, digital whiteboard sessions, and web interaction. Students then research, design, develop, deploy, and field-test their own data-collecting physical oceanography instruments in their classroom. The online interactive curriculum encourages active inquiry with intellectually stimulating problem-solving, enabling students to gain critical insight and skill while investigating some of the most provocative questions of our time, and seeing scientists as role- models. Recent science test scores with IFRR students have shown significant increases in classes where this curriculum has been implemented as compared to other classes where the traditional curriculum has been used. IFRR has provided students in the San Diego area with a unique opportunity for learning about oceanographic research, which could inspire students to become oceanographers or at least scientifically literate citizens - a benefit for a country that depends increasingly on technically proficient personnel, and a benefit for society at large.

Dal "San Marco" al "Vega". (English Title: From "San Marco" to Vega)

NASA Astrophysics Data System (ADS)

Savi, E.

2017-10-01

Apart from the two superpowers, among the other countries Italy has had an important role in astronautics. The roots of Italian astronautics' history runs deep in the hottest years of the Cold War, and it had its first remarkable achievement in the San Marco project..after years of advanced technologies testing, they achieved European cooperation and built VEGA, the current Arianespace light launcher.

Geometry Dynamics of α-Helices in Different Class I Major Histocompatibility Complexes

PubMed Central

Karch, Rudolf; Schreiner, Wolfgang

2015-01-01

MHC α-helices form the antigen-binding cleft and are of particular interest for immunological reactions. To monitor these helices in molecular dynamics simulations, we applied a parsimonious fragment-fitting method to trace the axes of the α-helices. Each resulting axis was fitted by polynomials in a least-squares sense and the curvature integral was computed. To find the appropriate polynomial degree, the method was tested on two artificially modelled helices, one performing a bending movement and another a hinge movement. We found that second-order polynomials retrieve predefined parameters of helical motion with minimal relative error. From MD simulations we selected those parts of α-helices that were stable and also close to the TCR/MHC interface. We monitored the curvature integral, generated a ruled surface between the two MHC α-helices, and computed interhelical area and surface torsion, as they changed over time. We found that MHC α-helices undergo rapid but small changes in conformation. The curvature integral of helices proved to be a sensitive measure, which was closely related to changes in shape over time as confirmed by RMSD analysis. We speculate that small changes in the conformation of individual MHC α-helices are part of the intrinsic dynamics induced by engagement with the TCR. PMID:26649324

Spatial modeling and classification of corneal shape.

PubMed

Marsolo, Keith; Twa, Michael; Bullimore, Mark A; Parthasarathy, Srinivasan

2007-03-01

One of the most promising applications of data mining is in biomedical data used in patient diagnosis. Any method of data analysis intended to support the clinical decision-making process should meet several criteria: it should capture clinically relevant features, be computationally feasible, and provide easily interpretable results. In an initial study, we examined the feasibility of using Zernike polynomials to represent biomedical instrument data in conjunction with a decision tree classifier to distinguish between the diseased and non-diseased eyes. Here, we provide a comprehensive follow-up to that work, examining a second representation, pseudo-Zernike polynomials, to determine whether they provide any increase in classification accuracy. We compare the fidelity of both methods using residual root-mean-square (rms) error and evaluate accuracy using several classifiers: neural networks, C4.5 decision trees, Voting Feature Intervals, and Naïve Bayes. We also examine the effect of several meta-learning strategies: boosting, bagging, and Random Forests (RFs). We present results comparing accuracy as it relates to dataset and transformation resolution over a larger, more challenging, multi-class dataset. They show that classification accuracy is similar for both data transformations, but differs by classifier. We find that the Zernike polynomials provide better feature representation than the pseudo-Zernikes and that the decision trees yield the best balance of classification accuracy and interpretability.

Logical definability and asymptotic growth in optimization and counting problems

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

Compton, K.

1994-12-31

There has recently been a great deal of interest in the relationship between logical definability and NP-optimization problems. Let MS{sub n} (resp. MP{sub n}) be the class of problems to compute, for given a finite structure A, the maximum number of tuples {bar x} in A satisfying a {Sigma}{sub n} (resp. II{sub n}) formula {psi}({bar x}, {bar S}) as {bar S} ranges over predicates on A. Kolaitis and Thakur showed that the classes MS{sub n} and MP{sub n} collapse to a hierarchy of four levels. Papadimitriou and Yannakakis previously showed that problems in the two lowest levels MS{sub 0} andmore » MS{sub 1} (which they called Max Snp and Max Np) are approximable to within a contrast factor in polynomial time. Similarly, Saluja, Subrahmanyam, and Thakur defined SS{sub n} (resp. SP{sub n}) to be the class of problems to compute, for given a finite structure A, the number of tuples ({bar T}, {bar S}) satisfying a given {Sigma}{sub n} (resp. II{sub n}) formula {psi}({bar T}, {bar c}) in A. They showed that the classes SS{sub n} and SP{sub n} collapse to a hierarchy of five levels and that problems in the two lowest levels SS{sub 0} and SS{sub 1} have a fully polynomial time randomized approximation scheme. We define extended classes MSF{sub n}, MPF{sub n} SSF{sub n}, and SPF{sub n} by allowing formulae to contain predicates definable in a logic known as least fixpoint logic. The resulting hierarchies classes collapse to the same number of levels and problems in the bottom levels can be approximated as before, but now some problems descend from the highest levels in the original hierarchies to the lowest levels in the new hierarchies. We introduce a method characterizing rates of growth of average solution sizes thereby showing a number of important problems do not belong MSF{sub 1} and SSF{sub 1}. This method is related to limit laws for logics and the probabilistic method from combinatorics.« less

MarCOs Cruise in Deep Space

NASA Image and Video Library

2018-03-29

An artist's rendering of the twin Mars Cube One (MarCO) spacecraft as they fly through deep space. The MarCOs will be the first CubeSats -- a kind of modular, mini-satellite -- attempting to fly to another planet. They're designed to fly along behind NASA's InSight lander on its cruise to Mars. If they make the journey, they will test a relay of data about InSight's entry, descent and landing back to Earth. Though InSight's mission will not depend on the success of the MarCOs, they will be a test of how CubeSats can be used in deep space. https://photojournal.jpl.nasa.gov/catalog/PIA22314

Alternate: MarCO Being Tested in Sunlight

NASA Image and Video Library

2018-03-29

Engineer Joel Steinkraus uses sunlight to test the solar arrays on one of the Mars Cube One (MarCO) spacecraft at NASA's Jet Propulsion Laboratory. The MarCOs will be the first CubeSats -- a kind of modular, mini-satellite -- flown into deep space. They're designed to fly along behind NASA's InSight lander on its cruise to Mars. If they make the journey, they will test a relay of data about InSight's entry, descent and landing back to Earth. Though InSight's mission will not depend on the success of the MarCOs, they will be a test of how CubeSats can be used in deep space. https://photojournal.jpl.nasa.gov/catalog/PIA22318

MarCO Being Tested in Sunlight

NASA Image and Video Library

2018-03-29

Engineer Joel Steinkraus uses sunlight to test the solar arrays on one of the Mars Cube One (MarCO) spacecraft at NASA's Jet Propulsion Laboratory. The MarCOs will be the first CubeSats -- a kind of modular, mini-satellite -- flown into deep space. They're designed to fly along behind NASA's InSight lander on its cruise to Mars. If they make the journey to Mars, they will test a relay of data about InSight's entry, descent and landing back to Earth. Though InSight's mission will not depend on the success of the MarCOs, they will be a test of how CubeSats can be used in deep space. https://photojournal.jpl.nasa.gov/catalog/PIA22317

Distant Perspective of MarCOs Cruise in Deep Space

NASA Image and Video Library

2018-03-29

An artist's rendering of the twin Mars Cube One (MarCO) spacecraft on their cruise in deep space. The MarCOs will be the first CubeSats -- a kind of modular, mini-satellite -- attempting to fly to another planet. They're designed to fly along behind NASA's InSight lander on its cruise to Mars. If they make the journey, they will test a relay of data about InSight's entry, descent and landing back to Earth. Though InSight's mission will not depend on the success of the MarCOs, they will be a test of how CubeSats can be used in deep space. https://photojournal.jpl.nasa.gov/catalog/PIA22315

San Marco D/L Post Launch Report No. 2

NASA Technical Reports Server (NTRS)

1988-01-01

The San Marco D/L spacecraft, utilizing a NASA supplied Scout expendable launch vehicle, was launched fran the San Marco Range, located off the coast of Kenya, Africa, on March 25, 1988 at 19:50 GMT. The launch was conducted by an Italian crew assisted by LaRC and LTV personnel. The San Marco D/L was the fifth in a series of Italian and United States satellites. The purpose of the mission is to explore the relationship between solar activity and the physics of the equatorial thermosphere and ionosphere. Information now being collected will augment, and be used in correlation with, data and information obtained from ground based facilities and other satellites.

San Marco C-2 Explorer

NASA Technical Reports Server (NTRS)

1974-01-01

The San Marco C-2 spacecraft will be launched no earlier than 18 February 1974 from the San Marco Range located off the coast of Kenya, Africa, by a Scout launch vehicle. The launch will be conducted by an Italian crew. The San Marco C-2 is the fourth cooperative satellite project between Italy and the United States. The purpose of the mission is to obtain measurements of the diurnal variations of the equatorial neutral atmosphere density, composition, and temperature and to use these data for correlation with AE-C (Explorer 51) data for studies of the physics and dynamics of the thermosphere. The San Marco C-2 project is a joint undertaking of the National Aeronautics and Space Administration (NASA) and the Italian Space Commission officially initiated with a Memorandum of Understanding in August of 1973. Project management responsibility for the Italian portion of the project has been assigned to the Centro Ricerche Aerospaziali (CRA) while the Goddard Space Flight Center (GSFC) has responsibility for the United States portion.

Origin and characteristics of discharge at San Marcos Springs based on hydrologic and geochemical data (2008-10), Bexar, Comal, and Hays Counties, Texas

USGS Publications Warehouse

Musgrove, MaryLynn; Crow, Cassi L.

2012-01-01

The Edwards aquifer in south-central Texas is a productive and important water resource. Several large springs issuing from the aquifer are major discharge points, popular locations for recreational activities, and habitat for threatened and endangered species. Discharges from Comal and San Marcos Springs, the first and second largest spring complexes in Texas, are used as thresholds in groundwater management strategies for the Edwards aquifer. Comal Springs is generally understood to be supplied by predominantly regional groundwater flow paths; the hydrologic connection of San Marcos Springs with the regional flow system, however, is less understood. During November 2008–December 2010, a hydrologic and geochemical investigation of San Marcos Springs was conducted by the U.S. Geological Survey (USGS) in cooperation with the San Antonio Water System. The primary objective of this study was to define and characterize sources of discharge from San Marcos Springs. During this study, hydrologic conditions transitioned from exceptional drought (the dry period, November 1, 2008 to September 8, 2009) to wetter than normal (the wet period, September 9, 2009 to December 31, 2010), which provided the opportunity to investigate the hydrogeology of San Marcos Springs under a wide range of hydrologic conditions. Water samples were collected from streams, groundwater wells, and springs at and in the vicinity of San Marcos Springs, including periodic (routine) sampling (every 3–7 weeks) and sampling in response to storms. Samples were analyzed for major ions, trace elements, nutrients, and selected stable and radiogenic isotopes (deuterium, oxygen, carbon, strontium). Additionally, selected physicochemical properties were measured continuously at several sites, and hydrologic data were compiled from other USGS efforts (stream and spring discharge). Potential aquifer recharge was evaluated from local streams, and daily recharge or gain/loss estimates were computed for several local streams. Local rainfall and recharge events were compared with physicochemical properties and geochemical variability at San Marcos Springs, with little evidence for dilution by local recharge.

Evaluation of acoustic doppler velocity meters to quantify flow from Comal Springs and San Marcos Springs, Texas

USGS Publications Warehouse

Gary, Marcus O.; Gary, Robin H.; Asquith, William H.

2008-01-01

Comal Springs and San Marcos Springs are the two largest springs in Texas, are major discharge points for the San Antonio segment of the Edwards aquifer, and provide habitat for several Federally listed endangered species that depend on adequate springflows for survival. It is therefore imperative that the Edwards Aquifer Authority have accurate and timely springflow data to guide resource management. Discharge points for Comal Springs and San Marcos Springs are submerged in Landa Lake and in Spring Lake, respectively. Flows from the springs currently (2008) are estimated by the U.S Geological Survey in real time as surface-water discharge from conventional stage-discharge ratings at sites downstream from each spring. Recent technological advances and availability of acoustic Doppler velocity meters (ADVMs) now provide tools to collect data (stream velocity) related to springflow that could increase accuracy of real-time estimates of the springflows. The U.S. Geological Survey, in cooperation with the Edwards Aquifer Authority, did a study during May 2006 through September 2007 to evaluate ADVMs to quantify flow from Comal and San Marcos Springs. The evaluation was based on two monitoring approaches: (1) placement of ADVMs in important spring orifices - spring run 3 and spring 7 at Comal Springs, and diversion spring at San Marcos Springs; and (2) placement of ADVMs at the nearest flowing streams - Comal River new and old channels for Comal Springs, Spring Lake west and east outflow channels and current (2008) San Marcos River streamflow-gaging site for San Marcos Springs. For Comal Springs, ADVM application at spring run 3 and spring 7 was intended to indicate whether the flows of spring run 3 and spring 7 can be related to total springflow. The findings indicate that velocity data from both discharge features, while reflecting changes in flow, do not reliably show a direct relation to measured streamflow and thus to total Comal Springs flow. ADVMs at the Comal River new channel and old channel sites provide data that potentially could yield more accurate real-time estimates of total Comal Springs flow than streamflow measured at the downstream Comal River site. For San Marcos Springs, the findings indicate shortcomings with ADVM installations at diversion spring and in the west and east outflow channels. However, the accuracy of streamflow measured at the San Marcos River gage as an estimate of real-time San Marcos Springs flow could potentially be increased through use of ADVM data from that site.

Aula Verde: art as experience in community-based environmental education.

PubMed

Abarca, Marco A

2010-01-01

After winning a class-action lawsuit against unconstitutional prison conditions in Puerto Rico, Marco Abarca managed to direct part of the fine monies accumulated throughout years of litigation toward an investment that would improve the living conditions in one of the largest and poorest housing projects in Puerto Rico. With the participation of parolees and probationers, he began to transform a mosquito-infested badland into a natural haven. Then, with the help of science educators, the group designed a workshop for elementary school children on urban ecology. As the participants organized, what developed was a community-based, self-employed enterprise known as Aula Verde.

Double Ramification Cycles and Quantum Integrable Systems

NASA Astrophysics Data System (ADS)

Buryak, Alexandr; Rossi, Paolo

2016-03-01

In this paper, we define a quantization of the Double Ramification Hierarchies of Buryak (Commun Math Phys 336:1085-1107, 2015) and Buryak and Rossi (Commun Math Phys, 2014), using intersection numbers of the double ramification cycle, the full Chern class of the Hodge bundle and psi-classes with a given cohomological field theory. We provide effective recursion formulae which determine the full quantum hierarchy starting from just one Hamiltonian, the one associated with the first descendant of the unit of the cohomological field theory only. We study various examples which provide, in very explicit form, new (1+1)-dimensional integrable quantum field theories whose classical limits are well-known integrable hierarchies such as KdV, Intermediate Long Wave, extended Toda, etc. Finally, we prove polynomiality in the ramification multiplicities of the integral of any tautological class over the double ramification cycle.

Southeast Asia Report

DTIC Science & Technology

1986-02-21

said Mr Marcos seemed to be delaying holding an official tally "until he knows how many additional votes he needs to win." Mr Marcos has stressed that...Feb 86) 66 Virata on Need for Dollar-Earning Cottage Industries ,. (BULLETIN TODAY, 3 Feb 86) 68 Marcos Says Government Managing Debt Well...that Dr Lim on 3 November returned from a tour of foreign countries during which he had a tumor in the thyroid gland surgically removed in America

History of San Marco

NASA Technical Reports Server (NTRS)

Caporale, A. J.

1968-01-01

A brief history is reported of the first San Marco project, a joint program of the United States and Italy. The Project was a three phase effort to investigate upper air density and associated ionosphere phenomena. The initial phase included the design and development of the spacecraft, the experiments, the launch complex, and a series of suborbital flights, from Wallops Island. The second phase, consisting of designing, fabricating, and testing a spacecraft for the first orbital mission, culminated in an orbital launch also from Wallops Island. The third phase consisted of further refining the experiments and spacecraft instrumentation and of establishing a full-bore scout complex in Kenya. The launch of San Marco B, in April 1967, from this complex into an equatorial orbit, concluded the initial San Marco effort.

Center manifolds for a class of degenerate evolution equations and existence of small-amplitude kinetic shocks

NASA Astrophysics Data System (ADS)

Pogan, Alin; Zumbrun, Kevin

2018-06-01

We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. Notably, for Boltzmann's equation, we show that elements of the center manifold decay in velocity at near-Maxwellian rate, in accord with the formal Chapman-Enskog picture of near-equilibrium flow as evolution along the manifold of Maxwellian states, or Grad moment approximation via Hermite polynomials in velocity. Our analysis is from a classical dynamical systems point of view, with a number of interesting modifications to accommodate ill-posedness of the underlying evolution equation.

Dynamics, integrability and topology for some classes of Kolmogorov Hamiltonian systems in R+4

NASA Astrophysics Data System (ADS)

Llibre, Jaume; Xiao, Dongmei

2017-02-01

In this paper we first give the sufficient and necessary conditions in order that two classes of polynomial Kolmogorov systems in R+4 are Hamiltonian systems. Then we study the integrability of these Hamiltonian systems in the Liouville sense. Finally, we investigate the global dynamics of the completely integrable Lotka-Volterra Hamiltonian systems in R+4. As an application of the invariant subsets of these systems, we obtain topological classifications of the 3-submanifolds in R+4 defined by the hypersurfaces axy + bzw + cx2 y + dxy2 + ez2 w + fzw2 = h, where a , b , c , d , e , f , w and h are real constants.

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

PubMed

Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

2014-10-01

Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

Comparison of random regression models with Legendre polynomials and linear splines for production traits and somatic cell score of Canadian Holstein cows.

PubMed

Bohmanova, J; Miglior, F; Jamrozik, J; Misztal, I; Sullivan, P G

2008-09-01

A random regression model with both random and fixed regressions fitted by Legendre polynomials of order 4 was compared with 3 alternative models fitting linear splines with 4, 5, or 6 knots. The effects common for all models were a herd-test-date effect, fixed regressions on days in milk (DIM) nested within region-age-season of calving class, and random regressions for additive genetic and permanent environmental effects. Data were test-day milk, fat and protein yields, and SCS recorded from 5 to 365 DIM during the first 3 lactations of Canadian Holstein cows. A random sample of 50 herds consisting of 96,756 test-day records was generated to estimate variance components within a Bayesian framework via Gibbs sampling. Two sets of genetic evaluations were subsequently carried out to investigate performance of the 4 models. Models were compared by graphical inspection of variance functions, goodness of fit, error of prediction of breeding values, and stability of estimated breeding values. Models with splines gave lower estimates of variances at extremes of lactations than the model with Legendre polynomials. Differences among models in goodness of fit measured by percentages of squared bias, correlations between predicted and observed records, and residual variances were small. The deviance information criterion favored the spline model with 6 knots. Smaller error of prediction and higher stability of estimated breeding values were achieved by using spline models with 5 and 6 knots compared with the model with Legendre polynomials. In general, the spline model with 6 knots had the best overall performance based upon the considered model comparison criteria.

Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle.

PubMed

Boligon, A A; Baldi, F; Mercadante, M E Z; Lobo, R B; Pereira, R J; Albuquerque, L G

2011-06-28

We quantified the potential increase in accuracy of expected breeding value for weights of Nelore cattle, from birth to mature age, using multi-trait and random regression models on Legendre polynomials and B-spline functions. A total of 87,712 weight records from 8144 females were used, recorded every three months from birth to mature age from the Nelore Brazil Program. For random regression analyses, all female weight records from birth to eight years of age (data set I) were considered. From this general data set, a subset was created (data set II), which included only nine weight records: at birth, weaning, 365 and 550 days of age, and 2, 3, 4, 5, and 6 years of age. Data set II was analyzed using random regression and multi-trait models. The model of analysis included the contemporary group as fixed effects and age of dam as a linear and quadratic covariable. In the random regression analyses, average growth trends were modeled using a cubic regression on orthogonal polynomials of age. Residual variances were modeled by a step function with five classes. Legendre polynomials of fourth and sixth order were utilized to model the direct genetic and animal permanent environmental effects, respectively, while third-order Legendre polynomials were considered for maternal genetic and maternal permanent environmental effects. Quadratic polynomials were applied to model all random effects in random regression models on B-spline functions. Direct genetic and animal permanent environmental effects were modeled using three segments or five coefficients, and genetic maternal and maternal permanent environmental effects were modeled with one segment or three coefficients in the random regression models on B-spline functions. For both data sets (I and II), animals ranked differently according to expected breeding value obtained by random regression or multi-trait models. With random regression models, the highest gains in accuracy were obtained at ages with a low number of weight records. The results indicate that random regression models provide more accurate expected breeding values than the traditionally finite multi-trait models. Thus, higher genetic responses are expected for beef cattle growth traits by replacing a multi-trait model with random regression models for genetic evaluation. B-spline functions could be applied as an alternative to Legendre polynomials to model covariance functions for weights from birth to mature age.

Association of total mixed ration particle fractions retained on the Penn State Particle Separator with milk, fat, and protein yield lactation curves at the cow level.

PubMed

Caccamo, M; Ferguson, J D; Veerkamp, R F; Schadt, I; Petriglieri, R; Azzaro, G; Pozzebon, A; Licitra, G

2014-01-01

As part of a larger project aiming to develop management evaluation tools based on results from test-day (TD) models, the objective of this study was to examine the effect of physical composition of total mixed rations (TMR) tested quarterly from March 2006 through December 2008 on milk, fat, and protein yield curves for 25 herds in Ragusa, Sicily. A random regression sire-maternal grandsire model was used to estimate variance components for milk, fat, and protein yields fitted on a full data set, including 241,153 TD records from 9,809 animals in 42 herds recorded from 1995 through 2008. The model included parity, age at calving, year at calving, and stage of pregnancy as fixed effects. Random effects were herd × test date, sire and maternal grandsire additive genetic effect, and permanent environmental effect modeled using third-order Legendre polynomials. Model fitting was carried out using ASREML. Afterward, for the 25 herds involved in the study, 9 particle size classes were defined based on the proportions of TMR particles on the top (19-mm) and middle (8-mm) screen of the Penn State Particle Separator. Subsequently, the model with estimated variance components was used to examine the influence of TMR particle size class on milk, fat, and protein yield curves. An interaction was included with the particle size class and days in milk. The effect of the TMR particle size class was modeled using a ninth-order Legendre polynomial. Lactation curves were predicted from the model while controlling for TMR chemical composition (crude protein content of 15.5%, neutral detergent fiber of 40.7%, and starch of 19.7% for all classes), to have pure estimates of particle distribution not confounded by nutrient content of TMR. We found little effect of class of particle proportions on milk yield and fat yield curves. Protein yield was greater for sieve classes with 10.4 to 17.4% of TMR particles retained on the top (19-mm) sieve. Optimal distributions different from those recommended may reflect regional differences based on climate and types and quality of forages fed. Copyright © 2014 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Britain, France and Germany: Priorities for the European Union’s Security and Defense Policy

DTIC Science & Technology

2009-12-01

Ronja Kempin and Marco Overhaus, Kein großer Sprung in der Entwicklung der ESVP: Lehren aus der Französischen EU- Ratspräsidentschaft (Berlin...Power," Survival 37, no. 3 (Autumn 1995), 82–103, 96. 144 Marco Overhaus, "German Foreign Policy and the Shadow of the Past," SAIS Review 25, no. 2...have enforced an arms embargo, Marco Overhaus, a research fellow at the German 171 Thomas

Poly-Frobenius-Euler polynomials

NASA Astrophysics Data System (ADS)

Kurt, Burak

2017-07-01

Hamahata [3] defined poly-Euler polynomials and the generalized poly-Euler polynomials. He proved some relations and closed formulas for the poly-Euler polynomials. By this motivation, we define poly-Frobenius-Euler polynomials. We give some relations for this polynomials. Also, we prove the relationships between poly-Frobenius-Euler polynomials and Stirling numbers of the second kind.

Remarks on a New Possible Discretization Scheme for Gauge Theories

NASA Astrophysics Data System (ADS)

Magnot, Jean-Pierre

2018-03-01

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

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.

On the theory of singular optimal controls in dynamic systems with control delay

NASA Astrophysics Data System (ADS)

Mardanov, M. J.; Melikov, T. K.

2017-05-01

An optimal control problem with a control delay is considered, and a more broad class of singular (in classical sense) controls is investigated. Various sequences of necessary conditions for the optimality of singular controls in recurrent form are obtained. These optimality conditions include analogues of the Kelley, Kopp-Moyer, R. Gabasov, and equality-type conditions. In the proof of the main results, the variation of the control is defined using Legendre polynomials.

Remarks on a New Possible Discretization Scheme for Gauge Theories

NASA Astrophysics Data System (ADS)

Magnot, Jean-Pierre

2018-07-01

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

On the Number of Periodic Solutions of Delay Differential Equations

NASA Astrophysics Data System (ADS)

Han, Maoan; Xu, Bing; Tian, Huanhuan; Bai, Yuzhen

In this paper, we consider the existence and number of periodic solutions for a class of delay differential equations of the form ẋ(t) = bx(t ‑ 1) + 𝜀f(x(t),x(t ‑ 1),𝜀), based on the Kaplan-Yorke method. Especially, we consider a kind of delay differential equations with f as a polynomial having parameters and find the number of periodic solutions with period 4 4k+1 or 4 4k+3.

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

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

Hong Luo; Yidong Xia; Robert Nourgaliev

2011-05-01

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison.more » Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.« less

Bounding the number of limit cycles of discontinuous differential systems by using Picard-Fuchs equations

NASA Astrophysics Data System (ADS)

Yang, Jihua; Zhao, Liqin

2018-05-01

In this paper, by using Picard-Fuchs equations and Chebyshev criterion, we study the upper bounds of the number of limit cycles given by the first order Melnikov function for discontinuous differential systems, which can bifurcate from the periodic orbits of quadratic reversible centers of genus one (r19): x ˙ = y - 12x2 + 16y2, y ˙ = - x - 16 xy, and (r20): x ˙ = y + 4x2, y ˙ = - x + 16 xy, and the periodic orbits of the quadratic isochronous centers (S1) : x ˙ = - y +x2 -y2, y ˙ = x + 2 xy, and (S2) : x ˙ = - y +x2, y ˙ = x + xy. The systems (r19) and (r20) are perturbed inside the class of polynomial differential systems of degree n and the system (S1) and (S2) are perturbed inside the class of quadratic polynomial differential systems. The discontinuity is the line y = 0. It is proved that the upper bounds of the number of limit cycles for systems (r19) and (r20) are respectively 4 n - 3 (n ≥ 4) and 4 n + 3 (n ≥ 3) counting the multiplicity, and the maximum numbers of limit cycles bifurcating from the period annuluses of the isochronous centers (S1) and (S2) are exactly 5 and 6 (counting the multiplicity) on each period annulus respectively.

Analytic complexity of functions of two variables

NASA Astrophysics Data System (ADS)

Beloshapka, V. K.

2007-09-01

The definition of analytic complexity of an analytic function of two variables is given. It is proved that the class of functions of a chosen complexity is a differentialalgebraic set. A differential polynomial defining the functions of first class is constructed. An algorithm for obtaining relations defining an arbitrary class is described. Examples of functions are given whose order of complexity is equal to zero, one, two, and infinity. It is shown that the formal order of complexity of the Cardano and Ferrari formulas is significantly higher than their analytic complexity. The complexity classes turn out to be invariant with respect to a certain infinite-dimensional transformation pseudogroup. In this connection, we describe the orbits of the action of this pseudogroup in the jets of orders one, two, and three. The notion of complexity order is extended to plane (or “planar”) 3-webs. It is discovered that webs of complexity order one are the hexagonal webs. Some problems are posed.

Concept of Operations for Deploying a Lander on the Secondary Body of Binary Asteroid 1996 FG3

NASA Astrophysics Data System (ADS)

Tardivel, Simon; Michel, P.; Scheeres, D.

2012-10-01

The European Space Agency is currently performing an assessment study of the MarcoPolo-R space mission, in the framework of the M3 class competition of its Cosmic Vision Program. MarcoPolo-R is a sample return mission to a primitive asteroid, whose baseline target is the binary asteroid 1996FG3. The baseline mission, including the sample, is focused on the primary of the binary system. To date, little has yet been considered for the investigation of the secondary, apart from remote observations from the spacecraft. However, MarcoPolo-R may carry an optional lander, and if such a lander could be accommodated it may be relevant to use it for a more detailed investigation of the secondary. This poster presents a strategy for deploying a lander using an unpowered trajectory towards the secondary. This ballistic deployment allows for the design of a light lander with minimum platform overhead and maximum payload. The deployment operations are shown to be very simple and require minimum preparation. The main spacecraft is set on an orbit that reaches a specific point near the binary system L2 Lagrange Point facing the far side of the secondary, about 220 meters from the secondary surface, with a relative speed of about 10cm/s. The lander is then jettisoned using a spring-release mechanism that sets it on an impact trajectory that robustly intersects with the secondary surface. On impact, the lander only needs to dissipate a small amount of kinetic energy in order to ensure that it is energetically and dynamically trapped on the surface. Considering errors on spacecraft GNC and on the spring-release mechanism, and very large uncertainties on the gravity field of the asteroids, the strategy presented here yields a successful landing in more than 99.9% of cases, while ensuring the absolute safety of the spacecraft before, during and after deployment operations.

