Mixed semiclassical-classical propagators for the Wigner phase space representation.

PubMed

Koda, Shin-Ichi

2016-04-21

We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency.

Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems

NASA Astrophysics Data System (ADS)

Demina, Maria V.

2018-05-01

The general structure of irreducible invariant algebraic curves for a polynomial dynamical system in C2 is found. Necessary conditions for existence of exponential factors related to an invariant algebraic curve are derived. As a consequence, all the cases when the classical force-free Duffing and Duffing-van der Pol oscillators possess Liouvillian first integrals are obtained. New exact solutions for the force-free Duffing-van der Pol system are constructed.

High-Order Polynomial Expansions (HOPE) for flux-vector splitting

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Steffen, Chris J., Jr.

1991-01-01

The Van Leer flux splitting is known to produce excessive numerical dissipation for Navier-Stokes calculations. Researchers attempt to remedy this deficiency by introducing a higher order polynomial expansion (HOPE) for the mass flux. In addition to Van Leer's splitting, a term is introduced so that the mass diffusion error vanishes at M = 0. Several splittings for pressure are proposed and examined. The effectiveness of the HOPE scheme is illustrated for 1-D hypersonic conical viscous flow and 2-D supersonic shock-wave boundary layer interactions.

On Schrödinger's equation, Hertz's mechanics and Van Vleck's determinant

NASA Astrophysics Data System (ADS)

Lopes Coelho, R.; Stachel, John

2013-07-01

There has been much research on Schrödinger's route to what we now call Schrödinger's equation. Various authors disagree as to the exact nature of the influence of each of the physicists he cites—and of some that he does not. This paper, intended for graduate students of and researchers in quantum theory, clarifies Schrödinger's original aims in formulating a wave equation for matter, discusses how far he fulfilled his original aspirations and in what respects he fell short of his goal. An analysis of Schrödinger's foundational paper enables us to distinguish between a formal and an epistemological part, and consider the input of the physicists cited on the basis of the part in which each reference occurs. It turns out, for instance, that Hamilton's optical-mechanical analogy belongs entirely to the epistemological part. Indeed, no element of this analogy plays any role in the formal part of Schrödinger's argument. Instead of basing his theory on this analogy, as is often done nowadays in the physics literature and even in the history of science, we maintain that the aim of Schrödinger's project was to represent wave phenomena by a ‘wave’ in configuration- or q-space, paralleling Hertz's treatment in his Mechanics (1894). The influence of this book on Schrödinger's foundational paper is demonstrated by an analysis of his unpublished paper: Hertz's Mechanics and Einstein's Theory of Gravitation. This approach enables us to dispense with the optical-mechanical analogy in tracing the route to Schrödinger's equation. We also discuss the curious role of the Van Vleck determinant as the ‘missing link’ in taking the classical limit of Schrödinger's wavefunction. A concluding section discusses the relation of some of Schrödinger's earlier and later work to the development of quantum field theory.

High-Order Polynomial Expansions (HOPE) for flux-vector splitting

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Steffen, Chris J., Jr.

1991-01-01

The Van Leer flux splitting is known to produce excessive numerical dissipation for Navier-Stokes calculations. Researchers attempt to remedy this deficiency by introducing a higher order polynomial expansion (HOPE) for the mass flux. In addition to Van Leer's splitting, a term is introduced so that the mass diffusion error vanishes at M equals 0. Several splittings for pressure are proposed and examined. The effectiveness of the HOPE scheme is illustrated for 1-D hypersonic conical viscous flow and 2-D supersonic shock-wave boundary layer interactions. Also, the authors give the weakness of the scheme and suggest areas for further investigation.

The first example of erbium triple-stranded helicates displaying SMM behaviour.

PubMed

Gorczyński, Adam; Kubicki, Maciej; Pinkowicz, Dawid; Pełka, Robert; Patroniak, Violetta; Podgajny, Robert

2015-10-14

A series of isostructural C3-symmetrical triple stranded dinuclear lanthanide [Ln2L3](NO3)3 molecules have been synthesized using subcomponent self-assembly of Ln(NO3)3 with 2-(methylhydrazino)benzimidazole and 4-tert-butyl-2,6-diformylphenol, where Ln = Tb (1), Dy (2), Ho (3), Er (4), Tm (5), and Yb (6). The temperature dependent and field dependent magnetic properties of 1-6 were modeled using the van Vleck approximation including the crystal field term HCF, the super-exchange term HSE and the Zeeman term HZE. Ferromagnetic interactions were found in 1, 2, 4 and 6, while antiferromagnetic interactions were found in 3 and 5. The erbium analogue reveals field induced SMM behaviour.

Polynomial decay rate of a thermoelastic Mindlin-Timoshenko plate model with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-02-01

In this article, we are concerned with the polynomial stabilization of a two-dimensional thermoelastic Mindlin-Timoshenko plate model with no mechanical damping. The model is subject to Dirichlet boundary conditions on the elastic as well as the thermal variables. The work complements our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 64:1305-1325, 2013) on the polynomial stabilization of a Mindlin-Timoshenko model in a radially symmetric domain under Dirichlet boundary conditions on the displacement and thermal variables and free boundary conditions on the shear angle variables. In particular, our aim is to investigate the effect of the Dirichlet boundary conditions on all the variables on the polynomial decay rate of the model. By once more applying a frequency domain method in which we make critical use of an inequality for the trace of Sobolev functions on the boundary of a bounded, open connected set we show that the decay is slower than in the model considered in the cited work. A comparison of our result with our polynomial decay result for a magnetoelastic Mindlin-Timoshenko model subject to Dirichlet boundary conditions on the elastic variables in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) also indicates a correlation between the robustness of the coupling between parabolic and hyperbolic dynamics and the polynomial decay rate in the two models.

CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae

NASA Astrophysics Data System (ADS)

van de Leur, Johan W.; Orlov, Alexander Yu.; Shiota, Takahiro

2012-06-01

We develop the theory of CKP hierarchy introduced in the papers of Kyoto school [Date E., Jimbo M., Kashiwara M., Miwa T., J. Phys. Soc. Japan 50 (1981), 3806-3812] (see also [Kac V.G., van de Leur J.W., Adv. Ser. Math. Phys., Vol. 7, World Sci. Publ., Teaneck, NJ, 1989, 369-406]). We present appropriate bosonization formulae. We show that in the context of the CKP theory certain orthogonal polynomials appear. These polynomials are polynomial both in even and odd (in Grassmannian sense) variables.

Polynomial-interpolation algorithm for van der Pauw Hall measurement in a metal hydride film

NASA Astrophysics Data System (ADS)

Koon, D. W.; Ares, J. R.; Leardini, F.; Fernández, J. F.; Ferrer, I. J.

2008-10-01

We apply a four-term polynomial-interpolation extension of the van der Pauw Hall measurement technique to a 330 nm Mg-Pd bilayer during both absorption and desorption of hydrogen at room temperature. We show that standard versions of the van der Pauw DC Hall measurement technique produce an error of over 100% due to a drifting offset signal and can lead to unphysical interpretations of the physical processes occurring in this film. The four-term technique effectively removes this source of error, even when the offset signal is drifting by an amount larger than the Hall signal in the time interval between successive measurements. This technique can be used to increase the resolution of transport studies of any material in which the resistivity is rapidly changing, particularly when the material is changing from metallic to insulating behavior.

Determination of the water vapor continuum absorption by THz-TDS and Molecular Response Theory.

PubMed

Yang, Yihong; Mandehgar, Mahboubeh; Grischkowsky, D

2014-02-24

Determination of the water vapor continuum absorption from 0.35 to 1 THz is reported. The THz pulses propagate though a 137 m long humidity-controlled chamber and are measured by THz time-domain spectroscopy (THz-TDS). The average relative humidity along the entire THz path is precisely obtained by measuring the difference between transit times of the sample and reference THz pulses to an accuracy of 0.1 ps. Using the measured total absorption and the calculated resonance line absorption with the Molecular Response Theory lineshape, based on physical principles and measurements, an accurate continuum absorption is obtained within four THz absorption windows, that agrees well with the empirical theory. The absorption is significantly smaller than that obtained using the van Vleck-Weisskopf lineshape with a 750 GHz cut-off.

Semiclassical propagation: Hilbert space vs. Wigner representation

NASA Astrophysics Data System (ADS)

Gottwald, Fabian; Ivanov, Sergei D.

2018-03-01

A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.

The calculation of rare-earth levels in layered cobaltates Rx/3CoO2 (x ≦ 1)

NASA Astrophysics Data System (ADS)

Novák, P.; Knížek, K.; Jirák, Z.; Buršík, J.

2015-05-01

We studied theoretically the crystal field and Zeeman split electronic levels of trivalent rare earths that are distributed over trigonal prismatic sites of the layered Rx/3CoO2 system (closely related to sodium cobaltate NaxCoO2). The calculations were done in the whole basis of 4fn configurations (up to 3000 many-electron determinantal functions) for the ideal trigonal symmetry D3h, as well as for the reduced symmetry C2v that takes into account a more distant neighborhood of the R-sites. Detailed data on the doublet and singlet states for Pr, Nd, Sm, Tb and Dy are presented. The obtained g-factor and the van Vleck susceptibility tensor components are used for calculations of anisotropic magnetic susceptibilities and their temperature dependencies.

Laboratory measurements of the microwave and millimeter-wave opacity of gaseous sulfur dioxide (SO2) under simulated conditions for the Venus atmosphere

NASA Technical Reports Server (NTRS)

Fahd, Antoine K.; Steffes, Paul G.

1992-01-01

Laboratory measurements have been conducted of the opacity of gaseous SO2 in a CO2 atmosphere at 12.3 cm, 1.32 cm, and 0.32 cm, with a view to the effects of this gas on the mm-wave emission of the Venus atmosphere. Close agreement is noted between the results obtained and the absorptivity predicted from a Van Vleck-Weisskopf formalism at the two shortest wavelengths, but not at the longest. These results have been incorporated into a radiative transfer model in order to infer an abundance profile for gaseous SO2 in Venus' middle atmosphere, and are also used to ascertain the effects of a SO2/CO2 gaseous mixture on the mm-wavelength spectrum of Venus.

Simulation of Ã(2)A(1)←X̃(2)E laser excitation spectrum of CH3O and CD3O.

PubMed

Nagesh, Jayashree; Sibert, Edwin L; Stanton, John F

2014-02-05

A theoretical calculation of the laser-induced fluorescence excitation spectrum from X̃(2)E→Ã(2)A1 is carried out for CH3O and CD3O using a transition dipole moment surface expanded up to second order. The vibronic form of these operators is obtained using symmetry arguments. The Ã(2)A1 vibrational levels are calculated using Van Vleck perturbation theory, and the latter is used to adjust harmonic constants of the potential to match experimental fundamentals. The CH3O fit force field is tested on CD3O. For both molecules the transition energies are well reproduced, but there are systematic differences between experimental and theoretical intensities. The origins of these differences are discussed. Copyright © 2013 Elsevier B.V. All rights reserved.

Semiclassical evaluation of quantum fidelity

NASA Astrophysics Data System (ADS)

Vanicek, Jiri

2004-03-01

We present a numerically feasible semiclassical method to evaluate quantum fidelity (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform semiclassical expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows a Monte-Carlo evaluation, this uniform expression is accurate at times where there are 10^70 semiclassical contributions. Remarkably, the method also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and thus provide a ``defense" of the linear response theory from the famous Van Kampen objection. We point out the potential use of our uniform expression in other areas because it gives a most direct link between the quantum Feynman propagator based on the path integral and the semiclassical Van Vleck propagator based on the sum over classical trajectories. Finally, we test the applicability of our method in integrable and mixed systems.

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.

Magnetism and structural chemistry of ternary borides RE2MB 6 ( RE = rare earth, M = Ru, Os)

NASA Astrophysics Data System (ADS)

Hiebl, K.; Rogl, P.; Nowotny, H.

1984-10-01

The magnetic behavior of the ternary borides RE2RuB 6 and RE2OsB 6 ( RE = Y, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) was studied in the temperature range 1.5 K < T < 1100 K. All compounds crystallize with the Y 2ReB 6-type structure and are characterized by direct RE- RE contacts and the formation of planar infinite two-dimensional rigid boron nets. The magnetic properties reveal a typical Van Vleck paramagnetism of free RE3+-ions at temperatures higher than 200 K with ferromagnetic interaction in the low-temperature range T < 55 K. The ferromagnetic ordering temperatures vary with the De Gennes factor. There is no indication for a magnetic contribution from the Ru(Os)-sublattice. Above 1.8 K none of the samples were found to be superconducting.

VizieR Online Data Catalog: Positions of 502 Stars in Pleiades Region (Eichhorn+ 1970)

NASA Astrophysics Data System (ADS)

Eichhorn, H.; Googe, W. D.; Lukac, C. F.; Murphy, J. K.

1996-01-01

The catalog contains the positions (equinox B1900.0 and epoch B1955.0) of 502 stars in a region of about 1.5 degrees square in the Pleiades cluster, centered on Eta Tau. These coordinates have been derived from measurements of stellar images obtained with 65 exposures of various durations on 14 photographic plates with two telescopes at McCormick Observatory and Van Vleck Observatory. The plates were reduced by the plate overlap method, which resulted in a high degree of systematic accuracy in the final positions. Data in the machine version include Hertzsprung number, color index, photovisual magnitude, right ascension and declination and their standard errors, proper motion, and differences between the present position and previous works. Data for exposures, plates, and images measured, present in the published catalog, are not included in the machine version. (1 data file).

Wavepacket propagation using time-sliced semiclassical initial value methods

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

Wallace, Brett B.; Reimers, Jeffrey R.; School of Chemistry, University of Sydney, Sydney NSW 2006

2004-12-22

A new semiclassical initial value representation (SC-IVR) propagator and a SC-IVR propagator originally introduced by Kay [J. Chem. Phys. 100, 4432 (1994)], are investigated for use in the split-operator method for solving the time-dependent Schroedinger equation. It is shown that the SC-IVR propagators can be derived from a procedure involving modified Filinov filtering of the Van Vleck expression for the semiclassical propagator. The two SC-IVR propagators have been selected for investigation because they avoid the need to perform a coherent state basis set expansion that is necessary in other time-slicing propagation schemes. An efficient scheme for solving the propagators ismore » introduced and can be considered to be a semiclassical form of the effective propagators of Makri [Chem. Phys. Lett. 159, 489 (1989)]. Results from applications to a one-dimensional, two-dimensional, and three-dimensional Hamiltonian for a double-well potential are presented.« less

Aspects of Quantum Theory

NASA Astrophysics Data System (ADS)

Salam, Abdus; Wigner, E. P.

2010-03-01

Preface; List of contributors; Bibliography of P. A. M. Dirac; 1. Dirac in Cambridge R. J. Eden and J. C. Polkinghorne; 2. Travels with Dirac in the Rockies J. H. Van Vleck; 3. 'The golden age of theoretical physics': P. A. M. Dirac's scientific work from 1924 to 1933 Jagdish Mehra; 4. Foundation of quantum field theory Res Jost; 5. The early history of the theory of electron: 1897-1947 A. Pais; 6. The Dirac equation A. S. Wightman; 7. Fermi-Dirac statistics Rudolph Peierls; 8. Indefinite metric in state space W. Heisenberg; 9. On bras and kets J. M. Jauch; 10. The Poisson bracket C. Lanczos; 11. La 'fonction' et les noyaux L. Schwartz; 12. On the Dirac magnetic poles Edoardo Amadli and Nicola Cabibbo; 13. The fundamental constants and their time variation Freeman J. Dyson; 14. On the time-energy uncertainty relation Eugene P. Wigner; 15. The path-integral quantisation of gravity Abdus Salam and J. Strathdee; Index; Plates.

Low-temperature anomalies in the dynamic elastic moduli of cubic AIIBVI crystals with 3d-transition metal impurities

NASA Astrophysics Data System (ADS)

Lonchakov, A. T.

2011-04-01

A negative paramagnetic contribution to the dynamic elastic moduli is identified in AIIBVI:3d wide band-gap compounds for the first time. It appears as a paramagnetic elastic, or, briefly, paraelastic, susceptibility. These compounds are found to have a linear temperature dependence for the inverse paraelastic susceptibility. This is explained by a contribution from the diagonal matrix elements of the orbit-lattice interaction operators in the energy of the spin-orbital states of the 3d-ion as a function of applied stress (by analogy with the Curie contribution to the magnetic susceptibility). The inverse paraelastic susceptibility of AIIBVI crystals containing non-Kramers 3d-ions is found to deviate from linearity with decreasing temperature and reaches saturation. This effect is explained by a contribution from nondiagonal matrix elements (analogous to the well known van Vleck contribution to the magnetic susceptibility of paramagnets).

Interview with Philip W. Anderson

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

Anderson, P.W.

1988-08-01

Phil Anderson, Professor of Physics at Princeton University, has devoted his career to research in theoretical physics. He is a member of the National Academy of Science and the American Academy of Arts and Sciences, a foreign member of the Royal Society, and a foreign associate of the Accademia Lincei in Rome. The Americal Physical Society awarded him the Oliver E. Buckley Solid State Physics Prize in 1964. In 1977 he won the Nobel Prize in Physics with J.H. van Vleck and N.F. Mott. His work has encompassed a broad range of subjects: quantum theory of condensed matter, broken symmetry,more » transport theory and localization, random statistical systems, spectral line broadening, superfluidity in helium and neutron stars, magnetism, and superconductivity. His avocations include ''hiking, the game of GO, Romanesque architecture, and the human condition.'' In this interview he explains his RVB theory of the oxide superconductors and its historical context.« less

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.

Hermite Functional Link Neural Network for Solving the Van der Pol-Duffing Oscillator Equation.

PubMed

Mall, Susmita; Chakraverty, S

2016-08-01

Hermite polynomial-based functional link artificial neural network (FLANN) is proposed here to solve the Van der Pol-Duffing oscillator equation. A single-layer hermite neural network (HeNN) model is used, where a hidden layer is replaced by expansion block of input pattern using Hermite orthogonal polynomials. A feedforward neural network model with the unsupervised error backpropagation principle is used for modifying the network parameters and minimizing the computed error function. The Van der Pol-Duffing and Duffing oscillator equations may not be solved exactly. Here, approximate solutions of these types of equations have been obtained by applying the HeNN model for the first time. Three mathematical example problems and two real-life application problems of Van der Pol-Duffing oscillator equation, extracting the features of early mechanical failure signal and weak signal detection problems, are solved using the proposed HeNN method. HeNN approximate solutions have been compared with results obtained by the well known Runge-Kutta method. Computed results are depicted in term of graphs. After training the HeNN model, we may use it as a black box to get numerical results at any arbitrary point in the domain. Thus, the proposed HeNN method is efficient. The results reveal that this method is reliable and can be applied to other nonlinear problems too.

Van-der-Waals interaction of atoms in dipolar Rydberg states

NASA Astrophysics Data System (ADS)

Kamenski, Aleksandr A.; Mokhnenko, Sergey N.; Ovsiannikov, Vitaly D.

2018-02-01

An asymptotic expression for the van-der-Waals constant C 6( n) ≈ -0.03 n 12 K p ( x) is derived for the long-range interaction between two highly excited hydrogen atoms A and B in their extreme Stark states of equal principal quantum numbers n A = n B = n ≫ 1 and parabolic quantum numbers n 1(2) = n - 1, n 2(1) = m = 0 in the case of collinear orientation of the Stark-state dipolar electric moments and the interatomic axis. The cubic polynomial K 3( x) in powers of reciprocal values of the principal quantum number x = 1/ n and quadratic polynomial K 2( y) in powers of reciprocal values of the principal quantum number squared y = 1/ n 2 were determined on the basis of the standard curve fitting polynomial procedure from the calculated data for C 6( n). The transformation of attractive van-der-Waals force ( C 6 > 0) for low-energy states n < 23 into repulsive force ( C 6 < 0) for all higher-energy states of n ≥ 23, is observed from the results of numerical calculations based on the second-order perturbation theory for the operator of the long-range interaction between neutral atoms. This transformation is taken into account in the asymptotic formulas (in both cases of p = 2, 3) by polynomials K p tending to unity at n → ∞ ( K p (0) = 1). The transformation from low- n attractive van-der-Waals force into high- n repulsive force demonstrates the gradual increase of the negative contribution to C 6( n) from the lower-energy two-atomic states, of the A(B)-atom principal quantum numbers n'A(B) = n-Δ n (where Δ n = 1, 2, … is significantly smaller than n for the terms providing major contribution to the second-order series), which together with the states of n″B(A) = n+Δ n make the joint contribution proportional to n 12. So, the hydrogen-like manifold structure of the energy spectrum is responsible for the transformation of the power-11 asymptotic dependence C 6( n) ∝ n 11of the low-angular-momenta Rydberg states in many-electron atoms into the power-12 dependence C 6( n) ∝ n 12 for the dipolar states of the Rydberg manifold.

Water budget and flow attenuation in a small montane meadow in the Sierra Nevada, California

NASA Astrophysics Data System (ADS)

Mancuso, L. A.; Cornwell, K.

2011-12-01

The purpose of this study was to assess how montane meadows aid in flow attenuation and store groundwater. The Van Vleck meadow, a 73 acre relatively healthy montane meadow in the Sierra Nevada of northern California was chosen for this analysis due to its protected status (in the Eldorado National Forest) and drainage infrastructure (culverts managing flow into and out of the meadow). A water budget for the meadow was developed to understand the quantity and timing of water entering and leaving the meadow throughout the 2009-2010 water year. The water storage capacity was estimated from data collected from piezometers, seismic refraction surveys and weirs. Flow attenuation parameters were assessed by comparing water reservoir increases and decreases during specific precipitation events. Results suggest that the meadow does slow down surface water pass through. An imbalance of surface flow in versus surface flow out suggests that surplus inflow waters may be recharging deeper aquifer systems via bedrock fractures although additional work is necessary to confirm this connection.

Semiclassical propagation of Wigner functions.

PubMed

Dittrich, T; Gómez, E A; Pachón, L A

2010-06-07

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrodinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

Numerical method based on transfer function for eliminating water vapor noise from terahertz spectra.

PubMed

Huang, Y; Sun, P; Zhang, Z; Jin, C

2017-07-10

Water vapor noise in the air affects the accuracy of optical parameters extracted from terahertz (THz) time-domain spectroscopy. In this paper, a numerical method was proposed to eliminate water vapor noise from the THz spectra. According to the Van Vleck-Weisskopf function and the linear absorption spectrum of water molecules in the HITRAN database, we simulated the water vapor absorption spectrum and real refractive index spectrum with a particular line width. The continuum effect of water vapor molecules was also considered. Theoretical transfer function of a different humidity was constructed through the theoretical calculation of the water vapor absorption coefficient and the real refractive index. The THz signal of the Lacidipine sample containing water vapor background noise in the continuous frequency domain of 0.5-1.8 THz was denoised by use of the method. The results show that the optical parameters extracted from the denoised signal are closer to the optical parameters in the dry nitrogen environment.

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

The millimeter-wavelength sulfur dioxide absorption spectra measured under simulated Venus conditions

NASA Astrophysics Data System (ADS)

Bellotti, Amadeo; Steffes, Paul G.

2015-07-01

Over 130 laboratory measurements of the 2-4 mm wavelength opacity of sulfur dioxide in a carbon dioxide atmosphere under simulated conditions for the upper Venus troposphere (temperatures between 308 and 343 K and pressures between 0.03 and 2 bar) have been made. These measurements along with the centimeter wavelength measurements by Steffes et al. (Steffes, P.G. et al. [2015]. Icarus 245, 153-161) have been used to empirically assess existing formalisms for sulfur dioxide opacity in a carbon dioxide atmosphere (Fahd, A.K., Steffes, P.G. [1992]. Icarus 97(2), 200-210; Suleiman, S.H. et al. [1996]. J. Geophys. Res.: Planets 101(E2), 4623-4635). The Van Vleck and Weisskopf Model (VVW) used by Fahd and Steffes with the JPL rotational line catalog (Pickett, H. et al. [1998]. J. Quant. Spectrosc. Radiat. Transfer 60(5), 499-890) was found to fit 85.88% of all 500 measurements within the 2-sigma uncertainty. This work will improve the confidence in retrievals of the atmospheric abundance of sulfur dioxide from millimeter-wavelength observations of the Venus atmosphere.

Study of magnetism in Cr doped (Bi1-xSbx)2Te3

NASA Astrophysics Data System (ADS)

Richardella, Anthony; Kandala, Abhinav; Kempinger, Susan; Samarth, Nitin; Grutter, Alex; Borchers, Julie

2015-03-01

The quantum anomalous Hall (QAH) effect was first observed in Cr doped films of the topological insulator (TI) (Bi1-xSbx)2Te3. This ferromagnetic TI opens a gap at the Dirac point and, when the Fermi energy lies inside this gap, a quantized QAH conductance can be observed. The origin of ferromagnetism in this material is still not well understood with the mechanism typically attributed to either a high van-Vleck susceptibility or a carrier mediated RKKY like interaction. To elucidate this we have studied Cry(Bi1-xSbx)2-yTe3 thin films grown by MBE on SrTiO3 (STO) substrates using polarized neutron reflectivity (PNR) while in-situ backgating the film to change the position of the Fermi energy. The films are also characterized by XRD, AFM, TEM and low temperature transport measurements. PNR measurements provide a direct measure of the depth dependent magnetization of a sample. We use this to study how the magnetization changes as the Fermi energy is moved towards the Dirac point. Funded by DARPA and ARO-MURI.

Synthesis and characterization of the divalent samarium Zintl-phases SmMg 2Bi 2 and SmMg 2Sb 2

DOE PAGES

Ramirez, D.; Gallagher, A.; Baumbach, R.; ...

2015-08-29

Here, single crystals of LnMg 2Bi 2 (Ln = Yb, Eu, Sm) and SmMg 2Sb 2 were synthesized using Mg-Bi metal and Mg-Sb metal fluxes, respectively. The crystal structures are of the CaAl 2Si 2 type with space group P3 m1 (#164, Z = 1): SmMg 2Bi 2 ( a = 4.7745(1)Å, c = 7.8490(2)Å), EuMg 2Bi 2 ( a = 4.7702(1)Å, c = 7.8457(2) Å), YbMg 2Bi 2 ( a = 4.7317(2)Å, c = 7.6524(3) Å), and SmMg 2Sb 2 ( a = 4.6861(1) Å, c = 7.7192(2) Å). Heat capacity, electrical transport, and magnetization of all bismuth containingmore » phases were measured. The materials behave as “poor metals” with resistivity between 2 and 10 mΩ·cm. Temperature independent Van Vleck paramagnetism is observed in SmMg 2Bi 2 indicative of divalent samarium (Sm 2+) ions.« less

Quasi-degenerate perturbation theory using matrix product states

NASA Astrophysics Data System (ADS)

Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali

2016-01-01

In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner's 2n + 1 rule. Further, our formulation satisfies Granovsky's requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

Universality of magnetic-field-induced Bose-Einstein condensation of magnons

NASA Astrophysics Data System (ADS)

Shirasawa, Kazuki; Kurita, Nobuyuki; Tanaka, Hidekazu

2017-10-01

CsFeBr3 is an S =1 hexagonal antiferromagnet that has a singlet ground state owing to its large easy-plane single-ion anisotropy. The critical behavior of the magnetic-field-induced phase transition for a magnetic field parallel to the c axis, which can be described by the Bose-Einstein condensation (BEC) of magnons under the U (1 ) symmetry, was investigated via magnetization and specific heat measurements down to 0.1 K. For the specific heat measurement, we have developed a method of effectively suppressing the torque acting on a sample with strong anisotropy that uses the spin dimer compound Ba2CoSi2O6Cl2 with large and anisotropic Van Vleck paramagnetism. The temperature dependence of the transition field Hc(T ) was found to follow the power-law Hc(T ) -Hc∝Tϕ with a critical exponent of ϕ =1.50 ±0.02 and critical field of Hc=2.60 T . This result verifies the universality of the three-dimensional BEC of magnons described by ϕBEC=3 /2 .

Observation of superconductivity in BaNb2S5

NASA Astrophysics Data System (ADS)

Smith, M. G.; Neumeier, J. J.

2018-06-01

Bulk superconductivity is reported in BaNb2S5 at the transition temperature Tc = 0.85(1) K. The electrical resistivity ρ versus T is metallic with ρ(2 K) = 42.4 μΩ cm. The magnetic susceptibility is paramagnetic, with temperature-independent contributions due to diamagnetism, Pauli paramagnetism, and Van Vleck paramagnetism; a Curie-Weiss contribution appears to be impurity related. Hall effect measurements show that the majority charge carriers are electrons with charge-carrier concentration n(3 K) = 2.40(2) × 1021 cm-3. Specific heat measurements reveal an electronic specific heat coefficient γ = 11.2(1) mJ/mol K2, a Debye temperature ΘD = 126.4(8) K, and an energy gap associated with the superconducting state of Eg = 0.184(4) meV. Measurements of ρ(T) in magnetic field provide the upper critical magnetic field of about 3055(74) Oe as T → 0 K, which was used to estimate the coherence length ξ = 6.21(15) nm. The results allow classification of BaNb2S5 as a Type II, BCS superconductor in the dirty limit.

Magneto-optical Kerr effect in Cr-doped (Bi,Sb)2Te3 Thin Films

NASA Astrophysics Data System (ADS)

Pan, Yu; Yao, Bing; Richardella, Anthony; Kandala, Abhinav; Fraleigh, Robert; Lee, Joon Sue; Samarth, Nitin; Yeats, Andrew; Awschalom, David D.

2014-03-01

When a three-dimensional (3D) topological insulator (TI) is interfaced with magnetism, the breaking of time reversal symmetry results in new phenomena such as the recently observed quantum anomalous Hall effect [C.-Z. Zhang et al., Science340, 167 (2013)]. Thus motivated, we use the polar-mode magneto-optical Kerr effect (MOKE) to probe the temperature- and field-dependent magnetization in molecular beam epitaxy grown Cr-doped thin films of the 3D TI (Bi,Sb)2Te3. Square MOKE hysteresis loops observed at low temperatures indicate robust ferromagnetism with a perpendicular magnetic anisotropy and Curie temperature that varies from ~ 5 K to ~ 150 K, depending on sample details. A key question is the nature of the ferromagnetism: is it a carrier-mediated mechanism, Van Vleck mechanism or due to extrinsic clusters? We address this issue by varying the magnetic ion concentration and carrier density via sample composition as well as by varying the chemical potential by back gating. Finally, we use spatially-resolved MOKE to image the magnetization in these samples. Supported by ONR and DARPA.

Information entropy of Gegenbauer polynomials and Gaussian quadrature

NASA Astrophysics Data System (ADS)

Sánchez-Ruiz, Jorge

2003-05-01

In a recent paper (Buyarov V S, López-Artés P, Martínez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549-60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C(lambda)n(x) in the case when lambda = l in Bbb N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary polynomials, P(x) and H(x), of degrees 2l - 2 and 2l - 4, respectively. Here it is shown that P(x) is related to the coefficients of the Gaussian quadrature formula for the Gegenbauer weights wl(x) = (1 - x2)l-1/2, and this fact is used to obtain the explicit expression of P(x). From this result, an explicit formula is also given for the polynomial S(x) = limnrightarrowinfty P(1 - x/(2n2)), which is relevant to the study of the asymptotic (n rightarrow infty with l fixed) behaviour of the entropy.

Should We Stop Developing Heuristics and Only Rely on Mixed Integer Programming Solvers in Automated Test Assembly? A Rejoinder to van der Linden and Li (2016).

PubMed

Chen, Pei-Hua

2017-05-01

This rejoinder responds to the commentary by van der Linden and Li entiled "Comment on Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach" on the article "Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach" by Chen. Van der Linden and Li made a strong statement calling for the cessation of test assembly heuristics development, and instead encouraged embracing mixed integer programming (MIP). This article points out the nondeterministic polynomial (NP)-hard nature of MIP problems and how solutions found using heuristics could be useful in an MIP context. Although van der Linden and Li provided several practical examples of test assembly supporting their view, the examples ignore the cases in which a slight change of constraints or item pool data might mean it would not be possible to obtain solutions as quickly as before. The article illustrates the use of heuristic solutions to improve both the performance of MIP solvers and the quality of solutions. Additional responses to the commentary by van der Linden and Li are included.

Exploration of the Memory Effect on the Photon-Assisted Tunneling via a Single Quantum Dot:. a Generalized Floquet Theoretical Approach

NASA Astrophysics Data System (ADS)

Chen, Hsing-Ta; Ho, Tak-San; Chu, Shih-I.

The generalized Floquet approach is developed to study memory effect on electron transport phenomena through a periodically driven single quantum dot in an electrode-multi-level dot-electrode nanoscale quantum device. The memory effect is treated using a multi-function Lorentzian spectral density (LSD) model that mimics the spectral density of each electrode in terms of multiple Lorentzian functions. For the symmetric single-function LSD model involving a single-level dot, the underlying single-particle propagator is shown to be related to a 2×2 effective time-dependent Hamiltonian that includes both the periodic external field and the electrode memory effect. By invoking the generalized Van Vleck (GVV) nearly degenerate perturbation theory, an analytical Tien-Gordon-like expression is derived for arbitrary order multi-photon resonance d.c. tunneling current. Numerically converged simulations and the GVV analytical results are in good agreement, revealing the origin of multi-photon coherent destruction of tunneling and accounting for the suppression of the staircase jumps of d.c. current due to the memory effect. Specially, a novel blockade phenomenon is observed, showing distinctive oscillations in the field-induced current in the large bias voltage limit.

Quantum Chemistry in Great Britain: Developing a Mathematical Framework for Quantum Chemistry

NASA Astrophysics Data System (ADS)

Simões, Ana; Gavroglu, Kostas

By 1935 quantum chemistry was already delineated as a distinct sub-discipline due to the contributions of Fritz London, Walter Heitler, Friedrich Hund, Erich Hückel, Robert Mulliken, Linus Pauling, John van Vleck and John Slater. These people are credited with showing that the application of quantum mechanics to the solution of chemical problems was, indeed, possible, especially so after the introduction of a number of new concepts and the adoption of certain approximation methods. And though a number of chemists had started talking of the formation of theoretical or, even, mathematical chemistry, a fully developed mathematical framework of quantum chemistry was still wanting. The work of three persons in particular-of John E. Lennard-Jones, Douglas R. Hartree, and Charles Alfred Coulson-has been absolutely crucial in the development of such a framework. In this paper we shall discuss the work of these three researchers who started their careers in the Cambridge tradition of mathematical physics and who at some point of their careers all became professors of applied mathematics. We shall argue that their work consisted of decisive contributions to the development of such a mathematical framework for quantum chemistry.

Polynomial law for controlling the generation of n-scroll chaotic attractors in an optoelectronic delayed oscillator

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

Márquez, Bicky A., E-mail: bmarquez@ivic.gob.ve; Suárez-Vargas, José J., E-mail: jjsuarez@ivic.gob.ve; Ramírez, Javier A.

2014-09-01

Controlled transitions between a hierarchy of n-scroll attractors are investigated in a nonlinear optoelectronic oscillator. Using the system's feedback strength as a control parameter, it is shown experimentally the transition from Van der Pol-like attractors to 6-scroll, but in general, this scheme can produce an arbitrary number of scrolls. The complexity of every state is characterized by Lyapunov exponents and autocorrelation coefficients.

Laboratory evaluation and application of microwave absorption properties under simulated conditions for planetary atmospheres

NASA Technical Reports Server (NTRS)

Steffes, P. G.

1985-01-01

Radio absorptivity data for planetary atmospheres obtained from spacecraft radio occultation experiments and Earth-based radio astronomical observations can be used to infer abundances of microwave absorbing atmospheric constituents in those atmospheres, as long as reliable information regarding the microwave absorbing properties of potential constituents is available. The use of theoretically-derived microwave absorption properties for such atmospheric constituents, or laboratory measurements of such properties under environmental conditions which are significantly different than those of the planetary atmosphere being studied, often lead to significant misinterpretation of available opacity data. Steffes and Eshleman showed that under environmental conditions corresponding to the middle atmosphere of Venus, the microwave absorption due to atmospheric SO2 was 50 percent greater than that calculated from Van Vleck-Weiskopff theory. Similarly, the opacity from gaseous H2SO4 was found to be a factor of 7 greater than theoretically predicted for conditions of the Venus middle atmosphere. The recognition of the need to make such measurements over a range of temperatures and pressures which correspond to the periapsis altitudes of radio occultation experiments, and over a range of frequencies which correspond to both radio occultation experiments and radio astronomical observations, has led to the development of a facility at Georgia Tech which is capable of making such measurements.

A Pilot Study of the Kinematics of the Open Cluster IC 4756.

NASA Astrophysics Data System (ADS)

Upgren, A. R.; Lee, J. T.; Weis, E. W.

1998-12-01

In 1982 a working group of I.A.U. Commission 24 was established in order to provide parallax standard fields (IAU Transactions, XVIIIB,127 1982). Three of these fields for regular trigonometric parallax observation are centered on open clusters; the Pleiades, Praesepe and IC4756. Very few studies on IC4756 have been made; one is by Herzog and Sanders (AAPS, 19, 211 1975). The Van Vleck Observatory began normal parallax observations of IC4756 with its 0.5m astrometric refractor in 1980. A few observations were also obtained in 1963. Using Yale PDS machine, Lee has measured two of these early plates and two from 1997-98. The proper motion differences among the stars from different plate pair solutions are about 0.0008"/yr, and the mean proper motion of member stars is about 0.003"/yr, with respect to the mean motion of the field stars. The epoch difference of 34 years appears sufficient for accurate measures of the internal motion of the member stars. This cluster has also been observed with the 1.5m reflector of the U.S. Naval Observatory and the 0.65m McCormick Observatory refractor. These observations may also become available for the motion study.

Crystal growth and magnetic anisotropy in the spin-chain ruthenate Na2RuO4

NASA Astrophysics Data System (ADS)

Balodhi, Ashiwini; Singh, Yogesh

2018-02-01

We report single-crystal growth, electrical resistivity ρ , anisotropic magnetic susceptibility χ , and heat capacity Cp measurements on the one-dimensional spin-chain ruthenate Na2RuO4 . We observe variable range hopping (VRH) behavior in ρ (T ) . The magnetic susceptibility with magnetic field perpendicular (χ⊥) and parallel (χ∥) to the spin chains is reported. The magnetic properties are anisotropic with χ⊥>χ∥ in the temperature range of measurements T ≈2 -305 K with χ⊥/χ∥≈1.4 at 305 K. From an analysis of the χ (T ) data we attempt to estimate the anisotropy in the g factor and Van Vleck paramagnetic contribution. An anomaly in χ (T ) and a corresponding step-like anomaly in Cp at TN=37 K confirms long-range antiferromagnetic ordering. This temperature is an order of magnitude smaller than the Weiss temperature θ ≈-250 K and points to suppression of long-range magnetic order due to low dimensionality. A fit of the experimental χ (T ) by a one-dimensional spin-chain model gave an estimate of the intrachain exchange interaction 2 J ≈-85 K and the magnitude of the interchain coupling |2 J⊥|≈3 K.

On Characterization of Barium Rare-Earth Antimonates: Ordered Perovskites Suitable as Substrates for Superconducting Films

NASA Astrophysics Data System (ADS)

Alonso, J. A.; Cascales, C.; García Casado, P.; Rasines, I.

1997-02-01

The crystal structure of the ordered perovskites Ba2(RSb)O6(R=Y, Ho) is refined from neutron powder diffraction data in the space groupFmoverline3m(No. 225),Z=4, with Ba at 8(c),Rat 4(b), Sb at 4(a), oxygen at 24(e), oxygen positional parameterx=0.2636(2) forR=Y and Ho, and unit cell dimensions ofa/Å=8.4240(3) and 8.4170(2) forR=Y and Ho, respectively. Bond-valence analysis explains how the highly covalent Sb-O bonds determine the overall structure of these perovskites in whichR-O and Ba-O bonds are under compressive and tensile stresses, respectively. The magnetic susceptibility of Ba2(HoSb)O6has been measured in the temperature range 2-350 K. From ana prioriestimation of the crystal-field parameters corresponding to the point site symmetry of the rare-earth,Oh, and using the wave functions associated with the energy levels obtained, the paramagnetic susceptibility and its evolution vs temperature is simulated according to the van Vleck formalism. The observed deviation from the Curie-Weiss behavior at low temperature, very well reproduced, reflects the splitting of the ground state of this cation under the influence of the crystal field.

The multi-reference retaining the excitation degree perturbation theory: A size-consistent, unitary invariant, and rapidly convergent wavefunction based ab initio approach

NASA Astrophysics Data System (ADS)

Fink, Reinhold F.

2009-02-01

The retaining the excitation degree (RE) partitioning [R.F. Fink, Chem. Phys. Lett. 428 (2006) 461(20 September)] is reformulated and applied to multi-reference cases with complete active space (CAS) reference wave functions. The generalised van Vleck perturbation theory is employed to set up the perturbation equations. It is demonstrated that this leads to a consistent and well defined theory which fulfils all important criteria of a generally applicable ab initio method: The theory is proven numerically and analytically to be size-consistent and invariant with respect to unitary orbital transformations within the inactive, active and virtual orbital spaces. In contrast to most previously proposed multi-reference perturbation theories the necessary condition for a proper perturbation theory to fulfil the zeroth order perturbation equation is exactly satisfied with the RE partitioning itself without additional projectors on configurational spaces. The theory is applied to several excited states of the benchmark systems CH2 , SiH2 , and NH2 , as well as to the lowest states of the carbon, nitrogen and oxygen atoms. In all cases comparisons are made with full configuration interaction results. The multi-reference (MR)-RE method is shown to provide very rapidly converging perturbation series. Energy differences between states of similar configurations converge even faster.

Spin correlations and spin-wave excitations in Dirac-Weyl semimetals

NASA Astrophysics Data System (ADS)

Araki, Yasufumi; Nomura, Kentaro

We study correlations among magnetic dopants in three-dimensional Dirac and Weyl semimetals. Effective field theory for localized magnetic moments is derived by integrating out the itinerant electron degrees of freedom. We find that spin correlation in the spatial direction parallel to local magnetization is more rigid than that in the perpendicular direction, reflecting spin-momentum locking nature of the Dirac Hamiltonian. Such an anisotropy becomes stronger for Fermi level close to the Dirac points, due to Van Vleck paramagnetism triggered by spin-orbit coupling. One can expect topologically nontrivial spin textures under this anisotropy, such as a hedgehog around a single point, or a radial vortex around an axis, as well as a uniform ferromagnetic order. We further investigate the characteristics of spin waves in the ferromagnetic state. Spin-wave dispersion also shows a spatial anisotropy, which is less dispersed in the direction transverse to the magnetization than that in the longitudinal direction. The spin-wave dispersion anisotropy can be traced back to the rigidity and flexibility of spin correlations discussed above. This work was supported by Grant-in-Aid for Scientific Research (Grants No.15H05854, No.26107505, and No.26400308) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

Effective Hamiltonians for correlated narrow energy band systems and magnetic insulators: Role of spin-orbit interactions in metal-insulator transitions and magnetic phase transitions

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

Chakraborty, Subrata; Vijay, Amrendra, E-mail: avijay@iitm.ac.in

Using a second-quantized many-electron Hamiltonian, we obtain (a) an effective Hamiltonian suitable for materials whose electronic properties are governed by a set of strongly correlated bands in a narrow energy range and (b) an effective spin-only Hamiltonian for magnetic materials. The present Hamiltonians faithfully include phonon and spin-related interactions as well as the external fields to study the electromagnetic response properties of complex materials and they, in appropriate limits, reduce to the model Hamiltonians due to Hubbard and Heisenberg. With the Hamiltonian for narrow-band strongly correlated materials, we show that the spin-orbit interaction provides a mechanism for metal-insulator transition, whichmore » is distinct from the Mott-Hubbard (driven by the electron correlation) and the Anderson mechanism (driven by the disorder). Next, with the spin-only Hamiltonian, we demonstrate the spin-orbit interaction to be a reason for the existence of antiferromagnetic phase in materials which are characterized by a positive isotropic spin-exchange energy. This is distinct from the Néel-VanVleck-Anderson paradigm which posits a negative spin-exchange for the existence of antiferromagnetism. We also find that the Néel temperature increases as the absolute value of the spin-orbit coupling increases.« less

Texas Teacher at Sea on the BOLIVAR Project Geophysical Cruise

NASA Astrophysics Data System (ADS)

Keelan, M.; Sullivan, S.; Ellins, K.

2004-12-01

UTIG provides K-12 teachers with research experiences in field programs that involve UTIG scientists. I am a 6th-9th grade science teacher in Van Vleck, Texas and in April 2004 I sailed to the southeastern Caribbean aboard the R/V Maurice Ewing as a member of the BOLIVAR Project alongside scientists from the U.S. and Venezuela. Our goal was collect seismic data to image the crust and mantle beneath the Caribbean as part of a study of the tectonic processes accompanying different stages of the Caribbean arc/South America continental collision process. Throughout the 52-day cruise I worked as a watch stander, interpreted newly collected seismic reflection data, helped deploy the streamer, maintained a cruise blog (a chronological journal weblog documenting personal thoughts about my experience), spoke with students in Texas with the telephone on loan from Iridium Satellite Solutions, and responded to email inquiries from shore-based students. It was hard work, but most importantly, a voyage of discovery. With guidance from scientists and GK-12 Fellows at UTIG, I am using my experience and the data collected as the basis for K-12 curriculum resources, including learning activities and a video documentary. Support for my participation and post-cruise activities was provided by the NSF and the Trull Foundation in Texas. If given the opportunity to do this again, I would, without reservation!