Improving children's menus in community restaurants: best food for families, infants, and toddlers (Best Food FITS) intervention, South Central Texas, 2010-2014.

PubMed

Crixell, Sylvia Hurd; Friedman, Bj; Fisher, Deborah Torrey; Biediger-Friedman, Lesli

2014-12-24

Approximately 32% of US children are overweight or obese. Restaurant and fast food meals contribute 18% of daily calories for children and adolescents aged 2 to 18 years. Changing children's menus may improve their diets. This case study describes Best Food for Families, Infants, and Toddlers (Best Food FITS), a community-based intervention designed to address childhood obesity. The objective of this study was to improve San Marcos children's access to healthy diets through partnerships with local restaurants, removing sugar-sweetened beverages, decreasing the number of energy-dense entrées, and increasing fruit and vegetable offerings on restaurant menus. San Marcos, Texas, the fastest growing US city, has more restaurants and fewer grocery stores than other Texas cities. San Marcos's population is diverse; 37.8% of residents and 70.3% of children are Hispanic. Overweight and obesity rates among school children exceed 50%; 40.3% of children live below the poverty level. This project received funding from the Texas Department of State Health Services Nutrition, Physical Activity, and Obesity Prevention Program to develop Best Food FITS. The case study consisted of developing a brand, engaging community stakeholders, reviewing existing children's menus in local restaurants, administering owner-manager surveys, collaborating with restaurants to improve menus, and assessing the process and outcomes of the intervention. Best Food FITS regularly participated in citywide health events and funded the construction of a teaching kitchen in a new community building where regular nutrition classes are held. Sixteen independent restaurants and 1 chain restaurant implemented new menus. Improving menus in restaurants can be a simple step toward changing children's food habits. The approach taken in this case study can be adapted to other communities. Minimal funding would be needed to facilitate development of promotional items to support brand recognition.

InSight MARCO Installation Cubesats

NASA Image and Video Library

2018-03-17

At Vandenberg Air Force Base in California, twin communications-relay CubeSats, called Mars Cube One (MarCO) are installed on an Atlas V rocket. MarCO constitutes a technology demonstration being built by NASA's Jet Propulsion Laboratory, Pasadena in California. They will launch in on the same United Launch Alliance Atlas V rocket as NASA's Interior Exploration using Seismic Investigations, Geodesy and Heat Transport, or InSight, spacecraft to land on Mars. CubeSats are a class of spacecraft based on a standardized small size and modular use of off-the-shelf technologies. Many have been made by university students, and dozens have been launched into Earth orbit using extra payload mass available on launches of larger spacecraft. InSight is the first mission to explore the Red Planet's deep interior. InSight is scheduled for liftoff May 5, 2018. InSight will be the first mission to look deep beneath the Martian surface. It will study the planet's interior by measuring its heat output and listen for marsquakes. InSight will use the seismic waves generated by marsquakes to develop a map of the planet’s deep interior. The resulting insight into Mars’ formation will provide a better understanding of how other rocky planets, including Earth, were created. NASA’s Jet Propulsion Laboratory in Pasadena, California, manages the InSight mission for the agency’s Science Mission Directorate. InSight is part of NASA's Discovery Program, managed by its Marshall Space Flight Center in Huntsville, Alabama. The spacecraft, including cruise stage and lander, was built and tested by Lockheed Martin Space in Denver. Several European partners, including France's space agency, the Centre National d'Étude Spatiales, and the German Aerospace Center, are supporting the mission. United Launch Alliance of Centennial, Colorado, is providing the Atlas V launch service. NASA’s Launch Services Program, based at its Kennedy Space Center in Florida, is responsible for launch management.

InSight Atlas V MARCO Cubesats Installation

NASA Image and Video Library

2018-03-17

At Vandenberg Air Force Base in California, twin communications-relay CubeSats, called Mars Cube One (MarCO) are prepared for installation on an Atlas V rocket. MarCO constitutes a technology demonstration being built by NASA's Jet Propulsion Laboratory, Pasadena in California. They will launch in on the same United Launch Alliance Atlas V rocket as NASA's Interior Exploration using Seismic Investigations, Geodesy and Heat Transport, or InSight, spacecraft to land on Mars. CubeSats are a class of spacecraft based on a standardized small size and modular use of off-the-shelf technologies. Many have been made by university students, and dozens have been launched into Earth orbit using extra payload mass available on launches of larger spacecraft. InSight is the first mission to explore the Red Planet's deep interior. InSight is scheduled for liftoff May 5, 2018. InSight will be the first mission to look deep beneath the Martian surface. It will study the planet's interior by measuring its heat output and listen for marsquakes. InSight will use the seismic waves generated by marsquakes to develop a map of the planet’s deep interior. The resulting insight into Mars’ formation will provide a better understanding of how other rocky planets, including Earth, were created. NASA’s Jet Propulsion Laboratory in Pasadena, California, manages the InSight mission for the agency’s Science Mission Directorate. InSight is part of NASA's Discovery Program, managed by its Marshall Space Flight Center in Huntsville, Alabama. The spacecraft, including cruise stage and lander, was built and tested by Lockheed Martin Space in Denver. Several European partners, including France's space agency, the Centre National d'Étude Spatiales, and the German Aerospace Center, are supporting the mission. United Launch Alliance of Centennial, Colorado, is providing the Atlas V launch service. NASA’s Launch Services Program, based at its Kennedy Space Center in Florida, is responsible for laun

InSight Atlas V MARCO Cubesats Installation

NASA Image and Video Library

2018-03-17

At Vandenberg Air Force Base in California, twin communications-relay CubeSats, called Mars Cube One (MarCO) are installed on an Atlas V rocket. MarCO constitutes a technology demonstration being built by NASA's Jet Propulsion Laboratory, Pasadena in California. They will launch in on the same United Launch Alliance Atlas V rocket as NASA's Interior Exploration using Seismic Investigations, Geodesy and Heat Transport, or InSight, spacecraft to land on Mars. CubeSats are a class of spacecraft based on a standardized small size and modular use of off-the-shelf technologies. Many have been made by university students, and dozens have been launched into Earth orbit using extra payload mass available on launches of larger spacecraft. InSight is the first mission to explore the Red Planet's deep interior. InSight is scheduled for liftoff May 5, 2018. InSight will be the first mission to look deep beneath the Martian surface. It will study the planet's interior by measuring its heat output and listen for marsquakes. InSight will use the seismic waves generated by marsquakes to develop a map of the planet’s deep interior. The resulting insight into Mars’ formation will provide a better understanding of how other rocky planets, including Earth, were created. NASA’s Jet Propulsion Laboratory in Pasadena, California, manages the InSight mission for the agency’s Science Mission Directorate. InSight is part of NASA's Discovery Program, managed by its Marshall Space Flight Center in Huntsville, Alabama. The spacecraft, including cruise stage and lander, was built and tested by Lockheed Martin Space in Denver. Several European partners, including France's space agency, the Centre National d'Étude Spatiales, and the German Aerospace Center, are supporting the mission. United Launch Alliance of Centennial, Colorado, is providing the Atlas V launch service. NASA’s Launch Services Program, based at its Kennedy Space Center in Florida, is responsible for launch management.

Philippine Counterinsurgency during the Presidencies of Magsaysay, Marcos, and Ramos: Challenges and Opportunities

DTIC Science & Technology

2016-06-10

80 Bresnan, Crisis in the Philippines , 76-77. 81 Ibid., 77. 82 Gerardo P. Sicat, “The Economic Legacy of Marcos,” UP School of Economics...of the Philippine University and later dropped out of school to organize the U.S. Tobacco Company union. He was killed, in the late of 1969, by a...insurgents- philippines -joint-agreement. Sicat, Gerardo P. “The Economic Legacy of Marcos.” UP School of Economics, November 2011. Accessed April 9, 2016

Size Contrast for Mars CubeSat

NASA Image and Video Library

2015-06-12

The full-scale mock-up of NASA's MarCO CubeSat held by Farah Alibay, a systems engineer at NASA's Jet Propulsion Laboratory, is dwarfed by the one-half-scale model of NASA's Mars Reconnaissance Orbiter behind her. MarCO, short for Mars Cube One, is the first interplanetary use of CubeSat technologies for small spacecraft. JPL is preparing two MarCO twins for launch in March 2016. They will ride along on an Atlas V launch vehicle lifting off from Vandenberg Air Force Base, California, with NASA's next Mars lander, InSight. MarCO is a technology demonstration aspect of the InSight mission. The mock-up in the photo is in a configuration to show the deployed position of components that correspond to MarCO's two solar panels and two antennas. During launch, those components will be stowed for a total vehicle size of about 14.4 inches (36.6 centimeters) by 9.5 inches (24.3 centimeters) by 4.6 inches (11.8 centimeters). After launch, the two MarCO CubeSats and InSight will be navigated separately to Mars. The MarCO twins will fly past the planet in September 2016 just as InSight is descending through the atmosphere and landing on the surface. MarCO is a technology demonstration to relay communications from InSight to Earth during InSight's descent and landing. InSight communications during that critical period will also be recorded by NASA's Mars Reconnaissance Orbiter for delayed transmission to Earth. InSight -- an acronym for Interior Exploration using Seismic Investigations, Geodesy and Heat Transport -- will study the interior of Mars to improve understanding of the processes that formed and shaped rocky planets, including Earth. Note: After thorough examination, NASA managers have decided to suspend the planned March 2016 launch of the Interior Exploration using Seismic Investigations Geodesy and Heat Transport (InSight) mission. The decision follows unsuccessful attempts to repair a leak in a section of the prime instrument in the science payload. http://photojournal.jpl.nasa.gov/catalog/PIA19671

Chaotic Behavior of a Generalized Sprott E Differential System

NASA Astrophysics Data System (ADS)

Oliveira, Regilene; Valls, Claudia

A chaotic system with only one equilibrium, a stable node-focus, was introduced by Wang and Chen [2012]. This system was found by adding a nonzero constant b to the Sprott E system [Sprott, 1994]. The coexistence of three types of attractors in this autonomous system was also considered by Braga and Mello [2013]. Adding a second parameter to the Sprott E differential system, we get the autonomous system ẋ = ayz + b,ẏ = x2 - y,ż = 1 - 4x, where a,b ∈ ℝ are parameters and a≠0. In this paper, we consider theoretically some global dynamical aspects of this system called here the generalized Sprott E differential system. This polynomial differential system is relevant because it is the first polynomial differential system in ℝ3 with two parameters exhibiting, besides the point attractor and chaotic attractor, coexisting stable limit cycles, demonstrating that this system is truly complicated and interesting. More precisely, we show that for b sufficiently small this system can exhibit two limit cycles emerging from the classical Hopf bifurcation at the equilibrium point p = (1/4, 1/16, 0). We also give a complete description of its dynamics on the Poincaré sphere at infinity by using the Poincaré compactification of a polynomial vector field in ℝ3, and we show that it has no first integrals in the class of Darboux functions.

On the degree conjecture for separability of multipartite quantum states

NASA Astrophysics Data System (ADS)

Hassan, Ali Saif M.; Joag, Pramod S.

2008-01-01

We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein et al. [Phys. Rev. A 73, 012320 (2006)]. The conjecture states that a multipartite quantum state is separable if and only if the degree matrix of the graph associated with the state is equal to the degree matrix of the partial transpose of this graph. We call this statement to be the strong form of the conjecture. In its weak version, the conjecture requires only the necessity, that is, if the state is separable, the corresponding degree matrices match. We prove the strong form of the conjecture for pure multipartite quantum states using the modified tensor product of graphs defined by Hassan and Joag [J. Phys. A 40, 10251 (2007)], as both necessary and sufficient condition for separability. Based on this proof, we give a polynomial-time algorithm for completely factorizing any pure multipartite quantum state. By polynomial-time algorithm, we mean that the execution time of this algorithm increases as a polynomial in m, where m is the number of parts of the quantum system. We give a counterexample to show that the conjecture fails, in general, even in its weak form, for multipartite mixed states. Finally, we prove this conjecture, in its weak form, for a class of multipartite mixed states, giving only a necessary condition for separability.

Tensor spherical harmonics theories on the exact nature of the elastic fields of a spherically anisotropic multi-inhomogeneous inclusion

NASA Astrophysics Data System (ADS)

Shodja, H. M.; Khorshidi, A.

2013-04-01

Eshelby's theories on the nature of the disturbance strains due to polynomial eigenstrains inside an isotropic ellipsoidal inclusion, and the form of homogenizing eigenstrains corresponding to remote polynomial loadings in the equivalent inclusion method (EIM) are not valid for spherically anisotropic inclusions and inhomogeneities. Materials with spherically anisotropic behavior are frequently encountered in nature, for example, some graphite particles or polyethylene spherulites. Moreover, multi-inclusions/inhomogeneities/inhomogeneous inclusions have abundant engineering and scientific applications and their exact theoretical treatment would be of great value. The present work is devoted to the development of a mathematical framework for the exact treatment of a spherical multi-inhomogeneous inclusion with spherically anisotropic constituents embedded in an unbounded isotropic matrix. The formulations herein are based on tensor spherical harmonics having orthogonality and completeness properties. For polynomial eigenstrain field and remote applied loading, several theorems on the exact closed-form expressions of the elastic fields associated with the matrix and all the phases of the inhomogeneous inclusion are stated and proved. Several classes of impotent eigenstrain fields associated to a generally anisotropic inclusion as well as isotropic and spherically anisotropic multi-inclusions are also introduced. The presented theories are useful for obtaining highly accurate solutions of desired accuracy when the constituent phases of the multi-inhomogeneous inclusion are made of functionally graded materials (FGMs).

Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images.

PubMed

Shukla, Rahul; Dragotti, Pier Luigi; Do, Minh N; Vetterli, Martin

2005-03-01

This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymptotic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one-dimensional case, our scheme is based on binary-tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying R-D behavior (D(R) - c(o)2(-c1R)), thus improving over classic wavelet schemes. We also prove that the computational complexity of the scheme is of O(N log N). We then show the extension of this scheme to the two-dimensional case using a quadtree. This quadtree-coding scheme also achieves an exponentially decaying R-D behavior, for the polygonal image model composed of a white polygon-shaped object against a uniform black background, with low computational cost of O(N log N). Again, the key is an R-D optimized prune and join strategy. Finally, we conclude with numerical results, which show that the proposed quadtree-coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp.

Characteristic classes of Q-manifolds: Classification and applications

NASA Astrophysics Data System (ADS)

Lyakhovich, S. L.; Mosman, E. A.; Sharapov, A. A.

2010-05-01

A Q-manifold M is a supermanifold endowed with an odd vector field Q squaring to zero. The Lie derivative LQ along Q makes the algebra of smooth tensor fields on M into a differential algebra. In this paper, we define and study the invariants of Q-manifolds called characteristic classes. These take values in the cohomology of the operator LQ and, given an affine symmetric connection with curvature R, can be represented by universal tensor polynomials in the repeated covariant derivatives of Q and R up to some finite order. As usual, the characteristic classes are proved to be independent of the choice of the affine connection used to define them. The main result of the paper is a complete classification of the intrinsic characteristic classes, which, by definition, do not vanish identically on flat Q-manifolds. As an illustration of the general theory we interpret some of the intrinsic characteristic classes as anomalies in the BV and BFV-BRST quantization methods of gauge theories. An application to the theory of (singular) foliations is also discussed.

Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos

DTIC Science & Technology

2001-09-11

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc...scheme, which is represented as a tree structure in figure 1 (following [24]), classifies the hypergeometric orthogonal polynomials and indicates the...2F0(1) 2F0(0) Figure 1: The Askey scheme of orthogonal polynomials The orthogonal polynomials associated with the generalized polynomial chaos,

SO(N) restricted Schur polynomials

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

Kemp, Garreth, E-mail: garreth.kemp@students.wits.ac.za

2015-02-15

We focus on the 1/4-BPS sector of free super Yang-Mills theory with an SO(N) gauge group. This theory has an AdS/CFT (an equivalence between a conformal field theory in d-1 dimensions and type II string theory defined on an AdS space in d-dimensions) dual in the form of type IIB string theory with AdS{sub 5}×RP{sup 5} geometry. With the aim of studying excited giant graviton dynamics, we construct an orthogonal basis for this sector of the gauge theory in this work. First, we demonstrate that the counting of states, as given by the partition function, and the counting of restrictedmore » Schur polynomials match by restricting to a particular class of Young diagram labels. We then give an explicit construction of these gauge invariant operators and evaluate their two-point function exactly. This paves the way to studying the spectral problem of these operators and their D-brane duals.« less

Solving the Swath Segment Selection Problem

NASA Technical Reports Server (NTRS)

Knight, Russell; Smith, Benjamin

2006-01-01

Several artificial-intelligence search techniques have been tested as means of solving the swath segment selection problem (SSSP) -- a real-world problem that is not only of interest in its own right, but is also useful as a test bed for search techniques in general. In simplest terms, the SSSP is the problem of scheduling the observation times of an airborne or spaceborne synthetic-aperture radar (SAR) system to effect the maximum coverage of a specified area (denoted the target), given a schedule of downlinks (opportunities for radio transmission of SAR scan data to a ground station), given the limit on the quantity of SAR scan data that can be stored in an onboard memory between downlink opportunities, and given the limit on the achievable downlink data rate. The SSSP is NP complete (short for "nondeterministic polynomial time complete" -- characteristic of a class of intractable problems that can be solved only by use of computers capable of making guesses and then checking the guesses in polynomial time).

Kirchhoff index of linear hexagonal chains

NASA Astrophysics Data System (ADS)

Yang, Yujun; Zhang, Heping

The resistance distance rij between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices. In this work, according to the decomposition theorem of Laplacian polynomial, we obtain that the Laplacian spectrum of linear hexagonal chain Ln consists of the Laplacian spectrum of path P2n+1 and eigenvalues of a symmetric tridiagonal matrix of order 2n + 1. By applying the relationship between roots and coefficients of the characteristic polynomial of the above matrix, explicit closed-form formula for Kirchhoff index of Ln is derived in terms of Laplacian spectrum. To our surprise, the Krichhoff index of Ln is approximately to one half of its Wiener index. Finally, we show that holds for all graphs G in a class of graphs including Ln.0

Graph traversals, genes, and matroids: An efficient case of the travelling salesman problem

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

Gusfield, D.; Stelling, P.; Wang, Lusheng

1996-12-31

In this paper the authors consider graph traversal problems that arise from a particular technology for DNA sequencing - sequencing by hybridization (SBH). They first explain the connection of the graph problems to SBH and then focus on the traversal problems. They describe a practical polynomial time solution to the Travelling Salesman Problem in a rich class of directed graphs (including edge weighted binary de Bruijn graphs), and provide a bounded-error approximation algorithm for the maximum weight TSP in a superset of those directed graphs. The authors also establish the existence of a matroid structure defined on the set ofmore » Euler and Hamilton paths in the restricted class of graphs. 8 refs., 5 figs.« less

5 CFR 531.603 - Locality pay areas.

Code of Federal Regulations, 2013 CFR

2013-01-01

... of the Sacramento—Arden-Arcade—Yuba City, CA-NV CSA, plus Carson City, NV; (30) San Diego-Carlsbad-San Marcos, CA—consisting of the San Diego-Carlsbad-San Marcos, CA MSA; (31) San Jose-San Francisco...

5 CFR 531.603 - Locality pay areas.

Code of Federal Regulations, 2014 CFR

2014-01-01

... of the Sacramento—Arden-Arcade—Yuba City, CA-NV CSA, plus Carson City, NV; (30) San Diego-Carlsbad-San Marcos, CA—consisting of the San Diego-Carlsbad-San Marcos, CA MSA; (31) San Jose-San Francisco...

5 CFR 531.603 - Locality pay areas.

Code of Federal Regulations, 2012 CFR

2012-01-01

... of the Sacramento—Arden-Arcade—Yuba City, CA-NV CSA, plus Carson City, NV; (30) San Diego-Carlsbad-San Marcos, CA—consisting of the San Diego-Carlsbad-San Marcos, CA MSA; (31) San Jose-San Francisco...

Lyapunov functions for a class of nonlinear systems using Caputo derivative

NASA Astrophysics Data System (ADS)

Fernandez-Anaya, G.; Nava-Antonio, G.; Jamous-Galante, J.; Muñoz-Vega, R.; Hernández-Martínez, E. G.

2017-02-01

This paper presents an extension of recent results that allow proving the stability of Caputo nonlinear and time-varying systems, by means of the fractional order Lyapunov direct method, using quadratic Lyapunov functions. This article introduces a new way of building polynomial Lyapunov functions of any positive integer order as a way of determining the stability of a greater variety of systems when the order of the derivative is 0 < α < 1. Some examples are given to validate these results.

Elegant Ince—Gaussian breathers in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

2012-06-01

A novel class of optical breathers, called elegant Ince—Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell's mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schrödinger equation.

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

2013-01-01

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

NASA Astrophysics Data System (ADS)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

Kinematics and dynamics of robotic systems with multiple closed loops

NASA Astrophysics Data System (ADS)

Zhang, Chang-De

The kinematics and dynamics of robotic systems with multiple closed loops, such as Stewart platforms, walking machines, and hybrid manipulators, are studied. In the study of kinematics, focus is on the closed-form solutions of the forward position analysis of different parallel systems. A closed-form solution means that the solution is expressed as a polynomial in one variable. If the order of the polynomial is less than or equal to four, the solution has analytical closed-form. First, the conditions of obtaining analytical closed-form solutions are studied. For a Stewart platform, the condition is found to be that one rotational degree of freedom of the output link is decoupled from the other five. Based on this condition, a class of Stewart platforms which has analytical closed-form solution is formulated. Conditions of analytical closed-form solution for other parallel systems are also studied. Closed-form solutions of forward kinematics for walking machines and multi-fingered grippers are then studied. For a parallel system with three three-degree-of-freedom subchains, there are 84 possible ways to select six independent joints among nine joints. These 84 ways can be classified into three categories: Category 3:3:0, Category 3:2:1, and Category 2:2:2. It is shown that the first category has no solutions; the solutions of the second category have analytical closed-form; and the solutions of the last category are higher order polynomials. The study is then extended to a nearly general Stewart platform. The solution is a 20th order polynomial and the Stewart platform has a maximum of 40 possible configurations. Also, the study is extended to a new class of hybrid manipulators which consists of two serially connected parallel mechanisms. In the study of dynamics, a computationally efficient method for inverse dynamics of manipulators based on the virtual work principle is developed. Although this method is comparable with the recursive Newton-Euler method for serial manipulators, its advantage is more noteworthy when applied to parallel systems. An approach of inverse dynamics of a walking machine is also developed, which includes inverse dynamic modeling, foot force distribution, and joint force/torque allocation.

Both MarCO Spacecraft

NASA Image and Video Library

2018-03-29

Engineer Joel Steinkraus stands with both of the Mars Cube One (MarCO) spacecraft at NASA's Jet Propulsion Laboratory. The one on the left is folded up the way it will be stowed on its rocket; the one on the right has its solar panels fully deployed, along with its high-gain antenna on top. The MarCOs will be the first CubeSats -- a kind of modular, mini-satellite -- flown in deep space. They're designed to fly along behind NASA's InSight lander on its cruise to Mars. If they make the journey, they will test a relay of data about InSight's entry, descent and landing back to Earth. Though InSight's mission will not depend on the success of the MarCOs, they will be a test of how CubeSats can be used in deep space. https://photojournal.jpl.nasa.gov/catalog/PIA22319

Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos

DTIC Science & Technology

2002-07-25

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc., AMS... orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener (1938). A Galerkin projection...1) by generalized polynomial chaos expansion, where the uncertainties can be introduced through κ, f , or g, or some combinations. It is worth

Orthonormal aberration polynomials for anamorphic optical imaging systems with circular pupils.

PubMed

Mahajan, Virendra N

2012-06-20

In a recent paper, we considered the classical aberrations of an anamorphic optical imaging system with a rectangular pupil, representing the terms of a power series expansion of its aberration function. These aberrations are inherently separable in the Cartesian coordinates (x,y) of a point on the pupil. Accordingly, there is x-defocus and x-coma, y-defocus and y-coma, and so on. We showed that the aberration polynomials orthonormal over the pupil and representing balanced aberrations for such a system are represented by the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point; for example, L(l)(x)L(m)(y), where l and m are positive integers (including zero) and L(l)(x), for example, represents an orthonormal Legendre polynomial of degree l in x. The compound two-dimensional (2D) Legendre polynomials, like the classical aberrations, are thus also inherently separable in the Cartesian coordinates of the pupil point. Moreover, for every orthonormal polynomial L(l)(x)L(m)(y), there is a corresponding orthonormal polynomial L(l)(y)L(m)(x) obtained by interchanging x and y. These polynomials are different from the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil. In this paper, we show that the orthonormal aberration polynomials for an anamorphic system with a circular pupil, obtained by the Gram-Schmidt orthogonalization of the 2D Legendre polynomials, are not separable in the two coordinates. Moreover, for a given polynomial in x and y, there is no corresponding polynomial obtained by interchanging x and y. For example, there are polynomials representing x-defocus, balanced x-coma, and balanced x-spherical aberration, but no corresponding y-aberration polynomials. The missing y-aberration terms are contained in other polynomials. We emphasize that the Zernike circle polynomials, although orthogonal over a circular pupil, are not suitable for an anamorphic system as they do not represent balanced aberrations for such a system.

Approximating exponential and logarithmic functions using polynomial interpolation

NASA Astrophysics Data System (ADS)

Gordon, Sheldon P.; Yang, Yajun

2017-04-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.

[A SAS marco program for batch processing of univariate Cox regression analysis for great database].

PubMed

Yang, Rendong; Xiong, Jie; Peng, Yangqin; Peng, Xiaoning; Zeng, Xiaomin

2015-02-01

To realize batch processing of univariate Cox regression analysis for great database by SAS marco program. We wrote a SAS macro program, which can filter, integrate, and export P values to Excel by SAS9.2. The program was used for screening survival correlated RNA molecules of ovarian cancer. A SAS marco program could finish the batch processing of univariate Cox regression analysis, the selection and export of the results. The SAS macro program has potential applications in reducing the workload of statistical analysis and providing a basis for batch processing of univariate Cox regression analysis.

Decision support system for diabetic retinopathy using discrete wavelet transform.

PubMed

Noronha, K; Acharya, U R; Nayak, K P; Kamath, S; Bhandary, S V

2013-03-01

Prolonged duration of the diabetes may affect the tiny blood vessels of the retina causing diabetic retinopathy. Routine eye screening of patients with diabetes helps to detect diabetic retinopathy at the early stage. It is very laborious and time-consuming for the doctors to go through many fundus images continuously. Therefore, decision support system for diabetic retinopathy detection can reduce the burden of the ophthalmologists. In this work, we have used discrete wavelet transform and support vector machine classifier for automated detection of normal and diabetic retinopathy classes. The wavelet-based decomposition was performed up to the second level, and eight energy features were extracted. Two energy features from the approximation coefficients of two levels and six energy values from the details in three orientations (horizontal, vertical and diagonal) were evaluated. These features were fed to the support vector machine classifier with various kernel functions (linear, radial basis function, polynomial of orders 2 and 3) to evaluate the highest classification accuracy. We obtained the highest average classification accuracy, sensitivity and specificity of more than 99% with support vector machine classifier (polynomial kernel of order 3) using three discrete wavelet transform features. We have also proposed an integrated index called Diabetic Retinopathy Risk Index using clinically significant wavelet energy features to identify normal and diabetic retinopathy classes using just one number. We believe that this (Diabetic Retinopathy Risk Index) can be used as an adjunct tool by the doctors during the eye screening to cross-check their diagnosis.

On the degree conjecture for separability of multipartite quantum states

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

Hassan, Ali Saif M.; Joag, Pramod S.

2008-01-15

We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein et al. [Phys. Rev. A 73, 012320 (2006)]. The conjecture states that a multipartite quantum state is separable if and only if the degree matrix of the graph associated with the state is equal to the degree matrix of the partial transpose of this graph. We call this statement to be the strong form of the conjecture. In its weak version, the conjecture requires only the necessity, that is, if the state is separable, the corresponding degree matricesmore » match. We prove the strong form of the conjecture for pure multipartite quantum states using the modified tensor product of graphs defined by Hassan and Joag [J. Phys. A 40, 10251 (2007)], as both necessary and sufficient condition for separability. Based on this proof, we give a polynomial-time algorithm for completely factorizing any pure multipartite quantum state. By polynomial-time algorithm, we mean that the execution time of this algorithm increases as a polynomial in m, where m is the number of parts of the quantum system. We give a counterexample to show that the conjecture fails, in general, even in its weak form, for multipartite mixed states. Finally, we prove this conjecture, in its weak form, for a class of multipartite mixed states, giving only a necessary condition for separability.« less

Preparing MarCO

NASA Image and Video Library

2018-04-19

Joel Steinkraus, MarCO lead mechanical engineer from JPL, makes an adjustment on the CubeSat prior to integration in a deployment box as seen inside the cleanroom lab at Cal Poly San Luis Obispo on Monday, March 12, 2018. https://photojournal.jpl.nasa.gov/catalog/PIA22321

Synchronization of a Class of Switched Neural Networks with Time-Varying Delays via Nonlinear Feedback Control.