Stepping Stone Mechanism: Carrier-Free Long-Range Magnetism Mediated by Magnetized Cation States in Quintuple Layer

NASA Astrophysics Data System (ADS)

Chan, Chunkai; Zhang, Xiaodong; Zhang, Yiou; Tse, Kinfai; Deng, Bei; Zhang, Jingzhao; Zhu, Junyi

2018-01-01

The long-range magnetism observed in group-V tellurides quintuple layers is the only working example of carrier-free dilute magnetic semiconductors (DMS), whereas the physical mechanism is unclear, except the speculation on the band topology enhanced van Vleck paramagnetism. Based on DFT calculations, we find a stable long-range ferromagnetic order in a single quintuple layer of Cr-doped Bi2Te3 or Sb2Te3, with the dopant separation more than 9 Å. This configuration is the global energy minimum among all configurations. Different from the conventional super exchange theory, the magnetism is facilitated by the lone pair derived anti-bonding states near the cations. Such anti-bonding states work as stepping stones merged in the electron sea and conduct magnetism. Further, spin orbit coupling induced band inversion is found to be insignificant in the magnetism. Therefore, our findings directly dismiss the common misbelief that band topology is the only factor that enhances the magnetism. We further demonstrate that removal of the lone pair derived states destroys the long-range magnetism. This novel mechanism sheds light on the fundamental understanding of long-range magnetism and may lead to discoveries of new classes of DMS. Supported by Chinese University of Hong Kong (CUHK) under Grant No 4053084, University Grants Committee of Hong Kong under Grant No 24300814, and the Start-up Funding of CUHK.

Magnetic-field-induced effects in the electronic structure of itinerant d- and f-metal systems

NASA Astrophysics Data System (ADS)

Grechnev, G. E.

2009-08-01

A paramagnetic response of transition metals and itinerant d- and f-metal compounds in an external magnetic field is studied by employing ab initio full-potential LMTO method in the framework of the local spin density approximation. Within this method the anisotropy of the magnetic susceptibility in hexagonal close-packed transition metals is evaluated for the first time. This anisotropy is owing to the orbital Van Vleck-like paramagnetic susceptibility, which is revealed to be substantial in transition-metal systems due to hybridization effects in the electronic structure. It is demonstrated that compounds TiCo, Ni3Al, YCo2, CeCo2, YNi5, LaNi5, and CeNi5 are strong paramagnets close to the quantum critical point. For these systems the Stoner approximation underestimates the spin susceptibility, whereas the calculated field-induced spin moments provide a good description of the large paramagnetic susceptibilities and magnetovolume effects. It is revealed that an itinerant description of hybridized f electrons produces magnetic properties of the compounds CeCo2, CeNi5, UAl3, UGa3, USi3, and UGe3 in close agreement with experiment. In the uranium compounds UX3 the strong spin-orbit coupling together with hybridization effects give rise to peculiar magnetic states in which the field-induced spin moments are antiparallel to the external field, and the magnetic response is dominated by the orbital contribution.

Theoretical Study of the IR Spectroscopy of BENZENE-(WATER)_N Clusters

NASA Astrophysics Data System (ADS)

Tabor, Daniel P.; Sibert, Edwin; Kusaka, Ryoji; Walsh, Patrick S.; Zwier, Timothy S.

2015-06-01

The local mode Hamiltonian that assigns RIDIR spectra for Bz-(H_2O)_6 and Bz-(H_2O)_7 is explored in detail for Bz-(H_2O)_n with n=3-7. In addition to contributions from OH stretches, the Hamiltonian includes the anharmonic coupling of each water monomer's bend overtone and its OH stretch fundamentals, which is necessary for accurately modeling 3150-3300 cm-1 region of the spectra. The parameters of the Hamiltonian can be calculated using either MP2 or density functional theory. The relative strengths and weaknesses of these two electronic structure approaches are examined to gain further physical understanding. Initial assignments of Bz-(H_2O)_6 and Bz-(H_2O)_7 were based on a linear scaling of M06-2X harmonic frequencies. In most cases, counterpoise-corrected MP2 calculations obtain similar frequencies (across all cluster sizes) if stretch anharmonicity is taken into account. Individual ``monomer Hamiltonians'' are constructed via the application of fourth order Van Vleck perturbation theory to MP2 potential energy surfaces. These calculations elucidate the sensitivity of intra-monomer couplings to chemical environment. The presence of benzene has particularly important consequences for the spectra of the Bz-(H_2O)3-5 clusters, in which the symmetry of the water cycles is broken by π-H-bonding to benzene. The nature of these perturbations is discussed.

Magnetic properties of rare-earth-doped La0.7Sr0.3MnO3.

PubMed

Veverka, Pavel; Kaman, Ondřej; Knížek, Karel; Novák, Pavel; Maryško, Miroslav; Jirák, Zdeněk

2017-01-25

Rare-earth-doped ferromagnetic manganites La 0.63 RE 0.07 Sr 0.30 MnO 3 (RE  =  Gd, Tb, Dy, and Ho) are synthesized in the form of sintered ceramics and nanocrystalline phases with the mean size of crystallites  ≈30 nm. The electronic states of the dopants are investigated by SQUID magnetometry and theoretically interpreted based on the calculations of the crystal field splitting of rare-earth energy levels. The samples show the orthorhombic perovskite structure of Ibmm symmetry, with a complete FM order of Mn spins in bulk and reduced order in nanoparticles. Non-zero moments are also detected at the perovskite A sites, which can be attributed to magnetic polarization of the rare-earth dopants. The measurements in external field up to 70 kOe show a standard Curie-type contribution of the spin-only moments of Gd 3+ ions, whereas Kramers ions Dy 3+ and non-Kramers ions Ho 3+ contribute by Ising moments due to their doublet ground states. The behaviour of non-Kramers ions Tb 3+ is anomalous, pointing to singlet ground state with giant Van Vleck paramagnetism. The Tb 3+ doping leads also to a notably increased coercivity compared to other La 0.63 RE 0.07 Sr 0.30 MnO 3 systems.

Improved Potential Energy Surface of Ozone Constructed Using the Fitting by Permutationally Invariant Polynomial Function

DOE PAGES

Ayouz, Mehdi; Babikov, Dmitri

2012-01-01

New global potential energy surface for the ground electronic state of ozone is constructed at the complete basis set level of the multireference configuration interaction theory. A method of fitting the data points by analytical permutationally invariant polynomial function is adopted. A small set of 500 points is preoptimized using the old surface of ozone. In this procedure the positions of points in the configuration space are chosen such that the RMS deviation of the fit is minimized. New ab initio calculations are carried out at these points and are used to build new surface. Additional points are added tomore » the vicinity of the minimum energy path in order to improve accuracy of the fit, particularly in the region where the surface of ozone exhibits a shallow van der Waals well. New surface can be used to study formation of ozone at thermal energies and its spectroscopy near the dissociation threshold.« less

Generalized closed form solutions for feasible dimension limit and pull-in characteristics of nanocantilever under the Influences of van der Waals and Casimir forces

NASA Astrophysics Data System (ADS)

Mukherjee, Banibrata; Sen, Siddhartha

2018-04-01

This paper presents generalized closed form expressions for determining the dimension limit for the basic design parameters as well as the pull-in characteristics of a nanocantilever beam under the influences of van der Waals and Casimir forces. The coupled nonlinear electromechanical problem of electrostatic nanocantilever is formulated in nondimensional form with Galerkin’s approximation considering the effects of these intermolecular forces and fringe field. The resulting integrals and higher order polynomials are solved numerically to derive the closed form expressions for maximum permissible detachment length, minimum feasible gap spacing and critical pull-in limit. The derived expressions are compared and validated as well with several reported literature showing reasonable agreement. The major advantages of the proposed closed form expressions are that, they do not contain any complex mathematical term or operation unlike in reported literature and thus they will serve as convenient tools for the NEMS community in successful design of various electrostatically actuated nanosystems.

Growth and magnetooptical properties of anisotropic TbF3 single crystals

NASA Astrophysics Data System (ADS)

Valiev, Uygun V.; Karimov, Denis N.; Burdick, Gary W.; Rakhimov, Rakhim; Pelenovich, Vasiliy O.; Fu, Dejun

2017-06-01

This paper investigates the Faraday effect and absorption and luminescence spectra of single-crystal TbF3 measured at 90 K and 300 K. The optical-quality single-phase TbF3 crystals (structural type β-YF3) were grown by the Bridgman technique. Faraday rotation angles were measured at remagnetization along the [100] crystallographic axis. Low temperature optical measurements were carried out along the [100] axis. "Quasi-doublet" sublevels with energy at 0 cm-1, 65 cm-1, and 190 cm-1, and also a singlet sublevel with energy at 114 cm-1 located in the ground 7F6 multiplet were determined from the low temperature luminescence spectra. The Van-Vleck behavior of the magnetic susceptibility χb can be satisfactorily explained by the magnetic mixing of wave functions belonging to the ground and first excited "quasi-doublet" sublevels at 0 and 65 cm-1, respectively. Analysis of the oscillation dependences of the rotation angle showed that the value of the natural birefringence (Δn ≈ 0.0186) remains nearly constant within the wavelength and temperature ranges under investigation. As the temperature decreases, we find significant increases in the oscillation amplitude of the rotation angle and in the Verdet constant V. The spectral dependences V(χ) are linear throughout the temperature range. The magnetooptical activity of TbF3 can be explained by means of the spin- and parity-allowed electric-dipole 4f → 5d transitions in the Tb3+ ions.

Local Moment Instability of Os in Honeycomb Li 2.15Os 0.85O 3

DOE PAGES

Wallace, M. K.; LaBarre, P. G.; Li, Jun; ...

2018-04-26

Compounds with honeycomb structures occupied by strong spin orbit coupled (SOC) moments are considered to be candidate Kitaev quantum spin liquids. Here we present the first example of Os on a honeycomb structure, Li 2.15(3)Os 0.85(3)O3 (C2/c, a = 5.09 Å, b = 8.81 Å, c = 9.83 Å, β = 99.3°). Neutron diffraction shows large site disorder in the honeycomb layer and X-ray absorption spectroscopy indicates a valence state of Os (4.7 ± 0.2), consistent with the nominal concentration. We observe a transport band gap of Δ = 243 ± 23 meV, a large van Vleck susceptibility, and anmore » effective moment of 0.85 μ B, much lower than expected from 70% Os(+5). No evidence of long range order is found above 0.10 K but a spin glass-like peak in ac-susceptibility is observed at 0.5 K. The specific heat displays an impurity spin contribution in addition to a power law ∝T (0.63±0.06). Applied density functional theory (DFT) leads to a reduced moment, suggesting incipient itineracy of the valence electrons, and finding evidence that Li over stoichiometry leads to Os(4+)–Os(5+) mixed valence. Lastly, this local picture is discussed in light of the site disorder and a possible underlying quantum spin liquid state.« less

Local Moment Instability of Os in Honeycomb Li 2.15Os 0.85O 3

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

Wallace, M. K.; LaBarre, P. G.; Li, Jun

Compounds with honeycomb structures occupied by strong spin orbit coupled (SOC) moments are considered to be candidate Kitaev quantum spin liquids. Here we present the first example of Os on a honeycomb structure, Li 2.15(3)Os 0.85(3)O3 (C2/c, a = 5.09 Å, b = 8.81 Å, c = 9.83 Å, β = 99.3°). Neutron diffraction shows large site disorder in the honeycomb layer and X-ray absorption spectroscopy indicates a valence state of Os (4.7 ± 0.2), consistent with the nominal concentration. We observe a transport band gap of Δ = 243 ± 23 meV, a large van Vleck susceptibility, and anmore » effective moment of 0.85 μ B, much lower than expected from 70% Os(+5). No evidence of long range order is found above 0.10 K but a spin glass-like peak in ac-susceptibility is observed at 0.5 K. The specific heat displays an impurity spin contribution in addition to a power law ∝T (0.63±0.06). Applied density functional theory (DFT) leads to a reduced moment, suggesting incipient itineracy of the valence electrons, and finding evidence that Li over stoichiometry leads to Os(4+)–Os(5+) mixed valence. Lastly, this local picture is discussed in light of the site disorder and a possible underlying quantum spin liquid state.« less

Use of density functional theory orbitals in the GVVPT2 variant of second-order multistate multireference perturbation theory.

PubMed

Hoffmann, Mark R; Helgaker, Trygve

2015-03-05

A new variation of the second-order generalized van Vleck perturbation theory (GVVPT2) for molecular electronic structure is suggested. In contrast to the established procedure, in which CASSCF or MCSCF orbitals are first obtained and subsequently used to define a many-electron model (or reference) space, the use of an orbital space obtained from the local density approximation (LDA) variant of density functional theory is considered. Through a final, noniterative diagonalization of an average Fock matrix within orbital subspaces, quasicanonical orbitals that are otherwise indistinguishable from quasicanonical orbitals obtained from a CASSCF or MCSCF calculation are obtained. Consequently, all advantages of the GVVPT2 method are retained, including use of macroconfigurations to define incomplete active spaces and rigorous avoidance of intruder states. The suggested variant is vetted on three well-known model problems: the symmetric stretching of the O-H bonds in water, the dissociation of N2, and the stretching of ground and excited states C2 to more than twice the equilibrium bond length of the ground state. It is observed that the LDA-based GVVPT2 calculations yield good results, of comparable quality to conventional CASSCF-based calculations. This is true even for the C2 model problem, in which the orbital space for each state was defined by the LDA orbitals. These results suggest that GVVPT2 can be applied to much larger problems than previously accessible.

Exponential stabilization of magnetoelastic waves in a Mindlin-Timoshenko plate by localized internal damping

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-08-01

This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.

Interfacial interactions between plastic particles in plastics flotation.

PubMed

Wang, Chong-qing; Wang, Hui; Gu, Guo-hua; Fu, Jian-gang; Lin, Qing-quan; Liu, You-nian

2015-12-01

Plastics flotation used for recycling of plastic wastes receives increasing attention for its industrial application. In order to study the mechanism of plastics flotation, the interfacial interactions between plastic particles in flotation system were investigated through calculation of Lifshitz-van der Waals (LW) function, Lewis acid-base (AB) Gibbs function, and the extended Derjaguin-Landau-Verwey-Overbeek potential energy profiles. The results showed that van der Waals force between plastic particles is attraction force in flotation system. The large hydrophobic attraction, caused by the AB Gibbs function, is the dominant interparticle force. Wetting agents present significant effects on the interfacial interactions between plastic particles. It is found that adsorption of wetting agents promotes dispersion of plastic particles and decreases the floatability. Pneumatic flotation may improve the recovery and purity of separated plastics through selective adsorption of wetting agents on plastic surface. The relationships between hydrophobic attraction and surface properties were also examined. It is revealed that there exists a three-order polynomial relationship between the AB Gibbs function and Lewis base component. Our finding provides some insights into mechanism of plastics flotation. Copyright © 2015 Elsevier Ltd. All rights reserved.

Generalization of the coherent-state path integrals and systematic derivation of semiclassical propagators

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

Koda, Shin-ichi; Takatsuka, Kazuo

The coherent path integral is generalized such that the identity operator represented in a complete (actually overcomplete) set of the coherent states with the ''time-variable'' exponents are inserted between two consecutive short-time propagators. Since such a complete set of any given exponent can constitute the identity operator, the exponent may be varied from time to time without loss of generality as long as it is set common to all the Gaussians. However, a finite truncation of the coherent state expansion should result in different values of the propagator depending on the choice of the exponents. Furthermore, approximation methodology to treatmore » with the exact propagator can also depend on this choice, and thereby many different semiclassical propagators may emerge from these combinations. Indeed, we show that the well-known semiclassical propagators such as those of Van Vleck, Herman-Kluk, Heller's thawed Gaussian, and many others can be derived in a systematic manner, which enables one to comprehend these semiclassical propagators from a unified point of view. We are particularly interested in our generalized form of the Herman-Kluk propagator, since the relative accuracy of this propagator has been well established by Kay, and since, nevertheless, its derivation was not necessarily clear. Thus our generalized Herman-Kluk propagator replaces the classical Hamiltonian with a Gaussian averaged quantum Hamiltonian, generating non-Newtonian trajectories. We perform a numerical test to assess the quality of such a family of generalized Herman-Kluk propagators and find that the original Herman-Kluk gives an accurate result. The reason why this has come about is also discussed.« less

Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators

NASA Astrophysics Data System (ADS)

Mikami, Takahiro; Kitamura, Sota; Yasuda, Kenji; Tsuji, Naoto; Oka, Takashi; Aoki, Hideo

2016-04-01

We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory, reproducing the quasienergies and eigenstates of the original Floquet Hamiltonian up to desired order in 1 /ω , with ω being the frequency of the drive. The advantage of the BW method is that it is not only efficient in deriving higher-order terms, but even enables us to write down the whole infinite series expansion, as compared to the van Vleck degenerate perturbation theory. The expansion is also free from a spurious dependence on the driving phase, which has been an obstacle in the Floquet-Magnus expansion. We apply the BW expansion to various models of noninteracting electrons driven by circularly polarized light. As the amplitude of the light is increased, the system undergoes a series of Floquet topological-to-topological phase transitions, whose phase boundary in the high-frequency regime is well explained by the BW expansion. As the frequency is lowered, the high-frequency expansion breaks down at some point due to band touching with nonzero-photon sectors, where we find numerically even more intricate and richer Floquet topological phases spring out. We have then analyzed, with the Floquet dynamical mean-field theory, the effects of electron-electron interaction and energy dissipation. We have specifically revealed that phase transitions from Floquet-topological to Mott insulators emerge, where the phase boundaries can again be captured with the high-frequency expansion.

Laboratory measurements of the W band (3.2 mm) properties of phosphine (PH3) and ammonia (NH3) under simulated conditions for the outer planets

NASA Astrophysics Data System (ADS)

Mohammed, Priscilla N.; Steffes, Paul G.

2004-07-01

A model, based on the Van Vleck-Weisskopf line shape, was developed for the centimeter-wavelength opacity of PH3, which provides an order of magnitude improvement over previous models [Hoffman et al., 2001]. New laboratory measurements indicate that the model is also accurate at 94 GHz (3.2 mm) under conditions for the outer planets. Measurements of the opacity and refractivity of PH3 in a hydrogen/helium (H2/He) atmosphere were conducted at 94 GHz (3.2 mm) at pressures of 0.5 and 2 bars and at temperatures of 293 K and 213 K. Additionally, new high-precision laboratory measurements of the opacity and refractivity of NH3 in an H2/He atmosphere were conducted at the same frequency at pressures from 0.5 to 2 bars and at temperatures of 204 K, 211 K, and 290 K. Results show that existing models, which predict NH3 opacity in an H2/He environment, understate the absorption due to the pressure broadened rotational lines. A new model is proposed for use at 94 GHz (3.2 mm) which uses a Ben-Reuven line shape [Ben-Reuven, 1966] for the inversion lines and a Kinetic line shape [Gross, 1955] for the rotational lines. Results of measurements of both PH3 and NH3 can be used to better interpret maps of Saturn's emission at this wavelength and can potentially be used to deduce spatial variations in the abundances of both gases in the atmosphere of Saturn.

A novel family of DG methods for diffusion problems

NASA Astrophysics Data System (ADS)

Johnson, Philip; Johnsen, Eric

2017-11-01

We describe and demonstrate a novel family of numerical schemes for handling elliptic/parabolic PDE behavior within the discontinuous Galerkin (DG) framework. Starting from the mixed-form approach commonly applied for handling diffusion (examples include Local DG and BR2), the new schemes apply the Recovery concept of Van Leer to handle cell interface terms. By applying recovery within the mixed-form approach, we have designed multiple schemes that show better accuracy than other mixed-form approaches while being more flexible and easier to implement than the Recovery DG schemes of Van Leer. While typical mixed-form approaches converge at rate 2p in the cell-average or functional error norms (where p is the order of the solution polynomial), many of our approaches achieve order 2p +2 convergence. In this talk, we will describe multiple schemes, including both compact and non-compact implementations; the compact approaches use only interface-connected neighbors to form the residual for each element, while the non-compact approaches add one extra layer to the stencil. In addition to testing the schemes on purely parabolic PDE problems, we apply them to handle the diffusive flux terms in advection-diffusion systems, such as the compressible Navier-Stokes equations.

The Time-Domain Matched Filter and the Spectral-Domain Matched Filter in 1-Dimensional NMR Spectroscopy.

PubMed

Spencer, Richard G

2010-09-01

A type of "matched filter" (MF), used extensively in the processing of one-dimensional spectra, is defined by multiplication of a free-induction decay (FID) by a decaying exponential with the same time constant as that of the FID. This maximizes, in a sense to be defined, the signal-to-noise ratio (SNR) in the spectrum obtained after Fourier transformation. However, a different entity known also as the matched filter was introduced by van Vleck in the context of pulse detection in the 1940's and has become widely integrated into signal processing practice. These two types of matched filters appear to be quite distinct. In the NMR case, the "filter", that is, the exponential multiplication, is defined by the characteristics of, and applied to, a time domain signal in order to achieve improved SNR in the spectral domain. In signal processing, the filter is defined by the characteristics of a signal in the spectral domain, and applied in order to improve the SNR in the temporal (pulse) domain. We reconcile these two distinct implementations of the matched filter, demonstrating that the NMR "matched filter" is a special case of the matched filter more rigorously defined in the signal processing literature. In addition, two limitations in the use of the MF are highlighted. First, application of the MF distorts resonance ratios as defined by amplitudes, although not as defined by areas. Second, the MF maximizes SNR with respect to resonance amplitude, while intensities are often more appropriately defined by areas. Maximizing the SNR with respect to area requires a somewhat different approach to matched filtering.

Low temperature synthesis of LnOF rare-earth oxyfluorides through reaction of the oxides with PTFE

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

Dutton, S.E., E-mail: sdutton@princeton.edu; Hirai, D.; Cava, R.J.