PubMed

Wang, Leimin; Shen, Yi; Zhang, Guodong

2016-10-01

This paper is concerned with the synchronization problem for a class of switched neural networks (SNNs) with time-varying delays. First, a new crucial lemma which includes and extends the classical exponential stability theorem is constructed. Then by using the lemma, new algebraic criteria of ψ -type synchronization (synchronization with general decay rate) for SNNs are established via the designed nonlinear feedback control. The ψ -type synchronization which is in a general framework is obtained by introducing a ψ -type function. It contains exponential synchronization, polynomial synchronization, and other synchronization as its special cases. The results of this paper are general, and they also complement and extend some previous results. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results.

Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width.

PubMed

De Sa, Christopher; Zhang, Ce; Olukotun, Kunle; Ré, Christopher

2015-12-01

Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be exponential in the number of variables. To help understand the behavior of Gibbs sampling, we introduce a new (hyper)graph property, called hierarchy width . We show that under suitable conditions on the weights, bounded hierarchy width ensures polynomial mixing time. Our study of hierarchy width is in part motivated by a class of factor graph templates, hierarchical templates , which have bounded hierarchy width-regardless of the data used to instantiate them. We demonstrate a rich application from natural language processing in which Gibbs sampling provably mixes rapidly and achieves accuracy that exceeds human volunteers.

Equivalences of the multi-indexed orthogonal polynomials

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

Odake, Satoru

2014-01-15

Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.

Classification of Dark Modified KdV Equation

NASA Astrophysics Data System (ADS)

Xiong, Na; Lou, Sen-Yue; Li, Biao; Chen, Yong

2017-07-01

The dark Korteweg-de Vries (KdV) systems are defined and classified by Kupershmidt sixteen years ago. However, there is no other classifications for other kinds of nonlinear systems. In this paper, a complete scalar classification for dark modified KdV (MKdV) systems is obtained by requiring the existence of higher order differential polynomial symmetries. Different to the nine classes of the dark KdV case, there exist twelve independent classes of the dark MKdV equations. Furthermore, for the every class of dark MKdV system, there is a free parameter. Only for a fixed parameter, the dark MKdV can be related to dark KdV via suitable Miura transformation. The recursion operators of two classes of dark MKdV systems are also given. Supported by the Global Change Research Program of China under Grant No. 2015Cb953904, National Natural Science Foundation of China under Grant Nos. 11675054, 11435005, 11175092, and 11205092 and Shanghai Knowledge Service Platform for Trustworthy Internet of Things (No. ZF1213) and K. C. Wong Magna Fund in Ningbo University

77 FR 42756 - Draft Environmental Impact Statement and Draft Habitat Conservation Plan for Incidental Take of...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-07-20

...), including the endangered fountain darter (Etheostoma fonticola), threatened San Marcos salamander (Eurycea nana), endangered San Marcos gambusia (Gambusia georgei), endangered Texas blind salamander...), Comal Springs salamander (Eurycea sp.), and Texas troglobitic water slater (Lirceolus smithii) in case...

First Image from MarCO-B

NASA Image and Video Library

2018-05-15

The first image captured by one of NASA's Mars Cube One (MarCO) CubeSats. The image, which shows both the CubeSat's unfolded high-gain antenna at right and the Earth and its moon in the center, was acquired by MarCO-B on May 9. MarCO is a pair of small spacecraft accompanying NASA's InSight (Interior Investigations Using Seismic Investigations, Geodesy and Heat Transport) lander. Together, MarCO-A and MarCO-B are the first CubeSats ever sent to deep space. InSight is the first mission to ever explore Mars' deep interior. If the MarCO CubeSats make the entire journey to Mars, they will attempt to relay data about InSight back to Earth as the lander enters the Martian atmosphere and lands. MarCO will not collect any science, but are intended purely as a technology demonstration. They could serve as a pathfinder for future CubeSat missions. An annotated version is available at https://photojournal.jpl.nasa.gov/catalog/PIA22323

Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials

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

Ho, Choon-Lin, E-mail: hcl@mail.tku.edu.tw

2011-04-15

Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it ismore » also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.« less

Solutions of interval type-2 fuzzy polynomials using a new ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

2015-10-01

A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

Coherent orthogonal polynomials

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

Celeghini, E., E-mail: celeghini@fi.infn.it; Olmo, M.A. del, E-mail: olmo@fta.uva.es

2013-08-15

We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory. We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard uncountable basis (|x〉), for an alternative countable basis (|n〉). The matrix elements that relatemore » these two bases are essentially the orthogonal polynomials: Hermite polynomials for the line and Laguerre and Legendre polynomials for the half-line and the line interval, respectively. Differential recurrence relations of orthogonal polynomials allow us to realize that they determine an infinite-dimensional irreducible representation of a non-compact Lie algebra, whose second order Casimir C gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl–Heisenberg algebra h(1) with C=0 for Hermite polynomials and su(1,1) with C=−1/4 for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the L{sup 2} functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space L{sup 2} and, in particular, generalized coherent polynomials are thus obtained. -- Highlights: •Fundamental characteristic of orthogonal polynomials (OP): existence of a Lie algebra. •Differential recurrence relations of OP determine a unitary representation of a non-compact Lie group. •2nd order Casimir originates a 2nd order differential equation that defines the corresponding OP family. •Generalized coherent polynomials are obtained from OP.« less

The Hom-Yang-Baxter equation and Hom-Lie algebras

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

Yau, Donald

2011-05-15

Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by Yau [J. Phys. A 42, 165202 (2009)]. In this paper, several more classes of solutions of the HYBE are constructed. Some of the solutions of the HYBE are closely related to the quantum enveloping algebra of sl(2), the Jones-Conway polynomial, and Yetter-Drinfel'd modules. Under some invertibility conditions, we construct a new infinite sequence of solutions of the HYBE from a given one.

Method of fuzzy inference for one class of MISO-structure systems with non-singleton inputs

NASA Astrophysics Data System (ADS)

Sinuk, V. G.; Panchenko, M. V.

2018-03-01

In fuzzy modeling, the inputs of the simulated systems can receive both crisp values and non-Singleton. Computational complexity of fuzzy inference with fuzzy non-Singleton inputs corresponds to an exponential. This paper describes a new method of inference, based on the theorem of decomposition of a multidimensional fuzzy implication and a fuzzy truth value. This method is considered for fuzzy inputs and has a polynomial complexity, which makes it possible to use it for modeling large-dimensional MISO-structure systems.

The simultaneous integration of many trajectories using nilpotent normal forms

NASA Technical Reports Server (NTRS)

Grayson, Matthew A.; Grossman, Robert

1990-01-01

Taylor's formula shows how to approximate a certain class of functions by polynomials. The approximations are arbitrarily good in some neighborhood whenever the function is analytic and they are easy to compute. The main goal is to give an efficient algorithm to approximate a neighborhood of the configuration space of a dynamical system by a nilpotent, explicitly integrable dynamical system. The major areas covered include: an approximating map; the generalized Baker-Campbell-Hausdorff formula; the Picard-Taylor method; the main theorem; simultaneous integration of trajectories; and examples.

Simple Proof of Jury Test for Complex Polynomials

NASA Astrophysics Data System (ADS)

Choo, Younseok; Kim, Dongmin

Recently some attempts have been made in the literature to give simple proofs of Jury test for real polynomials. This letter presents a similar result for complex polynomials. A simple proof of Jury test for complex polynomials is provided based on the Rouché's Theorem and a single-parameter characterization of Schur stability property for complex polynomials.

Computing Role Assignments of Proper Interval Graphs in Polynomial Time

NASA Astrophysics Data System (ADS)

Heggernes, Pinar; van't Hof, Pim; Paulusma, Daniël

A homomorphism from a graph G to a graph R is locally surjective if its restriction to the neighborhood of each vertex of G is surjective. Such a homomorphism is also called an R-role assignment of G. Role assignments have applications in distributed computing, social network theory, and topological graph theory. The Role Assignment problem has as input a pair of graphs (G,R) and asks whether G has an R-role assignment. This problem is NP-complete already on input pairs (G,R) where R is a path on three vertices. So far, the only known non-trivial tractable case consists of input pairs (G,R) where G is a tree. We present a polynomial time algorithm that solves Role Assignment on all input pairs (G,R) where G is a proper interval graph. Thus we identify the first graph class other than trees on which the problem is tractable. As a complementary result, we show that the problem is Graph Isomorphism-hard on chordal graphs, a superclass of proper interval graphs and trees.

On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2003-05-01

A formula expressing the Laguerre coefficients of a general-order derivative of an infinitely differentiable function in terms of its original coefficients is proved, and a formula expressing explicitly the derivatives of Laguerre polynomials of any degree and for any order as a linear combination of suitable Laguerre polynomials is deduced. A formula for the Laguerre coefficients of the moments of one single Laguerre polynomial of certain degree is given. Formulae for the Laguerre coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Laguerre coefficients are also obtained. A simple approach in order to build and solve recursively for the connection coefficients between Jacobi-Laguerre and Hermite-Laguerre polynomials is described. An explicit formula for these coefficients between Jacobi and Laguerre polynomials is given, of which the ultra-spherical polynomials of the first and second kinds and Legendre polynomials are important special cases. An analytical formula for the connection coefficients between Hermite and Laguerre polynomials is also obtained.

Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials

NASA Astrophysics Data System (ADS)

Chen, Zhixiang; Fu, Bin

This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a ΠΣΠ polynomial. We first prove that the first problem is #P-hard and then devise a O *(3 n s(n)) upper bound for this problem for any polynomial represented by an arithmetic circuit of size s(n). Later, this upper bound is improved to O *(2 n ) for ΠΣΠ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for ΠΣ polynomials. On the negative side, we prove that, even for ΠΣΠ polynomials with terms of degree ≤ 2, the first problem cannot be approximated at all for any approximation factor ≥ 1, nor "weakly approximated" in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time λ-approximation algorithm for ΠΣΠ polynomials with terms of degrees no more a constant λ ≥ 2. On the inapproximability side, we give a n (1 - ɛ)/2 lower bound, for any ɛ> 0, on the approximation factor for ΠΣΠ polynomials. When the degrees of the terms in these polynomials are constrained as ≤ 2, we prove a 1.0476 lower bound, assuming Pnot=NP; and a higher 1.0604 lower bound, assuming the Unique Games Conjecture.

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

NASA Astrophysics Data System (ADS)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Nodal Statistics for the Van Vleck Polynomials

NASA Astrophysics Data System (ADS)

Bourget, Alain

The Van Vleck polynomials naturally arise from the generalized Lamé equation as the polynomials of degree for which Eq. (1) has a polynomial solution of some degree k. In this paper, we compute the limiting distribution, as well as the limiting mean level spacings distribution of the zeros of any Van Vleck polynomial as N --> ∞.

78 FR 11218 - Final Environmental Impact Statement and Record of Decision on the Edwards Aquifer Recovery...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-02-15

... fonticola) Texas blind salamander (Eurycea [=Typhlomolge] rathbuni) San Marcos gambusia (Gambusia georgei) Threatened San Marcos salamander (Eurycea nana) Non-listed Species Texas cave diving beetle (Haideoporus texanus) Texas troglobitic water slater (Lirceolus smithii) Comal Springs salamander (Eurycea sp.) Take of...

Legendre modified moments for Euler's constant

NASA Astrophysics Data System (ADS)

Prévost, Marc

2008-10-01

Polynomial moments are often used for the computation of Gauss quadrature to stabilize the numerical calculation of the orthogonal polynomials, see [W. Gautschi, Computational aspects of orthogonal polynomials, in: P. Nevai (Ed.), Orthogonal Polynomials-Theory and Practice, NATO ASI Series, Series C: Mathematical and Physical Sciences, vol. 294. Kluwer, Dordrecht, 1990, pp. 181-216 [6]; W. Gautschi, On the sensitivity of orthogonal polynomials to perturbations in the moments, Numer. Math. 48(4) (1986) 369-382 [5]; W. Gautschi, On generating orthogonal polynomials, SIAM J. Sci. Statist. Comput. 3(3) (1982) 289-317 [4

On multiple orthogonal polynomials for discrete Meixner measures

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

Sorokin, Vladimir N

2010-12-07

The paper examines two examples of multiple orthogonal polynomials generalizing orthogonal polynomials of a discrete variable, meaning thereby the Meixner polynomials. One example is bound up with a discrete Nikishin system, and the other leads to essentially new effects. The limit distribution of the zeros of polynomials is obtained in terms of logarithmic equilibrium potentials and in terms of algebraic curves. Bibliography: 9 titles.

Direct calculation of modal parameters from matrix orthogonal polynomials

NASA Astrophysics Data System (ADS)

El-Kafafy, Mahmoud; Guillaume, Patrick

2011-10-01

The object of this paper is to introduce a new technique to derive the global modal parameter (i.e. system poles) directly from estimated matrix orthogonal polynomials. This contribution generalized the results given in Rolain et al. (1994) [5] and Rolain et al. (1995) [6] for scalar orthogonal polynomials to multivariable (matrix) orthogonal polynomials for multiple input multiple output (MIMO) system. Using orthogonal polynomials improves the numerical properties of the estimation process. However, the derivation of the modal parameters from the orthogonal polynomials is in general ill-conditioned if not handled properly. The transformation of the coefficients from orthogonal polynomials basis to power polynomials basis is known to be an ill-conditioned transformation. In this paper a new approach is proposed to compute the system poles directly from the multivariable orthogonal polynomials. High order models can be used without any numerical problems. The proposed method will be compared with existing methods (Van Der Auweraer and Leuridan (1987) [4] Chen and Xu (2003) [7]). For this comparative study, simulated as well as experimental data will be used.

The DeMarco factor: interview with a health policy advocate.

PubMed

Jernigan, David H

2010-05-01

An interview with Vincent DeMarco, President of the Maryland Citizen's Health Initiative, reviews the history and strategies used to win victories for public health on gun policy and tobacco taxes and to seek passage of higher alcohol taxes in the state of Maryland. DeMarco emphasizes the need to build broad coalitions, to engage policy makers at election time and not just or primarily during legislative sessions, and to take advantage of the power of the news media as a microphone for reaching millions of possible supporters. The interview concludes with recommendations for public health training and practitioners in order to become successful policy advocates in a rapidly changing media and political landscape.

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(ln ⁡ f) x and u = 2(ln ⁡ f) xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.

Open Quantum Random Walks on the Half-Line: The Karlin-McGregor Formula, Path Counting and Foster's Theorem

NASA Astrophysics Data System (ADS)

Jacq, Thomas S.; Lardizabal, Carlos F.

2017-11-01

In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the Karlin-McGregor formula. We focus on absorbing boundary conditions and, for simpler classes of examples, we consider path counting and the corresponding combinatorial tools. A non-commutative version of the gambler's ruin is studied by obtaining the probability of reaching a certain fortune and the mean time to reach a fortune or ruin in terms of generating functions. In the case of the Hadamard coin, a counting technique for boundary restricted paths in a lattice is also presented. We discuss an open quantum version of Foster's Theorem for the expected return time together with applications.

Control aspects of quantum computing using pure and mixed states.

PubMed

Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J

2012-10-13

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.

Multipartite Entanglement classes via Negativity Fonts

NASA Astrophysics Data System (ADS)

Sharma, Santosh Shelly; Sharma, Naresh Kumar

2012-02-01

The number and types of K-way negativity fonts in canonical form of an N-qubit state depends on the nature and amount of quantum coherences in the state. Non zero determinants of negativity fonts, characterizing a given state, are easily written down and reflect the entanglement microstructure of the superposition. A classification criterion for multipartite entangled states, based on negativity fonts in canonical state and decomposition of global partial transpose in terms of K-way partially transposed operators, is proposed. Inequivalent sub-classes are labelled by N-qubit local unitary invariants. A complete classification of four qubit states is obtained. The number of major families for N>3 is found to be 2^N-2N. Classification of four qubit states indicates that a small number of relevant polynomial invariants is enough to classify N-qubit states.

Control aspects of quantum computing using pure and mixed states

PubMed Central

Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J.

2012-01-01

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems. PMID:22946034

Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width

PubMed Central

De Sa, Christopher; Zhang, Ce; Olukotun, Kunle; Ré, Christopher

2016-01-01

Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be exponential in the number of variables. To help understand the behavior of Gibbs sampling, we introduce a new (hyper)graph property, called hierarchy width. We show that under suitable conditions on the weights, bounded hierarchy width ensures polynomial mixing time. Our study of hierarchy width is in part motivated by a class of factor graph templates, hierarchical templates, which have bounded hierarchy width—regardless of the data used to instantiate them. We demonstrate a rich application from natural language processing in which Gibbs sampling provably mixes rapidly and achieves accuracy that exceeds human volunteers. PMID:27279724

Two Sides of the Same Coin: Reaching Nontraditional Students

ERIC Educational Resources Information Center

Berg, Steven L.

2005-01-01

This paper presents interviews with Barbara Bonham, a Senior Researcher at the National Center for Developmental Education and a member of the faculty at the Kellogg Institute, Appalachian State University in Boone, North Carolina and Melanie Chu, the Outreach Librarian at Cal State San Marcos in San Marcos, California. In these interviews they…

76 FR 17 - Changes in Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2011-01-03

... 24, 2010 080101 1121). of Larimer County February 15, 2010; Johnson, Chair Pro-Tem, (09-08-0465P...: Collier (FEMA Docket No.: B- City of Marco Island February 19, 2010; Mr. Stephen T. Thompson, February 9, 2010 120426 1121). (09-04-7821P). February 26, 2010; Marco Island City Naples Daily News. Manager, 50...

Classification of Phylogenetic Profiles for Protein Function Prediction: An SVM Approach

NASA Astrophysics Data System (ADS)

Kotaru, Appala Raju; Joshi, Ramesh C.

Predicting the function of an uncharacterized protein is a major challenge in post-genomic era due to problems complexity and scale. Having knowledge of protein function is a crucial link in the development of new drugs, better crops, and even the development of biochemicals such as biofuels. Recently numerous high-throughput experimental procedures have been invented to investigate the mechanisms leading to the accomplishment of a protein’s function and Phylogenetic profile is one of them. Phylogenetic profile is a way of representing a protein which encodes evolutionary history of proteins. In this paper we proposed a method for classification of phylogenetic profiles using supervised machine learning method, support vector machine classification along with radial basis function as kernel for identifying functionally linked proteins. We experimentally evaluated the performance of the classifier with the linear kernel, polynomial kernel and compared the results with the existing tree kernel. In our study we have used proteins of the budding yeast saccharomyces cerevisiae genome. We generated the phylogenetic profiles of 2465 yeast genes and for our study we used the functional annotations that are available in the MIPS database. Our experiments show that the performance of the radial basis kernel is similar to polynomial kernel is some functional classes together are better than linear, tree kernel and over all radial basis kernel outperformed the polynomial kernel, linear kernel and tree kernel. In analyzing these results we show that it will be feasible to make use of SVM classifier with radial basis function as kernel to predict the gene functionality using phylogenetic profiles.

Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality

NASA Astrophysics Data System (ADS)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2008-10-01

We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form e-[phi](x), giving a unified treatment for the so-called Freud (i.e., when [phi] has polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) cases. In addition, we provide a new proof for the bound of the distance of the zeros to the convex hull of the support for these Sobolev orthogonal polynomials.

A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces

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

Vignat, C.; Lamberti, P. W.

2009-10-15

Recently, Carinena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positivemore » curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.« less

INSPIRE and MarCO - Technology Development for the First Deep Space CubeSats

NASA Astrophysics Data System (ADS)

Klesh, Andrew

2016-07-01

INSPIRE (Interplanetary NanoSpacecraft Pathfinder In a Relevant Environment) and MarCO (Mars Cube One) will open the door for tiny spacecraft to explore the solar system. INSPIRE serves as a trailblazer, designed to demonstrate new technology needed for deep space. MarCO will open the door for NanoSpacecraft to serve in support roles for much larger primary missions - in this case, providing a real-time relay of for the InSight project and will likely be the first CubeSats to reach deep space. Together, these four spacecraft (two for each mission) enable fundamental science objectives to be met with tiny vehicles. Originally designed for a March, 2016 launch with the InSight mission to Mars, the MarCO spacecraft are now complete and in storage. When launched with the InSight lander from Vandenberg Air Force Base, the spacecraft will begin a 6.5 month cruise to Mars. Soon after InSight itself separates from the upper stage of the launch vehicle, the two MarCO CubeSats will deploy and independently fly to Mars to support telecommunications relay for InSight's entry, descent, and landing sequence. These spacecraft will have onboard capability for deep space trajectory correction maneuvers; high-speed direct-to-Earth & DSN-compatible communications; an advanced navigation transponder; a large deployable reflect-array high gain antenna; and a robust software suite. This talk will present an overview of the INSPIRE and MarCO projects, including a concept of operations, details of the spacecraft and subsystem design, and lessons learned from integration and test. Finally, the talk will outline how lessons from these spacecraft are already being utilized in the next generation of interplanetary CubeSats, as well as a brief vision of their applicability for solar system exploration. The research described here was carried out at the Jet Propulsion Laboratory, Caltech, under a contract with the National Aeronautics and Space Administration (NASA).

Hadamard Factorization of Stable Polynomials

NASA Astrophysics Data System (ADS)

Loredo-Villalobos, Carlos Arturo; Aguirre-Hernández, Baltazar

2011-11-01

The stable (Hurwitz) polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p,q ∈ R[x]:p(x) = anxn+an-1xn-1+...+a1x+a0q(x) = bmx m+bm-1xm-1+...+b1x+b0the Hadamard product (p × q) is defined as (p×q)(x) = akbkxk+ak-1bk-1xk-1+...+a1b1x+a0b0where k = min(m,n). Some results (see [16]) shows that if p,q ∈R[x] are stable polynomials then (p×q) is stable, also, i.e. the Hadamard product is closed; however, the reciprocal is not always true, that is, not all stable polynomial has a factorization into two stable polynomials the same degree n, if n> 4 (see [15]).In this work we will give some conditions to Hadamard factorization existence for stable polynomials.

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.

Stable Numerical Approach for Fractional Delay Differential Equations

NASA Astrophysics Data System (ADS)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

Percolation critical polynomial as a graph invariant

DOE PAGES

Scullard, Christian R.

2012-10-18

Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0; 1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer withmore » increasing subgraph size. In this paper, I show how the critical polynomial can be viewed as a graph invariant like the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction p c = 0:52440572:::, which differs from the numerical value, p c = 0:52440503(5), by only 6:9 X 10 -7.« less

On Certain Wronskians of Multiple Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Zhang, Lun; Filipuk, Galina

2014-11-01

We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep a constant sign in some cases, while in some other cases oscillatory behavior appears, which generalizes classical results for orthogonal polynomials due to Karlin and Szegő. There are two applications of our results. The first application arises from the observation that the m-th moment of the average characteristic polynomials for multiple orthogonal polynomial ensembles can be expressed as a Wronskian of the type II multiple orthogonal polynomials. Hence, it is straightforward to obtain the distinct behavior of the moments for odd and even m in a special multiple orthogonal ensemble - the AT ensemble. As the second application, we derive some Turán type inequalities for m! ultiple Hermite and multiple Laguerre polynomials (of two kinds). Finally, we study numerically the geometric configuration of zeros for the Wronskians of these multiple orthogonal polynomials. We observe that the zeros have regular configurations in the complex plane, which might be of independent interest.

Evaluation Report of the San Marcos Independent School District's Bilingual Education Program.

ERIC Educational Resources Information Center

Harrison, Helene W.

The San Marcos Independent School District's Bilingual Education Program for 1972-73 was evaluated in this report. The program consisted of 684 students in grades K-5 in 4 elementary schools. The majority of these students were Mexican American with only 18% monolingual English speakers. The program's objectives were, first, to provide bilingual…

The Philippine Press after Marcos: Restored Freedoms and New Problems.

ERIC Educational Resources Information Center

Guimary, Donald L.

With the overthrow of Ferdinand Marcos from his 20-year rule of the Philippines, the news media regained its freedom and its voice, and now faces a new set of problems: low circulation, questionable ethical standards of reporters and their lack of experience, and ominous indications from the Corazon Aquino government that the administration might…

Determinants with orthogonal polynomial entries

NASA Astrophysics Data System (ADS)

Ismail, Mourad E. H.

2005-06-01

We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determinants formed by the orthogonal polynomials. We also study the Hankel determinants which start with pn on the top left-hand corner. As examples we evaluate the Hankel determinants whose entries are q-ultraspherical or Al-Salam-Chihara polynomials.

From sequences to polynomials and back, via operator orderings

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

Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu

2013-12-15

Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1985-01-01

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Higher derivative extensions of 3 d Chern-Simons models: conservation laws and stability

NASA Astrophysics Data System (ADS)

Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.

2015-11-01

We consider the class of higher derivative 3 d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.

Type II universal spacetimes

NASA Astrophysics Data System (ADS)

Hervik, S.; Málek, T.; Pravda, V.; Pravdová, A.

2015-12-01

We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbitrary order. We provide examples of type II universal metrics for all composite number dimensions. On the other hand, we have no examples for prime number dimensions and we prove the non-existence of type II universal spacetimes in five dimensions. We also present type II vacuum solutions of selected classes of gravitational theories, such as Lovelock, quadratic and L({{Riemann}}) gravities.

Surface Catalysis and Characterization of Proposed Candidate TPS for Access-to-Space Vehicles

NASA Technical Reports Server (NTRS)

Stewart, David A.

1997-01-01

Surface properties have been obtained on several classes of thermal protection systems (TPS) using data from both side-arm-reactor and arc-jet facilities. Thermochemical stability, optical properties, and coefficients for atom recombination were determined for candidate TPS proposed for single-stage-to-orbit vehicles. The systems included rigid fibrous insulations, blankets, reinforced carbon carbon, and metals. Test techniques, theories used to define arc-jet and side-arm-reactor flow, and material surface properties are described. Total hemispherical emittance and atom recombination coefficients for each candidate TPS are summarized in the form of polynomial and Arrhenius expressions.

Polynomial solutions of the Monge-Ampère equation

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

Aminov, Yu A

2014-11-30

The question of the existence of polynomial solutions to the Monge-Ampère equation z{sub xx}z{sub yy}−z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a polynomial. It is proved that if f is a polynomial of the second degree, which is positive for all values of its arguments and has a positive squared part, then no polynomial solution exists. On the other hand, a solution which is not polynomial but is analytic in the whole of the x, y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction ofmore » such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.« less

Solving the interval type-2 fuzzy polynomial equation using the ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim

2014-07-01

Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

NASA Astrophysics Data System (ADS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

Multiple zeros of polynomials

NASA Technical Reports Server (NTRS)

Wood, C. A.

1974-01-01

For polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is, either they fail to converge to some or all of the zeros, or they converge to very bad approximations of the polynomial's zeros. This material introduces two new methods, the greatest common divisor (G.C.D.) method and the repeated greatest common divisor (repeated G.C.D.) method, which are superior methods for numerically approximating the zeros of a polynomial having multiple zeros. These methods were programmed in FORTRAN 4 and comparisons in time and accuracy are given.

Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Yang, Yajun

2017-01-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

Interpolation and Polynomial Curve Fitting

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2014-01-01

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

A note on the zeros of Freud-Sobolev orthogonal polynomials

NASA Astrophysics Data System (ADS)

Moreno-Balcazar, Juan J.

2007-10-01

We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e-x4 on are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e-x4. Some numerical examples are shown.

A FAST POLYNOMIAL TRANSFORM PROGRAM WITH A MODULARIZED STRUCTURE

NASA Technical Reports Server (NTRS)

Truong, T. K.

1994-01-01

This program utilizes a fast polynomial transformation (FPT) algorithm applicable to two-dimensional mathematical convolutions. Two-dimensional convolution has many applications, particularly in image processing. Two-dimensional cyclic convolutions can be converted to a one-dimensional convolution in a polynomial ring. Traditional FPT methods decompose the one-dimensional cyclic polynomial into polynomial convolutions of different lengths. This program will decompose a cyclic polynomial into polynomial convolutions of the same length. Thus, only FPTs and Fast Fourier Transforms of the same length are required. This modular approach can save computational resources. To further enhance its appeal, the program is written in the transportable 'C' language. The steps in the algorithm are: 1) formulate the modulus reduction equations, 2) calculate the polynomial transforms, 3) multiply the transforms using a generalized fast Fourier transformation, 4) compute the inverse polynomial transforms, and 5) reconstruct the final matrices using the Chinese remainder theorem. Input to this program is comprised of the row and column dimensions and the initial two matrices. The matrices are printed out at all steps, ending with the final reconstruction. This program is written in 'C' for batch execution and has been implemented on the IBM PC series of computers under DOS with a central memory requirement of approximately 18K of 8 bit bytes. This program was developed in 1986.

AKLSQF - LEAST SQUARES CURVE FITTING

NASA Technical Reports Server (NTRS)

Kantak, A. V.

1994-01-01

The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.

Hydrodynamics-based functional forms of activity metabolism: a case for the power-law polynomial function in animal swimming energetics.

PubMed

Papadopoulos, Anthony

2009-01-01

The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined.