2012-03-15

Highlights: Black-Right-Pointing-Pointer Low temperature synthesis of LnOF rare-earth oxyfluorides from Ln{sub 2}O{sub 3} and PTFE (CF{sub 2}). Black-Right-Pointing-Pointer Rhombohedral LnOF is the major phase and forms as nanocrystals, 29-103 nm. Black-Right-Pointing-Pointer Expected lanthanide contraction observed in lattice parameters and bond lengths. Black-Right-Pointing-Pointer TbOF orders antiferromagnetically at 10 K and has a metamagnetic transition at 1.8 T. Black-Right-Pointing-Pointer GdOF orders antiferromagnetically at 5 K, other LnOF are paramagnetic. -- Abstract: A low temperature solid-state synthesis route, employing polytetrafluoroethylene (PTFE) and the rare-earth oxides, for the formation of the LnOF rare-earth oxyfluorides (Ln = Y, La, Pr, Nd, Sm, Eu, Gd, Tb,more » Dy, Ho, Er), is reported. With the exception of LaOF, which forms in a tetragonal variant, rhomobohedral LnOF is found to be the major product of the reaction. In the case of PrOF, a transition from the rhombohedral to the cubic fluorite phase is observed on heating in air to 500 Degree-Sign C. X-ray diffraction shows the expected lanthanide contraction in the lattice parameters and bond lengths. Magnetic susceptibility measurements show antiferromagnetic-like ordering in TbOF, T{sub m} = 10 K, with a metamagnetic transition at a field {mu}{sub 0}H{sub t} = 1.8 T at 2 K. An antiferromagnetic transition, T{sub N} = 4 K, is observed in GdOF. Paramagnetic behavior is observed above 2 K in PrOF, NdOF, DyOF, HoOF and ErOF. The magnetic susceptibility of EuOF is characteristic of Van Vleck paramagnetism.« less

Structural and Magnetic Properties of {Eu}(3+) Eu 3 + -Doped {CdNb}_{2} {O}_{6} CdNb 2 O 6 Powders

NASA Astrophysics Data System (ADS)

Topkaya, Ramazan; Boyraz, Cihat; Ekmekçi, Mete Kaan

2018-03-01

Europium-doped CdNb2O6 powders with the molar concentration of Eu^{3+} (0.5, 3 and 6 mol%) were successfully prepared at 900°C by using molten salt synthesis method. The effect of europium (Eu) molar concentration on the structural and temperature-dependent magnetic properties of CdNb2O6 powders has been investigated by using X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), vibrating sample magnetometer (VSM) and ferromagnetic resonance (FMR) techniques in the temperature range of 10-300 K. XRD results confirm that all the powders have orthorhombic crystal structure. It has been confirmed from VSM and FMR measurements that Eu^{3+}-doped CdNb2O6 powders have ferromagnetic behaviour for each Eu^{3+} molar concentration between 10 and 300 K. XRD and EDX analyses indicate that there is no magnetic impurity in Eu^{3+}-doped CdNb_2O_6 powders, supporting that the ferromagnetic behaviour of the powders arises from Eu^{3+} ions. The observed ferromagnetism was elucidated with the intrinsic exchange interactions between the magnetic moments associated with the unpaired 4 f electrons in Eu^{3+} ions. The saturation magnetization decreases with increasing Eu^{3+} molar concentration. The temperature-dependent magnetization behaviour was observed not to agree with Curie-Weiss law because europium obeys Van Vleck paramagnetism. Broad FMR spectra and a g-value higher than 2 were observed from FMR measurements, indicating the ferromagnetic behaviour of the powders. It was found that while the resonance field of FMR spectra decreases, the linewidth increases as a function of Eu^{3+} molar concentration.

Polyad quantum numbers and multiple resonances in anharmonic vibrational studies of polyatomic molecules

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

Krasnoshchekov, Sergey V.; Stepanov, Nikolay F.

2013-11-14

In the theory of anharmonic vibrations of a polyatomic molecule, mixing the zero-order vibrational states due to cubic, quartic and higher-order terms in the potential energy expansion leads to the appearance of more-or-less isolated blocks of states (also called polyads), connected through multiple resonances. Such polyads of states can be characterized by a common secondary integer quantum number. This polyad quantum number is defined as a linear combination of the zero-order vibrational quantum numbers, attributed to normal modes, multiplied by non-negative integer polyad coefficients, which are subject to definition for any particular molecule. According to Kellman's method [J. Chem. Phys.more » 93, 6630 (1990)], the corresponding formalism can be conveniently described using vector algebra. In the present work, a systematic consideration of polyad quantum numbers is given in the framework of the canonical Van Vleck perturbation theory (CVPT) and its numerical-analytic operator implementation for reducing the Hamiltonian to the quasi-diagonal form, earlier developed by the authors. It is shown that CVPT provides a convenient method for the systematic identification of essential resonances and the definition of a polyad quantum number. The method presented is generally suitable for molecules of significant size and complexity, as illustrated by several examples of molecules up to six atoms. The polyad quantum number technique is very useful for assembling comprehensive basis sets for the matrix representation of the Hamiltonian after removal of all non-resonance terms by CVPT. In addition, the classification of anharmonic energy levels according to their polyad quantum numbers provides an additional means for the interpretation of observed vibrational spectra.« less

Deformed Calogero-Sutherland model and fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

Atai, Farrokh; Langmann, Edwin

2017-01-01

The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.

VizieR Online Data Catalog: NIBLES. I. The Nancay HI survey (van Driel+, 2016)

NASA Astrophysics Data System (ADS)

van Driel, M.; Butcher, Z.; Schneider, S.; Lehnert, M.; Minchin, R.; Blyth, S.-L.; Chemin, L.; Hallet, N.; Joseph, T.; Kotze, P.; Kraan-Korteweg, R. C.; Olofsson, H.; Ramatsoku, M.

2016-11-01

HI 21cm line spectra of the 1870 clearly or marginally detected SDSS sources obtained for NIBLES at the Nancay Radio Telescope. Please note that these include the six detections with velocities below the 900 km/s lower limit for the NIBLES statistical sample, which are listed in Table A.5 (NIBLES sources 0347, 1572, 1734, 1897, 2259, and 2326). See Sect. 3 of the paper for further details on data acquisition and reduction. Data have been smoothed in velocity to 18 km/s resolution (see exact number in the spectrum headers). A fitted polynomial baseline was substracted from the observed spectra. Velocities (first column) are heliocentric in the optical convention in units of km/s and flux densities (second column) are in Janskys. (4 data files).

Supersymmetric Dirac Born Infeld action with self-dual mass term

NASA Astrophysics Data System (ADS)

Nishino, Hitoshi; Rajpoot, Subhash; Reed, Kevin

2005-05-01

We introduce a Dirac Born Infeld action to a self-dual N = 1 supersymmetric vector multiplet in three dimensions. This action is based on the supersymmetric generalized self-duality in odd dimensions developed originally by Townsend, Pilch and van Nieuwenhuizen. Even though such a self-duality had been supposed to be very difficult to generalize to a supersymmetrically interacting system, we show that the Dirac Born Infeld action is actually compatible with supersymmetry and self-duality in three dimensions, even though the original self-duality receives corrections by the Dirac Born Infeld action. The interactions can be further generalized to arbitrary (non)polynomial interactions. As a by-product, we also show that a third-rank field strength leads to a more natural formulation of self-duality in 3D. We also show an interesting role played by the third-rank field strength leading to supersymmetry breaking, in addition to accommodating a Chern Simons form.

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.

The challenges and frustrations of a veteran astronomical optician: Robert Lundin, 1880-1962

NASA Astrophysics Data System (ADS)

Briggs, John W.; Osterbrock, Donald E.

1998-12-01

Robert Lundin, apprenticed in nineteenth century optical craftsmanship but employed in twenty century fabrication and engineering, suffered many frustrations during a nonetheless productive career. Son of Carl A.R. Lundin, a senior optician at the famous American firm of Alvan Clark & Sons, Robert grew up building telescopes. As a teenager, he assisted with projects including the 1-m [40-inch] objective for Yerkes Observatory. After his father's death in 1915, he became manager of the Clark Corporation and was responsible for many smaller, successful refractors and reflectors. Lundin also completed major projects, including a highly praised 50.8-cm achromat for Van Vleck Observatory, as well as a successful 33-cm astrograph used at Lowell to discover Pluto. In 1929, a dispute with the owners of the Clark Corporation led to Lundin's resignation and his creation of a new business, "C.A. Robert Lundin and Associates." This short-lived firm built several observatory refractors, including a 26.7 cm for E.W. Rice, the retired chairman of General Electric. But none was entirely successful, and the Great Depression finished off the company. In 1933, Lundin took a job as head of Warner & Swasey's new optical shop, only to experience his greatest disasters. The 2.08-m [82-inch] reflector for McDonald Observatory was delayed for years until astronomers uncovered an error in Lundin's procedure for testing the primary mirror. A 38.1-cm photographic lens for the Naval Observatory was a complete failure. Under pressure to complete a 61-cm Schmidt camera, Lundin seems to have attempted to deceive visiting astronomers. After retirement in the mid 1940s, Lundin moved to Austin, Texas, the home of his daughter, where he died. His difficulties should not obscure his success with many instruments that continue to serve as important research and education tools.

Magnetic properties of the layered III-VI diluted magnetic semiconductor Ga{sub 1−x}Fe{sub x}Te

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

Pekarek, T. M.; Edwards, P. S.; Olejniczak, T. L.

2016-05-15

Magnetic properties of single crystalline Ga{sub 1−x}Fe{sub x}Te (x = 0.05) have been measured. GaTe and related layered III-VI semiconductors exhibit a rich collection of important properties for THz generation and detection. The magnetization versus field for an x = 0.05 sample deviates from the linear response seen previously in Ga{sub 1−x}Mn{sub x}Se and Ga{sub 1−x}Mn{sub x}S and reaches a maximum of 0.68 emu/g at 2 K in 7 T. The magnetization of Ga{sub 1−x}Fe{sub x}Te saturates rapidly even at room temperature where the magnetization reaches 50% of saturation in a field of only 0.2 T. In 0.1 T atmore » temperatures between 50 and 400 K, the magnetization drops to a roughly constant 0.22 emu/g. In 0 T, the magnetization drops to zero with no hysteresis present. The data is consistent with Van-Vleck paramagnetism combined with a pronounced crystalline anisotropy, which is similar to that observed for Ga{sub 1−x}Fe{sub x}Se. Neither the broad thermal hysteresis observed from 100-300 K in In{sub 1−x}Mn{sub x}Se nor the spin-glass behavior observed around 10.9 K in Ga{sub 1−x}Mn{sub x}S are observed in Ga{sub 1−x}Fe{sub x}Te. Single crystal x-ray diffraction data yield a rhombohedral space group bearing hexagonal axes, namely R3c. The unit cell dimensions were a = 5.01 Å, b = 5.01 Å, and c = 17.02 Å, with α = 90°, β = 90°, and γ = 120° giving a unit cell volume of 369 Å{sup 3}.« less

{beta}-K{sub 4}La{sub 6}I{sub 14}Os: A new structure type for rare-earth-metal cluster compounds that contains discrete tetrahedral K{sub 4}I{sup 3+} units

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

Uma, S.; Corbett, J.D.

1999-08-23

Suitable reactions of KI, La, LaI{sub 3}, and Os in niobium tubes at 800--850 C result in black, air- and moisture-sensitive crystals of the quaternary title phase. Isostructural K{sub 4}Pr{sub 6}I{sub 14}Z also exist for Z = Fe, Ru. The title phase was characterized by single-crystal X-ray diffraction (tetragonal, P4/ncc (No. 130), Z = 4; a = 13.117(3), c = 25.17(1) {angstrom} at 23 C). The important structural feature is the constitution (K{sub 4}I){sup 3+}(La{sub 6}I{sub 13}Os{sup 3{minus}}) with a new type of 3D anion network of [(La{sub 6}Os)I{sub 8}{sup i}I{sub 4/2}{sup i{minus}a}I{sub 4/2}{sup a{minus}i}I{sub 2/2}{sup a{minus}a}] clusters that aremore » connected into puckered layers through I{sup i{minus}a} and I{sup a{minus}i} atom pairs that bridge diagonally in the a-b plane. These cluster layers are further interlinked along {rvec c} at trans-vertexes through simple bridging I{sup a{minus}a}. The 14th iodine atom occurs in the unique K{sub 4}I{sup 3+} ions which lie in columns that interpenetrate the La{sub 6}OsI{sub 13} network along c. The present 16-e{sup {minus}} clusters, in contrast with the optimal 18-e{sup {minus}} octahedral cluster configuration, exhibit an uncommon tetragonal elongation and evidently become closed shell, with only a small temperature-independent (van Vleck-like) paramagnetism, {approximately}4 x 10{sup {minus}4} emu mol{sup {minus}1}.« less

Comparing the accuracy of perturbative and variational calculations for predicting fundamental vibrational frequencies of dihalomethanes

NASA Astrophysics Data System (ADS)

Krasnoshchekov, Sergey V.; Schutski, Roman S.; Craig, Norman C.; Sibaev, Marat; Crittenden, Deborah L.

2018-02-01

Three dihalogenated methane derivatives (CH2F2, CH2FCl, and CH2Cl2) were used as model systems to compare and assess the accuracy of two different approaches for predicting observed fundamental frequencies: canonical operator Van Vleck vibrational perturbation theory (CVPT) and vibrational configuration interaction (VCI). For convenience and consistency, both methods employ the Watson Hamiltonian in rectilinear normal coordinates, expanding the potential energy surface (PES) as a Taylor series about equilibrium and constructing the wavefunction from a harmonic oscillator product basis. At the highest levels of theory considered here, fourth-order CVPT and VCI in a harmonic oscillator basis with up to 10 quanta of vibrational excitation in conjunction with a 4-mode representation sextic force field (SFF-4MR) computed at MP2/cc-pVTZ with replacement CCSD(T)/aug-cc-pVQZ harmonic force constants, the agreement between computed fundamentals is closer to 0.3 cm-1 on average, with a maximum difference of 1.7 cm-1. The major remaining accuracy-limiting factors are the accuracy of the underlying electronic structure model, followed by the incompleteness of the PES expansion. Nonetheless, computed and experimental fundamentals agree to within 5 cm-1, with an average difference of 2 cm-1, confirming the utility and accuracy of both theoretical models. One exception to this rule is the formally IR-inactive but weakly allowed through Coriolis-coupling H-C-H out-of-plane twisting mode of dichloromethane, whose spectrum we therefore revisit and reassign. We also investigate convergence with respect to order of CVPT, VCI excitation level, and order of PES expansion, concluding that premature truncation substantially decreases accuracy, although VCI(6)/SFF-4MR results are still of acceptable accuracy, and some error cancellation is observed with CVPT2 using a quartic force field.

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.

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,

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.

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.

Optimal bounds and extremal trajectories for time averages in dynamical systems

NASA Astrophysics Data System (ADS)

Tobasco, Ian; Goluskin, David; Doering, Charles

2017-11-01

For systems governed by differential equations it is natural to seek extremal solution trajectories, maximizing or minimizing the long-time average of a given quantity of interest. A priori bounds on optima can be proved by constructing auxiliary functions satisfying certain point-wise inequalities, the verification of which does not require solving the underlying equations. We prove that for any bounded autonomous ODE, the problems of finding extremal trajectories on the one hand and optimal auxiliary functions on the other are strongly dual in the sense of convex duality. As a result, auxiliary functions provide arbitrarily sharp bounds on optimal time averages. Furthermore, nearly optimal auxiliary functions provide volumes in phase space where maximal and nearly maximal trajectories must lie. For polynomial systems, such functions can be constructed by semidefinite programming. We illustrate these ideas using the Lorenz system, producing explicit volumes in phase space where extremal trajectories are guaranteed to reside. Supported by NSF Award DMS-1515161, Van Loo Postdoctoral Fellowships, and the John Simon Guggenheim Foundation.

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

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.

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.

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

The statistics of relativistic electron pitch angle distribution in the Earth's radiation belt based on the Van Allen Probes measurements

NASA Astrophysics Data System (ADS)

Zhao, H.; Freidel, R. H. W.; Chen, Y.; Henderson, M. G.; Kanekal, S. G.; Baker, D. N.; Spence, H. E.; Reeves, G. D.

2015-12-01

The relativistic electron pitch angle distribution (PAD) is an important characteristic of radiation belt electrons, which can give information on source or loss processes in a specific region. Using data from MagEIS and REPT instruments onboard the Van Allen Probes, a statistical survey of relativistic electron pitch angle distribution (PAD) is performed. By fitting relativistic electron PADs to Legendre polynomials, an empirical model of PADs as a function of L (from 1.4 to 6), MLT, electron energy (~100 keV - 5 MeV), and geomagnetic activity is developed and many intriguing features are found. In the outer radiation belt, an unexpected dawn/dusk asymmetry of ultra-relativistic electrons is found during quiet times, with the asymmetry becoming stronger at higher energies and at higher L shells. This may indicate the existence of physical processes acting on the relativistic electrons on the order of drift period, or be a signature of the partial ring current. In the inner belt and slot region, 100s of keV pitch angle distributions with minima at 90° are shown to be persistent in the inner belt and appears in the slot region during storm times. The model also shows clear energy dependence and L shell dependence of 90°-minimum pitch angle distribution. On the other hand, the head-and-shoulder pitch angle distributions are found during quiet times in the slot region, and the energy, L shell and geomagnetic activity dependence of those PADs are consistent with the wave-particle interaction caused by hiss waves.

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.

Independence polynomial and matching polynomial of the Koch network

NASA Astrophysics Data System (ADS)

Liao, Yunhua; Xie, Xiaoliang

2015-11-01

The lattice gas model and the monomer-dimer model are two classical models in statistical mechanics. It is well known that the partition functions of these two models are associated with the independence polynomial and the matching polynomial in graph theory, respectively. Both polynomials have been shown to belong to the “#P-complete” class, which indicate the problems are computationally “intractable”. We consider these two polynomials of the Koch networks which are scale-free with small-world effects. Explicit recurrences are derived, and explicit formulae are presented for the number of independent sets of a certain type.

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

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

NASA Astrophysics Data System (ADS)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

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.

Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Malik, Pradeep; Swaminathan, A.

2010-11-01

In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

Relativistic GVVPT2 multireference perturbation theory description of the electronic states of Y2 and Tc2.

PubMed

Tamukong, Patrick K; Hoffmann, Mark R; Li, Zhendong; Liu, Wenjian

2014-02-27

The multireference generalized Van Vleck second-order perturbation theory (GVVPT2) method is used to describe full potential energy curves (PECs) of low-lying states of second-row transition metal dimers Y(2) and Tc(2), with scalar relativity included via the spin-free exact two-component (sf-X2C) Hamiltonian. Chemically motivated incomplete model spaces, of the style previously shown to describe complicated first-row transition metal diatoms well, were used and again shown to be effective. The studied states include the previously uncharacterized 2(1)Σ(g)(+) and 3(1)Σ(g)(+) PECs of Y(2). These states, together with 1(1)Σ(g)(+), are relevant to discussion of controversial results in the literature that suggest dissociation asymptotes that violate the noncrossing rule. The ground state of Y(2) was found to be X(5)Σ(u)(–) (similar to Sc(2)) with bond length R(e) = 2.80 Å, binding energy D(e) = 3.12 eV, and harmonic frequency ω(e) = 287.2 cm(–1), whereas the lowest 1(1)(g)(+) state of Y(2) was found to lie 0.67 eV above the quintet ground state and had spectroscopic constants R(e) = 3.21 Å, D(e) = 0.91 eV, and ω(e) = 140.0 cm(–1). Calculations performed on Tc(2) include study of the previously uncharacterized relatively low-lying 1(5)Σ(g)(+) and 1(9)Σ(g)(+) states (i.e., 0.70 and 1.84 eV above 1(1)Σ(g)(+), respectively). The ground state of Tc(2) was found to be X(3)Σ(g)(–) with R(e) = 2.13 Å, D(e) = 3.50 eV, and ω(e) = 336.6 cm(–1) (for the most stable isotope, Tc-98) whereas the lowest (1)Σ(g)(+) state, generally accepted to be the ground state symmetry for isovalent Mn(2) and Re(2), was found to lie 0.47 eV above the X(3)Σ(g)(–) state of Tc(2). The results broaden the range of demonstrated applicability of the GVVPT2 method.

Laguerre-Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two

NASA Astrophysics Data System (ADS)

Hounga, C.; Hounkonnou, M. N.; Ronveaux, A.

2006-10-01

In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.

The Gibbs Phenomenon for Series of Orthogonal Polynomials

ERIC Educational Resources Information Center

Fay, T. H.; Kloppers, P. Hendrik

2006-01-01

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

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.

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

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.

Optimal Chebyshev polynomials on ellipses in the complex plane

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland

1989-01-01

The design of iterative schemes for sparse matrix computations often leads to constrained polynomial approximation problems on sets in the complex plane. For the case of ellipses, we introduce a new class of complex polynomials which are in general very good approximations to the best polynomials and even optimal in most cases.

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.

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.

An Empirical Model of Radiation Belt Electron Pitch Angle Distributions Based On Van Allen Probes Measurements

NASA Astrophysics Data System (ADS)

Zhao, H.; Friedel, R. H. W.; Chen, Y.; Reeves, G. D.; Baker, D. N.; Li, X.; Jaynes, A. N.; Kanekal, S. G.; Claudepierre, S. G.; Fennell, J. F.; Blake, J. B.; Spence, H. E.

2018-05-01

Based on over 4 years of Van Allen Probes measurements, an empirical model of radiation belt electron equatorial pitch angle distribution (PAD) is constructed. The model, developed by fitting electron PADs with Legendre polynomials, provides the statistical PADs as a function of L-shell (L = 1-6), magnetic local time, electron energy ( 30 keV to 5.2 MeV), and geomagnetic activity (represented by the Dst index) and is also the first empirical PAD model in the inner belt and slot region. For megaelectron volt electrons, model results show more significant day-night PAD asymmetry of electrons with higher energies and during disturbed times, which is caused by geomagnetic field configuration and flux radial gradient changes. Steeper PADs with higher fluxes around 90° pitch angle and lower fluxes at lower pitch angles for higher-energy electrons and during active times are also present, which could be due to electromagnetic ion cyclotron wave scattering. For hundreds of kiloelectron volt electrons, cap PADs are generally present in the slot region during quiet times and their energy-dependent features are consistent with hiss wave scattering, while during active times, cap PADs are less significant especially at outer part of slot region, which could be due to the complex energizing and transport processes. The 90°-minimum PADs are persistently present in the inner belt and appear in the slot region during active times, and minima at 90° pitch angle are more significant for electrons with higher energies, which could be a critical evidence in identifying the underlying physical processes responsible for the formation of 90°-minimum PADs.

The 129Xe nuclear shielding surfaces for Xe interacting with linear molecules CO2, N2, and CO

NASA Astrophysics Data System (ADS)

de Dios, Angel C.; Jameson, Cynthia J.

1997-09-01

We have calculated the intermolecular nuclear magnetic shielding surfaces for 129Xe in the systems Xe-CO2, Xe-N2, and Xe-CO using a gauge-invariant ab initio method at the coupled Hartree-Fock level with gauge-including atomic orbitals (GIAO). Implementation of a large basis set (240 basis functions) on the Xe gives very small counterpoise corrections which indicates that the basis set superposition errors in the calculated shielding values are negligible. These are the first intermolecular shielding surfaces for Xe-molecule systems. The surfaces are highly anisotropic and can be described adequately by a sum of inverse even powers of the distance with explicit angle dependence in the coefficients expressed by Legendre polynomials P2n(cos θ), n=0-3, for Xe-CO2 and Xe-N2. The Xe-CO shielding surface is well described by a similar functional form, except that Pn(cos θ), n=0-4 were used. When averaged over the anisotropic potential function these shielding surfaces provide the second virial coefficient of the nuclear magnetic resonance (NMR) chemical shift observed in gas mixtures. The energies from the self-consistent field (SCF) calculations were used to construct potential surfaces, using a damped dispersion form. These potential functions are compared with existing potentials in their predictions of the second virial coefficients of NMR shielding, the pressure virial coefficients, the density coefficient of the mean-square torque from infrared absorption, and the rotational constants and other average properties of the van der Waals complexes. Average properties of the van der Waals complexes were obtained by quantum diffusion Monte Carlo solutions of the vibrational motion using the various potentials and compared with experiment.

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.