MarCO and Dispenser

NASA Image and Video Library

2018-04-19

One of the MarCO CubeSats inside a cleanroom at Cal Poly San Luis Obispo, before being placed into its deployment box. The deployment box will eject the briefcase-sized CubeSat into space after launch. It and its twin will accompany the InSight Mars lander when it lifts off from Vandenberg Air Force Base in May. https://photojournal.jpl.nasa.gov/catalog/PIA22322

Scaling Laws for Heterogeneous Wireless Networks

DTIC Science & Technology

2009-09-01

planned and the size of communication networks that are fundamentally understood. On the one hand, wireline networks (like the Internet) have grown from...Franceschetti, Marco D. Migliore, and Paolo Minero . The capacity of wireless networks: Information-theoretic and physical limits. In Proceedings of the...Allerton Conference on Communication, Control, and Computing, September 2007. [12] Massimo Franceschetti, Marco D. Migliore, and Paolo Minero . The

Design, implementation and evaluation of a practical pseudoknot folding algorithm based on thermodynamics

PubMed Central

Reeder, Jens; Giegerich, Robert

2004-01-01

Background The general problem of RNA secondary structure prediction under the widely used thermodynamic model is known to be NP-complete when the structures considered include arbitrary pseudoknots. For restricted classes of pseudoknots, several polynomial time algorithms have been designed, where the O(n6)time and O(n4) space algorithm by Rivas and Eddy is currently the best available program. Results We introduce the class of canonical simple recursive pseudoknots and present an algorithm that requires O(n4) time and O(n2) space to predict the energetically optimal structure of an RNA sequence, possible containing such pseudoknots. Evaluation against a large collection of known pseudoknotted structures shows the adequacy of the canonization approach and our algorithm. Conclusions RNA pseudoknots of medium size can now be predicted reliably as well as efficiently by the new algorithm. PMID:15294028

Symmetric digit sets for elliptic curve scalar multiplication without precomputation

PubMed Central

Heuberger, Clemens; Mazzoli, Michela

2014-01-01

We describe a method to perform scalar multiplication on two classes of ordinary elliptic curves, namely E:y2=x3+Ax in prime characteristic p≡1mod4, and E:y2=x3+B in prime characteristic p≡1mod3. On these curves, the 4-th and 6-th roots of unity act as (computationally efficient) endomorphisms. In order to optimise the scalar multiplication, we consider a width-w-NAF (Non-Adjacent Form) digit expansion of positive integers to the complex base of τ, where τ is a zero of the characteristic polynomial x2−tx+p of the Frobenius endomorphism associated to the curve. We provide a precomputationless algorithm by means of a convenient factorisation of the unit group of residue classes modulo τ in the endomorphism ring, whereby we construct a digit set consisting of powers of subgroup generators, which are chosen as efficient endomorphisms of the curve. PMID:25190900

Theoretical and observational constraints on Tachyon Inflation

NASA Astrophysics Data System (ADS)

Barbosa-Cendejas, Nandinii; De-Santiago, Josue; German, Gabriel; Hidalgo, Juan Carlos; Rigel Mora-Luna, Refugio

2018-03-01

We constrain several models in Tachyonic Inflation derived from the large-N formalism by considering theoretical aspects as well as the latest observational data. On the theoretical side, we assess the field range of our models by means of the excursion of the equivalent canonical field. On the observational side, we employ BK14+PLANCK+BAO data to perform a parameter estimation analysis as well as a Bayesian model selection to distinguish the most favoured models among all four classes here presented. We observe that the original potential V propto sech(T) is strongly disfavoured by observations with respect to a reference model with flat priors on inflationary observables. This realisation of Tachyon inflation also presents a large field range which may demand further quantum corrections. We also provide examples of potentials derived from the polynomial and the perturbative classes which are both statistically favoured and theoretically acceptable.

Continuous-Variable Instantaneous Quantum Computing is Hard to Sample.

PubMed

Douce, T; Markham, D; Kashefi, E; Diamanti, E; Coudreau, T; Milman, P; van Loock, P; Ferrini, G

2017-02-17

Instantaneous quantum computing is a subuniversal quantum complexity class, whose circuits have proven to be hard to simulate classically in the discrete-variable realm. We extend this proof to the continuous-variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of postselected circuits. In order to treat postselection in CVs, we consider finitely resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render postselected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.

Nonbinary Tree-Based Phylogenetic Networks.

PubMed

Jetten, Laura; van Iersel, Leo

2018-01-01

Rooted phylogenetic networks are used to describe evolutionary histories that contain non-treelike evolutionary events such as hybridization and horizontal gene transfer. In some cases, such histories can be described by a phylogenetic base-tree with additional linking arcs, which can, for example, represent gene transfer events. Such phylogenetic networks are called tree-based. Here, we consider two possible generalizations of this concept to nonbinary networks, which we call tree-based and strictly-tree-based nonbinary phylogenetic networks. We give simple graph-theoretic characterizations of tree-based and strictly-tree-based nonbinary phylogenetic networks. Moreover, we show for each of these two classes that it can be decided in polynomial time whether a given network is contained in the class. Our approach also provides a new view on tree-based binary phylogenetic networks. Finally, we discuss two examples of nonbinary phylogenetic networks in biology and show how our results can be applied to them.

The analysis of convolutional codes via the extended Smith algorithm

NASA Technical Reports Server (NTRS)

Mceliece, R. J.; Onyszchuk, I.

1993-01-01

Convolutional codes have been the central part of most error-control systems in deep-space communication for many years. Almost all such applications, however, have used the restricted class of (n,1), also known as 'rate 1/n,' convolutional codes. The more general class of (n,k) convolutional codes contains many potentially useful codes, but their algebraic theory is difficult and has proved to be a stumbling block in the evolution of convolutional coding systems. In this article, the situation is improved by describing a set of practical algorithms for computing certain basic things about a convolutional code (among them the degree, the Forney indices, a minimal generator matrix, and a parity-check matrix), which are usually needed before a system using the code can be built. The approach is based on the classic Forney theory for convolutional codes, together with the extended Smith algorithm for polynomial matrices, which is introduced in this article.

About the best approximations with trigonometric polynomials on the class W0Hω¯ of the space L, part I

NASA Astrophysics Data System (ADS)

Nikolova, Yanka

2012-11-01

In this paper we obtain estimation for the best approximation En(W0Hω)¯ in the L-metric, where W0Hω¯ is the conjugate of the class W0Hω, i.e. W0Hω¯def = {f¯,f∈W0Hω}. Our results concern evaluations of the function Φ(Ḡ; x) where Φ(G; x) is the so-called Σ-representation of the function G, as defined in [2, p. 144], and Ḡ(x) denotes the conjugate of the function G(x). We prove three theorems, necessary for the estimation of the functional Fω(ḡ) = sup/f∈Hω ∫ 02πf(t).ḡ(t)dt. Specially, in Theorem 4 we prove an inequality for this functional and show that estimation is exact, i.e. the inequality becomes equality for some specific conjugate functions.

A quantum approach to homomorphic encryption

PubMed Central

Tan, Si-Hui; Kettlewell, Joshua A.; Ouyang, Yingkai; Chen, Lin; Fitzsimons, Joseph F.

2016-01-01

Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum homomorphic encryption scheme that enables a broad class of quantum computation on encrypted data. The quantum data is encoded on bosons of distinct species in distinct spatial modes, and the quantum computations are manipulations of these bosons in a manner independent of their species. A particular instance of our encoding hides up to a constant fraction of the information encrypted. This fraction can be made arbitrarily close to unity with overhead scaling only polynomially in the message length. This highlights the potential of our protocol to hide a non-trivial amount of information, and is suggestive of a large class of encodings that might yield better security. PMID:27658349

Nonlinear Structured Growth Mixture Models in Mplus and OpenMx

PubMed Central

Grimm, Kevin J.; Ram, Nilam; Estabrook, Ryne

2014-01-01

Growth mixture models (GMMs; Muthén & Muthén, 2000; Muthén & Shedden, 1999) are a combination of latent curve models (LCMs) and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. GMMs are often fit with linear, latent basis, multiphase, or polynomial change models because of their common use, flexibility in modeling many types of change patterns, the availability of statistical programs to fit such models, and the ease of programming. In this paper, we present additional ways of modeling nonlinear change patterns with GMMs. Specifically, we show how LCMs that follow specific nonlinear functions can be extended to examine the presence of multiple latent classes using the Mplus and OpenMx computer programs. These models are fit to longitudinal reading data from the Early Childhood Longitudinal Study-Kindergarten Cohort to illustrate their use. PMID:25419006

Solving search problems by strongly simulating quantum circuits

PubMed Central

Johnson, T. H.; Biamonte, J. D.; Clark, S. R.; Jaksch, D.

2013-01-01

Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several efficient strong simulation techniques are known for restricted families of quantum circuits and we develop an additional technique in this article. Further, we show that strong simulation algorithms perform another fundamental task: solving search problems. Efficient strong simulation techniques allow solutions to a class of search problems to be counted and found efficiently. This enhances the utility of strong simulation methods, known or yet to be discovered, and extends the class of search problems known to be efficiently simulable. Relating strong simulation to search problems also bounds the computational power of efficiently strongly simulable circuits; if they could solve all problems in P this would imply that all problems in NP and #P could be solved in polynomial time. PMID:23390585

Tikekar superdense stars in electric fields

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Maharaj, S. D.

2007-04-01

We present exact solutions to the Einstein-Maxwell system of equations with a specified form of the electric field intensity by assuming that the hypersurface {t=constant} are spheroidal. The solution of the Einstein-Maxwell system is reduced to a recurrence relation with variable rational coefficients which can be solved in general using mathematical induction. New classes of solutions of linearly independent functions are obtained by restricting the spheroidal parameter K and the electric field intensity parameter α. Consequently, it is possible to find exact solutions in terms of elementary functions, namely, polynomials and algebraic functions. Our result contains models found previously including the superdense Tikekar neutron star model [J. Math. Phys. 31, 2454 (1990)] when K=-7 and α=0. Our class of charged spheroidal models generalize the uncharged isotropic Maharaj and Leach solutions [J. Math. Phys. 37, 430 (1996)]. In particular, we find an explicit relationship directly relating the spheroidal parameter K to the electromagnetic field.

Solving a class of generalized fractional programming problems using the feasibility of linear programs.

PubMed

Shen, Peiping; Zhang, Tongli; Wang, Chunfeng

2017-01-01

This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm.

MarCO CubeSat Model

NASA Image and Video Library

2016-01-20

Joel Steinkraus, lead mechanical engineer for the MarCO (Mars Cube One) CubeSat spacecraft, adjusts a model of one of the two spacecraft. The mock-up in the photo is in a configuration to show the deployed position of components that correspond to MarCO's two solar panels and two antennas. During launch, those components will be stowed for a total vehicle size of about 14.4 inches (36.6 centimeters) by 9.5 inches (24.3 centimeters) by 4.6 inches (11.8 centimeters). The briefcase-size MarCO twins were designed to ride along with NASA's next Mars lander, InSight. Its planned March 2016 launch was suspended. InSight -- an acronym for Interior Exploration using Seismic Investigations, Geodesy and Heat Transport -- will study the interior of Mars to improve understanding of the processes that formed and shaped rocky planets, including Earth. Note: After thorough examination, NASA managers have decided to suspend the planned March 2016 launch of the Interior Exploration using Seismic Investigations Geodesy and Heat Transport (InSight) mission. The decision follows unsuccessful attempts to repair a leak in a section of the prime instrument in the science payload. http://photojournal.jpl.nasa.gov/catalog/PIA20344

Stochastic Estimation via Polynomial Chaos

DTIC Science & Technology

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Vehicle Sprung Mass Estimation for Rough Terrain

DTIC Science & Technology

2011-03-01

distributions are greater than zero. The multivariate polynomials are functions of the Legendre polynomials (Poularikas (1999...developed methods based on polynomial chaos theory and on the maximum likelihood approach to estimate the most likely value of the vehicle sprung...mass. The polynomial chaos estimator is compared to benchmark algorithms including recursive least squares, recursive total least squares, extended

Degenerate r-Stirling Numbers and r-Bell Polynomials

NASA Astrophysics Data System (ADS)

Kim, T.; Yao, Y.; Kim, D. S.; Jang, G.-W.

2018-01-01

The purpose of this paper is to exploit umbral calculus in order to derive some properties, recurrence relations, and identities related to the degenerate r-Stirling numbers of the second kind and the degenerate r-Bell polynomials. Especially, we will express the degenerate r-Bell polynomials as linear combinations of many well-known families of special polynomials.

From Chebyshev to Bernstein: A Tour of Polynomials Small and Large

ERIC Educational Resources Information Center

Boelkins, Matthew; Miller, Jennifer; Vugteveen, Benjamin

2006-01-01

Consider the family of monic polynomials of degree n having zeros at -1 and +1 and all their other real zeros in between these two values. This article explores the size of these polynomials using the supremum of the absolute value on [-1, 1], showing that scaled Chebyshev and Bernstein polynomials give the extremes.

A Final Approach Trajectory Model for Current Operations

NASA Technical Reports Server (NTRS)

Gong, Chester; Sadovsky, Alexander

2010-01-01

Predicting accurate trajectories with limited intent information is a challenge faced by air traffic management decision support tools in operation today. One such tool is the FAA's Terminal Proximity Alert system which is intended to assist controllers in maintaining safe separation of arrival aircraft during final approach. In an effort to improve the performance of such tools, two final approach trajectory models are proposed; one based on polynomial interpolation, the other on the Fourier transform. These models were tested against actual traffic data and used to study effects of the key final approach trajectory modeling parameters of wind, aircraft type, and weight class, on trajectory prediction accuracy. Using only the limited intent data available to today's ATM system, both the polynomial interpolation and Fourier transform models showed improved trajectory prediction accuracy over a baseline dead reckoning model. Analysis of actual arrival traffic showed that this improved trajectory prediction accuracy leads to improved inter-arrival separation prediction accuracy for longer look ahead times. The difference in mean inter-arrival separation prediction error between the Fourier transform and dead reckoning models was 0.2 nmi for a look ahead time of 120 sec, a 33 percent improvement, with a corresponding 32 percent improvement in standard deviation.

MarCO Flight Hardware 2

NASA Image and Video Library

2016-01-20

One of the two MarCO (Mars Cube One) CubeSat spacecraft is seen at NASA's Jet Propulsion Laboratory, Pasadena, California. The briefcase-size MarCO twins were designed to ride along with NASA's next Mars lander, InSight. Its planned March 2016 launch was suspended. InSight -- an acronym for Interior Exploration using Seismic Investigations, Geodesy and Heat Transport -- will study the interior of Mars to improve understanding of the processes that formed and shaped rocky planets, including Earth. Note: After thorough examination, NASA managers have decided to suspend the planned March 2016 launch of the Interior Exploration using Seismic Investigations Geodesy and Heat Transport (InSight) mission. The decision follows unsuccessful attempts to repair a leak in a section of the prime instrument in the science payload. http://photojournal.jpl.nasa.gov/catalog/PIA20346

Umbral orthogonal polynomials

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

Lopez-Sendino, J. E.; del Olmo, M. A.

2010-12-23

We present an umbral operator version of the classical orthogonal polynomials. We obtain three families which are the umbral counterpart of the Jacobi, Laguerre and Hermite polynomials in the classical case.

Design and Use of a Learning Object for Finding Complex Polynomial Roots

ERIC Educational Resources Information Center

Benitez, Julio; Gimenez, Marcos H.; Hueso, Jose L.; Martinez, Eulalia; Riera, Jaime

2013-01-01

Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…

Extending a Property of Cubic Polynomials to Higher-Degree Polynomials

ERIC Educational Resources Information Center

Miller, David A.; Moseley, James

2012-01-01

In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

Formal language constrained path problems

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

Barrett, C.; Jacob, R.; Marathe, M.

1997-07-08

In many path finding problems arising in practice, certain patterns of edge/vertex labels in the labeled graph being traversed are allowed/preferred, while others are disallowed. Motivated by such applications as intermodal transportation planning, the authors investigate the complexity of finding feasible paths in a labeled network, where the mode choice for each traveler is specified by a formal language. The main contributions of this paper include the following: (1) the authors show that the problem of finding a shortest path between a source and destination for a traveler whose mode choice is specified as a context free language is solvablemore » efficiently in polynomial time, when the mode choice is specified as a regular language they provide algorithms with improved space and time bounds; (2) in contrast, they show that the problem of finding simple paths between a source and a given destination is NP-hard, even when restricted to very simple regular expressions and/or very simple graphs; (3) for the class of treewidth bounded graphs, they show that (i) the problem of finding a regular language constrained simple path between source and a destination is solvable in polynomial time and (ii) the extension to finding context free language constrained simple paths is NP-complete. Several extensions of these results are presented in the context of finding shortest paths with additional constraints. These results significantly extend the results in [MW95]. As a corollary of the results, they obtain a polynomial time algorithm for the BEST k-SIMILAR PATH problem studied in [SJB97]. The previous best algorithm was given by [SJB97] and takes exponential time in the worst case.« less

Computing Galois Groups of Eisenstein Polynomials Over P-adic Fields

NASA Astrophysics Data System (ADS)

Milstead, Jonathan

The most efficient algorithms for computing Galois groups of polynomials over global fields are based on Stauduhar's relative resolvent method. These methods are not directly generalizable to the local field case, since they require a field that contains the global field in which all roots of the polynomial can be approximated. We present splitting field-independent methods for computing the Galois group of an Eisenstein polynomial over a p-adic field. Our approach is to combine information from different disciplines. We primarily, make use of the ramification polygon of the polynomial, which is the Newton polygon of a related polynomial. This allows us to quickly calculate several invariants that serve to reduce the number of possible Galois groups. Algorithms by Greve and Pauli very efficiently return the Galois group of polynomials where the ramification polygon consists of one segment as well as information about the subfields of the stem field. Second, we look at the factorization of linear absolute resolvents to further narrow the pool of possible groups.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

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

Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei

The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl{sub -1}(2). The dual -1 Hahn polynomials are the bispectral polynomials of a discrete argument obtained from the q{yields}-1 limit of the dual q-Hahn polynomials. The Hopf algebra sl{sub -1}(2) has four generators including an involution, it is also a q{yields}-1 limit of the quantum algebra sl{sub q}(2) and furthermore, the dynamical algebra of the parabose oscillator. The algebra H, a two-parameter generalization of u(2) with an involution as additional generator, is first derived from the recurrence relation of themore » -1 Hahn polynomials. It is then shown that H can be realized in terms of the generators of two added sl{sub -1}(2) algebras, so that the Clebsch-Gordan coefficients of sl{sub -1}(2) are dual -1 Hahn polynomials. An irreducible representation of H involving five-diagonal matrices and connected to the difference equation of the dual -1 Hahn polynomials is constructed.« less

Bounds on the sample complexity for private learning and private data release

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

Kasiviswanathan, Shiva; Beime, Amos; Nissim, Kobbi

2009-01-01

Learning is a task that generalizes many of the analyses that are applied to collections of data, and in particular, collections of sensitive individual information. Hence, it is natural to ask what can be learned while preserving individual privacy. [Kasiviswanathan, Lee, Nissim, Raskhodnikova, and Smith; FOCS 2008] initiated such a discussion. They formalized the notion of private learning, as a combination of PAC learning and differential privacy, and investigated what concept classes can be learned privately. Somewhat surprisingly, they showed that, ignoring time complexity, every PAC learning task could be performed privately with polynomially many samples, and in many naturalmore » cases this could even be done in polynomial time. While these results seem to equate non-private and private learning, there is still a significant gap: the sample complexity of (non-private) PAC learning is crisply characterized in terms of the VC-dimension of the concept class, whereas this relationship is lost in the constructions of private learners, which exhibit, generally, a higher sample complexity. Looking into this gap, we examine several private learning tasks and give tight bounds on their sample complexity. In particular, we show strong separations between sample complexities of proper and improper private learners (such separation does not exist for non-private learners), and between sample complexities of efficient and inefficient proper private learners. Our results show that VC-dimension is not the right measure for characterizing the sample complexity of proper private learning. We also examine the task of private data release (as initiated by [Blum, Ligett, and Roth; STOC 2008]), and give new lower bounds on the sample complexity. Our results show that the logarithmic dependence on size of the instance space is essential for private data release.« less

Interbasis expansions in the Zernike system

NASA Astrophysics Data System (ADS)

Atakishiyev, Natig M.; Pogosyan, George S.; Wolf, Kurt Bernardo; Yakhno, Alexander

2017-10-01

The differential equation with free boundary conditions on the unit disk that was proposed by Frits Zernike in 1934 to find Jacobi polynomial solutions (indicated as I) serves to define a classical system and a quantum system which have been found to be superintegrable. We have determined two new orthogonal polynomial solutions (indicated as II and III) that are separable and involve Legendre and Gegenbauer polynomials. Here we report on their three interbasis expansion coefficients: between the I-II and I-III bases, they are given by F32(⋯|1 ) polynomials that are also special su(2) Clebsch-Gordan coefficients and Hahn polynomials. Between the II-III bases, we find an expansion expressed by F43(⋯|1 ) 's and Racah polynomials that are related to the Wigner 6j coefficients.

33 CFR 147.837 - Marco Polo Tension Leg Platform safety zone.

Code of Federal Regulations, 2010 CFR

2010-07-01

... Platform safety zone. (a) Description. Marco Polo Tension Leg Platform, Green Canyon 608 (GC 608), located at position 27°21′43.32″ N, 90°10′53.01″ W. The area within 500 meters (1640.4 feet) from each point on the structure's outer edge is a safety zone. These coordinates are based upon [NAD 83]. (b...

JPRS Report, Latin America

DTIC Science & Technology

1987-07-02

70 MDN Prepares for Second Assembly ( Hubert de Ronceray Interview; HAITI LIBEREE, 28 Apr 87) 71 Briefs PUCH Statement 74 - c PARAGUAY...director of the INPE, Marco Antonio Raupp, said that apart from sharing the use of the satellite, Brazil will also provide China with various other types...included: Castillo Barajas and Marco Antonio Ventura from the Ministry of Economy; Willy Zapata from the Bank of Guatemala; and Haroldo Rodas Melgar

Continental Scientific Drilling Program.

DTIC Science & Technology

1979-01-01

Institute of Technology ALBERT W. BALLY, Shell Oil Company, Houston HUBERT L. BARNES, Pennsylvania State University ARTHUR L. BOETTCHER, University of...San Marcos arch near Victoria, Texas. Information from a hole would answer fundamental questions about ancient continental margins and would complement...did the uplift begin in this area? Is the crust continental or oceanic? Area 3 (Figure A-7), positioned upon the San Marcos arch to avoid the thick

Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

NASA Astrophysics Data System (ADS)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2009-12-01

We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.

Combinatorial theory of Macdonald polynomials I: proof of Haglund's formula.

PubMed

Haglund, J; Haiman, M; Loehr, N

2005-02-22

Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H(mu). We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H(mu). As corollaries, we obtain the cocharge formula of Lascoux and Schutzenberger for Hall-Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization of this result to the integral Macdonald polynomials J(mu), a formula for H(mu) in terms of Lascoux-Leclerc-Thibon polynomials, and combinatorial expressions for the Kostka-Macdonald coefficients K(lambda,mu) when mu is a two-column shape.

Multi-indexed (q-)Racah polynomials

NASA Astrophysics Data System (ADS)

Odake, Satoru; Sasaki, Ryu

2012-09-01

As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of ‘discrete quantum mechanics’ with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials by the multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of ‘virtual state’ vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the ‘solutions’ of the matrix Schrödinger equation with negative ‘eigenvalues’, except for one of the two boundary points.

Conformal Galilei algebras, symmetric polynomials and singular vectors

NASA Astrophysics Data System (ADS)

Křižka, Libor; Somberg, Petr

2018-01-01

We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras cga_ℓ (d,C) with d=1 for any integer value ℓ \\in N. The homomorphisms are uniquely determined by singular vectors as solutions of certain differential operators of flag type and identified with specific polynomials arising as coefficients in the expansion of a parametric family of symmetric polynomials into power sum symmetric polynomials.

Identities associated with Milne-Thomson type polynomials and special numbers.

PubMed

Simsek, Yilmaz; Cakic, Nenad

2018-01-01

The purpose of this paper is to give identities and relations including the Milne-Thomson polynomials, the Hermite polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy numbers. By using fermionic and bosonic p -adic integrals, we derive some new relations and formulas related to these numbers and polynomials, and also the combinatorial sums.

MarCO Flight Hardware 1

NASA Image and Video Library

2016-01-20

One of the two MarCO (Mars Cube One) CubeSat spacecraft, with its insides displayed, is seen at NASA's Jet Propulsion Laboratory, Pasadena, California. The briefcase-size MarCO twins were designed to ride along with NASA's next Mars lander, InSight. Its planned March 2016 launch was suspended. InSight -- an acronym for Interior Exploration using Seismic Investigations, Geodesy and Heat Transport -- will study the interior of Mars to improve understanding of the processes that formed and shaped rocky planets, including Earth. Note: After thorough examination, NASA managers have decided to suspend the planned March 2016 launch of the Interior Exploration using Seismic Investigations Geodesy and Heat Transport (InSight) mission. The decision follows unsuccessful attempts to repair a leak in a section of the prime instrument in the science payload. http://photojournal.jpl.nasa.gov/catalog/PIA20345

Parameter reduction in nonlinear state-space identification of hysteresis

NASA Astrophysics Data System (ADS)

Fakhrizadeh Esfahani, Alireza; Dreesen, Philippe; Tiels, Koen; Noël, Jean-Philippe; Schoukens, Johan

2018-05-01

Recent work on black-box polynomial nonlinear state-space modeling for hysteresis identification has provided promising results, but struggles with a large number of parameters due to the use of multivariate polynomials. This drawback is tackled in the current paper by applying a decoupling approach that results in a more parsimonious representation involving univariate polynomials. This work is carried out numerically on input-output data generated by a Bouc-Wen hysteretic model and follows up on earlier work of the authors. The current article discusses the polynomial decoupling approach and explores the selection of the number of univariate polynomials with the polynomial degree. We have found that the presented decoupling approach is able to reduce the number of parameters of the full nonlinear model up to about 50%, while maintaining a comparable output error level.

Learning polynomial feedforward neural networks by genetic programming and backpropagation.

PubMed

Nikolaev, N Y; Iba, H

2003-01-01

This paper presents an approach to learning polynomial feedforward neural networks (PFNNs). The approach suggests, first, finding the polynomial network structure by means of a population-based search technique relying on the genetic programming paradigm, and second, further adjustment of the best discovered network weights by an especially derived backpropagation algorithm for higher order networks with polynomial activation functions. These two stages of the PFNN learning process enable us to identify networks with good training as well as generalization performance. Empirical results show that this approach finds PFNN which outperform considerably some previous constructive polynomial network algorithms on processing benchmark time series.

Quasi-kernel polynomials and convergence results for quasi-minimal residual iterations

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1992-01-01

Recently, Freund and Nachtigal have proposed a novel polynominal-based iteration, the quasi-minimal residual algorithm (QMR), for solving general nonsingular non-Hermitian linear systems. Motivated by the QMR method, we have introduced the general concept of quasi-kernel polynomials, and we have shown that the QMR algorithm is based on a particular instance of quasi-kernel polynomials. In this paper, we continue our study of quasi-kernel polynomials. In particular, we derive bounds for the norms of quasi-kernel polynomials. These results are then applied to obtain convergence theorems both for the QMR method and for a transpose-free variant of QMR, the TFQMR algorithm.

On universal knot polynomials

NASA Astrophysics Data System (ADS)

Mironov, A.; Mkrtchyan, R.; Morozov, A.

2016-02-01

We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, respectively and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.

Zernike Basis to Cartesian Transformations

NASA Astrophysics Data System (ADS)

Mathar, R. J.

2009-12-01

The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle) defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

Universal Racah matrices and adjoint knot polynomials: Arborescent knots

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2016-04-01

By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.

Imaging characteristics of Zernike and annular polynomial aberrations.

PubMed

Mahajan, Virendra N; Díaz, José Antonio

2013-04-01

The general equations for the point-spread function (PSF) and optical transfer function (OTF) are given for any pupil shape, and they are applied to optical imaging systems with circular and annular pupils. The symmetry properties of the PSF, the real and imaginary parts of the OTF, and the modulation transfer function (MTF) of a system with a circular pupil aberrated by a Zernike circle polynomial aberration are derived. The interferograms and PSFs are illustrated for some typical polynomial aberrations with a sigma value of one wave, and 3D PSFs and MTFs are shown for 0.1 wave. The Strehl ratio is also calculated for polynomial aberrations with a sigma value of 0.1 wave, and shown to be well estimated from the sigma value. The numerical results are compared with the corresponding results in the literature. Because of the same angular dependence of the corresponding annular and circle polynomial aberrations, the symmetry properties of systems with annular pupils aberrated by an annular polynomial aberration are the same as those for a circular pupil aberrated by a corresponding circle polynomial aberration. They are also illustrated with numerical examples.

APPROXIMATION OF SOLUTIONS OF THE EQUATION \\overline\\partial^jf=0, j\\geq1, IN DOMAINS WITH QUASICONFORMAL BOUNDARY

NASA Astrophysics Data System (ADS)

Andrievskiĭ, V. V.; Belyĭ, V. I.; Maĭmeskul, V. V.

1991-02-01

This article establishes direct and inverse theorems of approximation theory (of the same type as theorems of Dzyadyk) that describe the quantitative connection between the smoothness properties of solutions of the equation \\overline\\partial^jf=0, j\\geq1, and the rate of their approximation by "module" polynomials of the form \\displaystyle P_N(z)=\\sum_{n=0}^{j-1}\\sum_{m=0}^{N-n}a_{m,n}z^m\\overline{z}^n,\\qquad N\\geq j-1.In particular, a constructive characterization is obtained for generalized Hölder classes of such functions on domains with quasiconformal boundary.Bibliography: 19 titles.

Parametric instabilities of finite-amplitude, circularly polarized Alfven waves in an anisotropic plasma

NASA Technical Reports Server (NTRS)

Hamabata, Hiromitsu

1993-01-01

A class of parametric instabilities of finite-amplitude, circularly polarized Alfven waves in a plasma with pressure anisotropy is studied by application of the CGL equations. A linear perturbation analysis is used to find the dispersion relation governing the instabilities, which is a fifth-order polynomial and is solved numerically. A large-amplitude, circularly polarized wave is unstable with respect to decay into three waves: one sound-like wave and two side-band Alfven-like waves. It is found that, in addition to the decay instability, two new instabilities that are absent in the framework of the MHD equations can occur, depending on the plasma parameters.

On chaos synchronization and secure communication.

PubMed

Kinzel, W; Englert, A; Kanter, I

2010-01-28

Chaos synchronization, in particular isochronal synchronization of two chaotic trajectories to each other, may be used to build a means of secure communication over a public channel. In this paper, we give an overview of coupling schemes of Bernoulli units deduced from chaotic laser systems, different ways to transmit information by chaos synchronization and the advantage of bidirectional over unidirectional coupling with respect to secure communication. We present the protocol for using dynamical private commutative filters for tap-proof transmission of information that maps the task of a passive attacker to the class of non-deterministic polynomial time-complete problems. This journal is © 2010 The Royal Society

Applications of polynomial optimization in financial risk investment

NASA Astrophysics Data System (ADS)

Zeng, Meilan; Fu, Hongwei

2017-09-01

Recently, polynomial optimization has many important applications in optimization, financial economics and eigenvalues of tensor, etc. This paper studies the applications of polynomial optimization in financial risk investment. We consider the standard mean-variance risk measurement model and the mean-variance risk measurement model with transaction costs. We use Lasserre's hierarchy of semidefinite programming (SDP) relaxations to solve the specific cases. The results show that polynomial optimization is effective for some financial optimization problems.

A Stochastic Mixed Finite Element Heterogeneous Multiscale Method for Flow in Porous Media

DTIC Science & Technology

2010-08-01

applicable for flow in porous media has drawn significant interest in the last few years. Several techniques like generalized polynomial chaos expansions (gPC...represents the stochastic solution as a polynomial approxima- tion. This interpolant is constructed via independent function calls to the de- terministic...of orthogonal polynomials [34,38] or sparse grid approximations [39–41]. It is well known that the global polynomial interpolation cannot resolve lo

A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or 6 - j Symbols.

DTIC Science & Technology

1978-03-01

Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. [11] D. Stanton, Some basic hypergeometric polynomials arising from... Some bas ic hypergeometr ic an a logues of the classical orthogonal polynomials and applications , to appear. [3] C. de Boor and G. H. Golub , The...Report #1833 A SET OF ORTHOGONAL POLYNOMIALS THAT GENERALIZE THE RACAR COEFFICIENTS OR 6 — j SYMBOLS Richard Askey and James Wilson •

Tutte polynomial in functional magnetic resonance imaging

NASA Astrophysics Data System (ADS)

García-Castillón, Marlly V.

2015-09-01

Methods of graph theory are applied to the processing of functional magnetic resonance images. Specifically the Tutte polynomial is used to analyze such kind of images. Functional Magnetic Resonance Imaging provide us connectivity networks in the brain which are represented by graphs and the Tutte polynomial will be applied. The problem of computing the Tutte polynomial for a given graph is #P-hard even for planar graphs. For a practical application the maple packages "GraphTheory" and "SpecialGraphs" will be used. We will consider certain diagram which is depicting functional connectivity, specifically between frontal and posterior areas, in autism during an inferential text comprehension task. The Tutte polynomial for the resulting neural networks will be computed and some numerical invariants for such network will be obtained. Our results show that the Tutte polynomial is a powerful tool to analyze and characterize the networks obtained from functional magnetic resonance imaging.

On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

NASA Astrophysics Data System (ADS)

Doha, E. H.

2002-02-01

An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

Genetic analyses of protein yield in dairy cows applying random regression models with time-dependent and temperature x humidity-dependent covariates.

PubMed

Brügemann, K; Gernand, E; von Borstel, U U; König, S

2011-08-01

Data used in the present study included 1,095,980 first-lactation test-day records for protein yield of 154,880 Holstein cows housed on 196 large-scale dairy farms in Germany. Data were recorded between 2002 and 2009 and merged with meteorological data from public weather stations. The maximum distance between each farm and its corresponding weather station was 50 km. Hourly temperature-humidity indexes (THI) were calculated using the mean of hourly measurements of dry bulb temperature and relative humidity. On the phenotypic scale, an increase in THI was generally associated with a decrease in daily protein yield. For genetic analyses, a random regression model was applied using time-dependent (d in milk, DIM) and THI-dependent covariates. Additive genetic and permanent environmental effects were fitted with this random regression model and Legendre polynomials of order 3 for DIM and THI. In addition, the fixed curve was modeled with Legendre polynomials of order 3. Heterogeneous residuals were fitted by dividing DIM into 5 classes, and by dividing THI into 4 classes, resulting in 20 different classes. Additive genetic variances for daily protein yield decreased with increasing degrees of heat stress and were lowest at the beginning of lactation and at extreme THI. Due to higher additive genetic variances, slightly higher permanent environment variances, and similar residual variances, heritabilities were highest for low THI in combination with DIM at the end of lactation. Genetic correlations among individual values for THI were generally >0.90. These trends from the complex random regression model were verified by applying relatively simple bivariate animal models for protein yield measured in 2 THI environments; that is, defining a THI value of 60 as a threshold. These high correlations indicate the absence of any substantial genotype × environment interaction for protein yield. However, heritabilities and additive genetic variances from the random regression model tended to be slightly higher in the THI range corresponding to cows' comfort zone. Selecting such superior environments for progeny testing can contribute to an accurate genetic differentiation among selection candidates. Copyright © 2011 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

On a Family of Multivariate Modified Humbert Polynomials

PubMed Central

Aktaş, Rabia; Erkuş-Duman, Esra

2013-01-01

This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials. PMID:23935411

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

Lue Xing; Sun Kun; Wang Pan

In the framework of Bell-polynomial manipulations, under investigation hereby are three single-field bilinearizable equations: the (1+1)-dimensional shallow water wave model, Boiti-Leon-Manna-Pempinelli model, and (2+1)-dimensional Sawada-Kotera model. Based on the concept of scale invariance, a direct and unifying Bell-polynomial scheme is employed to achieve the Baecklund transformations and Lax pairs associated with those three soliton equations. Note that the Bell-polynomial expressions and Bell-polynomial-typed Baecklund transformations for those three soliton equations can be, respectively, cast into the bilinear equations and bilinear Baecklund transformations with symbolic computation. Consequently, it is also shown that the Bell-polynomial-typed Baecklund transformations can be linearized into the correspondingmore » Lax pairs.« less

An O(log sup 2 N) parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1989-01-01

An O(log sup 2 N) parallel algorithm is presented for computing the eigenvalues of a symmetric tridiagonal matrix using a parallel algorithm for computing the zeros of the characteristic polynomial. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The exact behavior of the polynomials at the interval endpoints is used to eliminate the usual problems induced by finite precision arithmetic.

238,234U contents on Lepomis Cyanellus from San Marcos dam located in a uraniferous area

NASA Astrophysics Data System (ADS)

Lares, Magaly Cabral; Luna-Porres, Mayra Y.; Montero-Cabrera, María E.; Renteria-Villalobos, Marusia

2014-07-01

Fish species are suitable biomonitors of radioisotopes in aquatic systems. In the present study, it was made the determination of uranium isotopic contents on fish fillet (Lepomis Cyanellus) from San Marcos dam which is located in uranium mineralized zone. Uranium activity concentrations (AC) in fish samples were obtained on wet weight (ww), using liquid scintillation. 238U and 234U AC in fish fillet ranged from 0.0004 to 0.0167 Bq kg-1, and from 0.0013 to 0.0394 Bq kg-1, respectively. The activity ratio (234U/overflow="scroll">238U) in fish fillet ranged from 2.2 to 8.8. Lepomis cyanellus from San Marcos dam shows bioaccumulation factor (FB) of 0.6 L kg-1. The results suggest that the Lepomis Cyanellus in environments with high U contents tends to have a greater bioaccumulation compared to others.

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

Polynomial time blackbox identity testers for depth-3 circuits : the field doesn't matter.

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

Seshadhri, Comandur; Saxena, Nitin

Let C be a depth-3 circuit with n variables, degree d and top fanin k (called {Sigma}{Pi}{Sigma}(k, d, n) circuits) over base field F. It is a major open problem to design a deterministic polynomial time blackbox algorithm that tests if C is identically zero. Klivans & Spielman (STOC 2001) observed that the problem is open even when k is a constant. This case has been subjected to a serious study over the past few years, starting from the work of Dvir & Shpilka (STOC 2005). We give the first polynomial time blackbox algorithm for this problem. Our algorithm runsmore » in time poly(n)d{sup k}, regardless of the base field. The only field for which polynomial time algorithms were previously known is F = Q (Kayal & Saraf, FOCS 2009, and Saxena & Seshadhri, FOCS 2010). This is the first blackbox algorithm for depth-3 circuits that does not use the rank based approaches of Karnin & Shpilka (CCC 2008). We prove an important tool for the study of depth-3 identities. We design a blackbox polynomial time transformation that reduces the number of variables in a {Sigma}{Pi}{Sigma}(k, d, n) circuit to k variables, but preserves the identity structure. Polynomial identity testing (PIT) is a major open problem in theoretical computer science. The input is an arithmetic circuit that computes a polynomial p(x{sub 1}, x{sub 2},..., x{sub n}) over a base field F. We wish to check if p is the zero polynomial, or in other words, is identically zero. We may be provided with an explicit circuit, or may only have blackbox access. In the latter case, we can only evaluate the polynomial p at various domain points. The main goal is to devise a deterministic blackbox polynomial time algorithm for PIT.« less

Analysis on the misalignment errors between Hartmann-Shack sensor and 45-element deformable mirror

NASA Astrophysics Data System (ADS)

Liu, Lihui; Zhang, Yi; Tao, Jianjun; Cao, Fen; Long, Yin; Tian, Pingchuan; Chen, Shangwu

2017-02-01

Aiming at 45-element adaptive optics system, the model of 45-element deformable mirror is truly built by COMSOL Multiphysics, and every actuator's influence function is acquired by finite element method. The process of this system correcting optical aberration is simulated by making use of procedure, and aiming for Strehl ratio of corrected diffraction facula, in the condition of existing different translation and rotation error between Hartmann-Shack sensor and deformable mirror, the system's correction ability for 3-20 Zernike polynomial wave aberration is analyzed. The computed result shows: the system's correction ability for 3-9 Zernike polynomial wave aberration is higher than that of 10-20 Zernike polynomial wave aberration. The correction ability for 3-20 Zernike polynomial wave aberration does not change with misalignment error changing. With rotation error between Hartmann-Shack sensor and deformable mirror increasing, the correction ability for 3-20 Zernike polynomial wave aberration gradually goes down, and with translation error increasing, the correction ability for 3-9 Zernike polynomial wave aberration gradually goes down, but the correction ability for 10-20 Zernike polynomial wave aberration behave up-and-down depression.

Stability analysis of fuzzy parametric uncertain systems.

PubMed

Bhiwani, R J; Patre, B M

2011-10-01

In this paper, the determination of stability margin, gain and phase margin aspects of fuzzy parametric uncertain systems are dealt. The stability analysis of uncertain linear systems with coefficients described by fuzzy functions is studied. A complexity reduced technique for determining the stability margin for FPUS is proposed. The method suggested is dependent on the order of the characteristic polynomial. In order to find the stability margin of interval polynomials of order less than 5, it is not always necessary to determine and check all four Kharitonov's polynomials. It has been shown that, for determining stability margin of FPUS of order five, four, and three we require only 3, 2, and 1 Kharitonov's polynomials respectively. Only for sixth and higher order polynomials, a complete set of Kharitonov's polynomials are needed to determine the stability margin. Thus for lower order systems, the calculations are reduced to a large extent. This idea has been extended to determine the stability margin of fuzzy interval polynomials. It is also shown that the gain and phase margin of FPUS can be determined analytically without using graphical techniques. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

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.

On the coefficients of differentiated expansions of ultraspherical polynomials

NASA Technical Reports Server (NTRS)

Karageorghis, Andreas; Phillips, Timothy N.

1989-01-01

A formula expressing the coefficients of an expression of ultraspherical polynomials which has been differentiated an arbitrary number of times in terms of the coefficients of the original expansion is proved. The particular examples of Chebyshev and Legendre polynomials are considered.

On Polynomial Solutions of Linear Differential Equations with Polynomial Coefficients

ERIC Educational Resources Information Center

Si, Do Tan

1977-01-01

Demonstrates a method for solving linear differential equations with polynomial coefficients based on the fact that the operators z and D + d/dz are known to be Hermitian conjugates with respect to the Bargman and Louck-Galbraith scalar products. (MLH)

Algorithms for computing solvents of unilateral second-order matrix polynomials over prime finite fields using lambda-matrices

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-01-01

The paper considers algorithms for finding diagonalizable and non-diagonalizable roots (so called solvents) of monic arbitrary unilateral second-order matrix polynomial over prime finite field. These algorithms are based on polynomial matrices (lambda-matrices). This is an extension of existing general methods for computing solvents of matrix polynomials over field of complex numbers. We analyze how techniques for complex numbers can be adapted for finite field and estimate asymptotic complexity of the obtained algorithms.

On the Analytical and Numerical Properties of the Truncated Laplace Transform I

DTIC Science & Technology

2014-09-05

contains generalizations and conclusions. 2 2 Preliminaries 2.1 The Legendre Polynomials In this subsection we summarize some of the properties of the the...standard Legendre Polynomi - als, and restate these properties for shifted and normalized forms of the Legendre Polynomials . We define the Shifted... Legendre Polynomial of degree k = 0, 1, ..., which we will be denoting by P ∗k , by the formula P ∗k (x) = Pk(2x− 1), (5) where Pk is the Legendre

Development of Fast Deterministic Physically Accurate Solvers for Kinetic Collision Integral for Applications of Near Space Flight and Control Devices

DTIC Science & Technology

2015-08-31

following functions were used: where are the Legendre polynomials of degree . It is assumed that the coefficient standing with has the form...enforce relaxation rates of high order moments, higher order polynomial basis functions are used. The use of high order polynomials results in strong...enforced while only polynomials up to second degree were used in the representation of the collision frequency. It can be seen that the new model

Effects of Air Drag and Lunar Third-Body Perturbations on Motion Near a Reference KAM Torus

DTIC Science & Technology

2011-03-01

body m 1) mass of satellite; 2) order of associated Legendre polynomial n 1) mean motion; 2) degree of associated Legendre polynomial n3 mean motion...physical momentum pi ith physical momentum Pmn associated Legendre polynomial of order m and degree n q̇ physical coordinate derivatives vector, [q̇1...are constants specifying the shape of the gravitational field; and Pmn are associated Legendre polynomials . When m = n = 0, the geopotential function

Polynomial compensation, inversion, and approximation of discrete time linear systems

NASA Technical Reports Server (NTRS)

Baram, Yoram

1987-01-01

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Recurrence relations for orthogonal polynomials for PDEs in polar and cylindrical geometries.

PubMed

Richardson, Megan; Lambers, James V

2016-01-01

This paper introduces two families of orthogonal polynomials on the interval (-1,1), with weight function [Formula: see text]. The first family satisfies the boundary condition [Formula: see text], and the second one satisfies the boundary conditions [Formula: see text]. These boundary conditions arise naturally from PDEs defined on a disk with Dirichlet boundary conditions and the requirement of regularity in Cartesian coordinates. The families of orthogonal polynomials are obtained by orthogonalizing short linear combinations of Legendre polynomials that satisfy the same boundary conditions. Then, the three-term recurrence relations are derived. Finally, it is shown that from these recurrence relations, one can efficiently compute the corresponding recurrences for generalized Jacobi polynomials that satisfy the same boundary conditions.

Gaussian quadrature for multiple orthogonal polynomials

NASA Astrophysics Data System (ADS)

Coussement, Jonathan; van Assche, Walter

2005-06-01

We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.

Frequency domain system identification methods - Matrix fraction description approach

NASA Technical Reports Server (NTRS)

Horta, Luca G.; Juang, Jer-Nan

1993-01-01

This paper presents the use of matrix fraction descriptions for least-squares curve fitting of the frequency spectra to compute two matrix polynomials. The matrix polynomials are intermediate step to obtain a linearized representation of the experimental transfer function. Two approaches are presented: first, the matrix polynomials are identified using an estimated transfer function; second, the matrix polynomials are identified directly from the cross/auto spectra of the input and output signals. A set of Markov parameters are computed from the polynomials and subsequently realization theory is used to recover a minimum order state space model. Unevenly spaced frequency response functions may be used. Results from a simple numerical example and an experiment are discussed to highlight some of the important aspect of the algorithm.

f( R) gravity modifications: from the action to the data

NASA Astrophysics Data System (ADS)

Lazkoz, Ruth; Ortiz-Baños, María; Salzano, Vincenzo

2018-03-01

It is a very well established matter nowadays that many modified gravity models can offer a sound alternative to General Relativity for the description of the accelerated expansion of the universe. But it is also equally well known that no clear and sharp discrimination between any alternative theory and the classical one has been found so far. In this work, we attempt at formulating a different approach starting from the general class of f( R) theories as test probes: we try to reformulate f( R) Lagrangian terms as explicit functions of the redshift, i.e., as f( z). In this context, the f( R) setting to the consensus cosmological model, the Λ CDM model, can be written as a polynomial including just a constant and a third-order term. Starting from this result, we propose various different polynomial parameterizations f( z), including new terms which would allow for deviations from Λ CDM, and we thoroughly compare them with observational data. While on the one hand we have found no statistically preference for our proposals (even if some of them are as good as Λ CDM by using Bayesian Evidence comparison), we think that our novel approach could provide a different perspective for the development of new and observationally reliable alternative models of gravity.

The Karlin-McGregor formula for a variant of a discrete version of Walsh's spider

NASA Astrophysics Data System (ADS)

Grünbaum, F. Alberto

2009-10-01

We consider a variant of a discrete space version of Walsh's spider, see Walsh (1978 Temps Locaux, Asterisque vol 52-53 (Paris: Soc. Math. de France)) as well as Evans and Sowers (2003 Ann. Probab. 31 486-527 and its references). This process can be seen as an instance of a quasi-birth-and-death process, a class of random walks for which the classical theory of Karlin and McGregor can be nicely adapted as in Dette, Reuther, Studden and Zygmunt (2006 SIAM J. Matrix Anal. Appl. 29 117-42), Grünbaum (2007 Probability, Geometry and Integrable Systems ed Pinsky and Birnir vol 55 (Berkeley, CA: MSRI publication) pp. 241-60, see also arXiv math PR/0703375), Grünbaum (2007 Dagstuhl Seminar Proc. 07461 on Numerical Methods in Structured Markov Chains ed Bini), Grünbaum (2008 Proceedings of IWOTA) and Grünbaum and de la Iglesia (2008 SIAM J. Matrix Anal. Appl. 30 741-63). We give here a weight matrix that makes the corresponding matrix-valued orthogonal polynomials orthogonal to each other. We also determine the polynomials themselves and thus obtain all the ingredients to apply a matrix-valued version of the Karlin-McGregor formula. Dedicated to Jack Schwartz, who passed away on March 2, 2009.

Theoretical Analysis of Local Search and Simple Evolutionary Algorithms for the Generalized Travelling Salesperson Problem.

PubMed

Pourhassan, Mojgan; Neumann, Frank

2018-06-22

The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem for which meta-heuristics, such as local search and evolutionary algorithms, have been used very successfully. Two hierarchical approaches with different neighbourhood structures, namely a Cluster-Based approach and a Node-Based approach, have been proposed by Hu and Raidl (2008) for solving this problem. In this paper, local search algorithms and simple evolutionary algorithms based on these approaches are investigated from a theoretical perspective. For local search algorithms, we point out the complementary abilities of the two approaches by presenting instances where they mutually outperform each other. Afterwards, we introduce an instance which is hard for both approaches when initialized on a particular point of the search space, but where a variable neighbourhood search combining them finds the optimal solution in polynomial time. Then we turn our attention to analysing the behaviour of simple evolutionary algorithms that use these approaches. We show that the Node-Based approach solves the hard instance of the Cluster-Based approach presented in Corus et al. (2016) in polynomial time. Furthermore, we prove an exponential lower bound on the optimization time of the Node-Based approach for a class of Euclidean instances.

Modeling of driver's collision avoidance maneuver based on controller switching model.

PubMed

Kim, Jong-Hae; Hayakawa, Soichiro; Suzuki, Tatsuya; Hayashi, Koji; Okuma, Shigeru; Tsuchida, Nuio; Shimizu, Masayuki; Kido, Shigeyuki

2005-12-01

This paper presents a modeling strategy of human driving behavior based on the controller switching model focusing on the driver's collision avoidance maneuver. The driving data are collected by using the three-dimensional (3-D) driving simulator based on the CAVE Automatic Virtual Environment (CAVE), which provides stereoscopic immersive virtual environment. In our modeling, the control scenario of the human driver, that is, the mapping from the driver's sensory information to the operation of the driver such as acceleration, braking, and steering, is expressed by Piecewise Polynomial (PWP) model. Since the PWP model includes both continuous behaviors given by polynomials and discrete logical conditions, it can be regarded as a class of Hybrid Dynamical System (HDS). The identification problem for the PWP model is formulated as the Mixed Integer Linear Programming (MILP) by transforming the switching conditions into binary variables. From the obtained results, it is found that the driver appropriately switches the "control law" according to the sensory information. In addition, the driving characteristics of the beginner driver and the expert driver are compared and discussed. These results enable us to capture not only the physical meaning of the driving skill but the decision-making aspect (switching conditions) in the driver's collision avoidance maneuver as well.

A simplified procedure for correcting both errors and erasures of a Reed-Solomon code using the Euclidean algorithm

NASA Technical Reports Server (NTRS)

Truong, T. K.; Hsu, I. S.; Eastman, W. L.; Reed, I. S.

1987-01-01

It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial and the error evaluator polynomial in Berlekamp's key equation needed to decode a Reed-Solomon (RS) code. A simplified procedure is developed and proved to correct erasures as well as errors by replacing the initial condition of the Euclidean algorithm by the erasure locator polynomial and the Forney syndrome polynomial. By this means, the errata locator polynomial and the errata evaluator polynomial can be obtained, simultaneously and simply, by the Euclidean algorithm only. With this improved technique the complexity of time domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches. As a consequence, decoders for correcting both errors and erasures of RS codes can be made more modular, regular, simple, and naturally suitable for both VLSI and software implementation. An example illustrating this modified decoding procedure is given for a (15, 9) RS code.

Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

PubMed

Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

2016-01-01

Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

Minimum Sobolev norm interpolation of scattered derivative data

NASA Astrophysics Data System (ADS)

Chandrasekaran, S.; Gorman, C. H.; Mhaskar, H. N.

2018-07-01

We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data of the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of two variables with total degree ≤n given the values of the polynomial and some of its derivatives at exactly the same number of points as the dimension of the polynomial space is sometimes impossible, we show that such a problem always has a solution in a very general situation if the degree of the polynomials is sufficiently large. We give estimates on how large the degree should be, and give explicit constructions for such a polynomial even in a far more general case. As the number of sampling points at which the data is available increases, our polynomials converge to the target function on the set where the sampling points are dense. Numerical examples in single and double precision show that this method is stable, efficient, and of high-order.

The earliest maize from San Marcos Tehuacán is a partial domesticate with genomic evidence of inbreeding

PubMed Central

Vallebueno-Estrada, Miguel; Rodríguez-Arévalo, Isaac; Rougon-Cardoso, Alejandra; Martínez González, Javier; García Cook, Angel; Vielle-Calzada, Jean-Philippe

2016-01-01

Pioneering archaeological expeditions lead by Richard MacNeish in the 1960s identified the valley of Tehuacán as an important center of early Mesoamerican agriculture, providing by far the widest collection of ancient crop remains, including maize. In 2012, a new exploration of San Marcos cave (Tehuacán, Mexico) yielded nonmanipulated maize specimens dating at a similar age of 5,300–4,970 calibrated y B.P. On the basis of shotgun sequencing and genomic comparisons to Balsas teosinte and modern maize, we show herein that the earliest maize from San Marcos cave was a partial domesticate diverging from the landraces and containing ancestral allelic variants that are absent from extant maize populations. Whereas some domestication loci, such as teosinte branched1 (tb1) and brittle endosperm2 (bt2), had already lost most of the nucleotide variability present in Balsas teosinte, others, such as teosinte glume architecture1 (tga1) and sugary1 (su1), conserved partial levels of nucleotide variability that are absent from extant maize. Genetic comparisons among three temporally convergent samples revealed that they were homozygous and identical by descent across their genome. Our results indicate that the earliest maize from San Marcos was already inbred, opening the possibility for Tehuacán maize cultivation evolving from reduced founder populations of isolated and perhaps self-pollinated individuals. PMID:27872313

The earliest maize from San Marcos Tehuacán is a partial domesticate with genomic evidence of inbreeding.

PubMed

Vallebueno-Estrada, Miguel; Rodríguez-Arévalo, Isaac; Rougon-Cardoso, Alejandra; Martínez González, Javier; García Cook, Angel; Montiel, Rafael; Vielle-Calzada, Jean-Philippe

2016-12-06

Pioneering archaeological expeditions lead by Richard MacNeish in the 1960s identified the valley of Tehuacán as an important center of early Mesoamerican agriculture, providing by far the widest collection of ancient crop remains, including maize. In 2012, a new exploration of San Marcos cave (Tehuacán, Mexico) yielded nonmanipulated maize specimens dating at a similar age of 5,300-4,970 calibrated y B.P. On the basis of shotgun sequencing and genomic comparisons to Balsas teosinte and modern maize, we show herein that the earliest maize from San Marcos cave was a partial domesticate diverging from the landraces and containing ancestral allelic variants that are absent from extant maize populations. Whereas some domestication loci, such as teosinte branched1 (tb1) and brittle endosperm2 (bt2), had already lost most of the nucleotide variability present in Balsas teosinte, others, such as teosinte glume architecture1 (tga1) and sugary1 (su1), conserved partial levels of nucleotide variability that are absent from extant maize. Genetic comparisons among three temporally convergent samples revealed that they were homozygous and identical by descent across their genome. Our results indicate that the earliest maize from San Marcos was already inbred, opening the possibility for Tehuacán maize cultivation evolving from reduced founder populations of isolated and perhaps self-pollinated individuals.

Ranked solutions to a class of combinatorial optimizations - with applications in mass spectrometry based peptide sequencing

NASA Astrophysics Data System (ADS)

Doerr, Timothy; Alves, Gelio; Yu, Yi-Kuo

2006-03-01

Typical combinatorial optimizations are NP-hard; however, for a particular class of cost functions the corresponding combinatorial optimizations can be solved in polynomial time. This suggests a way to efficiently find approximate solutions - - find a transformation that makes the cost function as similar as possible to that of the solvable class. After keeping many high-ranking solutions using the approximate cost function, one may then re-assess these solutions with the full cost function to find the best approximate solution. Under this approach, it is important to be able to assess the quality of the solutions obtained, e.g., by finding the true ranking of kth best approximate solution when all possible solutions are considered exhaustively. To tackle this statistical issue, we provide a systematic method starting with a scaling function generated from the fininte number of high- ranking solutions followed by a convergent iterative mapping. This method, useful in a variant of the directed paths in random media problem proposed here, can also provide a statistical significance assessment for one of the most important proteomic tasks - - peptide sequencing using tandem mass spectrometry data.

Modeling State-Space Aeroelastic Systems Using a Simple Matrix Polynomial Approach for the Unsteady Aerodynamics

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S.

2008-01-01

A simple matrix polynomial approach is introduced for approximating unsteady aerodynamics in the s-plane and ultimately, after combining matrix polynomial coefficients with matrices defining the structure, a matrix polynomial of the flutter equations of motion (EOM) is formed. A technique of recasting the matrix-polynomial form of the flutter EOM into a first order form is also presented that can be used to determine the eigenvalues near the origin and everywhere on the complex plane. An aeroservoelastic (ASE) EOM have been generalized to include the gust terms on the right-hand side. The reasons for developing the new matrix polynomial approach are also presented, which are the following: first, the "workhorse" methods such as the NASTRAN flutter analysis lack the capability to consistently find roots near the origin, along the real axis or accurately find roots farther away from the imaginary axis of the complex plane; and, second, the existing s-plane methods, such as the Roger s s-plane approximation method as implemented in ISAC, do not always give suitable fits of some tabular data of the unsteady aerodynamics. A method available in MATLAB is introduced that will accurately fit generalized aerodynamic force (GAF) coefficients in a tabular data form into the coefficients of a matrix polynomial form. The root-locus results from the NASTRAN pknl flutter analysis, the ISAC-Roger's s-plane method and the present matrix polynomial method are presented and compared for accuracy and for the number and locations of roots.