Comparison of thermal signatures of a mine buried in mineral and organic soils

NASA Astrophysics Data System (ADS)

Lamorski, K.; Pregowski, Piotr; Swiderski, Waldemar; Usowicz, B.; Walczak, R. T.

2001-10-01

Values of thermal signature of a mine buried in soils, which ave different properties, were compared using mathematical- statistical modeling. There was applied a model of transport phenomena in the soil, which takes into consideration water and energy transfer. The energy transport is described using Fourier's equation. Liquid phase transport of water is calculated using Richard's model of water flow in porous medium. For the comparison, there were selected two soils: mineral and organic, which differs significantly in thermal and hydrological properties. The heat capacity of soil was estimated using de Vries model. The thermal conductivity was calculated using a statistical model, which incorprates fundamental soil physical properties. The model of soil thermal conductivity was built on the base of heat resistance, two Kirchhoff's laws and polynomial distribution. Soil hydrological properties were described using Mualem-van Genuchten model. The impact of thermal properties of the medium in which a mien had been placed on its thermal signature in the conditions of heat input was presented. The dependence was stated between observed thermal signature of a mine and thermal parameters of the medium.

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…

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

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.

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.

Approximating smooth functions using algebraic-trigonometric polynomials

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

Sharapudinov, Idris I

2011-01-14

The problem under consideration is that of approximating classes of smooth functions by algebraic-trigonometric polynomials of the form p{sub n}(t)+{tau}{sub m}(t), where p{sub n}(t) is an algebraic polynomial of degree n and {tau}{sub m}(t)=a{sub 0}+{Sigma}{sub k=1}{sup m}a{sub k} cos k{pi}t + b{sub k} sin k{pi}t is a trigonometric polynomial of order m. The precise order of approximation by such polynomials in the classes W{sup r}{sub {infinity}(}M) and an upper bound for similar approximations in the class W{sup r}{sub p}(M) with 4/3

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.

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.

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.

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 •

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

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.

Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

NASA Astrophysics Data System (ADS)

Recchioni, Maria Cristina

2001-12-01

This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

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.

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

Luigi Gatteschi's work on asymptotics of special functions and their zeros

NASA Astrophysics Data System (ADS)

Gautschi, Walter; Giordano, Carla

2008-12-01

A good portion of Gatteschi's research publications-about 65%-is devoted to asymptotics of special functions and their zeros. Most prominently among the special functions studied figure classical orthogonal polynomials, notably Jacobi polynomials and their special cases, Laguerre polynomials, and Hermite polynomials by implication. Other important classes of special functions dealt with are Bessel functions of the first and second kind, Airy functions, and confluent hypergeometric functions, both in Tricomi's and Whittaker's form. This work is reviewed here, and organized along methodological lines.

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.

dPotFit: A computer program to fit diatomic molecule spectral data to potential energy functions

NASA Astrophysics Data System (ADS)

Le Roy, Robert J.

2017-01-01

This paper describes program dPotFit, which performs least-squares fits of diatomic molecule spectroscopic data consisting of any combination of microwave, infrared or electronic vibrational bands, fluorescence series, and tunneling predissociation level widths, involving one or more electronic states and one or more isotopologs, and for appropriate systems, second virial coefficient data, to determine analytic potential energy functions defining the observed levels and other properties of each state. Four families of analytical potential functions are available for fitting in the current version of dPotFit: the Expanded Morse Oscillator (EMO) function, the Morse/Long-Range (MLR) function, the Double-Exponential/Long-Range (DELR) function, and the 'Generalized Potential Energy Function' (GPEF) of Šurkus, which incorporates a variety of polynomial functional forms. In addition, dPotFit allows sets of experimental data to be tested against predictions generated from three other families of analytic functions, namely, the 'Hannover Polynomial' (or "X-expansion") function, and the 'Tang-Toennies' and Scoles-Aziz 'HFD', exponential-plus-van der Waals functions, and from interpolation-smoothed pointwise potential energies, such as those obtained from ab initio or RKR calculations. dPotFit also allows the fits to determine atomic-mass-dependent Born-Oppenheimer breakdown functions, and singlet-state Λ-doubling, or 2Σ splitting radial strength functions for one or more electronic states. dPotFit always reports both the 95% confidence limit uncertainty and the "sensitivity" of each fitted parameter; the latter indicates the number of significant digits that must be retained when rounding fitted parameters, in order to ensure that predictions remain in full agreement with experiment. It will also, if requested, apply a "sequential rounding and refitting" procedure to yield a final parameter set defined by a minimum number of significant digits, while ensuring no significant loss of accuracy in the predictions yielded by those parameters.

Polynomial fuzzy observer designs: a sum-of-squares approach.

PubMed

Tanaka, Kazuo; Ohtake, Hiroshi; Seo, Toshiaki; Tanaka, Motoyasu; Wang, Hua O

2012-10-01

This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.

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.

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.

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.

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.

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.

Discrete Painlevé equations for a class of PVI τ-functions given as U(N) averages

NASA Astrophysics Data System (ADS)

Forrester, P. J.; Witte, N. S.

2005-09-01

In a recent work, difference equations (Laguerre-Freud equations) for the bi-orthogonal polynomials and related quantities corresponding to the weight on the unit circle w(z)=\\prod^m_{j=1}(z-z_j(t))^{\\rho_j} were derived. It is shown here that in the case m = 3, these difference equations, when applied to the calculation of the underlying U(N) average, reduce to a coupled system identifiable with that obtained by Adler and van Moerbeke, using the methods of the Toeplitz lattice and Virasoro constraints. Moreover, it is shown that this coupled system can be reduced to yield the discrete fifth Painlevé equation dPV as it occurs in the theory of the sixth Painlevé system. Methods based on affine Weyl group symmetries of Bäcklund transformations have previously yielded the dPV equation, but with different parameters for the same problem. We find an explicit mapping between the two forms. Applications of our results are made to give recurrences for the gap probabilities and moments in the circular unitary ensemble of random matrices, and to the diagonal spin-spin correlation function of the square lattice Ising model.

Animating Nested Taylor Polynomials to Approximate a Function

ERIC Educational Resources Information Center

Mazzone, Eric F.; Piper, Bruce R.

2010-01-01

The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…

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

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.

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.

High-Nuclearity Magnetic Clusters: Generalized Spin Hamiltonian and Its Use for the Calculation of the Energy Levels, Bulk Magnetic Properties, and Inelastic Neutron Scattering Spectra.

PubMed

Borrás-Almenar, J. J.; Clemente-Juan, J. M.; Coronado, E.; Tsukerblat, B. S.

1999-12-27

A general solution of the exchange problem in the high-nuclearity spin clusters (HNSC) containing arbitrary number of exchange-coupled centers and topology is developed. All constituent magnetic centers are supposed to possess well-isolated orbitally non-degenerate ground states so that the isotropic Heisenberg-Dirac-Van Vleck (HDVV) term is the leading part of the exchange spin Hamiltonian. Along with the HDVV term, we consider higher-order isotropic exchange terms (biquadratic exchange), as well as the anisotropic terms (anisotropic and antisymmetric exchange interactions and local single-ion anisotropies). All these terms are expressed as irreducible tensor operators (ITO). This allows us to take full advantage of the spin symmetry of the system. At the same time, we have also benefitted by taking into account the point group symmetry of the cluster, which allows us to work with symmetrized spin functions. This results in an additional reduction of the matrices to diagonalize. The approach developed here is accompanied by an efficient computational procedure that allows us to calculate the bulk magnetic properties (magnetic susceptibility, magnetization, and magnetic specific heat) as well as the spectroscopic properties of HNSC. Special attention is paid to calculate the magnetic excitations observed by inelastic neutron scattering (INS), their intensities, and their Q and temperature dependencies. This spectroscopic technique provides direct access to the energies and wave functions of the different spin states of the cluster; thus, it can be applied to spin clusters in order to obtain deep and detailed information on the nature of the magnetic exchange phenomenon. The general expression for the INS cross-section of spin clusters interacting by all kinds of exchange interactions, including also the single-ion zero-field splitting term, is derived for the first time. A closed-form expression is also derived for the particular case in which only the isotropic exchange interactions are involved. Finally this approach has been used to model the magnetic properties as well as the INS spectra of the polyoxometalate anion [Ni(9)(OH)(3)(H(2)O)(6)(HPO(4))(2)(PW(9)O(34))(3)](16)(-), which contains a central magnetic cluster formed by nine exchange-coupled Ni(II) ions surrounded by diamagnetic phosphotungstate ligands (PW(9)O(34))(9)(-).

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.

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.

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

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

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.

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.

Design of polynomial fuzzy observer-controller for nonlinear systems with state delay: sum of squares approach

NASA Astrophysics Data System (ADS)

Gassara, H.; El Hajjaji, A.; Chaabane, M.

2017-07-01

This paper investigates the problem of observer-based control for two classes of polynomial fuzzy systems with time-varying delay. The first class concerns a special case where the polynomial matrices do not depend on the estimated state variables. The second one is the general case where the polynomial matrices could depend on unmeasurable system states that will be estimated. For the last case, two design procedures are proposed. The first one gives the polynomial fuzzy controller and observer gains in two steps. In the second procedure, the designed gains are obtained using a single-step approach to overcome the drawback of a two-step procedure. The obtained conditions are presented in terms of sum of squares (SOS) which can be solved via the SOSTOOLS and a semi-definite program solver. Illustrative examples show the validity and applicability of the proposed results.

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.

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…

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.

A general method for constructing multidimensional molecular potential energy surfaces from {ital ab} {ital initio} calculations

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

Ho, T.; Rabitz, H.

1996-02-01

A general interpolation method for constructing smooth molecular potential energy surfaces (PES{close_quote}s) from {ital ab} {ital initio} data are proposed within the framework of the reproducing kernel Hilbert space and the inverse problem theory. The general expression for an {ital a} {ital posteriori} error bound of the constructed PES is derived. It is shown that the method yields globally smooth potential energy surfaces that are continuous and possess derivatives up to second order or higher. Moreover, the method is amenable to correct symmetry properties and asymptotic behavior of the molecular system. Finally, the method is generic and can be easilymore » extended from low dimensional problems involving two and three atoms to high dimensional problems involving four or more atoms. Basic properties of the method are illustrated by the construction of a one-dimensional potential energy curve of the He{endash}He van der Waals dimer using the exact quantum Monte Carlo calculations of Anderson {ital et} {ital al}. [J. Chem. Phys. {bold 99}, 345 (1993)], a two-dimensional potential energy surface of the HeCO van der Waals molecule using recent {ital ab} {ital initio} calculations by Tao {ital et} {ital al}. [J. Chem. Phys. {bold 101}, 8680 (1994)], and a three-dimensional potential energy surface of the H{sup +}{sub 3} molecular ion using highly accurate {ital ab} {ital initio} calculations of R{umlt o}hse {ital et} {ital al}. [J. Chem. Phys. {bold 101}, 2231 (1994)]. In the first two cases the constructed potentials clearly exhibit the correct asymptotic forms, while in the last case the constructed potential energy surface is in excellent agreement with that constructed by R{umlt o}hse {ital et} {ital al}. using a low order polynomial fitting procedure. {copyright} {ital 1996 American Institute of Physics.}« less

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.

vanC Cluster of Vancomycin-Resistant Enterococcus gallinarum BM4174

PubMed Central

Arias, Cesar A.; Courvalin, Patrice; Reynolds, Peter E.

2000-01-01

Glycopeptide-resistant enterococci of the VanC type synthesize UDP-muramyl-pentapeptide[d-Ser] for cell wall assembly and prevent synthesis of peptidoglycan precursors ending in d-Ala. The vanC cluster of Enterococcus gallinarum BM4174 consists of five genes: vanC-1, vanXYC, vanT, vanRC, and vanSC. Three genes are sufficient for resistance: vanC-1 encodes a ligase that synthesizes the dipeptide d-Ala-d-Ser for addition to UDP-MurNAc-tripeptide, vanXYC encodes a d,d-dipeptidase–carboxypeptidase that hydrolyzes d-Ala-d-Ala and removes d-Ala from UDP-MurNAc-pentapeptide[d-Ala], and vanT encodes a membrane-bound serine racemase that provides d-Ser for the synthetic pathway. The three genes are clustered: the start codons of vanXYC and vanT overlap the termination codons of vanC-1 and vanXYC, respectively. Two genes which encode proteins with homology to the VanS-VanR two-component regulatory system were present downstream from the resistance genes. The predicted amino acid sequence of VanRC exhibited 50% identity to VanR and 33% identity to VanRB. VanSC had 40% identity to VanS over a region of 308 amino acids and 24% identity to VanSB over a region of 285 amino acids. All residues with important functions in response regulators and histidine kinases were conserved in VanRC and VanSC, respectively. Induction experiments based on the determination of d,d-carboxypeptidase activity in cytoplasmic extracts confirmed that the genes were expressed constitutively. Using a promoter-probing vector, regions upstream from the resistance and regulatory genes were identified that have promoter activity. PMID:10817725

Pointwise convergence of derivatives of Lagrange interpolation polynomials for exponential weights

NASA Astrophysics Data System (ADS)

Damelin, S. B.; Jung, H. S.

2005-01-01

For a general class of exponential weights on the line and on (-1,1), we study pointwise convergence of the derivatives of Lagrange interpolation. Our weights include even weights of smooth polynomial decay near +/-[infinity] (Freud weights), even weights of faster than smooth polynomial decay near +/-[infinity] (Erdos weights) and even weights which vanish strongly near +/-1, for example Pollaczek type weights.

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

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.

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.

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.

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

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

Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation.

PubMed

Välimäki, Vesa; Pekonen, Jussi; Nam, Juhan

2012-01-01

Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz. © 2012 Acoustical Society of America.

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.

Genetics Home Reference: achromatopsia

MedlinePlus

... NW, Roosing S, van Schooneveld MJ, van Lith-Verhoeven JJ, van Moll-Ramirez N, van den Born LI, ... van Schooneveld MJ, Strom TM, van Lith-Verhoeven JJ, Lotery AJ, van Moll-Ramirez N, Leroy BP, ...

Glycopeptide Resistance vanA Operons in Paenibacillus Strains Isolated from Soil

PubMed Central

Guardabassi, Luca; Perichon, Bruno; van Heijenoort, Jean; Blanot, Didier; Courvalin, Patrice

2005-01-01

The sequence and gene organization of the van operons in vancomycin (MIC of >256 μg/ml)- and teicoplanin (MIC of ≥32 μg/ml)-resistant Paenibacillus thiaminolyticus PT-2B1 and Paenibacillus apiarius PA-B2B isolated from soil were determined. Both operons had regulatory (vanR and vanS), resistance (vanH, vanA, and vanX), and accessory (vanY, vanZ, and vanW) genes homologous to the corresponding genes in enterococcal vanA and vanB operons. The vanAPT operon in P. thiaminolyticus PT-2B1 had the same gene organization as that of vanA operons whereas vanAPA in P. apiarius PA-B2B resembled vanB operons due to the presence of vanW upstream from the vanHAX cluster but was closer to vanA operons in sequence. Reference P. apiarius strains NRRL B-4299 and NRRL B-4188 were found to harbor operons indistinguishable from vanAPA by PCR mapping, restriction fragment length polymorphism, and partial sequencing, suggesting that this operon was species specific. As in enterococci, resistance was inducible by glycopeptides and associated with the synthesis of pentadepsipeptide peptidoglycan precursors ending in d-Ala-d-Lac, as demonstrated by d,d-dipeptidase activities, high-pressure liquid chromatography, and mass spectrometry. The precursors differed from those in enterococci by the presence of diaminopimelic acid instead of lysine in the peptide chain. Altogether, the results are compatible with the notion that van operons in soil Paenibacillus strains and in enterococci have evolved from a common ancestor. PMID:16189102

Glycopeptide resistance vanA operons in Paenibacillus strains isolated from soil.

PubMed

Guardabassi, Luca; Perichon, Bruno; van Heijenoort, Jean; Blanot, Didier; Courvalin, Patrice

2005-10-01

The sequence and gene organization of the van operons in vancomycin (MIC of >256 microg/ml)- and teicoplanin (MIC of > or =32 microg/ml)-resistant Paenibacillus thiaminolyticus PT-2B1 and Paenibacillus apiarius PA-B2B isolated from soil were determined. Both operons had regulatory (vanR and vanS), resistance (vanH, vanA, and vanX), and accessory (vanY, vanZ, and vanW) genes homologous to the corresponding genes in enterococcal vanA and vanB operons. The vanA(PT) operon in P. thiaminolyticus PT-2B1 had the same gene organization as that of vanA operons whereas vanA(PA) in P. apiarius PA-B2B resembled vanB operons due to the presence of vanW upstream from the vanHAX cluster but was closer to vanA operons in sequence. Reference P. apiarius strains NRRL B-4299 and NRRL B-4188 were found to harbor operons indistinguishable from vanA(PA) by PCR mapping, restriction fragment length polymorphism, and partial sequencing, suggesting that this operon was species specific. As in enterococci, resistance was inducible by glycopeptides and associated with the synthesis of pentadepsipeptide peptidoglycan precursors ending in D-Ala-D-Lac, as demonstrated by D,D-dipeptidase activities, high-pressure liquid chromatography, and mass spectrometry. The precursors differed from those in enterococci by the presence of diaminopimelic acid instead of lysine in the peptide chain. Altogether, the results are compatible with the notion that van operons in soil Paenibacillus strains and in enterococci have evolved from a common ancestor.

Diversity of Tn1546 in vanA-positive Enterococcus faecium clinical isolates with VanA, VanB, and VanD phenotypes and susceptibility to vancomycin.

PubMed

Cha, J O; Yoo, J I; Kim, H K; Kim, H S; Yoo, J S; Lee, Y S; Jung, Y H

2013-10-01

To investigate diversity in the vanA cluster in Enterococcus faecium isolates from nontertiary hospitals. We identified 43 vanA-positive Ent. faecium isolates, including two vancomycin-susceptible isolates, from hospitals between 2003 and 2006. Of these isolates, >85% were resistant to ampicillin, erythromycin and ciprofloxacin. The vanA cluster was classified into six types using overlapping PCR, but the prototype transposon Tn1546 was not found. Most vanA-positive vancomycin-resistant Enterococcus (VRE) carried IS1216V and belonged to Type III (58·1%) or Type II (20·9%). vanY, vanZ and IS1216V were observed in the left and right ends of Type III with long-range PCR. IS1216V was also observed within vanS and vanX in the two vancomycin-susceptible isolates and in two vancomycin-resistant isolates. No VRE isolates with VanB and VanD phenotypes contained point mutations in vanS, unlike in previous reports. Sequence types (STs) of all isolates belonged to clonal complex 17, and ST78 was predominant. Insertion sequences, especially IS1216V, cause structural variation in the vanA cluster. We report the first observation of vanY and vanZ at the left end of Tn1546 in clinical isolates. This is the first report of the frequency of vancomycin resistance and diversity of Tn1546 in vanA-positive Ent. faecium isolates from nontertiary hospitals. © 2013 The Society for Applied Microbiology.

An Introduction to Lagrangian Differential Calculus.

ERIC Educational Resources Information Center

Schremmer, Francesca; Schremmer, Alain

1990-01-01

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Development and Evaluation of a Hydrostatic Dynamical Core Using the Spectral Element/Discontinuous Galerkin Methods

DTIC Science & Technology

2014-04-01

The CG and DG horizontal discretization employs high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...and DG horizontal discretization employs high-order nodal basis functions 29 associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...Inside 235 each element we build ( 1)N + Gauss-Lobatto- Legendre (GLL) quadrature points, where N 236 indicate the polynomial order of the basis

Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

PubMed Central

Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

2014-01-01

In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293

The s-Ordered Fock Space Projectors Gained by the General Ordering Theorem

NASA Astrophysics Data System (ADS)

Farid, Shähandeh; Mohammad, Reza Bazrafkan; Mahmoud, Ashrafi

2012-09-01

Employing the general ordering theorem (GOT), operational methods and incomplete 2-D Hermite polynomials, we derive the t-ordered expansion of Fock space projectors. Using the result, the general ordered form of the coherent state projectors is obtained. This indeed gives a new integration formula regarding incomplete 2-D Hermite polynomials. In addition, the orthogonality relation of the incomplete 2-D Hermite polynomials is derived to resolve Dattoli's failure.

Baecklund transformation, Lax pair, and solutions for the Caudrey-Dodd-Gibbon equation

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

Qu Qixing; Sun Kun; Jiang Yan

2011-01-15

By using Bell polynomials and symbolic computation, we investigate the Caudrey-Dodd-Gibbon equation analytically. Through a generalization of Bells polynomials, its bilinear form is derived, based on which, the periodic wave solution and soliton solutions are presented. And the soliton solutions with graphic analysis are also given. Furthermore, Baecklund transformation and Lax pair are derived via the Bells exponential polynomials. Finally, the Ablowitz-Kaup-Newell-Segur system is constructed.

OMEGACAM and Gravitational Lensing

NASA Astrophysics Data System (ADS)

Christen, Fabrice Frédéric Thiébaut

2007-04-01

Het proefschrift van Fabrice Christen gaat over de ontwikkeling van nieuwe methoden voor het corrigeren van (digitale) foto's van melkwegstelsels. Met deze methoden kunnen de beelden uit het heelal beter worden geanalyseerd. Het eerste gedeelte is gewijd aan het werk dat bij ESO is uitgevoerd aan de CCD's van de OmegaCAM camera, het enige instrument van de VST. OmegaCAM is een optische groothoekcamera met een beeldveld van een vierkante graad, opgebouwd uit een mozaiek van 8 bij 4 CCD's. Van elk onderdeel moeten alle kenmerken volledig bekend zijn voordat het in het CCD mozaiek geplaatst kan worden. In het tweede deel van dit proefschrift wordt de ontwikkeling van een nieuwe methode voor het corrigeren van de ``point-spread function'' (PSF) en schatten van de ellipticiteit van de melkwegstelsels besproken. De nieuwe techniek wordt getest en vergeleken met een door sterrenkundigen algemeen gebruikte methode in het veld van zwaartekrachtslenzen, de Kaiser, Squire en Broadhurst (KSB) methode. De nieuwe methode, gebaseerd op shapelet ontleding (vergelijkbaar met wavelet ontleding), gaat verder, en is sneller en theoretisch preciezer dan de KSB methode. Door gebruik te maken van de gecorrigeerde ellipticiteit, kunnen we een statistische analyse uitvoeren om er een kosmisch vervormingssignaal uit te halen. De licht vervormde beelden van de melkwegstelsels bewij zen dat de niet-homogene massaverdeling op megaparsec-schaal voornamelijk bestaat uit grote hoeveelheden donkere materie. Verder vergelijken we de schattingen van de ellipticiteit van de shapelet en KSB methode. Bovendien voeren we ook nog een melkwegstelsel-melkwegstelsel lens analyse uit op de 50 VLT Fors1 afbeeldingen en slagen we erin de belangrijkste eigenschappen van de halo's van de stelsels, die zich op een afstand van een- tot tweeduizend megaparsec (1 parsec = 3,26 lichtjaar = 3,085 x 10^16 meter) bevinden, te bepalen door gebruik te maken van twee modellen van melkwegstelselhalo's. Vergeleken met andere overzichtsmetingen vinden we vergelijkbare resultaten.