Numerical solutions for Helmholtz equations using Bernoulli polynomials

NASA Astrophysics Data System (ADS)

Bicer, Kubra Erdem; Yalcinbas, Salih

2017-07-01

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

Elasticity solutions for a class of composite laminate problems with stress singularities

NASA Technical Reports Server (NTRS)

Wang, S. S.

1983-01-01

A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.

Improved Results for Route Planning in Stochastic Transportation Networks

NASA Technical Reports Server (NTRS)

Boyan, Justin; Mitzenmacher, Michael

2000-01-01

In the bus network problem, the goal is to generate a plan for getting from point X to point Y within a city using buses in the smallest expected time. Because bus arrival times are not determined by a fixed schedule but instead may be random. the problem requires more than standard shortest path techniques. In recent work, Datar and Ranade provide algorithms in the case where bus arrivals are assumed to be independent and exponentially distributed. We offer solutions to two important generalizations of the problem, answering open questions posed by Datar and Ranade. First, we provide a polynomial time algorithm for a much wider class of arrival distributions, namely those with increasing failure rate. This class includes not only exponential distributions but also uniform, normal, and gamma distributions. Second, in the case where bus arrival times are independent and geometric discrete random variable,. we provide an algorithm for transportation networks of buses and trains, where trains run according to a fixed schedule.

Translation of Bernstein Coefficients Under an Affine Mapping of the Unit Interval

NASA Technical Reports Server (NTRS)

Alford, John A., II

2012-01-01

We derive an expression connecting the coefficients of a polynomial expanded in the Bernstein basis to the coefficients of an equivalent expansion of the polynomial under an affine mapping of the domain. The expression may be useful in the calculation of bounds for multi-variate polynomials.

On polynomial selection for the general number field sieve

NASA Astrophysics Data System (ADS)

Kleinjung, Thorsten

2006-12-01

The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records.

Graphical Solution of Polynomial Equations

ERIC Educational Resources Information Center

Grishin, Anatole

2009-01-01

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

Evaluation of more general integrals involving universal associated Legendre polynomials

NASA Astrophysics Data System (ADS)

You, Yuan; Chen, Chang-Yuan; Tahir, Farida; Dong, Shi-Hai

2017-05-01

We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. We present a popular integral formula which includes universal associated Legendre polynomials and we also evaluate some important integrals involving the product of two universal associated Legendre polynomials Pl' m'(x ) , Pk' n'(x ) and x2 a(1-x2 ) -p -1, xb(1±x2 ) -p, and xc(1-x2 ) -p(1±x ) -1, where l'≠k' and m'≠n'. Their selection rules are also mentioned.

Neck curve polynomials in neck rupture model

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

Kurniadi, Rizal; Perkasa, Yudha S.; Waris, Abdul

2012-06-06

The Neck Rupture Model is a model that explains the scission process which has smallest radius in liquid drop at certain position. Old fashion of rupture position is determined randomly so that has been called as Random Neck Rupture Model (RNRM). The neck curve polynomials have been employed in the Neck Rupture Model for calculation the fission yield of neutron induced fission reaction of {sup 280}X{sub 90} with changing of order of polynomials as well as temperature. The neck curve polynomials approximation shows the important effects in shaping of fission yield curve.

More on rotations as spin matrix polynomials

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

Curtright, Thomas L.

2015-09-15

Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful framework to meet this challenge. Central factorial numbers play a key role in the theoretical development. Explicit polynomial coefficients for rotations expressed either as exponentials or as rational Cayley transforms are considered here. Structural features of the results are discussed and compared, and large j limits of the coefficients are examined.

Robust stability of fractional order polynomials with complicated uncertainty structure

PubMed Central

Şenol, Bilal; Pekař, Libor

2017-01-01

The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition. PMID:28662173

Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials

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

Zhang, Hong-Biao, E-mail: zhanghb017@nenu.edu.cn; Lu, Lu

2013-12-15

Two novel polynomial su(1, 1) algebras for the physical systems with the first and second Pöschl-Teller (PT) potentials are constructed, and their specific representations are presented. Meanwhile, these polynomial su(1, 1) algebras are used as an algebraic technique to solve eigenvalues and eigenfunctions of the Hamiltonians associated with the first and second PT potentials. The algebraic approach explores an appropriate new pair of raising and lowing operators K-circumflex{sub ±} of polynomial su(1, 1) algebra as a pair of shift operators of our Hamiltonians. In addition, two usual su(1, 1) algebras associated with the first and second PT potentials are derivedmore » naturally from the polynomial su(1, 1) algebras built by us.« less

Polynomials to model the growth of young bulls in performance tests.

PubMed

Scalez, D C B; Fragomeni, B O; Passafaro, T L; Pereira, I G; Toral, F L B

2014-03-01

The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) polynomials. In general, the Legendre and quadratic B-spline models that included more covariance parameters provided a better fit with the data. When comparing models with the same number of parameters, the quadratic B-spline provided a better fit than the Legendre polynomials. The quadratic B-spline with four intervals provided the best fit for the Nellore and MA groups. The fitting of random regression models with different types of polynomials (Legendre polynomials or B-spline) affected neither the genetic parameters estimates nor the ranking of the Nellore young bulls. However, fitting different type of polynomials affected the genetic parameters estimates and the ranking of the MA young bulls. Parsimonious Legendre or quadratic B-spline models could be used for genetic evaluation of body weight of Nellore young bulls in performance tests, whereas these parsimonious models were less efficient for animals of the MA genetic group owing to limited data at the extreme ages.

Cylinder surface test with Chebyshev polynomial fitting method

NASA Astrophysics Data System (ADS)

Yu, Kui-bang; Guo, Pei-ji; Chen, Xi

2017-10-01

Zernike polynomials fitting method is often applied in the test of optical components and systems, used to represent the wavefront and surface error in circular domain. Zernike polynomials are not orthogonal in rectangular region which results in its unsuitable for the test of optical element with rectangular aperture such as cylinder surface. Applying the Chebyshev polynomials which are orthogonal among the rectangular area as an substitution to the fitting method, can solve the problem. Corresponding to a cylinder surface with diameter of 50 mm and F number of 1/7, a measuring system has been designed in Zemax based on Fizeau Interferometry. The expressions of the two-dimensional Chebyshev polynomials has been given and its relationship with the aberration has been presented. Furthermore, Chebyshev polynomials are used as base items to analyze the rectangular aperture test data. The coefficient of different items are obtained from the test data through the method of least squares. Comparing the Chebyshev spectrum in different misalignment, it show that each misalignment is independence and has a certain relationship with the certain Chebyshev terms. The simulation results show that, through the Legendre polynomials fitting method, it will be a great improvement in the efficient of the detection and adjustment of the cylinder surface test.

Generating the patterns of variation with GeoGebra: the case of polynomial approximations

NASA Astrophysics Data System (ADS)

Attorps, Iiris; Björk, Kjell; Radic, Mirko

2016-01-01

In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students' learning opportunities in the study group compared with the control group.

Service-Oriented Architectures and Project Optimization for a Special Cost Management Problem Creating Synergies for Informed Change between Qualitative and Quantitative Strategic Management Processes

DTIC Science & Technology

2010-05-01

Science, Werner Heisenberg -Weg 39,85577 Neubiberg, Germany,CA,93943 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S...University of the Federal Armed Forces of Germany Institute for Theoretic Computer Science Mathematics and Operations Research Werner Heisenberg -Weg...Research Werner Heisenberg -Weg 39 85577 Neubiberg, Germany Phone +49 89 6004 2400 Marco Schuler—Marco Schuler is an active Officer of the Federal

NASA/DOD Aerospace Knowledge Diffusion Research Project. Paper Sixty Eight, Who is Managing Knowledge? The Implications for Knowledge Production and Management of Global Strategic Alliances in Knowledge-Dependent Industries

DTIC Science & Technology

1998-03-01

United States. Pittsburgh, PA: Carnegie Mellon University Press (August). Cohen, S.S., S . Halimi , and J. Zysman. 1986. "Institutions, Politics, and...San Marcos 333 S . Twin Oaks Valley Rd. San Marcos, CA 92096-0001 vgolich@csusm.edu Thomas E. Pinelli Technology & Distance Learning Officer NASA...1991; Chesnais, 1993; Cohen 1977; Cohen, Halimi , and Zysman, 1986 Crossland, 1975; Gillispie, 1980; Gilpin 1968; Golich

Dr. Marco Marra: Pioneer and Visionary in Cancer Genomics Research | Office of Cancer Genomics

Cancer.gov

Dr. Marco Marra is a highly distinguished genomics and bioinformatics researcher. He is the Director of Canada’s Michael Smith Genome Sciences Centre at the BC Cancer Agency and holds a faculty position at the University of British Columbia. The Centre is a state-of-the-art sequencing facility in Vancouver, Canada, with a major focus on the study of cancers.  Many of their research projects are undertaken in collaborations with other Canadian and international institutions.

Marco Todeschini - Space Dynamics and Psycho-Biophysics

NASA Astrophysics Data System (ADS)

Teodorani, M.

2006-03-01

This book is dedicated to the theoretical and experimental research carried out in the 20-th century, by Italian engineer and technical physicist Marco Todeschini. It describes the subjects of "space dynamics" and "psycho-biophysics" - two related physical sciences - whose foundations lay in the existence of the ether and of the vortexes that all bodies with mass produce in it. An entirely new cosmology is derived in which all the bodies in the universe - elementary particles, astronomical bodies, and the human being - are strictly related together.

Strategic Planning for Comprehensive Security in the European Union’s Military Operations: EUFOR RD Congo, EUFOR Tchad/RCA, and EUNAVFOR Somalia

DTIC Science & Technology

2010-06-01

Globalization and Environmental Challenges: Reconceptualizing Security in the 21st Century, 947. 11 Marco A. Ferroni and Ashoka Mody, International Public...Security and Defence Policy, 67–70; Howorth, Security and Defence Policy in the European Union, 152–154. 47 Hubert Zimmermann, “Security Exporters...consilium.europa.eu/showPage.aspx?id=1519&lang=en (accessed 12 March 2010). Ferroni, Marco A. and Ashoka Mody. International Public Goods: Incentives

Joint Force Quarterly. Issue 60, 1st Quarter 2011

DTIC Science & Technology

2011-01-01

John J. Church, D.M.A Internet Publications Editor Joanna E. Seich Design Nicholas Crawford and Marco Marchegiani, U.S. Government Printing Office...agency of the Federal Government . n d u p r e s s . n d u . e d u About the covers Front cover: Corporal Bethany Hess, USMC, assigned to the 3d Battalion...Crawford and Marco Marchegiani, U.S. Government Printing Office Printed in St. Louis, Missouri by NDU Press is the National Defense University’s

A new class of exact solutions of the Klein-Gordon equation of a charged particle interacting with an electromagnetic plane wave in a medium

NASA Astrophysics Data System (ADS)

Varró, Sándor

2014-01-01

Exact solutions are presented of the Klein-Gordon equation of a charged particle moving in a transverse monochromatic plasmon wave of arbitrary high amplitude, which propagates in an underdense plasma. These solutions are expressed in terms of Ince polynomials, forming a doubly infinite set, parametrized by discrete momentum components of the charged particle’s de Broglie wave along the polarization vector and along the propagation direction of the plasmon radiation. The envelope of the exact wavefunctions describes a high-contrast periodic structure of the particle density on the plasma length scale, which may have relevance in novel particle acceleration mechanisms.

Hamiltonian BVMs (HBVMs): Implementation Details and Applications

NASA Astrophysics Data System (ADS)

Brugnano, Luigi; Iavernaro, Felice; Susca, Tiziana

2009-09-01

Hamiltonian Boundary Value Methods are one step schemes of high order where the internal stages are partly exploited to impose the order conditions (fundamental stages) and partly to confer the formula the property of conserving the Hamiltonian function when this is a polynomial with a given degree v. The term "silent stages" has been coined for these latter set of extra-stages to mean that their presence does not cause an increase of the dimension of the associated nonlinear system to be solved at each step. By considering a specific method in this class, we give some details about how the solution of the nonlinear system may be conveniently carried out and how to compensate the effect of roundoff errors.

A general U-block model-based design procedure for nonlinear polynomial control systems

NASA Astrophysics Data System (ADS)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Two-dimensional orthonormal trend surfaces for prospecting

NASA Astrophysics Data System (ADS)

Sarma, D. D.; Selvaraj, J. B.

Orthonormal polynomials have distinct advantages over conventional polynomials: the equations for evaluating trend coefficients are not ill-conditioned and the convergence power of this method is greater compared to the least-squares approximation and therefore the approach by orthonormal functions provides a powerful alternative to the least-squares method. In this paper, orthonormal polynomials in two dimensions are obtained using the Gram-Schmidt method for a polynomial series of the type: Z = 1 + x + y + x2 + xy + y2 + … + yn, where x and y are the locational coordinates and Z is the value of the variable under consideration. Trend-surface analysis, which has wide applications in prospecting, has been carried out using the orthonormal polynomial approach for two sample sets of data from India concerned with gold accumulation from the Kolar Gold Field, and gravity data. A comparison of the orthonormal polynomial trend surfaces with those obtained by the classical least-squares method has been made for the two data sets. In both the situations, the orthonormal polynomial surfaces gave an improved fit to the data. A flowchart and a FORTRAN-IV computer program for deriving orthonormal polynomials of any order and for using them to fit trend surfaces is included. The program has provision for logarithmic transformation of the Z variable. If log-transformation is performed the predicted Z values are reconverted to the original units and the trend-surface map generated for use. The illustration of gold assay data related to the Champion lode system of Kolar Gold Fields, for which a 9th-degree orthonormal trend surface was fit, could be used for further prospecting the area.

Polynomial Conjoint Analysis of Similarities: A Model for Constructing Polynomial Conjoint Measurement Algorithms.

ERIC Educational Resources Information Center

Young, Forrest W.

A model permitting construction of algorithms for the polynomial conjoint analysis of similarities is presented. This model, which is based on concepts used in nonmetric scaling, permits one to obtain the best approximate solution. The concepts used to construct nonmetric scaling algorithms are reviewed. Finally, examples of algorithmic models for…

Dual exponential polynomials and linear differential equations

NASA Astrophysics Data System (ADS)

Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

2018-01-01

We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

Polynomial Graphs and Symmetry

ERIC Educational Resources Information Center

Goehle, Geoff; Kobayashi, Mitsuo

2013-01-01

Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

Why the Faulhaber Polynomials Are Sums of Even or Odd Powers of (n + 1/2)

ERIC Educational Resources Information Center

Hersh, Reuben

2012-01-01

By extending Faulhaber's polynomial to negative values of n, the sum of the p'th powers of the first n integers is seen to be an even or odd polynomial in (n + 1/2) and therefore expressible in terms of the sum of the first n integers.

Self-Replicating Quadratics

ERIC Educational Resources Information Center

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo; Circi, Christian

2018-05-01

In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth-Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated.

Orbifold E-functions of dual invertible polynomials

NASA Astrophysics Data System (ADS)

Ebeling, Wolfgang; Gusein-Zade, Sabir M.; Takahashi, Atsushi

2016-08-01

An invertible polynomial is a weighted homogeneous polynomial with the number of monomials coinciding with the number of variables and such that the weights of the variables and the quasi-degree are well defined. In the framework of the search for mirror symmetric orbifold Landau-Ginzburg models, P. Berglund and M. Henningson considered a pair (f , G) consisting of an invertible polynomial f and an abelian group G of its symmetries together with a dual pair (f ˜ , G ˜) . We consider the so-called orbifold E-function of such a pair (f , G) which is a generating function for the exponents of the monodromy action on an orbifold version of the mixed Hodge structure on the Milnor fibre of f. We prove that the orbifold E-functions of Berglund-Henningson dual pairs coincide up to a sign depending on the number of variables and a simple change of variables. The proof is based on a relation between monomials (say, elements of a monomial basis of the Milnor algebra of an invertible polynomial) and elements of the whole symmetry group of the dual polynomial.

Local polynomial estimation of heteroscedasticity in a multivariate linear regression model and its applications in economics.

PubMed

Su, Liyun; Zhao, Yanyong; Yan, Tianshun; Li, Fenglan

2012-01-01

Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations.

Symmetric polynomials in information theory: Entropy and subentropy

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

Jozsa, Richard; Mitchison, Graeme

2015-06-15

Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore, we see that H and the intrinsically quantum informational quantitymore » Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials, we also derive a series of further properties of H and Q.« less

Recursive approach to the moment-based phase unwrapping method.

PubMed

Langley, Jason A; Brice, Robert G; Zhao, Qun

2010-06-01

The moment-based phase unwrapping algorithm approximates the phase map as a product of Gegenbauer polynomials, but the weight function for the Gegenbauer polynomials generates artificial singularities along the edge of the phase map. A method is presented to remove the singularities inherent to the moment-based phase unwrapping algorithm by approximating the phase map as a product of two one-dimensional Legendre polynomials and applying a recursive property of derivatives of Legendre polynomials. The proposed phase unwrapping algorithm is tested on simulated and experimental data sets. The results are then compared to those of PRELUDE 2D, a widely used phase unwrapping algorithm, and a Chebyshev-polynomial-based phase unwrapping algorithm. It was found that the proposed phase unwrapping algorithm provides results that are comparable to those obtained by using PRELUDE 2D and the Chebyshev phase unwrapping algorithm.

A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials

NASA Astrophysics Data System (ADS)

Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing

2015-09-01

The accuracy of metamodelling is determined by both the sampling and approximation. This article proposes a new sampling method based on the zeros of Chebyshev polynomials to capture the sampling information effectively. First, the zeros of one-dimensional Chebyshev polynomials are applied to construct Chebyshev tensor product (CTP) sampling, and the CTP is then used to construct high-order multi-dimensional metamodels using the 'hypercube' polynomials. Secondly, the CTP sampling is further enhanced to develop Chebyshev collocation method (CCM) sampling, to construct the 'simplex' polynomials. The samples of CCM are randomly and directly chosen from the CTP samples. Two widely studied sampling methods, namely the Smolyak sparse grid and Hammersley, are used to demonstrate the effectiveness of the proposed sampling method. Several numerical examples are utilized to validate the approximation accuracy of the proposed metamodel under different dimensions.

A solver for General Unilateral Polynomial Matrix Equation with Second-Order Matrices Over Prime Finite Fields

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-03-01

The paper firstly considers the problem of finding solvents for arbitrary unilateral polynomial matrix equations with second-order matrices over prime finite fields from the practical point of view: we implement the solver for this problem. The solver’s algorithm has two step: the first is finding solvents, having Jordan Normal Form (JNF), the second is finding solvents among the rest matrices. The first step reduces to the finding roots of usual polynomials over finite fields, the second is essentially exhaustive search. The first step’s algorithms essentially use the polynomial matrices theory. We estimate the practical duration of computations using our software implementation (for example that one can’t construct unilateral matrix polynomial over finite field, having any predefined number of solvents) and answer some theoretically-valued questions.

Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes

DOE PAGES

Zlotnikov, Michael

2016-08-24

We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for n scattering particles into a σ-moduli multivariate polynomial of what we call the standard form. We show that a standard form polynomial must have a specific ladder type monomial structure, which has finite size at any n, with highest multivariate degree given by (n – 3)(n – 4)/2. This set of monomials spans a complete basis for polynomials with rational coefficients in kinematic data on the support of scattering equations. Subsequently, at tree and one-loop level, we employ the global residue theorem to derive amore » prescription that evaluates any CHY amplitude by means of collecting simple residues at infinity only. Furthermore, the prescription is then applied explicitly to some tree and one-loop amplitude examples.« less

A polynomial based model for cell fate prediction in human diseases.

PubMed

Ma, Lichun; Zheng, Jie

2017-12-21

Cell fate regulation directly affects tissue homeostasis and human health. Research on cell fate decision sheds light on key regulators, facilitates understanding the mechanisms, and suggests novel strategies to treat human diseases that are related to abnormal cell development. In this study, we proposed a polynomial based model to predict cell fate. This model was derived from Taylor series. As a case study, gene expression data of pancreatic cells were adopted to test and verify the model. As numerous features (genes) are available, we employed two kinds of feature selection methods, i.e. correlation based and apoptosis pathway based. Then polynomials of different degrees were used to refine the cell fate prediction function. 10-fold cross-validation was carried out to evaluate the performance of our model. In addition, we analyzed the stability of the resultant cell fate prediction model by evaluating the ranges of the parameters, as well as assessing the variances of the predicted values at randomly selected points. Results show that, within both the two considered gene selection methods, the prediction accuracies of polynomials of different degrees show little differences. Interestingly, the linear polynomial (degree 1 polynomial) is more stable than others. When comparing the linear polynomials based on the two gene selection methods, it shows that although the accuracy of the linear polynomial that uses correlation analysis outcomes is a little higher (achieves 86.62%), the one within genes of the apoptosis pathway is much more stable. Considering both the prediction accuracy and the stability of polynomial models of different degrees, the linear model is a preferred choice for cell fate prediction with gene expression data of pancreatic cells. The presented cell fate prediction model can be extended to other cells, which may be important for basic research as well as clinical study of cell development related diseases.

Generalized Freud's equation and level densities with polynomial potential

NASA Astrophysics Data System (ADS)

Boobna, Akshat; Ghosh, Saugata

2013-08-01

We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.

FIT: Computer Program that Interactively Determines Polynomial Equations for Data which are a Function of Two Independent Variables

NASA Technical Reports Server (NTRS)

Arbuckle, P. D.; Sliwa, S. M.; Roy, M. L.; Tiffany, S. H.

1985-01-01

A computer program for interactively developing least-squares polynomial equations to fit user-supplied data is described. The program is characterized by the ability to compute the polynomial equations of a surface fit through data that are a function of two independent variables. The program utilizes the Langley Research Center graphics packages to display polynomial equation curves and data points, facilitating a qualitative evaluation of the effectiveness of the fit. An explanation of the fundamental principles and features of the program, as well as sample input and corresponding output, are included.

First Instances of Generalized Expo-Rational Finite Elements on Triangulations

NASA Astrophysics Data System (ADS)

Dechevsky, Lubomir T.; Zanaty, Peter; Laksa˚, Arne; Bang, Børre

2011-12-01

In this communication we consider a construction of simplicial finite elements on triangulated two-dimensional polygonal domains. This construction is, in some sense, dual to the construction of generalized expo-rational B-splines (GERBS). The main result is in the obtaining of new polynomial simplicial patches of the first several lowest possible total polynomial degrees which exhibit Hermite interpolatory properties. The derivation of these results is based on the theory of piecewise polynomial GERBS called Euler Beta-function B-splines. We also provide 3-dimensional visualization of the graphs of the new polynomial simplicial patches and their control polygons.

The Translated Dowling Polynomials and Numbers.

PubMed

Mangontarum, Mahid M; Macodi-Ringia, Amila P; Abdulcarim, Normalah S

2014-01-01

More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.

Análisis del futuro marco de referencia internacional

NASA Astrophysics Data System (ADS)

Cionco, G. R.; Arias, E. F.

La técnica de interferometría de muy larga línea de base (VLBI) se aplica hoy a la astrometría para el cálculo de posiciones precisas de radiofuentes extragalácticas. Por tratarse de objetos lejanos, sus movimientos propios aparentes pueden considerarse nulos; esta propiedad hace que los catálogos de radiofuentes extragalácticas VLBI constituyan la mejor materialización de un sistema de referencia celeste inercial definido cinemáticamente. La Unión Astronómica Internacional (IAU) recomendó la adopción de un nuevo sistema de referencia celeste internacional materializado por las coordenadas ecuatoriales de objetos extragalácticos observados con le técnica VLBI. Para superar la precisión astrométrica actual es necesaria una mejora en la modelización de aquellos fenómenos que pueden introducir desviaciones sistemáticas en el marco de referencia celeste. El objetivo de este trabajo es poner de manifiesto las sistematicidades presentes en los distintos marcos de referencia elaborados con el próposito de materializar el nuevo sistema de referencia celeste de la IAU. Para la comparación de los distintos marcos de referencia se propone un modelo de tres rotaciones diferenciales más un término lineal que procura absorber los efectos sistemáticos presentes en las coordenadas. Se analiza igualmente la estabilidad de la solución cuando se utilizan distintos conjuntos de objetos de definición.

Accurate Estimation of Solvation Free Energy Using Polynomial Fitting Techniques

PubMed Central

Shyu, Conrad; Ytreberg, F. Marty

2010-01-01

This report details an approach to improve the accuracy of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable λ) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy of the free energy difference estimates. Previously, we introduced the use of polynomial regression technique to fit thermodynamic integration data (Shyu and Ytreberg, J Comput Chem 30: 2297–2304, 2009). In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy of the interpolation approach. We also use both interpolation and regression methods to determine a small molecule solvation free energy. Our simulations show that, using such polynomial techniques and non-equidistant λ values, the solvation free energy can be estimated with high accuracy without using soft-core scaling and separate simulations for Lennard-Jones and partial charges. The results from our study suggest these polynomial techniques, especially with use of non-equidistant λ values, improve the accuracy for ΔF estimates without demanding additional simulations. We also provide general guidelines for use of polynomial fitting to estimate free energy. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software. PMID:20623657

Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials

PubMed Central

Corteel, Sylvie; Williams, Lauren K.

2010-01-01

We introduce some combinatorial objects called staircase tableaux, which have cardinality 4nn !, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. The ASEP is a model from statistical mechanics introduced in the late 1960s, which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with open boundaries. It has been cited as a model for traffic flow and translation in protein synthesis. In its most general form, particles may enter and exit at the left with probabilities α and γ, and they may exit and enter at the right with probabilities β and δ. In the bulk, the probability of hopping left is q times the probability of hopping right. Our first result is a formula for the stationary distribution of the ASEP with all parameters general, in terms of staircase tableaux. Our second result is a formula for the moments of (the weight function of) Askey-Wilson polynomials, also in terms of staircase tableaux. Since the 1980s there has been a great deal of work giving combinatorial formulas for moments of classical orthogonal polynomials (e.g. Hermite, Charlier, Laguerre); among these polynomials, the Askey-Wilson polynomials are the most important, because they are at the top of the hierarchy of classical orthogonal polynomials. PMID:20348417

Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials.

PubMed

Corteel, Sylvie; Williams, Lauren K

2010-04-13

We introduce some combinatorial objects called staircase tableaux, which have cardinality 4(n)n!, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. The ASEP is a model from statistical mechanics introduced in the late 1960s, which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with open boundaries. It has been cited as a model for traffic flow and translation in protein synthesis. In its most general form, particles may enter and exit at the left with probabilities alpha and gamma, and they may exit and enter at the right with probabilities beta and delta. In the bulk, the probability of hopping left is q times the probability of hopping right. Our first result is a formula for the stationary distribution of the ASEP with all parameters general, in terms of staircase tableaux. Our second result is a formula for the moments of (the weight function of) Askey-Wilson polynomials, also in terms of staircase tableaux. Since the 1980s there has been a great deal of work giving combinatorial formulas for moments of classical orthogonal polynomials (e.g. Hermite, Charlier, Laguerre); among these polynomials, the Askey-Wilson polynomials are the most important, because they are at the top of the hierarchy of classical orthogonal polynomials.

Impact of a Tutored Theoretical-Practical Training to Develop Undergraduate Students' Skills for the Detection of Caries Lesions: Study Protocol for a Multicenter Controlled Randomized Study.