Improving multivariate Horner schemes with Monte Carlo tree search

NASA Astrophysics Data System (ADS)

Kuipers, J.; Plaat, A.; Vermaseren, J. A. M.; van den Herik, H. J.

2013-11-01

Optimizing the cost of evaluating a polynomial is a classic problem in computer science. For polynomials in one variable, Horner's method provides a scheme for producing a computationally efficient form. For multivariate polynomials it is possible to generalize Horner's method, but this leaves freedom in the order of the variables. Traditionally, greedy schemes like most-occurring variable first are used. This simple textbook algorithm has given remarkably efficient results. Finding better algorithms has proved difficult. In trying to improve upon the greedy scheme we have implemented Monte Carlo tree search, a recent search method from the field of artificial intelligence. This results in better Horner schemes and reduces the cost of evaluating polynomials, sometimes by factors up to two.

Assessing the suitability of fractional polynomial methods in health services research: a perspective on the categorization epidemic.

PubMed

Williams, Jennifer Stewart

2011-07-01

To show how fractional polynomial methods can usefully replace the practice of arbitrarily categorizing data in epidemiology and health services research. A health service setting is used to illustrate a structured and transparent way of representing non-linear data without arbitrary grouping. When age is a regressor its effects on an outcome will be interpreted differently depending upon the placing of cutpoints or the use of a polynomial transformation. Although it is common practice, categorization comes at a cost. Information is lost, and accuracy and statistical power reduced, leading to spurious statistical interpretation of the data. The fractional polynomial method is widely supported by statistical software programs, and deserves greater attention and use.

Magnetic Resonance Imaging-derived Flow Parameters for the Analysis of Cardiovascular Diseases and Drug Development.

PubMed

Michael, Dada O; Bamidele, Awojoyogbe O; Adewale, Adesola O; Karem, Boubaker

2013-01-01

Nuclear magnetic resonance (NMR) allows for fast, accurate and noninvasive measurement of fluid flow in restricted and non-restricted media. The results of such measurements may be possible for a very small B 0 field and can be enhanced through detailed examination of generating functions that may arise from polynomial solutions of NMR flow equations in terms of Legendre polynomials and Boubaker polynomials. The generating functions of these polynomials can present an array of interesting possibilities that may be useful for understanding the basic physics of extracting relevant NMR flow information from which various hemodynamic problems can be carefully studied. Specifically, these results may be used to develop effective drugs for cardiovascular-related diseases.

Magnetic Resonance Imaging-derived Flow Parameters for the Analysis of Cardiovascular Diseases and Drug Development

PubMed Central

Michael, Dada O.; Bamidele, Awojoyogbe O.; Adewale, Adesola O.; Karem, Boubaker

2013-01-01

Nuclear magnetic resonance (NMR) allows for fast, accurate and noninvasive measurement of fluid flow in restricted and non-restricted media. The results of such measurements may be possible for a very small B0 field and can be enhanced through detailed examination of generating functions that may arise from polynomial solutions of NMR flow equations in terms of Legendre polynomials and Boubaker polynomials. The generating functions of these polynomials can present an array of interesting possibilities that may be useful for understanding the basic physics of extracting relevant NMR flow information from which various hemodynamic problems can be carefully studied. Specifically, these results may be used to develop effective drugs for cardiovascular-related diseases. PMID:25114546

Asymptotic formulae for the zeros of orthogonal polynomials

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

Badkov, V M

2012-09-30

Let p{sub n}(t) be an algebraic polynomial that is orthonormal with weight p(t) on the interval [-1, 1]. When p(t) is a perturbation (in certain limits) of the Chebyshev weight of the first kind, the zeros of the polynomial p{sub n}( cos {tau}) and the differences between pairs of (not necessarily consecutive) zeros are shown to satisfy asymptotic formulae as n{yields}{infinity}, which hold uniformly with respect to the indices of the zeros. Similar results are also obtained for perturbations of the Chebyshev weight of the second kind. First, some preliminary results on the asymptotic behaviour of the difference between twomore » zeros of an orthogonal trigonometric polynomial, which are needed, are established. Bibliography: 15 titles.« less

Parametric analysis of ATM solar array.

NASA Technical Reports Server (NTRS)

Singh, B. K.; Adkisson, W. B.

1973-01-01

The paper discusses the methods used for the calculation of ATM solar array performance characteristics and provides the parametric analysis of solar panels used in SKYLAB. To predict the solar array performance under conditions other than test conditions, a mathematical model has been developed. Four computer programs have been used to convert the solar simulator test data to the parametric curves. The first performs module summations, the second determines average solar cell characteristics which will cause a mathematical model to generate a curve matching the test data, the third is a polynomial fit program which determines the polynomial equations for the solar cell characteristics versus temperature, and the fourth program uses the polynomial coefficients generated by the polynomial curve fit program to generate the parametric data.

Beslisbevoegdheden en Verantwoordelijkheden van de Uitgestegen Soldaat. Deel A: Verplaatsen van Beslisbevoegdheden (Authority and Responsibility of the Dismounted Soldier. Part A. Empowering the Dismounted Soldier)

DTIC Science & Technology

2007-04-01

en verantwoordelijkheden van de uitgestegen soldaat Deel A: verplaatsen van beslisbevoegdheden Datumn april 2007 Auteur (s) R. de Bruin ITE. van Bernmel...Admiraal, Bureau SMP Auteur (s) R. de Bruin Program maleider Projectleider I.E. van Bemnmel dr. W.A. Lotens, A.J. van Vliet, A.J. van Vijet TNO Defensie en...Leadership Theory en wordt relevant geacht voor de ontvangers van aanvullende beslisbevoegdheden. 2.1.3 Het oogmerk van de hogere commandant Een ander

A distinctive dual-channel quorum-sensing system operates in Vibrio anguillarum.

PubMed

Croxatto, Antony; Pride, John; Hardman, Andrea; Williams, Paul; Cámara, Miguel; Milton, Debra L

2004-06-01

Many bacterial cells communicate using diffusible signal molecules to monitor cell population density via a process termed quorum sensing. In marine Vibrio species, the Vibrio harveyi-type LuxR protein is a key player in a quorum-sensing phosphorelay cascade, which controls the expression of virulence, symbiotic and survival genes. Previously, we characterized Vibrio anguillarum homologues of LuxR (VanT) and LuxMN (VanMN) and, in this study, we have identified homologues of LuxPQ (VanPQ) and LuxOU (VanOU). In contrast to other Vibrio species, vanT was expressed at low cell density and showed no significant induction as the cell number increased. In addition, although the loss of VanO increased vanT expression, the loss of VanU, unexpectedly, decreased it. Both VanN and VanQ were required for repression of vanT even in a vanU mutant, suggesting an alternative route for VanNQ signal transduction other than via VanU. VanT negatively regulated its own expression by binding and repressing the vanT promoter and by binding and activating the vanOU promoter. The signal relay results in a cellular response as expression of the metalloprotease, empA, was altered similar to that of vanT in all the mutants. Consequently, the V. anguillarum quorum-sensing phosphorelay systems work differently from those of V. harveyi and may be used to limit rather than induce vanT expression.

Dutch Anthropometry for Vehicle Design and Evaluation

DTIC Science & Technology

2008-10-01

middelen Beschrijving van de werkzaamheden Uitgaande van afmetingen van Nederlanders zijn grenswaarden voor negen paspoppen. met vanSrende...vastgesteld voor het jaar 2015 Hierbij is uitgegaan van een Nederlands antropometrisch bestand (NedScan) Resultaten en conclusies Het resultaat is een kort... Nederlands antropometrisch bestand (NedScan) en van lichaamsafmetingen van goedgekeurde K.L rekruten. De grenswaarden omvatten 95% van dat Nederlandse

19 CFR 10.41a - Lift vans, cargo vans, shipping tanks, skids, pallets, and similar instruments of international...

Code of Federal Regulations, 2011 CFR

2011-04-01

... 19 Customs Duties 1 2011-04-01 2011-04-01 false Lift vans, cargo vans, shipping tanks, skids... Traffic § 10.41a Lift vans, cargo vans, shipping tanks, skids, pallets, and similar instruments of international traffic; repair components. (a)(1) Lift vans, cargo vans, shipping tanks, skids, pallets, caul...

19 CFR 10.41a - Lift vans, cargo vans, shipping tanks, skids, pallets, and similar instruments of international...

Code of Federal Regulations, 2010 CFR

2010-04-01

... 19 Customs Duties 1 2010-04-01 2010-04-01 false Lift vans, cargo vans, shipping tanks, skids... Traffic § 10.41a Lift vans, cargo vans, shipping tanks, skids, pallets, and similar instruments of international traffic; repair components. (a)(1) Lift vans, cargo vans, shipping tanks, skids, pallets, caul...

A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry

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

Kersaudy, Pierric, E-mail: pierric.kersaudy@orange.com; Whist Lab, 38 avenue du Général Leclerc, 92130 Issy-les-Moulineaux; ESYCOM, Université Paris-Est Marne-la-Vallée, 5 boulevard Descartes, 77700 Marne-la-Vallée

2015-04-01

In numerical dosimetry, the recent advances in high performance computing led to a strong reduction of the required computational time to assess the specific absorption rate (SAR) characterizing the human exposure to electromagnetic waves. However, this procedure remains time-consuming and a single simulation can request several hours. As a consequence, the influence of uncertain input parameters on the SAR cannot be analyzed using crude Monte Carlo simulation. The solution presented here to perform such an analysis is surrogate modeling. This paper proposes a novel approach to build such a surrogate model from a design of experiments. Considering a sparse representationmore » of the polynomial chaos expansions using least-angle regression as a selection algorithm to retain the most influential polynomials, this paper proposes to use the selected polynomials as regression functions for the universal Kriging model. The leave-one-out cross validation is used to select the optimal number of polynomials in the deterministic part of the Kriging model. The proposed approach, called LARS-Kriging-PC modeling, is applied to three benchmark examples and then to a full-scale metamodeling problem involving the exposure of a numerical fetus model to a femtocell device. The performances of the LARS-Kriging-PC are compared to an ordinary Kriging model and to a classical sparse polynomial chaos expansion. The LARS-Kriging-PC appears to have better performances than the two other approaches. A significant accuracy improvement is observed compared to the ordinary Kriging or to the sparse polynomial chaos depending on the studied case. This approach seems to be an optimal solution between the two other classical approaches. A global sensitivity analysis is finally performed on the LARS-Kriging-PC model of the fetus exposure problem.« less

Zernike expansion of derivatives and Laplacians of the Zernike circle polynomials.

PubMed

Janssen, A J E M

2014-07-01

The partial derivatives and Laplacians of the Zernike circle polynomials occur in various places in the literature on computational optics. In a number of cases, the expansion of these derivatives and Laplacians in the circle polynomials are required. For the first-order partial derivatives, analytic results are scattered in the literature. Results start as early as 1942 in Nijboer's thesis and continue until present day, with some emphasis on recursive computation schemes. A brief historic account of these results is given in the present paper. By choosing the unnormalized version of the circle polynomials, with exponential rather than trigonometric azimuthal dependence, and by a proper combination of the two partial derivatives, a concise form of the expressions emerges. This form is appropriate for the formulation and solution of a model wavefront sensing problem of reconstructing a wavefront on the level of its expansion coefficients from (measurements of the expansion coefficients of) the partial derivatives. It turns out that the least-squares estimation problem arising here decouples per azimuthal order m, and per m the generalized inverse solution assumes a concise analytic form so that singular value decompositions are avoided. The preferred version of the circle polynomials, with proper combination of the partial derivatives, also leads to a concise analytic result for the Zernike expansion of the Laplacian of the circle polynomials. From these expansions, the properties of the Laplacian as a mapping from the space of circle polynomials of maximal degree N, as required in the study of the Neumann problem associated with the transport-of-intensity equation, can be read off within a single glance. Furthermore, the inverse of the Laplacian on this space is shown to have a concise analytic form.

A Polynomial Subset-Based Efficient Multi-Party Key Management System for Lightweight Device Networks.

PubMed

Mahmood, Zahid; Ning, Huansheng; Ghafoor, AtaUllah

2017-03-24

Wireless Sensor Networks (WSNs) consist of lightweight devices to measure sensitive data that are highly vulnerable to security attacks due to their constrained resources. In a similar manner, the internet-based lightweight devices used in the Internet of Things (IoT) are facing severe security and privacy issues because of the direct accessibility of devices due to their connection to the internet. Complex and resource-intensive security schemes are infeasible and reduce the network lifetime. In this regard, we have explored the polynomial distribution-based key establishment schemes and identified an issue that the resultant polynomial value is either storage intensive or infeasible when large values are multiplied. It becomes more costly when these polynomials are regenerated dynamically after each node join or leave operation and whenever key is refreshed. To reduce the computation, we have proposed an Efficient Key Management (EKM) scheme for multiparty communication-based scenarios. The proposed session key management protocol is established by applying a symmetric polynomial for group members, and the group head acts as a responsible node. The polynomial generation method uses security credentials and secure hash function. Symmetric cryptographic parameters are efficient in computation, communication, and the storage required. The security justification of the proposed scheme has been completed by using Rubin logic, which guarantees that the protocol attains mutual validation and session key agreement property strongly among the participating entities. Simulation scenarios are performed using NS 2.35 to validate the results for storage, communication, latency, energy, and polynomial calculation costs during authentication, session key generation, node migration, secure joining, and leaving phases. EKM is efficient regarding storage, computation, and communication overhead and can protect WSN-based IoT infrastructure.

A Polynomial Subset-Based Efficient Multi-Party Key Management System for Lightweight Device Networks

PubMed Central

Mahmood, Zahid; Ning, Huansheng; Ghafoor, AtaUllah

2017-01-01

Wireless Sensor Networks (WSNs) consist of lightweight devices to measure sensitive data that are highly vulnerable to security attacks due to their constrained resources. In a similar manner, the internet-based lightweight devices used in the Internet of Things (IoT) are facing severe security and privacy issues because of the direct accessibility of devices due to their connection to the internet. Complex and resource-intensive security schemes are infeasible and reduce the network lifetime. In this regard, we have explored the polynomial distribution-based key establishment schemes and identified an issue that the resultant polynomial value is either storage intensive or infeasible when large values are multiplied. It becomes more costly when these polynomials are regenerated dynamically after each node join or leave operation and whenever key is refreshed. To reduce the computation, we have proposed an Efficient Key Management (EKM) scheme for multiparty communication-based scenarios. The proposed session key management protocol is established by applying a symmetric polynomial for group members, and the group head acts as a responsible node. The polynomial generation method uses security credentials and secure hash function. Symmetric cryptographic parameters are efficient in computation, communication, and the storage required. The security justification of the proposed scheme has been completed by using Rubin logic, which guarantees that the protocol attains mutual validation and session key agreement property strongly among the participating entities. Simulation scenarios are performed using NS 2.35 to validate the results for storage, communication, latency, energy, and polynomial calculation costs during authentication, session key generation, node migration, secure joining, and leaving phases. EKM is efficient regarding storage, computation, and communication overhead and can protect WSN-based IoT infrastructure. PMID:28338632

The polynomial form of the scattering equations is an H -basis

NASA Astrophysics Data System (ADS)

Bosma, Jorrit; Søgaard, Mads; Zhang, Yang

2016-08-01

We prove that the polynomial form of the scattering equations is a Macaulay H -basis. We demonstrate that this H -basis facilitates integrand reduction and global residue computations in a way very similar to using a Gröbner basis, but circumvents the heavy computation of the latter. As an example, we apply the H -basis to prove the conjecture that the dual basis of the polynomial scattering equations must contain one constant term.

Analytical Solutions for the Resonance Response of Goupillaud-type Elastic Media Using Z-transform Methods

DTIC Science & Technology

2012-02-01

using z-transform methods. The determinant of the resulting global system matrix in the z-space |Am| is a palindromic polynomial with real...resulting global system matrix in the z-space |Am| is a palindromic polynomial with real coefficients. The zeros of the palindromic polynomial are distinct...Goupillaud-type multilayered media. In addition, the present treatment uses a global matrix method that is attributed to Knopoff [16], rather than the

Distortion theorems for polynomials on a circle

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

Dubinin, V N

2000-12-31

Inequalities for the derivatives with respect to {phi}=arg z the functions ReP(z), |P(z)|{sup 2} and arg P(z) are established for an algebraic polynomial P(z) at points on the circle |z|=1. These estimates depend, in particular, on the constant term and the leading coefficient of the polynomial P(z) and improve the classical Bernstein and Turan inequalities. The method of proof is based on the techniques of generalized reduced moduli.

Quantized vortices in the ideal bose gas: a physical realization of random polynomials.

PubMed

Castin, Yvan; Hadzibabic, Zoran; Stock, Sabine; Dalibard, Jean; Stringari, Sandro

2006-02-03

We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials, and observed in the density profile of the gas.

A quadratic regression modelling on paddy production in the area of Perlis

NASA Astrophysics Data System (ADS)

Goh, Aizat Hanis Annas; Ali, Zalila; Nor, Norlida Mohd; Baharum, Adam; Ahmad, Wan Muhamad Amir W.

2017-08-01

Polynomial regression models are useful in situations in which the relationship between a response variable and predictor variables is curvilinear. Polynomial regression fits the nonlinear relationship into a least squares linear regression model by decomposing the predictor variables into a kth order polynomial. The polynomial order determines the number of inflexions on the curvilinear fitted line. A second order polynomial forms a quadratic expression (parabolic curve) with either a single maximum or minimum, a third order polynomial forms a cubic expression with both a relative maximum and a minimum. This study used paddy data in the area of Perlis to model paddy production based on paddy cultivation characteristics and environmental characteristics. The results indicated that a quadratic regression model best fits the data and paddy production is affected by urea fertilizer application and the interaction between amount of average rainfall and percentage of area defected by pest and disease. Urea fertilizer application has a quadratic effect in the model which indicated that if the number of days of urea fertilizer application increased, paddy production is expected to decrease until it achieved a minimum value and paddy production is expected to increase at higher number of days of urea application. The decrease in paddy production with an increased in rainfall is greater, the higher the percentage of area defected by pest and disease.

Computing border bases using mutant strategies

NASA Astrophysics Data System (ADS)

Ullah, E.; Abbas Khan, S.

2014-01-01

Border bases, a generalization of Gröbner bases, have actively been addressed during recent years due to their applicability to industrial problems. In cryptography and coding theory a useful application of border based is to solve zero-dimensional systems of polynomial equations over finite fields, which motivates us for developing optimizations of the algorithms that compute border bases. In 2006, Kehrein and Kreuzer formulated the Border Basis Algorithm (BBA), an algorithm which allows the computation of border bases that relate to a degree compatible term ordering. In 2007, J. Ding et al. introduced mutant strategies bases on finding special lower degree polynomials in the ideal. The mutant strategies aim to distinguish special lower degree polynomials (mutants) from the other polynomials and give them priority in the process of generating new polynomials in the ideal. In this paper we develop hybrid algorithms that use the ideas of J. Ding et al. involving the concept of mutants to optimize the Border Basis Algorithm for solving systems of polynomial equations over finite fields. In particular, we recall a version of the Border Basis Algorithm which is actually called the Improved Border Basis Algorithm and propose two hybrid algorithms, called MBBA and IMBBA. The new mutants variants provide us space efficiency as well as time efficiency. The efficiency of these newly developed hybrid algorithms is discussed using standard cryptographic examples.

Cosmographic analysis with Chebyshev polynomials

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; D'Agostino, Rocco; Luongo, Orlando

2018-05-01

The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parametrize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Padé series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Padé approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the Joint Light-curve Analysis supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.

Fast Determination of the Element Excitation of an Active Phased Array Antenna

DTIC Science & Technology

1991-03-01

elementenexcitatie te, bepalen: de amplitude en fase van het elektrische ven-e veld moeten gemeten warden in slechts I richting in het verre veld van de ...Page 3 rapport no FEL-91-BO38 titel Een snelle bepaling van de excitatie van de elenienten van cen actieve phased array antenne auteur(s) I. J.G. van...van der Spek Onderzoek uItgevoerd door Ir. J.G. van Hezewijk SAMENVATIING (ONGERUBRICEERD) Het verre veld stralingsdiagram van een actieve phased array

Neutron spectroscopy with scintillation detectors using wavelets

NASA Astrophysics Data System (ADS)

Hartman, Jessica

The purpose of this research was to study neutron spectroscopy using the EJ-299-33A plastic scintillator. This scintillator material provided a novel means of detection for fast neutrons, without the disadvantages of traditional liquid scintillation materials. EJ-299-33A provided a more durable option to these materials, making it less likely to be damaged during handling. Unlike liquid scintillators, this plastic scintillator was manufactured from a non-toxic material, making it safer to use, as well as easier to design detectors. The material was also manufactured with inherent pulse shape discrimination abilities, making it suitable for use in neutron detection. The neutron spectral unfolding technique was developed in two stages. Initial detector response function modeling was carried out through the use of the MCNPX Monte Carlo code. The response functions were developed for a monoenergetic neutron flux. Wavelets were then applied to smooth the response function. The spectral unfolding technique was applied through polynomial fitting and optimization techniques in MATLAB. Verification of the unfolding technique was carried out through the use of experimentally determined response functions. These were measured on the neutron source based on the Van de Graff accelerator at the University of Kentucky. This machine provided a range of monoenergetic neutron beams between 0.1 MeV and 24 MeV, making it possible to measure the set of response functions of the EJ-299-33A plastic scintillator detector to neutrons of specific energies. The response of a plutonium-beryllium (PuBe) source was measured using the source available at the University of Nevada, Las Vegas. The neutron spectrum reconstruction was carried out using the experimentally measured response functions. Experimental data was collected in the list mode of the waveform digitizer. Post processing of this data focused on the pulse shape discrimination analysis of the recorded response functions to remove the effects of photons and allow for source characterization based solely on the neutron response. The unfolding technique was performed through polynomial fitting and optimization techniques in MATLAB, and provided an energy spectrum for the PuBe source.

On High-Order Upwind Methods for Advection

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2017-01-01

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom ?? per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2??-1, which is higher than the expected order of ??.

Explicit formulae for Chern-Simons invariants of the twist-knot orbifolds and edge polynomials of twist knots

NASA Astrophysics Data System (ADS)

Ham, J.-Y.; Lee, J.

2016-09-01

We calculate the Chern-Simons invariants of twist-knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of twist knot cone-manifold structures. Following the general instruction of Hilden, Lozano, and Montesinos-Amilibia, we here present concrete formulae and calculations. We use the Pythagorean Theorem, which was used by Ham, Mednykh and Petrov, to relate the complex length of the longitude and the complex distance between the two axes fixed by two generators. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic twist-knot orbifolds. We also derive some interesting results. The explicit formulae of the A-polynomials of twist knots are obtained from the complex distance polynomials. Hence the edge polynomials corresponding to the edges of the Newton polygons of the A-polynomials of twist knots can be obtained. In particular, the number of boundary components of every incompressible surface corresponding to slope -4n+2 turns out to be 2. Bibliography: 39 titles.