PubMed

Braga, Mariana Minatel; Lenzi, Tathiane Larissa; Ferreira, Fernanda Rosche; Mendes, Fausto Medeiros; Raggio, Daniela Prócida; Imparato, José Carlos; Bonecker, Marcelo; Magalhães, Ana Carolina; Wang, Linda; Rios, Daniela; Pessan, Juliano Pelim; Duque, Cristiane; Rebelo, Maria Augusta Bessa; Alves Filho, Ary Oliveira; Lima, Marina De Deus Moura; Moura, Marcoeli Silva; De Carli, Alessandro Diogo; Sanabe, Mariane Emi; Cenci, Maximiliano Sergio; Oliveira, Elenara Ferreira; Correa, Marcos Britto; Rocha, Rachel Oliveira; Zenkner, Julio Eduardo; Murisí, Pedroza Uribe; Martignon, Stefania; Lara, Juan Sebastian; Aquino, Fatima Gabriela; Carrillo, Alfredo; Chu, Chun Hung; Deery, Chris; Ricketts, David; Melo, Paulo; Antunes, José Leopoldo Ferreira; Ekstrand, Kim Rud

2017-08-16

Tutored laboratorial activities could be a manner of improving the competency development of students. However, its impact over conventional theoretical classes has not yet been tested. Additionally, different university contexts could influence this issue and should be explored. To assess the impact of a tutored theoretical-practical training for teaching undergraduate students to detect caries lesions as compared with theoretical teaching activities. The impact of these teaching/learning activities will be assessed in terms of efficacy, cost/benefit, retention of knowledge/acquired competences, and student acceptability. Sixteen centers (7 centers from Brazil and 9 centers from other countries throughout the world) are involved in the inclusion of subjects for this protocol. A randomized controlled study with parallel groups will be conducted. One group (control) will be exposed to a 60- to 90-minute conventional theoretical class and the other group (test) will be exposed to the same theoretical class and also a 90-minute laboratory class, including exercises and discussions based on the evaluation of a pool of images and extracted teeth. The mentioned outcomes will be evaluated immediately after the teaching activities and also in medium- and long-term analyses. To compare the long-term outcomes, students who enrolled in the university before the participating students will be interviewed for data collection and these data will be used as a control and compared with the trained group. This stage will be a nonrandomized phase of this study, nested in the main study. Appropriate statistical analysis will be performed according to the aims of this study. Variables related to the centers will also be analyzed and used to model adjustment as possible sources of variability among results. This ongoing study is funded by a Brazilian national funding agency (CNPq- 400736/2014-4). We expect that the tutored theoretical-practical training will improve the undergraduate students' performance in the detection of caries lesions and subsequent treatment decisions, mainly in terms of long-term retention of knowledge. Our hypothesis is that tutored theoretical-practical training is a more cost-effective option for teaching undergraduate students to detect caries lesions. If our hypothesis is confirmed, the use of laboratory training in conjunction with theoretical classes could be used as an educational strategy in Cariology to improve the development of undergraduate students' skills in the detection of caries lesions and clinical decision-making. ©Mariana Minatel Braga, Tathiane Larissa Lenzi, Fernanda Rosche Ferreira, Fausto Medeiros Mendes, Daniela Prócida Raggio, José Carlos Imparato, Marcelo Bonecker, Ana Carolina Magalhães, Linda Wang, Daniela Rios, Juliano Pelim Pessan, Cristiane Duque, Maria Augusta Bessa Rebelo, Ary Oliveira Alves Filho, Marina De Deus Moura Lima, Marcoeli Silva Moura, Alessandro Diogo De Carli, Mariane Emi Sanabe, Maximiliano Sergio Cenci, Elenara Ferreira Oliveira, Marcos Britto Correa, Rachel Oliveira Rocha, Julio Eduardo Zenkner, Pedroza Uribe Murisí, Stefania Martignon, Juan Sebastian Lara, Fatima Gabriela Aquino, Alfredo Carrillo, Chun Hung Chu, Chris Deery, David Ricketts, Paulo Melo, José Leopoldo Ferreira Antunes, Kim Rud Ekstrand, IuSTC Group. Originally published in JMIR Research Protocols (http://www.researchprotocols.org), 16.08.2017.

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information

NASA Astrophysics Data System (ADS)

Boros, Endre; Elbassioni, Khaled; Gurvich, Vladimir; Makino, Kazuhisa

In this paper, we consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V = V B ∪ V W ∪ V R , E), with local rewards r: E to { R}, and three types of vertices: black V B , white V W , and random V R . The game is played by two players, White and Black: When the play is at a white (black) vertex v, White (Black) selects an outgoing arc (v,u). When the play is at a random vertex v, a vertex u is picked with the given probability p(v,u). In all cases, Black pays White the value r(v,u). The play continues forever, and White aims to maximize (Black aims to minimize) the limiting mean (that is, average) payoff. It was recently shown in [7] that BWR-games are polynomially equivalent with the classical Gillette games, which include many well-known subclasses, such as cyclic games, simple stochastic games (SSG's), stochastic parity games, and Markov decision processes. In this paper, we give a new algorithm for solving BWR-games in the ergodic case, that is when the optimal values do not depend on the initial position. Our algorithm solves a BWR-game by reducing it, using a potential transformation, to a canonical form in which the optimal strategies of both players and the value for every initial position are obvious, since a locally optimal move in it is optimal in the whole game. We show that this algorithm is pseudo-polynomial when the number of random nodes is constant. We also provide an almost matching lower bound on its running time, and show that this bound holds for a wider class of algorithms. Let us add that the general (non-ergodic) case is at least as hard as SSG's, for which no pseudo-polynomial algorithm is known.

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle.

PubMed

Baldi, F; Alencar, M M; Albuquerque, L G

2010-12-01

The objective of this work was to estimate covariance functions using random regression models on B-splines functions of animal age, for weights from birth to adult age in Canchim cattle. Data comprised 49,011 records on 2435 females. The model of analysis included fixed effects of contemporary groups, age of dam as quadratic covariable and the population mean trend taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were modelled through a step function with four classes. The direct and maternal additive genetic effects, and animal and maternal permanent environmental effects were included as random effects in the model. A total of seventeen analyses, considering linear, quadratic and cubic B-splines functions and up to seven knots, were carried out. B-spline functions of the same order were considered for all random effects. Random regression models on B-splines functions were compared to a random regression model on Legendre polynomials and with a multitrait model. Results from different models of analyses were compared using the REML form of the Akaike Information criterion and Schwarz' Bayesian Information criterion. In addition, the variance components and genetic parameters estimated for each random regression model were also used as criteria to choose the most adequate model to describe the covariance structure of the data. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most adequate to describe the covariance structure of the data. Random regression models using B-spline functions as base functions fitted the data better than Legendre polynomials, especially at mature ages, but higher number of parameters need to be estimated with B-splines functions. © 2010 Blackwell Verlag GmbH.

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows.

PubMed

Bignardi, A B; El Faro, L; Torres Júnior, R A A; Cardoso, V L; Machado, P F; Albuquerque, L G

2011-10-31

We analyzed 152,145 test-day records from 7317 first lactations of Holstein cows recorded from 1995 to 2003. Our objective was to model variations in test-day milk yield during the first lactation of Holstein cows by random regression model (RRM), using various functions in order to obtain adequate and parsimonious models for the estimation of genetic parameters. Test-day milk yields were grouped into weekly classes of days in milk, ranging from 1 to 44 weeks. The contemporary groups were defined as herd-test-day. The analyses were performed using a single-trait RRM, including the direct additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. The mean trend of milk yield was modeled with a fourth-order orthogonal Legendre polynomial. The additive genetic and permanent environmental covariance functions were estimated by random regression on two parametric functions, Ali and Schaeffer and Wilmink, and on B-spline functions of days in milk. The covariance components and the genetic parameters were estimated by the restricted maximum likelihood method. Results from RRM parametric and B-spline functions were compared to RRM on Legendre polynomials and with a multi-trait analysis, using the same data set. Heritability estimates presented similar trends during mid-lactation (13 to 31 weeks) and between week 37 and the end of lactation, for all RRM. Heritabilities obtained by multi-trait analysis were of a lower magnitude than those estimated by RRM. The RRMs with a higher number of parameters were more useful to describe the genetic variation of test-day milk yield throughout the lactation. RRM using B-spline and Legendre polynomials as base functions appears to be the most adequate to describe the covariance structure of the data.

Design and development by direct polishing of the WFXT thin polynomial mirror shells

NASA Astrophysics Data System (ADS)

Proserpio, L.; Campana, S.; Citterio, O.; Civitani, M.; Combrinck, H.; Conconi, P.; Cotroneo, V.; Freeman, R.; Mattini, E.; Langstrof, P.; Morton, R.; Motta, G.; Oberle, O.; Pareschi, G.; Parodi, G.; Pels, C.; Schenk, C.; Stock, R.; Tagliaferri, G.

2017-11-01

The Wide Field X-ray Telescope (WFXT) is a medium class mission proposed to address key questions about cosmic origins and physics of the cosmos through an unprecedented survey of the sky in the soft X-ray band (0.2-6 keV) [1], [2]. In order to get the desired angular resolution of 10 arcsec (5 arcsec goal) on the entire 1 degrees Field Of View (FOV), the design of the optical system is based on nested grazing-incidence polynomial profiles mirrors, and assumes a focal plane curvature and plate scale corrections among the shells. This design guarantees an increased angular resolution also at large off-axis positions with respect to the usually adopted Wolter I configuration. In order to meet the requirements in terms of mass and effective area (less than 1200 kg, 6000 cm2 @ 1 keV), the nested shells are thin and made of quartz glass. The telescope assembly is composed by three identical modules of 78 nested shells each, with diameter up to 1.1 m, length in the range of 200-440 mm and thickness of less than 2.2 mm. At this regard, a deterministic direct polishing method is under investigation to manufacture the WFXT thin grazing-incidence mirrors made of quartz. The direct polishing method has already been used for past missions (as Einstein, Rosat, Chandra) but based on much thicker shells (10 mm ore more). The technological challenge for WFXT is to apply the same approach but for 510 times thinner shells. The proposed approach is based on two main steps: first, quartz glass tubes available on the market are ground to conical profiles; second the pre-shaped shells are polished to the required polynomial profiles using a CNC polishing machine. In this paper, preliminary results on the direct grinding and polishing of prototypes shells made by quartz glass with low thickness, representative of the WFXT optical design, are presented.

Wilson-Racah quantum system

NASA Astrophysics Data System (ADS)

Alhaidari, A. D.; Taiwo, T. J.

2017-02-01

Using a recent formulation of quantum mechanics without a potential function, we present a four-parameter system associated with the Wilson and Racah polynomials. The continuum scattering states are written in terms of the Wilson polynomials whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Racah polynomials.

On the Waring problem for polynomial rings

PubMed Central

Fröberg, Ralf; Ottaviani, Giorgio; Shapiro, Boris

2012-01-01

In this note we discuss an analog of the classical Waring problem for . Namely, we show that a general homogeneous polynomial of degree divisible by k≥2 can be represented as a sum of at most kn k-th powers of homogeneous polynomials in . Noticeably, kn coincides with the number obtained by naive dimension count. PMID:22460787

A DDDAS Framework for Volcanic Ash Propagation and Hazard Analysis

DTIC Science & Technology

2012-01-01

probability distribution for the input variables (for example, Hermite polynomials for normally distributed parameters, or Legendre for uniformly...parameters and windfields will drive our simulations. We will use uncertainty quantification methodology – polynomial chaos quadrature in combination...quantification methodology ? polynomial chaos quadrature in combination with data integration to complete the DDDAS loop. 15. SUBJECT TERMS 16. SECURITY

On computation of Gröbner bases for linear difference systems

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.

2006-04-01

In this paper, we present an algorithm for computing Gröbner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The algorithm is an adaptation to difference ideals of our polynomial algorithm based on Janet-like reductions.

A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

NASA Astrophysics Data System (ADS)

Deift, P.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Venakides, S.; Zhou, X.

2001-08-01

A few years ago the authors introduced a new approach to study asymptotic questions for orthogonal polynomials. In this paper we give an overview of our method and review the results which have been obtained in Deift et al. (Internat. Math. Res. Notices (1997) 759, Comm. Pure Appl. Math. 52 (1999) 1491, 1335), Deift (Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes, Vol. 3, New York University, 1999), Kriecherbauer and McLaughlin (Internat. Math. Res. Notices (1999) 299) and Baik et al. (J. Amer. Math. Soc. 12 (1999) 1119). We mainly consider orthogonal polynomials with respect to weights on the real line which are either (1) Freud-type weights d[alpha](x)=e-Q(x) dx (Q polynomial or Q(x)=x[beta], [beta]>0), or (2) varying weights d[alpha]n(x)=e-nV(x) dx (V analytic, limx-->[infinity] V(x)/logx=[infinity]). We obtain Plancherel-Rotach-type asymptotics in the entire complex plane as well as asymptotic formulae with error estimates for the leading coefficients, for the recurrence coefficients, and for the zeros of the orthogonal polynomials. Our proof starts from an observation of Fokas et al. (Comm. Math. Phys. 142 (1991) 313) that the orthogonal polynomials can be determined as solutions of certain matrix valued Riemann-Hilbert problems. We analyze the Riemann-Hilbert problems by a steepest descent type method introduced by Deift and Zhou (Ann. Math. 137 (1993) 295) and further developed in Deift and Zhou (Comm. Pure Appl. Math. 48 (1995) 277) and Deift et al. (Proc. Nat. Acad. Sci. USA 95 (1998) 450). A crucial step in our analysis is the use of the well-known equilibrium measure which describes the asymptotic distribution of the zeros of the orthogonal polynomials.

Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere

NASA Astrophysics Data System (ADS)

Miller, W., Jr.; Li, Q.

2015-04-01

The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L2 of H in terms of an eigenbasis of another symmetry operator L1, but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions.

Piecewise polynomial representations of genomic tracks.

PubMed

Tarabichi, Maxime; Detours, Vincent; Konopka, Tomasz

2012-01-01

Genomic data from micro-array and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewise-polynomial curves. We present a general framework for building piecewise polynomial representations of genome-scale signals and illustrate some of its applications via examples. We show that piecewise constant segmentation, a typical step in copy-number analyses, can be carried out within this framework for both array and (DNA) sequencing data offering advantages over existing methods in each case. Higher-order polynomial curves can be used, for example, to detect trends and/or discontinuities in transcription levels from RNA-seq data. We give a concrete application of piecewise linear functions to diagnose and quantify alignment quality at exon borders (splice sites). Our software (source and object code) for building piecewise polynomial models is available at http://sourceforge.net/projects/locsmoc/.

Where are the roots of the Bethe Ansatz equations?

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Lima-Santos, A.

2015-10-01

Changing the variables in the Bethe Ansatz Equations (BAE) for the XXZ six-vertex model we had obtained a coupled system of polynomial equations. This provided a direct link between the BAE deduced from the Algebraic Bethe Ansatz (ABA) and the BAE arising from the Coordinate Bethe Ansatz (CBA). For two magnon states this polynomial system could be decoupled and the solutions given in terms of the roots of some self-inversive polynomials. From theorems concerning the distribution of the roots of self-inversive polynomials we made a thorough analysis of the two magnon states, which allowed us to find the location and multiplicity of the Bethe roots in the complex plane, to discuss the completeness and singularities of Bethe's equations, the ill-founded string-hypothesis concerning the location of their roots, as well as to find an interesting connection between the BAE with Salem's polynomials.

Lifting q-difference operators for Askey-Wilson polynomials and their weight function

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

Atakishiyeva, M. K.; Atakishiyev, N. M., E-mail: natig_atakishiyev@hotmail.com

2011-06-15

We determine an explicit form of a q-difference operator that transforms the continuous q-Hermite polynomials H{sub n}(x | q) of Rogers into the Askey-Wilson polynomials p{sub n}(x; a, b, c, d | q) on the top level in the Askey q-scheme. This operator represents a special convolution-type product of four one-parameter q-difference operators of the form {epsilon}{sub q}(c{sub q}D{sub q}) (where c{sub q} are some constants), defined as Exton's q-exponential function {epsilon}{sub q}(z) in terms of the Askey-Wilson divided q-difference operator D{sub q}. We also determine another q-difference operator that lifts the orthogonality weight function for the continuous q-Hermite polynomialsH{submore » n}(x | q) up to the weight function, associated with the Askey-Wilson polynomials p{sub n}(x; a, b, c, d | q).« less

New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

PubMed Central

Abd-Elhameed, W. M.

2014-01-01

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. PMID:25386599

Combining freeform optics and curved detectors for wide field imaging: a polynomial approach over squared aperture.

PubMed

Muslimov, Eduard; Hugot, Emmanuel; Jahn, Wilfried; Vives, Sebastien; Ferrari, Marc; Chambion, Bertrand; Henry, David; Gaschet, Christophe

2017-06-26

In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which are very compact and free of obscuration. However, the field of freeform surfaces design techniques still remains underexplored. In the present paper we use the mathematical apparatus of orthogonal polynomials defined over a square aperture, which was developed before for the tasks of wavefront reconstruction, to describe shape of a mirror surface. Two cases, namely Legendre polynomials and generalization of the Zernike polynomials on a square, are considered. The potential advantages of these polynomials sets are demonstrated on example of a three-mirror unobscured telescope with F/# = 2.5 and FoV = 7.2x7.2°. In addition, we discuss possibility of use of curved detectors in such a design.

Inequalities for a polynomial and its derivative

NASA Astrophysics Data System (ADS)

Chanam, Barchand; Dewan, K. K.

2007-12-01

Let , 1[less-than-or-equals, slant][mu][less-than-or-equals, slant]n, be a polynomial of degree n such that p(z)[not equal to]0 in z0, then for 0

Quantization of gauge fields, graph polynomials and graph homology

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

Kreimer, Dirk, E-mail: kreimer@physik.hu-berlin.de; Sars, Matthias; Suijlekom, Walter D. van

2013-09-15

We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology.more » -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.« less

An algorithmic approach to solving polynomial equations associated with quantum circuits

NASA Astrophysics Data System (ADS)

Gerdt, V. P.; Zinin, M. V.

2009-12-01

In this paper we present two algorithms for reducing systems of multivariate polynomial equations over the finite field F 2 to the canonical triangular form called lexicographical Gröbner basis. This triangular form is the most appropriate for finding solutions of the system. On the other hand, the system of polynomials over F 2 whose variables also take values in F 2 (Boolean polynomials) completely describes the unitary matrix generated by a quantum circuit. In particular, the matrix itself can be computed by counting the number of solutions (roots) of the associated polynomial system. Thereby, efficient construction of the lexicographical Gröbner bases over F 2 associated with quantum circuits gives a method for computing their circuit matrices that is alternative to the direct numerical method based on linear algebra. We compare our implementation of both algorithms with some other software packages available for computing Gröbner bases over F 2.

Recurrence approach and higher order polynomial algebras for superintegrable monopole systems

NASA Astrophysics Data System (ADS)

Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong

2018-05-01

We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in a generalized Taub-Newman-Unti-Tamburino (NUT) space. The Schrödinger equation of this model is solved in spherical coordinates in the framework of Stäckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show that the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model.

Polynomial interpolation and sums of powers of integers

NASA Astrophysics Data System (ADS)

Cereceda, José Luis

2017-02-01

In this note, we revisit the problem of polynomial interpolation and explicitly construct two polynomials in n of degree k + 1, Pk(n) and Qk(n), such that Pk(n) = Qk(n) = fk(n) for n = 1, 2,… , k, where fk(1), fk(2),… , fk(k) are k arbitrarily chosen (real or complex) values. Then, we focus on the case that fk(n) is given by the sum of powers of the first n positive integers Sk(n) = 1k + 2k + ṡṡṡ + nk, and show that Sk(n) admits the polynomial representations Sk(n) = Pk(n) and Sk(n) = Qk(n) for all n = 1, 2,… , and k ≥ 1, where the first representation involves the Eulerian numbers, and the second one the Stirling numbers of the second kind. Finally, we consider yet another polynomial formula for Sk(n) alternative to the well-known formula of Bernoulli.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Botti, Lorenzo; Di Pietro, Daniele A.

2018-10-01

We propose and validate a novel extension of Hybrid High-Order (HHO) methods to meshes featuring curved elements. HHO methods are based on discrete unknowns that are broken polynomials on the mesh and its skeleton. We propose here the use of physical frame polynomials over mesh elements and reference frame polynomials over mesh faces. With this choice, the degree of face unknowns must be suitably selected in order to recover on curved meshes the same convergence rates as on straight meshes. We provide an estimate of the optimal face polynomial degree depending on the element polynomial degree and on the so-called effective mapping order. The estimate is numerically validated through specifically crafted numerical tests. All test cases are conducted considering two- and three-dimensional pure diffusion problems, and include comparisons with discontinuous Galerkin discretizations. The extension to agglomerated meshes with curved boundaries is also considered.

Multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials

NASA Astrophysics Data System (ADS)

Odake, Satoru; Sasaki, Ryu

2017-04-01

As the fourth stage of the project multi-indexed orthogonal polynomials, we present the multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials in the framework of ‘discrete quantum mechanics’ with real shifts defined on the semi-infinite lattice in one dimension. They are obtained, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier, from the quantum mechanical systems corresponding to the original orthogonal polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of virtual state vectors. The virtual state vectors are the solutions of the matrix Schrödinger equation on all the lattice points having negative energies and infinite norm. This is in good contrast to the (q-)Racah systems defined on a finite lattice, in which the ‘virtual state’ vectors satisfy the matrix Schrödinger equation except for one of the two boundary points.

Using Tutte polynomials to analyze the structure of the benzodiazepines

NASA Astrophysics Data System (ADS)

Cadavid Muñoz, Juan José

2014-05-01

Graph theory in general and Tutte polynomials in particular, are implemented for analyzing the chemical structure of the benzodiazepines. Similarity analysis are used with the Tutte polynomials for finding other molecules that are similar to the benzodiazepines and therefore that might show similar psycho-active actions for medical purpose, in order to evade the drawbacks associated to the benzodiazepines based medicine. For each type of benzodiazepines, Tutte polynomials are computed and some numeric characteristics are obtained, such as the number of spanning trees and the number of spanning forests. Computations are done using the computer algebra Maple's GraphTheory package. The obtained analytical results are of great importance in pharmaceutical engineering. As a future research line, the usage of the chemistry computational program named Spartan, will be used to extent and compare it with the obtained results from the Tutte polynomials of benzodiazepines.

Multiple-trait random regression models for the estimation of genetic parameters for milk, fat, and protein yield in buffaloes.

PubMed

Borquis, Rusbel Raul Aspilcueta; Neto, Francisco Ribeiro de Araujo; Baldi, Fernando; Hurtado-Lugo, Naudin; de Camargo, Gregório M F; Muñoz-Berrocal, Milthon; Tonhati, Humberto

2013-09-01

In this study, genetic parameters for test-day milk, fat, and protein yield were estimated for the first lactation. The data analyzed consisted of 1,433 first lactations of Murrah buffaloes, daughters of 113 sires from 12 herds in the state of São Paulo, Brazil, with calvings from 1985 to 2007. Ten-month classes of lactation days were considered for the test-day yields. The (co)variance components for the 3 traits were estimated using the regression analyses by Bayesian inference applying an animal model by Gibbs sampling. The contemporary groups were defined as herd-year-month of the test day. In the model, the random effects were additive genetic, permanent environment, and residual. The fixed effects were contemporary group and number of milkings (1 or 2), the linear and quadratic effects of the covariable age of the buffalo at calving, as well as the mean lactation curve of the population, which was modeled by orthogonal Legendre polynomials of fourth order. The random effects for the traits studied were modeled by Legendre polynomials of third and fourth order for additive genetic and permanent environment, respectively, the residual variances were modeled considering 4 residual classes. The heritability estimates for the traits were moderate (from 0.21-0.38), with higher estimates in the intermediate lactation phase. The genetic correlation estimates within and among the traits varied from 0.05 to 0.99. The results indicate that the selection for any trait test day will result in an indirect genetic gain for milk, fat, and protein yield in all periods of the lactation curve. The accuracy associated with estimated breeding values obtained using multi-trait random regression was slightly higher (around 8%) compared with single-trait random regression. This difference may be because to the greater amount of information available per animal. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

The Fixed-Links Model in Combination with the Polynomial Function as a Tool for Investigating Choice Reaction Time Data

ERIC Educational Resources Information Center

Schweizer, Karl

2006-01-01

A model with fixed relations between manifest and latent variables is presented for investigating choice reaction time data. The numbers for fixation originate from the polynomial function. Two options are considered: the component-based (1 latent variable for each component of the polynomial function) and composite-based options (1 latent…

Credible Set Estimation, Analysis, and Applications in Synthetic Aperture Radar Canonical Feature Extraction

DTIC Science & Technology

2015-03-26

depicting the CSE implementation for use with CV Domes data. . . 88 B.1 Validation results for N = 1 observation at 1.0 interval. Legendre polynomial of... Legendre polynomial of order Nl = 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 B.3 Validation results for N = 1 observation at...0.01 interval. Legendre polynomial of order Nl = 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 B.4 Validation results for N

Some Curious Properties and Loci Problems Associated with Cubics and Other Polynomials

ERIC Educational Resources Information Center

de Alwis, Amal

2012-01-01

The article begins with a well-known property regarding tangent lines to a cubic polynomial that has distinct, real zeros. We were then able to generalize this property to any polynomial with distinct, real zeros. We also considered a certain family of cubics with two fixed zeros and one variable zero, and explored the loci of centroids of…

Networked Guidance and Control for Mobile Multi-Agent Systems: A Multi-Terminal (Network) Information Theoretic Approach

DTIC Science & Technology

2014-11-04

maximization. A numerical example is provided to illustrate these ideas. [2] Marcos M. Vasconcelos and Nuno C. Martins, “Remote Estimation Games...and bias are affected by current and past outputs. (Working papers to be submitted until the end of 2014) [7] Marcos M. Vasconcelos and Nuno C...4.  Personnel:     Students  partially   funded  by  this  grant  E.  Arvelo,  S.  Park,  D.  Ward,  M.   Vasconcelos

Studies of the Origin and Evolution of Ionospheric Irregularities and Their Effects on AF Systems

DTIC Science & Technology

2008-06-30

34The JB2006 empirical thermospheric density model," by B . R. Bowman, W. K . Tobiska, F. A. Marcos, and C. E. Valladares, J. Atm. and Solar-Terr...during the super geomagnetic storm on 20 November 2003, Ann. Geophys, 25, 863-873, 2007. Bowman, B . R., W. K . Tobiska, F. A. Marcos, and C. E...at middle and equatorial latitudes, J. Geophys. Res., 106, 30,389. Devasia, C. V., N. Jyoti, K . S. V. Subbarao , K . S. Viswanathan, D. Tiwari, and R

Generalized clustering conditions of Jack polynomials at negative Jack parameter {alpha}

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

Bernevig, B. Andrei; Department of Physics, Princeton University, Princeton, New Jersey 08544; Haldane, F. D. M.

We present several conjectures on the behavior and clustering properties of Jack polynomials at a negative parameter {alpha}=-(k+1/r-1), with partitions that violate the (k,r,N)- admissibility rule of [Feigin et al. [Int. Math. Res. Notices 23, 1223 (2002)]. We find that the ''highest weight'' Jack polynomials of specific partitions represent the minimum degree polynomials in N variables that vanish when s distinct clusters of k+1 particles are formed, where s and k are positive integers. Explicit counting formulas are conjectured. The generalized clustering conditions are useful in a forthcoming description of fractional quantum Hall quasiparticles.

Direct solution for thermal stresses in a nose cap under an arbitrary axisymmetric temperature distribution

NASA Technical Reports Server (NTRS)

Davis, Randall C.

1988-01-01

The design of a nose cap for a hypersonic vehicle is an iterative process requiring a rapid, easy to use and accurate stress analysis. The objective of this paper is to develop such a stress analysis technique from a direct solution of the thermal stress equations for a spherical shell. The nose cap structure is treated as a thin spherical shell with an axisymmetric temperature distribution. The governing differential equations are solved by expressing the stress solution to the thermoelastic equations in terms of a series of derivatives of the Legendre polynomials. The process of finding the coefficients for the series solution in terms of the temperature distribution is generalized by expressing the temperature along the shell and through the thickness as a polynomial in the spherical angle coordinate. Under this generalization the orthogonality property of the Legendre polynomials leads to a sequence of integrals involving powers of the spherical shell coordinate times the derivative of the Legendre polynomials. The coefficients of the temperature polynomial appear outside of these integrals. Thus, the integrals are evaluated only once and their values tabulated for use with any arbitrary polynomial temperature distribution.

Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator

NASA Astrophysics Data System (ADS)

Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.

2017-10-01

In position dependent mass (PDM) problems, the quantum dynamics of the associated systems have been understood well in the literature for particular orderings. However, no efforts seem to have been made to solve such PDM problems for general orderings to obtain a global picture. In this connection, we here consider the general ordered quantum Hamiltonian of an interesting position dependent mass problem, namely, the Mathews-Lakshmanan oscillator, and try to solve the quantum problem for all possible orderings including Hermitian and non-Hermitian ones. The other interesting point in our study is that for all possible orderings, although the Schrödinger equation of this Mathews-Lakshmanan oscillator is uniquely reduced to the associated Legendre differential equation, their eigenfunctions cannot be represented in terms of the associated Legendre polynomials with integral degree and order. Rather the eigenfunctions are represented in terms of associated Legendre polynomials with non-integral degree and order. We here explore such polynomials and represent the discrete and continuum states of the system. We also exploit the connection between associated Legendre polynomials with non-integral degree with other orthogonal polynomials such as Jacobi and Gegenbauer polynomials.

Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

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

Degroote, M.; Henderson, T. M.; Zhao, J.

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero.more » Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.« less

Model-based estimates of long-term persistence of induced HPV antibodies: a flexible subject-specific approach.

PubMed

Aregay, Mehreteab; Shkedy, Ziv; Molenberghs, Geert; David, Marie-Pierre; Tibaldi, Fabián

2013-01-01

In infectious diseases, it is important to predict the long-term persistence of vaccine-induced antibodies and to estimate the time points where the individual titers are below the threshold value for protection. This article focuses on HPV-16/18, and uses a so-called fractional-polynomial model to this effect, derived in a data-driven fashion. Initially, model selection was done from among the second- and first-order fractional polynomials on the one hand and from the linear mixed model on the other. According to a functional selection procedure, the first-order fractional polynomial was selected. Apart from the fractional polynomial model, we also fitted a power-law model, which is a special case of the fractional polynomial model. Both models were compared using Akaike's information criterion. Over the observation period, the fractional polynomials fitted the data better than the power-law model; this, of course, does not imply that it fits best over the long run, and hence, caution ought to be used when prediction is of interest. Therefore, we point out that the persistence of the anti-HPV responses induced by these vaccines can only be ascertained empirically by long-term follow-up analysis.

On Using Homogeneous Polynomials To Design Anisotropic Yield Functions With Tension/Compression Symmetry/Assymetry

NASA Astrophysics Data System (ADS)

Soare, S.; Yoon, J. W.; Cazacu, O.