Wavefront analysis from its slope data

NASA Astrophysics Data System (ADS)

Mahajan, Virendra N.; Acosta, Eva

2017-08-01

In the aberration analysis of a wavefront over a certain domain, the polynomials that are orthogonal over and represent balanced wave aberrations for this domain are used. For example, Zernike circle polynomials are used for the analysis of a circular wavefront. Similarly, the annular polynomials are used to analyze the annular wavefronts for systems with annular pupils, as in a rotationally symmetric two-mirror system, such as the Hubble space telescope. However, when the data available for analysis are the slopes of a wavefront, as, for example, in a Shack- Hartmann sensor, we can integrate the slope data to obtain the wavefront data, and then use the orthogonal polynomials to obtain the aberration coefficients. An alternative is to find vector functions that are orthogonal to the gradients of the wavefront polynomials, and obtain the aberration coefficients directly as the inner products of these functions with the slope data. In this paper, we show that an infinite number of vector functions can be obtained in this manner. We show further that the vector functions that are irrotational are unique and propagate minimum uncorrelated additive random noise from the slope data to the aberration coefficients.

The NonConforming Virtual Element Method for the Stokes Equations

DOE PAGES

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

2016-01-01

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

Polynomial probability distribution estimation using the method of moments

PubMed Central

Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram–Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation. PMID:28394949

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

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

Influence of surface error on electromagnetic performance of reflectors based on Zernike polynomials

NASA Astrophysics Data System (ADS)

Li, Tuanjie; Shi, Jiachen; Tang, Yaqiong

2018-04-01

This paper investigates the influence of surface error distribution on the electromagnetic performance of antennas. The normalized Zernike polynomials are used to describe a smooth and continuous deformation surface. Based on the geometrical optics and piecewise linear fitting method, the electrical performance of reflector described by the Zernike polynomials is derived to reveal the relationship between surface error distribution and electromagnetic performance. Then the relation database between surface figure and electric performance is built for ideal and deformed surfaces to realize rapidly calculation of far-field electric performances. The simulation analysis of the influence of Zernike polynomials on the electrical properties for the axis-symmetrical reflector with the axial mode helical antenna as feed is further conducted to verify the correctness of the proposed method. Finally, the influence rules of surface error distribution on electromagnetic performance are summarized. The simulation results show that some terms of Zernike polynomials may decrease the amplitude of main lobe of antenna pattern, and some may reduce the pointing accuracy. This work extracts a new concept for reflector's shape adjustment in manufacturing process.

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.

PubMed

Kulkarni, Rishikesh; Rastogi, Pramod

2018-02-01

A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.

Polynomial probability distribution estimation using the method of moments.

PubMed

Munkhammar, Joakim; Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram-Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.

Orthonormal vector polynomials in a unit circle, Part I: Basis set derived from gradients of Zernike polynomials.

PubMed

Zhao, Chunyu; Burge, James H

2007-12-24

Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. These functions are generated from gradients of Zernike polynomials, made orthonormal using the Gram- Schmidt technique. This set provides a complete basis for representing vector fields that can be defined as a gradient of some scalar function. It is then efficient to transform from the coefficients of the vector functions to the scalar Zernike polynomials that represent the function whose gradient was fit. These new vector functions have immediate application for fitting data from a Shack-Hartmann wavefront sensor or for fitting mapping distortion for optical testing. A subsequent paper gives an additional set of vector functions consisting only of rotational terms with zero divergence. The two sets together provide a complete basis that can represent all vector distributions in a circular domain.

Local Composite Quantile Regression Smoothing for Harris Recurrent Markov Processes

PubMed Central

Li, Degui; Li, Runze

2016-01-01

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general Harris recurrent Markov process which includes both the stationary (positive recurrent) and nonstationary (null recurrent) cases. Under some mild conditions, we establish the asymptotic theory for the proposed local polynomial CQR estimator of the mean regression function, and show that the convergence rate for the estimator in nonstationary case is slower than that in stationary case. Furthermore, a weighted type local polynomial CQR estimator is provided to improve the estimation efficiency, and a data-driven bandwidth selection is introduced to choose the optimal bandwidth involved in the nonparametric estimators. Finally, we give some numerical studies to examine the finite sample performance of the developed methodology and theory. PMID:27667894

A Reconstructed Discontinuous Galerkin Method for the Compressible Euler Equations on Arbitrary Grids

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

Hong Luo; Luquing Luo; Robert Nourgaliev

2009-06-01

A reconstruction-based discontinuous Galerkin (DG) method is presented for the solution of the compressible Euler equations on arbitrary grids. By taking advantage of handily available and yet invaluable information, namely the derivatives, in the context of the discontinuous Galerkin methods, a solution polynomial of one degree higher is reconstructed using a least-squares method. The stencils used in the reconstruction involve only the van Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The resulting DG method can be regarded as an improvement of a recovery-based DG method in the sense that it shares the samemore » nice features as the recovery-based DG method, such as high accuracy and efficiency, and yet overcomes some of its shortcomings such as a lack of flexibility, compactness, and robustness. The developed DG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate the accuracy and efficiency of the method. The numerical results indicate that this reconstructed DG method is able to obtain a third-order accurate solution at a slightly higher cost than its second-order DG method and provide an increase in performance over the third order DG method in terms of computing time and storage requirement.« less

Amino acid substitutions in the VanS sensor of the VanA-type vancomycin-resistant Enterococcus strains result in high-level vancomycin resistance and low-level teicoplanin resistance.

PubMed

Hashimoto, Y; Tanimoto, K; Ozawa, Y; Murata, T; Ike, Y

2000-04-15

The vancomycin-resistant enterococci GV1, GV2 and GV3, which were isolated from droppings from broiler farms in Japan have been characterized as VanA-type VRE, which express high-level vancomycin resistance (256 or 512 microg ml(-1), MIC) and low-level teicoplanin resistance (1 or 2 microg ml(-1), MIC). The vancomycin resistances were encoded on plasmids. The vancomycin resistance conjugative plasmid pMG2 was isolated from the GV2 strain. The VanA determinant of pMG2 showed the same genetic organization as that of the VanA genes encoded on the representative transposon Tn1546, which comprises vanRSHAXYZ. The nucleotide sequences of all the genes, except the gene related to the vanS gene on Tn1546, were completely identical to the genes encoded on Tn1546. Three amino acid substitutions in the N-terminal region of the deduced VanS were detected in the nucleotide sequence of vanS encoded on pMG2. There were also three amino acid substitutions in the vanS gene of the GV1 and GV3 strains in the same positions as in the vanS gene of pMG2. Vancomycin induced the increased teicoplanin resistance in these strains.

Presence of the vancomycin resistance gene cluster vanC1, vanXYc, and vanT in Enterococcus casseliflavus.

PubMed

Hölzel, Christina; Bauer, Johann; Stegherr, Eva-Maria; Schwaiger, Karin

2014-04-01

The three chromosomally located clustered genes vanC1, vanXYc, and vanT confer intrinsic resistance to vancomycin and are used for species identification of Enterococcus gallinarum. In this study, 28 strains belonging to the E. gallinarum/casseliflavus group isolated from cloacal swabs from laying hens were screened for the presence of vanC1. As confirmed by species-specific multiplex PCR, 11 vanC1-positive strains were identified as E. gallinarum. Surprisingly, one yellow pigmented strain, verified as E. casseliflavus by species-specific multiplex PCR, was also vanC1 positive; vanXYc and vanT were additionally detectable in this strain. To our knowledge, this is the first report of vanC1, vanXYc, and vanT in E. casseliflavus. The minimum inhibitory concentration of vancomycin was 4 mg/L. Real-time reverse transcription-PCR revealed that none of the clustered genes was expressed in this strain. Even if the genes seem not to be active, there is a certain risk that they will be transferred to other bacteria where they might be functionally expressed. Therefore, it may be advisable to expand the search for vanC1, vanXYc, and vanT from E. gallinarum to other (enterococcal) species. This study confirms that enterococci live up to their name as being reservoir bacteria and should therefore always be closely monitored.

Stabilization of an inverted pendulum-cart system by fractional PI-state feedback.

PubMed

Bettayeb, M; Boussalem, C; Mansouri, R; Al-Saggaf, U M

2014-03-01

This paper deals with pole placement PI-state feedback controller design to control an integer order system. The fractional aspect of the control law is introduced by a dynamic state feedback as u(t)=K(p)x(t)+K(I)I(α)(x(t)). The closed loop characteristic polynomial is thus fractional for which the roots are complex to calculate. The proposed method allows us to decompose this polynomial into a first order fractional polynomial and an integer order polynomial of order n-1 (n being the order of the integer system). This new stabilization control algorithm is applied for an inverted pendulum-cart test-bed, and the effectiveness and robustness of the proposed control are examined by experiments. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.

Computational algebraic geometry for statistical modeling FY09Q2 progress.

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

Thompson, David C.; Rojas, Joseph Maurice; Pebay, Philippe Pierre

2009-03-01

This is a progress report on polynomial system solving for statistical modeling. This is a progress report on polynomial system solving for statistical modeling. This quarter we have developed our first model of shock response data and an algorithm for identifying the chamber cone containing a polynomial system in n variables with n+k terms within polynomial time - a significant improvement over previous algorithms, all having exponential worst-case complexity. We have implemented and verified the chamber cone algorithm for n+3 and are working to extend the implementation to handle arbitrary k. Later sections of this report explain chamber cones inmore » more detail; the next section provides an overview of the project and how the current progress fits into it.« less

A comparison of VLSI architectures for time and transform domain decoding of Reed-Solomon codes

NASA Technical Reports Server (NTRS)

Hsu, I. S.; Truong, T. K.; Deutsch, L. J.; Satorius, E. H.; Reed, I. S.

1988-01-01

It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial needed to decode a Reed-Solomon (RS) code. It is shown that this algorithm can be used for both time and transform domain decoding by replacing its initial conditions with the Forney syndromes and the erasure locator polynomial. By this means both the errata locator polynomial and the errate evaluator polynomial can be obtained with the Euclidean algorithm. With these ideas, both time and transform domain Reed-Solomon decoders for correcting errors and erasures are simplified and compared. As a consequence, the architectures of Reed-Solomon decoders for correcting both errors and erasures can be made more modular, regular, simple, and naturally suitable for VLSI implementation.

Verifying the error bound of numerical computation implemented in computer systems

DOEpatents

Sawada, Jun

2013-03-12

A verification tool receives a finite precision definition for an approximation of an infinite precision numerical function implemented in a processor in the form of a polynomial of bounded functions. The verification tool receives a domain for verifying outputs of segments associated with the infinite precision numerical function. The verification tool splits the domain into at least two segments, wherein each segment is non-overlapping with any other segment and converts, for each segment, a polynomial of bounded functions for the segment to a simplified formula comprising a polynomial, an inequality, and a constant for a selected segment. The verification tool calculates upper bounds of the polynomial for the at least two segments, beginning with the selected segment and reports the segments that violate a bounding condition.

Pulse transmission transmitter including a higher order time derivate filter

DOEpatents

Dress, Jr., William B.; Smith, Stephen F.

2003-09-23

Systems and methods for pulse-transmission low-power communication modes are disclosed. A pulse transmission transmitter includes: a clock; a pseudorandom polynomial generator coupled to the clock, the pseudorandom polynomial generator having a polynomial load input; an exclusive-OR gate coupled to the pseudorandom polynomial generator, the exclusive-OR gate having a serial data input; a programmable delay circuit coupled to both the clock and the exclusive-OR gate; a pulse generator coupled to the programmable delay circuit; and a higher order time derivative filter coupled to the pulse generator. The systems and methods significantly reduce lower-frequency emissions from pulse transmission spread-spectrum communication modes, which reduces potentially harmful interference to existing radio frequency services and users and also simultaneously permit transmission of multiple data bits by utilizing specific pulse shapes.

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

Zlotnikov, Michael

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

Euler polynomials and identities for non-commutative operators

NASA Astrophysics Data System (ADS)

De Angelis, Valerio; Vignat, Christophe

2015-12-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

Torus Knot Polynomials and Susy Wilson Loops

NASA Astrophysics Data System (ADS)

Giasemidis, Georgios; Tierz, Miguel

2014-12-01

We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of ( n, m) torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result, the symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang-Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang-Mills theory, which is known to give averages of Wilson loops in = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones-Rosso representation in terms of q-harmonic oscillators.

The Local Group in LCDM - Shapes and masses of dark halos

NASA Astrophysics Data System (ADS)

Vera-Ciro, Carlos Andrés

2013-01-01

In dit proefschrift bestuderen we de eigenschappen van donkere materie halo's in het LCDM paradigma. Het eerste deel richt zich op de vorm van de massadistributie van dergelijke objecten. We hebben gevonden dat de vorm van ge"isoleerde Melkweg-achtige donkere materie halo's significant afwijkt van bolsymmetrie. De lokale omgeving heeft invloed op de halo's en deze worden daarbij sterk be"invloed door de manier waarop massa aangroeit. We hebben ook de structuur en de baanstructuur van de satellieten van dergelijke halo's in detail onderzocht. In het algemeen zijn deze objecten sferischer dan de halo's zelf. Ze vertonen ook duidelijke afdrukken van getijdenwerking in zowel hun geometrische vorm als in de baanstructuur. Daarna gebruiken we het aantal massieve objecten rond de Melkweg om limieten te zetten op de totale massa van de donkere materie halo van de Melkweg. De eigenschappen van de massaverdeling van de Melkweg worden verder onderzocht in het laatste hoofdstuk. Daar maken we gebruik van de Sagittarius sterstroom om de vorm van de galactische potentiaal beter te bepalen. We komen met een nieuw model dat rekening houdt met de galactische schijf en de invloed van satellietstelsels en die bovendien consistent is met het LCDM paradigma.

Co-colonization of vanA and vanB Enterococcus faecium of clonal complex 17 in a patient with bacteremia due to vanA E. faecium.

PubMed

Seol, Chang Ahn; Park, Jeong Su; Sung, Heungsup; Kim, Mi-Na

2014-06-01

A 53-year-old Vietnamese man with liver cirrhosis was transferred from a Vietnamese hospital to our tertiary care hospital in Korea in order to undergo a liver transplantation. Bacteremia due to vanA Enterococcus faecium was diagnosed, and stool surveillance cultures for vancomycin-resistant enterococci (VRE) were positive for both vanA and vanB E. faecium. Pulsed-field gel electrophoresis analysis revealed that the 2 vanA VRE isolates from the blood and stool were clonal, but the vanB VRE was unrelated to the vanA VRE. vanA and vanB VRE were ST64 and ST18, single-allele variations of clonal complex 17, respectively. This is the first case report of vanA VRE bacteremia in a Vietnamese patient and demonstrates the reemergence of vanB VRE since a single outbreak occurred 15years ago in Korea. The reemergence of vanB VRE emphasizes the importance of VRE genotyping to prevent the spread of new VRE strains. Copyright © 2014 Elsevier Inc. All rights reserved.

Constant-Round Concurrent Zero Knowledge From Falsifiable Assumptions

DTIC Science & Technology

2013-01-01

assumptions (e.g., [DS98, Dam00, CGGM00, Gol02, PTV12, GJO+12]), or in alternative models (e.g., super -polynomial-time simulation [Pas03b, PV10]). In the...T (·)-time computations, where T (·) is some “nice” (slightly) super -polynomial function (e.g., T (n) = nlog log logn). We refer to such proof...put a cap on both using a (slightly) super -polynomial function, and thus to guarantee soundness of the concurrent zero-knowledge protocol, we need

On the Existence of Non-Oscillatory Phase Functions for Second Order Ordinary Differential Equations in the High-Frequency Regime

DTIC Science & Technology

2014-08-04

Chebyshev coefficients of both r and q decay exponentially, although those of r decay at a slightly slower rate. 10.2. Evaluation of Legendre polynomials ...In this experiment, we compare the cost of evaluating Legendre polynomials of large order using the standard recurrence relation with the cost of...doing so with a nonoscillatory phase function. For any integer n ě 0, the Legendre polynomial Pnpxq of order n is a solution of the second order

A Near to Far Transformation using Spherical Expansions Phase 1: Verification on Simulated Antennas

DTIC Science & Technology

2014-09-01

Antenna Pattern Range. . . . . 75 List of Tables 1 Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Legendre polynomials ...first kind Pmn (x) are [3, Equation 12.84 and footnote]: Pmn (x) := (−1)m(1− x2)m/2 dm dxm Pn(x), where Pn(x)’s are the Legendre polynomials . There is the...n ) (4) 9 that computes Pmn (x) = 0 for m > n (5) Table 2 lists the initial Legendre polynomials and their derivatives. Figure 8 plots the first few

New separated polynomial solutions to the Zernike system on the unit disk and interbasis expansion.

PubMed

Pogosyan, George S; Wolf, Kurt Bernardo; Yakhno, Alexander

2017-10-01

The differential equation proposed by Frits Zernike to obtain a basis of polynomial orthogonal solutions on the unit disk to classify wavefront aberrations in circular pupils is shown to have a set of new orthonormal solution bases involving Legendre and Gegenbauer polynomials in nonorthogonal coordinates, close to Cartesian ones. We find the overlaps between the original Zernike basis and a representative of the new set, which turn out to be Clebsch-Gordan coefficients.

Impacts of Sigma Coordinates on the Euler and Navier-Stokes Equations using Continuous Galerkin Methods

DTIC Science & Technology

2009-03-01

the 1- D local basis functions. The 1-D Lagrange polynomial local basis function, using Legendre -Gauss-Lobatto interpolation points, was defined by...cases were run using 10th order polynomials , with contours from -0.05 to 0.525 K with an interval of 0.025 K...after 700 s for reso- lutions: (a) 20, (b) 10, and (c) 5 m. All cases were run using 10th order polynomials , with contours from -0.05 to 0.525 K

Distortion theorems for polynomials on a circle

NASA Astrophysics Data System (ADS)

Dubinin, V. N.

2000-12-01

Inequalities for the derivatives with respect to \\varphi=\\arg z the functions \\operatorname{Re}P(z), \\vert P(z)\\vert^2 and \\arg P(z) are established for an algebraic polynomial P(z) at points on the circle \\vert z\\vert=1. These estimates depend, in particular, on the constant term and the leading coefficient of the polynomial P(z) and improve the classical Bernstein and Turan inequalities. The method of proof is based on the techniques of generalized reduced moduli.

On the coefficients of integrated expansions of Bessel polynomials

NASA Astrophysics Data System (ADS)

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

2006-03-01

A new formula expressing explicitly the integrals of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another new explicit formula relating the Bessel coefficients of an expansion for 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 also established. An application of these formulae for solving ordinary differential equations with varying coefficients is discussed.

Orthogonal Polynomials Associated with Complementary Chain Sequences

NASA Astrophysics Data System (ADS)

Behera, Kiran Kumar; Sri Ranga, A.; Swaminathan, A.

2016-07-01

Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using the relation between these complementary chain sequences and the corresponding Verblunsky coefficients, the para-orthogonal polynomials and the associated Szegő polynomials are analyzed. Two illustrations, one involving Gaussian hypergeometric functions and the other involving Carathéodory functions are also provided. A connection between these two illustrations by means of complementary chain sequences is also observed.

Biochemical and Genetic Characterization of the vanC-2 Vancomycin Resistance Gene Cluster of Enterococcus casseliflavus ATCC 25788

PubMed Central

Dutta, Ireena; Reynolds, Peter E.

2002-01-01

The vanC-2 cluster of Enterococcus casseliflavus ATCC 25788 consisted of five genes (vanC-2, vanXYC-2, vanTC-2, vanRC-2, and vanSC-2) and shared the same organization as the vanC cluster of E. gallinarum BM4174. The proteins encoded by these genes displayed a high degree of amino acid identity to the proteins encoded within the vanC gene cluster. The putative d,d-dipeptidase-d,d-carboxypeptidase, VanXYC-2, exhibited 81% amino acid identity to VanXYC, and VanTC-2 displayed 65% amino acid identity to the serine racemase, VanT. VanRC-2 and VanSC-2 displayed high degrees of identity to VanRC and VanSC, respectively, and contained the conserved residues identified as important to their function as a response regulator and histidine kinase, respectively. Resistance to vancomycin was expressed inducibly in E. casseliflavus ATCC 25788 and required an extended period of induction. Analysis of peptidoglycan precursors revealed that UDP-N-acetylmuramyl-l-Ala-δ-d-Glu-l-Lys-d-Ala-d-Ser could not be detected until several hours after the addition of vancomycin, and its appearance coincided with the resumption of growth. The introduction of additional copies of the vanTC-2 gene, encoding a putative serine racemase, and the presence of supplementary d-serine in the growth medium both significantly reduced the period before growth resumed after addition of vancomycin. This suggested that the availability of d-serine plays an important role in the induction process. PMID:12234834

Orthogonal sets of data windows constructed from trigonometric polynomials

NASA Technical Reports Server (NTRS)

Greenhall, C. A.

1989-01-01

Suboptimal, easily computable substitutes for the discrete prolate-spheroidal windows used by Thomson for spectral estimation are given. Trigonometric coefficients and energy leakages of the window polynomials are tabulated.

Characterisation of the selective binding of antibiotics vancomycin and teicoplanin by the VanS receptor regulating type A vancomycin resistance in the enterococci.

PubMed

Hughes, C S; Longo, E; Phillips-Jones, M K; Hussain, R

2017-08-01

A-type resistance towards "last-line" glycopeptide antibiotic vancomycin in the leading hospital acquired infectious agent, the enterococci, is the most common in the UK. Resistance is regulated by the VanR A S A two-component system, comprising the histidine sensor kinase VanS A and the partner response regulator VanR A . The nature of the activating ligand for VanS A has not been identified, therefore this work sought to identify and characterise ligand(s) for VanS A . In vitro approaches were used to screen the structural and activity effects of a range of potential ligands with purified VanS A protein. Of the screened ligands (glycopeptide antibiotics vancomycin and teicoplanin, and peptidoglycan components N-acetylmuramic acid, D-Ala-D-Ala and Ala-D-y-Glu-Lys-D-Ala-D-Ala) only glycopeptide antibiotics vancomycin and teicoplanin were found to bind VanS A with different affinities (vancomycin 70μM; teicoplanin 30 and 170μM), and were proposed to bind via exposed aromatic residues tryptophan and tyrosine. Furthermore, binding of the antibiotics induced quicker, longer-lived phosphorylation states for VanS A , proposing them as activators of type A vancomycin resistance in the enterococci. Copyright © 2017 Diamond Light Source Ltd. Published by Elsevier B.V. All rights reserved.

Hermite polynomials and quasi-classical asymptotics

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

Ali, S. Twareque, E-mail: twareque.ali@concordia.ca; Engliš, Miroslav, E-mail: englis@math.cas.cz

2014-04-15

We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.

Schur Stability Regions for Complex Quadratic Polynomials

ERIC Educational Resources Information Center

Cheng, Sui Sun; Huang, Shao Yuan

2010-01-01

Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

Members of the Genera Paenibacillus and Rhodococcus Harbor Genes Homologous to Enterococcal Glycopeptide Resistance Genes vanA and vanB

PubMed Central

Guardabassi, L.; Christensen, H.; Hasman, H.; Dalsgaard, A.