2007-05-01

With few exceptions, non-quadratic homogeneous polynomials have received little attention as possible candidates for yield functions. One reason might be that not every such polynomial is a convex function. In this paper we show that homogeneous polynomials can be used to develop powerful anisotropic yield criteria, and that imposing simple constraints on the identification process leads, aposteriori, to the desired convexity property. It is shown that combinations of such polynomials allow for modeling yielding properties of metallic materials with any crystal structure, i.e. both cubic and hexagonal which display strength differential effects. Extensions of the proposed criteria to 3D stress states are also presented. We apply these criteria to the description of the aluminum alloy AA2090T3. We prove that a sixth order orthotropic homogeneous polynomial is capable of a satisfactory description of this alloy. Next, applications to the deep drawing of a cylindrical cup are presented. The newly proposed criteria were implemented as UMAT subroutines into the commercial FE code ABAQUS. We were able to predict six ears on the AA2090T3 cup's profile. Finally, we show that a tension/compression asymmetry in yielding can have an important effect on the earing profile.

Algebraic approach to solve ttbar dilepton equations

NASA Astrophysics Data System (ADS)

Sonnenschein, Lars

2006-01-01

The set of non-linear equations describing the Standard Model kinematics of the top quark an- tiqark production system in the dilepton decay channel has at most a four-fold ambiguity due to two not fully reconstructed neutrinos. Its most precise and robust solution is of major importance for measurements of top quark properties like the top quark mass and t t spin correlations. Simple algebraic operations allow to transform the non-linear equations into a system of two polynomial equations with two unknowns. These two polynomials of multidegree eight can in turn be an- alytically reduced to one polynomial with one unknown by means of resultants. The obtained univariate polynomial is of degree sixteen and the coefficients are free of any singularity. The number of its real solutions is determined analytically by means of Sturm’s theorem, which is as well used to isolate each real solution into a unique pairwise disjoint interval. The solutions are polished by seeking the sign change of the polynomial in a given interval through binary brack- eting. Further a new Ansatz - exploiting an accidental cancelation in the process of transforming the equations - is presented. It permits to transform the initial system of equations into two poly- nomial equations with two unknowns. These two polynomials of multidegree two can be reduced to one univariate polynomial of degree four by means of resultants. The obtained quartic equation can be solved analytically. The analytical solution has singularities which can be circumvented by the algebraic approach described above.

Charactering baseline shift with 4th polynomial function for portable biomedical near-infrared spectroscopy device

NASA Astrophysics Data System (ADS)

Zhao, Ke; Ji, Yaoyao; Pan, Boan; Li, Ting

2018-02-01

The continuous-wave Near-infrared spectroscopy (NIRS) devices have been highlighted for its clinical and health care applications in noninvasive hemodynamic measurements. The baseline shift of the deviation measurement attracts lots of attentions for its clinical importance. Nonetheless current published methods have low reliability or high variability. In this study, we found a perfect polynomial fitting function for baseline removal, using NIRS. Unlike previous studies on baseline correction for near-infrared spectroscopy evaluation of non-hemodynamic particles, we focused on baseline fitting and corresponding correction method for NIRS and found that the polynomial fitting function at 4th order is greater than the function at 2nd order reported in previous research. Through experimental tests of hemodynamic parameters of the solid phantom, we compared the fitting effect between the 4th order polynomial and the 2nd order polynomial, by recording and analyzing the R values and the SSE (the sum of squares due to error) values. The R values of the 4th order polynomial function fitting are all higher than 0.99, which are significantly higher than the corresponding ones of 2nd order, while the SSE values of the 4th order are significantly smaller than the corresponding ones of the 2nd order. By using the high-reliable and low-variable 4th order polynomial fitting function, we are able to remove the baseline online to obtain more accurate NIRS measurements.

On Some Algebraic and Combinatorial Properties of Dunkl Elements

NASA Astrophysics Data System (ADS)

Kirillov, Anatol N.

2013-06-01

We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the β-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.

Exact solutions of massive gravity in three dimensions

NASA Astrophysics Data System (ADS)

Chakhad, Mohamed

In recent years, there has been an upsurge in interest in three-dimensional theories of gravity. In particular, two theories of massive gravity in three dimensions hold strong promise in the search for fully consistent theories of quantum gravity, an understanding of which will shed light on the problems of quantum gravity in four dimensions. One of these theories is the "old" third-order theory of topologically massive gravity (TMG) and the other one is a "new" fourth-order theory of massive gravity (NMG). Despite this increase in research activity, the problem of finding and classifying solutions of TMG and NMG remains a wide open area of research. In this thesis, we provide explicit new solutions of massive gravity in three dimensions and suggest future directions of research. These solutions belong to the Kundt class of spacetimes. A systematic analysis of the Kundt solutions with constant scalar polynomial curvature invariants provides a glimpse of the structure of the spaces of solutions of the two theories of massive gravity. We also find explicit solutions of topologically massive gravity whose scalar polynomial curvature invariants are not all constant, and these are the first such solutions. A number of properties of Kundt solutions of TMG and NMG, such as an identification of solutions which lie at the intersection of the full nonlinear and linearized theories, are also derived.

CS-AMPPred: An Updated SVM Model for Antimicrobial Activity Prediction in Cysteine-Stabilized Peptides

PubMed Central

Porto, William F.; Pires, Állan S.; Franco, Octavio L.

2012-01-01

The antimicrobial peptides (AMP) have been proposed as an alternative to control resistant pathogens. However, due to multifunctional properties of several AMP classes, until now there has been no way to perform efficient AMP identification, except through in vitro and in vivo tests. Nevertheless, an indication of activity can be provided by prediction methods. In order to contribute to the AMP prediction field, the CS-AMPPred (Cysteine-Stabilized Antimicrobial Peptides Predictor) is presented here, consisting of an updated version of the Support Vector Machine (SVM) model for antimicrobial activity prediction in cysteine-stabilized peptides. The CS-AMPPred is based on five sequence descriptors: indexes of (i) α-helix and (ii) loop formation; and averages of (iii) net charge, (iv) hydrophobicity and (v) flexibility. CS-AMPPred was based on 310 cysteine-stabilized AMPs and 310 sequences extracted from PDB. The polynomial kernel achieves the best accuracy on 5-fold cross validation (85.81%), while the radial and linear kernels achieve 84.19%. Testing in a blind data set, the polynomial and radial kernels achieve an accuracy of 90.00%, while the linear model achieves 89.33%. The three models reach higher accuracies than previously described methods. A standalone version of CS-AMPPred is available for download at and runs on any Linux machine. PMID:23240023

On Some Algebraic and Combinatorial Properties of Dunkl Elements

NASA Astrophysics Data System (ADS)

Kirillov, Anatol N.

2012-11-01

We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the β-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.

STATLIB: NSWC Library of Statistical Programs and Subroutines

DTIC Science & Technology

1989-08-01

Uncorrelated Weighted Polynomial Regression 41 .WEPORC Correlated Weighted Polynomial Regression 45 MROP Multiple Regression Using Orthogonal Polynomials ...could not and should not be con- NSWC TR 89-97 verted to the new general purpose computer (the current CDC 995). Some were designed tu compute...personal computers. They are referred to as SPSSPC+, BMDPC, and SASPC and in general are less comprehensive than their mainframe counterparts. The basic

Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs. NBER Working Paper No. 20405

ERIC Educational Resources Information Center

Gelman, Andrew; Imbens, Guido

2014-01-01

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use estimators based on local linear or quadratic polynomials or…

Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)

NASA Astrophysics Data System (ADS)

Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.

2018-05-01

A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.

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.

Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

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

Konakli, Katerina, E-mail: konakli@ibk.baug.ethz.ch; Sudret, Bruno

2016-09-15

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely themore » exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input dimension, a situation that is often encountered in real-life problems. By introducing the conditional generalization error, we further demonstrate that canonical LRA tend to outperform sparse PCE in the prediction of extreme model responses, which is critical in reliability analysis.« less

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.

Time-varying higher order spectra

NASA Astrophysics Data System (ADS)

Boashash, Boualem; O'Shea, Peter

1991-12-01

A general solution for the problem of time-frequency signal representation of nonlinear FM signals is provided, based on a generalization of the Wigner-Ville distribution. The Wigner- Ville distribution (WVD) is a second order time-frequency representation. That is, it is able to give ideal energy concentration for quadratic phase signals and its ensemble average is a second order time-varying spectrum. The same holds for Cohen's class of time-frequency distributions, which are smoothed versions of the WVD. The WVD may be extended so as to achieve ideal energy concentration for higher order phase laws, and such that the expectation is a time-varying higher order spectrum. The usefulness of these generalized Wigner-Ville distributions (GWVD) is twofold. Firstly, because they achieve ideal energy concentration for polynomial phase signals, they may be used for optimal instantaneous frequency estimation. Second, they are useful for discriminating between nonstationary processes of differing higher order moments. In the same way that the WVD is generalized, we generalize Cohen's class of TFDs by defining a class of generalized time-frequency distributions (GTFDs) obtained by a two dimensional smoothing of the GWVD. Another results derived from this approach is a method based on higher order spectra which allows the separation of cross-terms and auto- terms in the WVD.

Uranium series isotopes concentration in sediments at San Marcos and Luis L. Leon reservoirs, Chihuahua, Mexico

NASA Astrophysics Data System (ADS)

Méndez-García, C.; Renteria-Villalobos, M.; García-Tenorio, R.; Montero-Cabrera, M. E.

2014-07-01

Spatial and temporal distribution of the radioisotopes concentrations were determined in sediments near the surface and core samples extracted from two reservoirs located in an arid region close to Chihuahua City, Mexico. At San Marcos reservoir one core was studied, while from Luis L. Leon reservoir one core from the entrance and another one close to the wall were investigated. 232Th-series, 238U-series, 40K and 137Cs activity concentrations (AC, Bq kg-1) were determined by gamma spectrometry with a high purity Ge detector. 238U and 234U ACs were obtained by liquid scintillation and alpha spectrometry with a surface barrier detector. Dating of core sediments was performed applying CRS method to 210Pb activities. Results were verified by 137Cs AC. Resulting activity concentrations were compared among corresponding surface and core sediments. High 238U-series AC values were found in sediments from San Marcos reservoir, because this site is located close to the Victorino uranium deposit. Low AC values found in Luis L. Leon reservoir suggest that the uranium present in the source of the Sacramento - Chuviscar Rivers is not transported up to the Conchos River. Activity ratios (AR) 234U/overflow="scroll">238U and 238U/overflow="scroll">226Ra in sediments have values between 0.9-1.2, showing a behavior close to radioactive equilibrium in the entire basin. 232Th/overflow="scroll">238U, 228Ra/overflow="scroll">226Ra ARs are witnesses of the different geological origin of sediments from San Marcos and Luis L. Leon reservoirs.

New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

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

Marquette, Ian; Quesne, Christiane

2013-04-15

In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant. In this paper, we construct from Hermite and Laguerre EOP and their related quantum systems new 2D superintegrable Hamiltonians with higher-order integrals of motion and the polynomial algebras generated by their integrals of motion. We obtain the finite-dimensional unitary representations of the polynomial algebras and the corresponding energy spectrum. We also point out a new type of degeneracies of the energy levels of these systems that is associated with holes in sequencesmore » of EOP.« less

Vector-valued Jack polynomials and wavefunctions on the torus

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

2017-06-01

The Hamiltonian of the quantum Calogero-Sutherland model of N identical particles on the circle with 1/r 2 interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials taking values in modules of the symmetric group and the matrix solution of a system of linear differential equations one constructs novel eigenfunctions of the Hamiltonian. Like the usual wavefunctions each eigenfunction determines a symmetric probability density on the N-torus. The construction applies to any irreducible representation of the symmetric group. The methods depend on the theory of generalized Jack polynomials due to Griffeth, and the Yang-Baxter graph approach of Luque and the author.

Phase demodulation method from a single fringe pattern based on correlation with a polynomial form.

PubMed

Robin, Eric; Valle, Valéry; Brémand, Fabrice

2005-12-01

The method presented extracts the demodulated phase from only one fringe pattern. Locally, this method approaches the fringe pattern morphology with the help of a mathematical model. The degree of similarity between the mathematical model and the real fringe is estimated by minimizing a correlation function. To use an optimization process, we have chosen a polynomial form such as a mathematical model. However, the use of a polynomial form induces an identification procedure with the purpose of retrieving the demodulated phase. This method, polynomial modulated phase correlation, is tested on several examples. Its performance, in terms of speed and precision, is presented on very noised fringe patterns.

Recognition and Quantification of Area Damaged by Oligonychus Perseae in Avocado Leaves

NASA Astrophysics Data System (ADS)

Díaz, Gloria; Romero, Eduardo; Boyero, Juan R.; Malpica, Norberto

The measure of leaf damage is a basic tool in plant epidemiology research. Measuring the area of a great number of leaves is subjective and time consuming. We investigate the use of machine learning approaches for the objective segmentation and quantification of leaf area damaged by mites in avocado leaves. After extraction of the leaf veins, pixels are labeled with a look-up table generated using a Support Vector Machine with a polynomial kernel of degree 3, on the chrominance components of YCrCb color space. Spatial information is included in the segmentation process by rating the degree of membership to a certain class and the homogeneity of the classified region. Results are presented on real images with different degrees of damage.

A color-coded vision scheme for robotics

NASA Technical Reports Server (NTRS)

Johnson, Kelley Tina

1991-01-01

Most vision systems for robotic applications rely entirely on the extraction of information from gray-level images. Humans, however, regularly depend on color to discriminate between objects. Therefore, the inclusion of color in a robot vision system seems a natural extension of the existing gray-level capabilities. A method for robot object recognition using a color-coding classification scheme is discussed. The scheme is based on an algebraic system in which a two-dimensional color image is represented as a polynomial of two variables. The system is then used to find the color contour of objects. In a controlled environment, such as that of the in-orbit space station, a particular class of objects can thus be quickly recognized by its color.

Logic integer programming models for signaling networks.

PubMed

Haus, Utz-Uwe; Niermann, Kathrin; Truemper, Klaus; Weismantel, Robert

2009-05-01

We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this, we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in molecular biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.

Integrable cosmological potentials

NASA Astrophysics Data System (ADS)

Sokolov, V. V.; Sorin, A. S.

2017-09-01

The problem of classification of the Einstein-Friedman cosmological Hamiltonians H with a single scalar inflaton field φ, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint H=0, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential V(φ). In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed.

Public channel cryptography: chaos synchronization and Hilbert's tenth problem.

PubMed

Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang

2008-08-22

The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.

On the Critical Behaviour, Crossover Point and Complexity of the Exact Cover Problem

NASA Technical Reports Server (NTRS)

Morris, Robin D.; Smelyanskiy, Vadim N.; Shumow, Daniel; Koga, Dennis (Technical Monitor)

2003-01-01

Research into quantum algorithms for NP-complete problems has rekindled interest in the detailed study a broad class of combinatorial problems. A recent paper applied the quantum adiabatic evolution algorithm to the Exact Cover problem for 3-sets (EC3), and provided an empirical evidence that the algorithm was polynomial. In this paper we provide a detailed study of the characteristics of the exact cover problem. We present the annealing approximation applied to EC3, which gives an over-estimate of the phase transition point. We also identify empirically the phase transition point. We also study the complexity of two classical algorithms on this problem: Davis-Putnam and Simulated Annealing. For these algorithms, EC3 is significantly easier than 3-SAT.

Stability analysis of spectral methods for hyperbolic initial-boundary value systems

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Lustman, L.; Tadmor, E.

1986-01-01

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

Optimal approach to quantum communication using dynamic programming.

PubMed

Jiang, Liang; Taylor, Jacob M; Khaneja, Navin; Lukin, Mikhail D

2007-10-30

Reliable preparation of entanglement between distant systems is an outstanding problem in quantum information science and quantum communication. In practice, this has to be accomplished by noisy channels (such as optical fibers) that generally result in exponential attenuation of quantum signals at large distances. A special class of quantum error correction protocols, quantum repeater protocols, can be used to overcome such losses. In this work, we introduce a method for systematically optimizing existing protocols and developing more efficient protocols. Our approach makes use of a dynamic programming-based searching algorithm, the complexity of which scales only polynomially with the communication distance, letting us efficiently determine near-optimal solutions. We find significant improvements in both the speed and the final-state fidelity for preparing long-distance entangled states.

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

New formulae between Jacobi polynomials and some fractional Jacobi functions generalizing some connection formulae

NASA Astrophysics Data System (ADS)

Abd-Elhameed, W. M.

2017-07-01

In this paper, a new formula relating Jacobi polynomials of arbitrary parameters with the squares of certain fractional Jacobi functions is derived. The derived formula is expressed in terms of a certain terminating hypergeometric function of the type _4F3(1) . With the aid of some standard reduction formulae such as Pfaff-Saalschütz's and Watson's identities, the derived formula can be reduced in simple forms which are free of any hypergeometric functions for certain choices of the involved parameters of the Jacobi polynomials and the Jacobi functions. Some other simplified formulae are obtained via employing some computer algebra algorithms such as the algorithms of Zeilberger, Petkovsek and van Hoeij. Some connection formulae between some Jacobi polynomials are deduced. From these connection formulae, some other linearization formulae of Chebyshev polynomials are obtained. As an application to some of the introduced formulae, a numerical algorithm for solving nonlinear Riccati differential equation is presented and implemented by applying a suitable spectral method.

State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates

NASA Astrophysics Data System (ADS)

Zheng, Mingfang; He, Cunfu; Lu, Yan; Wu, Bin

2018-01-01

We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact solution to the problem in the form of the Legendre polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre polynomials. The Legendre polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.

Computing Tutte polynomials of contact networks in classrooms

NASA Astrophysics Data System (ADS)

Hincapié, Doracelly; Ospina, Juan

2013-05-01

Objective: The topological complexity of contact networks in classrooms and the potential transmission of an infectious disease were analyzed by sex and age. Methods: The Tutte polynomials, some topological properties and the number of spanning trees were used to algebraically compute the topological complexity. Computations were made with the Maple package GraphTheory. Published data of mutually reported social contacts within a classroom taken from primary school, consisting of children in the age ranges of 4-5, 7-8 and 10-11, were used. Results: The algebraic complexity of the Tutte polynomial and the probability of disease transmission increases with age. The contact networks are not bipartite graphs, gender segregation was observed especially in younger children. Conclusion: Tutte polynomials are tools to understand the topology of the contact networks and to derive numerical indexes of such topologies. It is possible to establish relationships between the Tutte polynomial of a given contact network and the potential transmission of an infectious disease within such network

A Formally-Verified Decision Procedure for Univariate Polynomial Computation Based on Sturm's Theorem

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony J.; Munoz, Cesar A.

2014-01-01

Sturm's Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semiopen interval. This paper presents a formalization of this theorem in the PVS theorem prover, as well as a decision procedure that checks whether a polynomial is always positive, nonnegative, nonzero, negative, or nonpositive on any input interval. The soundness and completeness of the decision procedure is proven in PVS. The procedure and its correctness properties enable the implementation of a PVS strategy for automatically proving existential and universal univariate polynomial inequalities. Since the decision procedure is formally verified in PVS, the soundness of the strategy depends solely on the internal logic of PVS rather than on an external oracle. The procedure itself uses a combination of Sturm's Theorem, an interval bisection procedure, and the fact that a polynomial with exactly one root in a bounded interval is always nonnegative on that interval if and only if it is nonnegative at both endpoints.

Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard

NASA Astrophysics Data System (ADS)

Roquet, F.; Madec, G.; McDougall, Trevor J.; Barker, Paul M.

2015-06-01

A new set of approximations to the standard TEOS-10 equation of state are presented. These follow a polynomial form, making it computationally efficient for use in numerical ocean models. Two versions are provided, the first being a fit of density for Boussinesq ocean models, and the second fitting specific volume which is more suitable for compressible models. Both versions are given as the sum of a vertical reference profile (6th-order polynomial) and an anomaly (52-term polynomial, cubic in pressure), with relative errors of ∼0.1% on the thermal expansion coefficients. A 75-term polynomial expression is also presented for computing specific volume, with a better accuracy than the existing TEOS-10 48-term rational approximation, especially regarding the sound speed, and it is suggested that this expression represents a valuable approximation of the TEOS-10 equation of state for hydrographic data analysis. In the last section, practical aspects about the implementation of TEOS-10 in ocean models are discussed.

Trajectory Optimization for Helicopter Unmanned Aerial Vehicles (UAVs)

DTIC Science & Technology

2010-06-01

the Nth-order derivative of the Legendre Polynomial ( )NL t . Using this method, the range of integration is transformed universally to [-1,+1...which is the interval for Legendre Polynomials . Although the LGL interpolation points are not evenly spaced, they are symmetric about the midpoint 0...the vehicle’s kinematic constraints are parameterized in terms of polynomials of sufficient order, (2) A collision-free criterion is developed and

Near Real-Time Closed-Loop Optimal Control Feedback for Spacecraft Attitude Maneuvers

DTIC Science & Technology

2009-03-01

60 3.8 Positive ωi Static Thrust Fan Characterization Polynomial Coefficients . . 62 3.9 Negative ωi Static Thrust Fan...Characterization Polynomial Coefficients . 62 4.1 Coefficients for SimSAT II’s Air Drag Polynomial Function . . . . . . . . . . . 78 5.1 OLOC Simulation...maneuver. Researchers using OCT identified that naturally occurring aerodynamic drag and gravity forces could be exploited in such a way that the CMGs

On the best mean-square approximations to a planet's gravitational potential

NASA Astrophysics Data System (ADS)

Lobkova, N. I.

1985-02-01

The continuous problem of approximating the gravitational potential of a planet in the form of polynomials of solid spherical functions is considered. The best mean-square polynomials, referred to different parts of space, are compared with each other. The harmonic coefficients corresponding to the surface of a planet are shown to be unstable with respect to the degree of the polynomial and to differ from the Stokes constants.

Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials

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

Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu; Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408; Roy, Pinaki, E-mail: pinaki@isical.ac.in

We construct energy-dependent potentials for which the Schrödinger equations admit solutions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations of exceptional Hermite, Jacobi and Laguerre polynomials. We present several examples of boundary-value problems with energy-dependent potentials that admit a discrete spectrum and the corresponding normalizable solutions in closed form.

Algorithms for Solvents and Spectral Factors of Matrix Polynomials

DTIC Science & Technology

1981-01-01

spectral factors of matrix polynomials LEANG S. SHIEHt, YIH T. TSAYt and NORMAN P. COLEMANt A generalized Newton method , based on the contracted gradient...of a matrix poly- nomial, is derived for solving the right (left) solvents and spectral factors of matrix polynomials. Two methods of selecting initial...estimates for rapid convergence of the newly developed numerical method are proposed. Also, new algorithms for solving complete sets of the right

Roots of polynomials by ratio of successive derivatives

NASA Technical Reports Server (NTRS)

Crouse, J. E.; Putt, C. W.

1972-01-01

An order of magnitude study of the ratios of successive polynomial derivatives yields information about the number of roots at an approached root point and the approximate location of a root point from a nearby point. The location approximation improves as a root is approached, so a powerful convergence procedure becomes available. These principles are developed into a computer program which finds the roots of polynomials with real number coefficients.

Least-Squares Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Kantak, Anil V.

1990-01-01

Least Squares Curve Fitting program, AKLSQF, easily and efficiently computes polynomial providing least-squares best fit to uniformly spaced data. Enables user to specify tolerable least-squares error in fit or degree of polynomial. AKLSQF returns polynomial and actual least-squares-fit error incurred in operation. Data supplied to routine either by direct keyboard entry or via file. Written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler.

Polynomial Interpolation and Sums of Powers of Integers

ERIC Educational Resources Information Center

Cereceda, José Luis

2017-01-01

In this note, we revisit the problem of polynomial interpolation and explicitly construct two polynomials in n of degree k + 1, P[subscript k](n) and Q[subscript k](n), such that P[subscript k](n) = Q[subscript k](n) = f[subscript k](n) for n = 1, 2,… , k, where f[subscript k](1), f[subscript k](2),… , f[subscript k](k) are k arbitrarily chosen…

On direct theorems for best polynomial approximation

NASA Astrophysics Data System (ADS)

Auad, A. A.; AbdulJabbar, R. S.

2018-05-01

This paper is to obtain similarity for the best approximation degree of functions, which are unbounded in L p,α (A = [0,1]), which called weighted space by algebraic polynomials. {E}nH{(f)}p,α and the best approximation degree in the same space on the interval [0,2π] by trigonometric polynomials {E}nT{(f)}p,α of direct wellknown theorems in forms the average modules.

Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

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

Hampton, Jerrad; Doostan, Alireza, E-mail: alireza.doostan@colorado.edu

2015-01-01

Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter, referred to as coherence, yields a bound on the number of samples necessary to identify coefficients in a sparse PC expansion via solution to an ℓ{sub 1}-minimization problem. Utilizing results for orthogonal polynomials, we bound the coherence parameter for polynomials of Hermite and Legendre type under their respective natural sampling distribution. In both polynomial bases we identify an importance sampling distribution which yields a bound with weaker dependence onmore » the order of the approximation. For more general orthonormal bases, we propose the coherence-optimal sampling: a Markov Chain Monte Carlo sampling, which directly uses the basis functions under consideration to achieve a statistical optimality among all sampling schemes with identical support. We demonstrate these different sampling strategies numerically in both high-order and high-dimensional, manufactured PC expansions. In addition, the quality of each sampling method is compared in the identification of solutions to two differential equations, one with a high-dimensional random input and the other with a high-order PC expansion. In both cases, the coherence-optimal sampling scheme leads to similar or considerably improved accuracy.« less

Long-time uncertainty propagation using generalized polynomial chaos and flow map composition

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

Luchtenburg, Dirk M., E-mail: dluchten@cooper.edu; Brunton, Steven L.; Rowley, Clarence W.

2014-10-01

We present an efficient and accurate method for long-time uncertainty propagation in dynamical systems. Uncertain initial conditions and parameters are both addressed. The method approximates the intermediate short-time flow maps by spectral polynomial bases, as in the generalized polynomial chaos (gPC) method, and uses flow map composition to construct the long-time flow map. In contrast to the gPC method, this approach has spectral error convergence for both short and long integration times. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be well represented by a relatively low-degree basis. The compositionmore » of these low-degree polynomial bases then accurately describes the uncertainty behavior for long integration times. The key to the method is that the degree of the resulting polynomial approximation increases exponentially in the number of time intervals, while the number of polynomial coefficients either remains constant (for an autonomous system) or increases linearly in the number of time intervals (for a non-autonomous system). The findings are illustrated on several numerical examples including a nonlinear ordinary differential equation (ODE) with an uncertain initial condition, a linear ODE with an uncertain model parameter, and a two-dimensional, non-autonomous double gyre flow.« less

Jack Polynomials as Fractional Quantum Hall States and the Betti Numbers of the ( k + 1)-Equals Ideal

NASA Astrophysics Data System (ADS)

Zamaere, Christine Berkesch; Griffeth, Stephen; Sam, Steven V.

2014-08-01

We show that for Jack parameter α = -( k + 1)/( r - 1), certain Jack polynomials studied by Feigin-Jimbo-Miwa-Mukhin vanish to order r when k + 1 of the coordinates coincide. This result was conjectured by Bernevig and Haldane, who proposed that these Jack polynomials are model wavefunctions for fractional quantum Hall states. Special cases of these Jack polynomials include the wavefunctions of Laughlin and Read-Rezayi. In fact, along these lines we prove several vanishing theorems known as clustering properties for Jack polynomials in the mathematical physics literature, special cases of which had previously been conjectured by Bernevig and Haldane. Motivated by the method of proof, which in the case r = 2 identifies the span of the relevant Jack polynomials with the S n -invariant part of a unitary representation of the rational Cherednik algebra, we conjecture that unitary representations of the type A Cherednik algebra have graded minimal free resolutions of Bernstein-Gelfand-Gelfand type; we prove this for the ideal of the ( k + 1)-equals arrangement in the case when the number of coordinates n is at most 2 k + 1. In general, our conjecture predicts the graded S n -equivariant Betti numbers of the ideal of the ( k + 1)-equals arrangement with no restriction on the number of ambient dimensions.

On Using Homogeneous Polynomials To Design Anisotropic Yield Functions With Tension/Compression Symmetry/Assymetry

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

Soare, S.; Cazacu, O.; Yoon, J. W.

With few exceptions, non-quadratic homogeneous polynomials have received little attention as possible candidates for yield functions. One reason might be that not every such polynomial is a convex function. In this paper we show that homogeneous polynomials can be used to develop powerful anisotropic yield criteria, and that imposing simple constraints on the identification process leads, aposteriori, to the desired convexity property. It is shown that combinations of such polynomials allow for modeling yielding properties of metallic materials with any crystal structure, i.e. both cubic and hexagonal which display strength differential effects. Extensions of the proposed criteria to 3D stressmore » states are also presented. We apply these criteria to the description of the aluminum alloy AA2090T3. We prove that a sixth order orthotropic homogeneous polynomial is capable of a satisfactory description of this alloy. Next, applications to the deep drawing of a cylindrical cup are presented. The newly proposed criteria were implemented as UMAT subroutines into the commercial FE code ABAQUS. We were able to predict six ears on the AA2090T3 cup's profile. Finally, we show that a tension/compression asymmetry in yielding can have an important effect on the earing profile.« less