2004-01-01

Genes homologous to enterococcal glycopeptide resistance genes vanA and vanB were found in glycopeptide-resistant Paenibacillus and Rhodococcus strains from soil. The putative d-Ala:d-Lac ligase genes in Paenibacillus thiaminolyticus PT-2B1 and Paenibacillus apiarius PA-B2B were closely related to vanA (92 and 87%) and flanked by genes homologous to vanH and vanX in vanA operons. PMID:15561881

Members of the genera Paenibacillus and Rhodococcus harbor genes homologous to enterococcal glycopeptide resistance genes vanA and vanB.

PubMed

Guardabassi, L; Christensen, H; Hasman, H; Dalsgaard, A

2004-12-01

Genes homologous to enterococcal glycopeptide resistance genes vanA and vanB were found in glycopeptide-resistant Paenibacillus and Rhodococcus strains from soil. The putative D-Ala:D-Lac ligase genes in Paenibacillus thiaminolyticus PT-2B1 and Paenibacillus apiarius PA-B2B were closely related to vanA (92 and 87%) and flanked by genes homologous to vanH and vanX in vanA operons.

Biochemical and genetic characterization of the vanC-2 vancomycin resistance gene cluster of Enterococcus casseliflavus ATCC 25788.

PubMed

Dutta, Ireena; Reynolds, Peter E

2002-10-01

The vanC-2 cluster of Enterococcus casseliflavus ATCC 25788 consisted of five genes (vanC-2, vanXY(C-2), vanT(C-2), vanR(C-2), and vanS(C-2)) and shared the same organization as the vanC cluster of E. gallinarum BM4174. The proteins encoded by these genes displayed a high degree of amino acid identity to the proteins encoded within the vanC gene cluster. The putative D,D-dipeptidase-D,D-carboxypeptidase, VanXY(C-2), exhibited 81% amino acid identity to VanXY(C), and VanT(C-2) displayed 65% amino acid identity to the serine racemase, VanT. VanR(C-2) and VanS(C-2) displayed high degrees of identity to VanR(C) and VanS(C), respectively, and contained the conserved residues identified as important to their function as a response regulator and histidine kinase, respectively. Resistance to vancomycin was expressed inducibly in E. casseliflavus ATCC 25788 and required an extended period of induction. Analysis of peptidoglycan precursors revealed that UDP-N-acetylmuramyl-L-Ala-delta-D-Glu-L-Lys-D-Ala-D-Ser could not be detected until several hours after the addition of vancomycin, and its appearance coincided with the resumption of growth. The introduction of additional copies of the vanT(C-2) gene, encoding a putative serine racemase, and the presence of supplementary D-serine in the growth medium both significantly reduced the period before growth resumed after addition of vancomycin. This suggested that the availability of D-serine plays an important role in the induction process.

Stitching interferometry of a full cylinder without using overlap areas

NASA Astrophysics Data System (ADS)

Peng, Junzheng; Chen, Dingfu; Yu, Yingjie

2017-08-01

Traditional stitching interferometry requires finding out the overlap correspondence and computing the discrepancies in the overlap regions, which makes it complex and time-consuming to obtain the 360° form map of a cylinder. In this paper, we develop a cylinder stitching model based on a new set of orthogonal polynomials, termed Legendre Fourier (LF) polynomials. With these polynomials, individual subaperture data can be expanded as a composition of the inherent form of a partial cylinder surface and additional misalignment parameters. Then the 360° form map can be acquired by simultaneously fitting all subaperture data with the LF polynomials. A metal shaft was measured to experimentally verify the proposed method. In contrast to traditional stitching interferometry, our technique does not require overlapping of adjacent subapertures, thus significantly reducing the measurement time and making the stitching algorithm simple.

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

PubMed

Mahajan, Virendra N

2010-12-20

The classical aberrations of an anamorphic optical imaging system, representing the terms of a power-series expansion of its aberration function, are separable in the Cartesian coordinates of a point on its pupil. We discuss the balancing of a classical aberration of a certain order with one or more such aberrations of lower order to minimize its variance across a rectangular pupil of such a system. We show that the balanced aberrations are the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point. The compound Legendre polynomials are orthogonal across a rectangular pupil and, like the classical aberrations, are inherently separable in the Cartesian coordinates of the pupil point. They are different from the balanced aberrations and the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil.

Symmetries and Invariants of Twisted Quantum Algebras and Associated Poisson Algebras

NASA Astrophysics Data System (ADS)

Molev, A. I.; Ragoucy, E.

We construct an action of the braid group BN on the twisted quantized enveloping algebra U q'( {o}N) where the elements of BN act as automorphisms. In the classical limit q → 1, we recover the action of BN on the polynomial functions on the space of upper triangular matrices with ones on the diagonal. The action preserves the Poisson bracket on the space of polynomials which was introduced by Nelson and Regge in their study of quantum gravity and rediscovered in the mathematical literature. Furthermore, we construct a Poisson bracket on the space of polynomials associated with another twisted quantized enveloping algebra U q'( {sp}2n). We use the Casimir elements of both twisted quantized enveloping algebras to reproduce and construct some well-known and new polynomial invariants of the corresponding Poisson algebras.

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland W.

1992-01-01

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed, which aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, we investigate the use of Bernstein-Szego weights.

Polynomial approximations of thermodynamic properties of arbitrary gas mixtures over wide pressure and density ranges

NASA Technical Reports Server (NTRS)

Allison, D. O.

1972-01-01

Computer programs for flow fields around planetary entry vehicles require real-gas equilibrium thermodynamic properties in a simple form which can be evaluated quickly. To fill this need, polynomial approximations were found for thermodynamic properties of air and model planetary atmospheres. A coefficient-averaging technique was used for curve fitting in lieu of the usual least-squares method. The polynomials consist of terms up to the ninth degree in each of two variables (essentially pressure and density) including all cross terms. Four of these polynomials can be joined to cover, for example, a range of about 1000 to 11000 K and 0.00001 to 1 atmosphere (1 atm = 1.0133 x 100,000 N/m sq) for a given thermodynamic property. Relative errors of less than 1 percent are found over most of the applicable range.

Measurement of EUV lithography pupil amplitude and phase variation via image-based methodology

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

Levinson, Zachary; Verduijn, Erik; Wood, Obert R.

2016-04-01

Here, an approach to image-based EUV aberration metrology using binary mask targets and iterative model-based solutions to extract both the amplitude and phase components of the aberrated pupil function is presented. The approach is enabled through previously developed modeling, fitting, and extraction algorithms. We seek to examine the behavior of pupil amplitude variation in real-optical systems. Optimized target images were captured under several conditions to fit the resulting pupil responses. Both the amplitude and phase components of the pupil function were extracted from a zone-plate-based EUV mask microscope. The pupil amplitude variation was expanded in three different bases: Zernike polynomials,more » Legendre polynomials, and Hermite polynomials. It was found that the Zernike polynomials describe pupil amplitude variation most effectively of the three.« less

Polynomial solution of quantum Grassmann matrices

NASA Astrophysics Data System (ADS)

Tierz, Miguel

2017-05-01

We study a model of quantum mechanical fermions with matrix-like index structure (with indices N and L) and quartic interactions, recently introduced by Anninos and Silva. We compute the partition function exactly with q-deformed orthogonal polynomials (Stieltjes-Wigert polynomials), for different values of L and arbitrary N. From the explicit evaluation of the thermal partition function, the energy levels and degeneracies are determined. For a given L, the number of states of different energy is quadratic in N, which implies an exponential degeneracy of the energy levels. We also show that at high-temperature we have a Gaussian matrix model, which implies a symmetry that swaps N and L, together with a Wick rotation of the spectral parameter. In this limit, we also write the partition function, for generic L and N, in terms of a single generalized Hermite polynomial.

Genetic parameters of legendre polynomials for first parity lactation curves.

PubMed

Pool, M H; Janss, L L; Meuwissen, T H

2000-11-01

Variance components of the covariance function coefficients in a random regression test-day model were estimated by Legendre polynomials up to a fifth order for first-parity records of Dutch dairy cows using Gibbs sampling. Two Legendre polynomials of equal order were used to model the random part of the lactation curve, one for the genetic component and one for permanent environment. Test-day records from cows registered between 1990 to 1996 and collected by regular milk recording were available. For the data set, 23,700 complete lactations were selected from 475 herds sired by 262 sires. Because the application of a random regression model is limited by computing capacity, we investigated the minimum order needed to fit the variance structure in the data sufficiently. Predictions of genetic and permanent environmental variance structures were compared with bivariate estimates on 30-d intervals. A third-order or higher polynomial modeled the shape of variance curves over DIM with sufficient accuracy for the genetic and permanent environment part. Also, the genetic correlation structure was fitted with sufficient accuracy by a third-order polynomial, but, for the permanent environmental component, a fourth order was needed. Because equal orders are suggested in the literature, a fourth-order Legendre polynomial is recommended in this study. However, a rank of three for the genetic covariance matrix and of four for permanent environment allows a simpler covariance function with a reduced number of parameters based on the eigenvalues and eigenvectors.

A model-based 3D phase unwrapping algorithm using Gegenbauer polynomials.

PubMed

Langley, Jason; Zhao, Qun

2009-09-07

The application of a two-dimensional (2D) phase unwrapping algorithm to a three-dimensional (3D) phase map may result in an unwrapped phase map that is discontinuous in the direction normal to the unwrapped plane. This work investigates the problem of phase unwrapping for 3D phase maps. The phase map is modeled as a product of three one-dimensional Gegenbauer polynomials. The orthogonality of Gegenbauer polynomials and their derivatives on the interval [-1, 1] are exploited to calculate the expansion coefficients. The algorithm was implemented using two well-known Gegenbauer polynomials: Chebyshev polynomials of the first kind and Legendre polynomials. Both implementations of the phase unwrapping algorithm were tested on 3D datasets acquired from a magnetic resonance imaging (MRI) scanner. The first dataset was acquired from a homogeneous spherical phantom. The second dataset was acquired using the same spherical phantom but magnetic field inhomogeneities were introduced by an external coil placed adjacent to the phantom, which provided an additional burden to the phase unwrapping algorithm. Then Gaussian noise was added to generate a low signal-to-noise ratio dataset. The third dataset was acquired from the brain of a human volunteer. The results showed that Chebyshev implementation and the Legendre implementation of the phase unwrapping algorithm give similar results on the 3D datasets. Both implementations of the phase unwrapping algorithm compare well to PRELUDE 3D, 3D phase unwrapping software well recognized for functional MRI.

Reachability Analysis in Probabilistic Biological Networks.

PubMed

Gabr, Haitham; Todor, Andrei; Dobra, Alin; Kahveci, Tamer

2015-01-01

Extra-cellular molecules trigger a response inside the cell by initiating a signal at special membrane receptors (i.e., sources), which is then transmitted to reporters (i.e., targets) through various chains of interactions among proteins. Understanding whether such a signal can reach from membrane receptors to reporters is essential in studying the cell response to extra-cellular events. This problem is drastically complicated due to the unreliability of the interaction data. In this paper, we develop a novel method, called PReach (Probabilistic Reachability), that precisely computes the probability that a signal can reach from a given collection of receptors to a given collection of reporters when the underlying signaling network is uncertain. This is a very difficult computational problem with no known polynomial-time solution. PReach represents each uncertain interaction as a bi-variate polynomial. It transforms the reachability problem to a polynomial multiplication problem. We introduce novel polynomial collapsing operators that associate polynomial terms with possible paths between sources and targets as well as the cuts that separate sources from targets. These operators significantly shrink the number of polynomial terms and thus the running time. PReach has much better time complexity than the recent solutions for this problem. Our experimental results on real data sets demonstrate that this improvement leads to orders of magnitude of reduction in the running time over the most recent methods. Availability: All the data sets used, the software implemented and the alignments found in this paper are available at http://bioinformatics.cise.ufl.edu/PReach/.

Efficient computer algebra algorithms for polynomial matrices in control design

NASA Technical Reports Server (NTRS)

Baras, J. S.; Macenany, D. C.; Munach, R.

1989-01-01

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

Incidence of Acute Kidney Injury among Patients Treated with Piperacillin-Tazobactam or Meropenem in Combination with Vancomycin.

PubMed

Rutter, W Cliff; Burgess, David S

2018-07-01

Acute kidney injury (AKI) increases during empirical antimicrobial therapy with the combination of piperacillin-tazobactam (TZP) and vancomycin (VAN) compared to the number of incidences with monotherapy or the combination of cefepime and VAN. Limited data regarding the impact of meropenem (MEM) combined with VAN exist. This study examined the AKI incidence among patients treated with MEM plus VAN (MEM+VAN) or TZP+VAN. Data were collected from the University of Kentucky Center for Clinical and Translational Science Enterprise Data Trust from September 2007 through October 2015. Adults without previous renal disease who received MEM+VAN or TZP+VAN for at least 2 days were included. AKI was assessed using risk, injury, failure, loss, and end-stage (RIFLE) criteria. Inverse probability of treatment weighting was utilized to control for differences between groups. In total, 10,236 patients met inclusion criteria, with 9,898 receiving TZP+VAN and 338 receiving MEM+VAN. AKI occurred in 15.4% of MEM+VAN patients and in 27.4% of TZP+VAN patients ( P < 0.001). TZP+VAN was associated with increased AKI compared to the level with MEM+VAN (odds ratio [OR], 2.53; 95% confidence interval [CI], 1.82 to 3.52), after controlling for confounders. Use of MEM+VAN should be considered an appropriate alternative therapy to TZP+VAN if nephrotoxicity is a major concern. The results of this study demonstrate that judicial use of TZP+VAN for empirical coverage of infection is needed. Copyright © 2018 American Society for Microbiology.

Revision of the subfamily Opiinae (Hymenoptera, Braconidae) from Hunan (China), including thirty-six new species and two new genera

PubMed Central

Li, Xi-Ying; van Achterberg, Cornelis; Tan, Ji-Cai

2013-01-01

Abstract The species of the subfamily Opiinae (Hymenoptera: Braconidae) from Hunan (Oriental China) are revised and illustrated. Thirty-six new species are described: Apodesmia bruniclypealis Li & van Achterberg, sp. n., Apodesmia melliclypealis Li & van Achterberg, sp. n., Areotetes albiferus Li & van Achterberg, sp. n., Areotetes carinuliferus Li & van Achterberg, sp. n., Areotetes striatiferus Li & van Achterberg, sp. n., Coleopioides diversinotum Li & van Achterberg, sp. n., Coleopioides postpectalis Li & van Achterberg, sp. n., Fopius dorsopiferus Li, van Achterberg & Tan, sp. n., Indiopius chenae Li & van Achterberg, sp. n., Opiognathus aulaciferus Li & van Achterberg, sp. n., Opiognathus brevibasalis Li & van Achterberg, sp. n., Opius crenuliferus Li & van Achterberg, sp. n., Opius malarator Li, van Achterberg & Tan, sp. n., Opius monilipalpis Li & van Achterberg, sp. n., Opius pachymerus Li & van Achterberg, sp. n., Opius songi Li & van Achterberg, sp. n., Opius youi Li & van Achterberg, sp. n., Opius zengi Li & van Achterberg, sp. n., Phaedrotoma acuticlypeata Li & van Achterberg, sp. n., Phaedrotoma angiclypeata Li & van Achterberg, sp. n., Phaedrotoma antenervalis Li & van Achterberg, sp. n., Phaedrotoma depressiclypealis Li & van Achterberg, sp. n., Phaedrotoma flavisoma Li & van Achterberg, sp. n., Phaedrotoma nigrisoma Li & van Achterberg, sp. n., Phaedrotoma protuberator Li & van Achterberg, sp. n., Phaedrotoma rugulifera Li & van Achterberg, sp. n., Li & van Achterberg,Phaedrotoma striatinota Li & van Achterberg, sp. n., Phaedrotoma vermiculifera Li & van Achterberg, sp. n., Rhogadopsis latipennis Li & van Achterberg, sp. n., Rhogadopsis longicaudifera Li & van Achterberg, sp. n., Rhogadopsis maculosa Li, van Achterberg & Tan, sp. n., Rhogadopsis obliqua Li & van Achterberg, sp. n., Rhogadopsis sculpturator Li & van Achterberg, sp. n., Utetes longicarinatus Li & van Achterberg, sp. n. and Xynobius notauliferus Li & van Achterberg, sp. n. Areotetes van Achterberg & Li, gen. n. (type species: Areotetes carinuliferus sp. n.) and Coleopioides van Achterberg & Li, gen. n. (type species: Coleopioides postpectalis sp. n. are described. All species are illustrated and keyed. In total 30 species of Opiinae are sequenced and the cladograms are presented. Neopius Gahan, 1917, Opiognathus Fischer, 1972, Opiostomus Fischer, 1972, and Rhogadopsis Brèthes, 1913, are treated as a valid genera based on molecular and morphological differences. Opius vittata Chen & Weng, 2005 (not Opius vittatus Ruschka, 1915), Opius ambiguus Weng & Chen, 2005 (not Wesmael, 1835) and Opius mitis Chen & Weng, 2005 (not Fischer, 1963) are primary homonymsandarerenamed into Phaedrotoma depressa Li & van Achterberg, nom. n., Opius cheni Li & van Achterberg, nom. n. andOpius wengi Li & van Achterberg, nom. n., respectively. Phaedrotoma terga (Chen & Weng, 2005) comb. n.,Diachasmimorpha longicaudata (Ashmead, 1905) and Biosteres pavitita Chen & Weng, 2005, are reported new for Hunan, Opiostomus aureliae (Fischer, 1957) comb. n. is new for China and Hunan; Xynobius maculipennis(Enderlein, 1912) comb. n. is new for Hunan and continental China and Rhogadopsis longuria (Chen & Weng, 2005) comb. n. is new for Hunan. The following new combinations are given: Apodesmia puncta (Weng & Chen, 2005) comb. n., Apodesmia tracta (Weng & Chen, 2005) comb. n., Areotetes laevigatus (Weng & Chen, 2005) comb. n., Phaedrotoma dimidia (Chen & Weng, 2005) comb. n., Phaedrotoma improcera (Weng & Chen, 2005) comb. n., Phaedrotoma amputata (Weng & Chen, 2005) comb. n., Phaedrotoma larga (Weng & Chen, 2005) comb. n., Phaedrotoma osculas (Weng & Chen, 2005) comb. n., Phaedrotoma postuma (Chen & Weng, 2005) comb. n., Phaedrotoma rugulosa (Chen & Weng, 2005) comb. n., Phaedrotoma tabularis (Weng & Chen, 2005) comb. n., Rhogadopsis apii (Chen & Weng, 2005) comb. n., Rhogadopsis dimidia (Chen & Weng, 2005) comb. n., Rhogadopsis diutia (Chen & Weng, 2005) comb. n., Rhogadopsis longuria (Chen & Weng, 2005) comb. n., Rhogadopsis pratellae(Weng & Chen, 2005) comb. n., Rhogadopsis pratensis (Weng & Chen, 2005) comb. n., Rhogadopsis sculpta (Chen & Weng, 2005) comb. n., Rhogadopsis sulcifer (Fischer, 1975) comb. n., Rhogadopsis tabidula(Weng & Chen, 2005) comb. n., Xynobius complexus (Weng & Chen, 2005) comb. n., Xynobius indagatrix (Weng & Chen, 2005) comb. n., Xynobius multiarculatus (Chen & Weng, 2005) comb. n. The following (sub)genera are synonymised: Snoflakopius Fischer, 1972, Jucundopius Fischer, 1984, Opiotenes Fischer, 1998, and Oetztalotenes Fischer, 1998, with Opiostomus Fischer, 1971; Xynobiotenes Fischer, 1998, with Xynobius Foerster, 1862; Allotypus Foerster, 1862, Lemnaphilopius Fischer, 1972, Agnopius Fischer, 1982, and Cryptognathopius Fischer, 1984, with Apodesmia Foerster, 1862; Nosopoea Foerster, 1862, Tolbia Cameron, 1907, Brachycentrus Szépligeti, 1907, Baeocentrum Schulz, 1911, Hexaulax Cameron, 1910, Coeloreuteus Roman, 1910, Neodiospilus Szépligeti, 1911, Euopius Fischer, 1967, Gerius Fischer, 1972, Grimnirus Fischer, 1972, Hoenirus Fischer, 1972, Mimirus Fischer, 1972, Gastrosema Fischer, 1972, Merotrachys Fischer, 1972, Phlebosema Fischer, 1972, Neoephedrus Samanta, Tamili, Saha & Raychaudhuri, 1983, Adontopius Fischer, 1984, Kainopaeopius Fischer, 1986, Millenniopius Fischer, 1996, and Neotropopius Fischer, 1999, with Phaedrotoma Foerster, 1862. PMID:23653521

Scatterometry

NASA Astrophysics Data System (ADS)

Stoffelen, Adrianus Cornelis Maria

1996-10-01

Een veelheid aan meteorologische metingen is dagelijks beschikbaar. De meeste van deze waarnemingen bevinden zich echter boven land, en met name windwaarnemingen boven de (Noord Atlantische) oceaan zijn schaars. Bij een westelijke luchtstroming is dit een duidelijke beperking voor de weers- en golfverwachtingen ten behoeve van Nederland. Juist dan is het gevaar voor bijvoorbeeld storm of overstroming het grootst. Ook in het aardse klimaatsysteem speelt de wind aan het oppervlak een grote rol en is de belangrijkste factor voor de aandrijving van de oceaancirculatie. De oceaancirculatie op zijn beurt is cruciaal voor de verschijnselen die samenhangen met bijvoorbeeld El Niño. Dit proefschift gaat over het scatterometer instrument dat vanuit de ruimte, zelfs onder een wolkendek, nauwkeurige en betrouwbare informatie geeft over de wind aan het oceaanoppervlak met een hoge mate van ruimtelijke consistentie. Tijdens de tweede wereldoorlog werden radars aan boord van schepen veelvuldig gebruikt voor de opsporing van vijandige vaartuigen. Hierbij werd vastgesteld dat de detectie slechter werd naarmate de wind aan het zeeoppervlak groter was. Proefondervindelijk was hiermee het principe van een wind scatterometer aangetoond. Al snel ontwikkelde zich dan ook de idee de wind aan het zeeoppervlak te meten met behulp van radar. Vanuit een vliegtuig of een satelliet word dan een microgolfbundel onder een schuine hoek naar het zeeoppervlak gestuurd. De microgolfstraling, met gewoonlijk een golflengte van enkele centimeters, wordt verstrooid aan het ruwe oppervlak, en een klein gedeelte van de uitgezonden puls keert terug naar het detectorgedeelte van de scatterometer. Het fysische fenomeen van belang voor de werking van de scatterometer is de aanwezigheid van zogeheten capillaire gavitatiegolven op het zeeoppervlak. Deze golven hebben een golflengte van enkele centimeters en reageren vrijwel instantaan op de sterkte van de wind. De verstrooiing van microgolven is op zijn beurt weer sterk afhankelijk van de amplitude van de capillaire golven. Bovendien blijken de capillaire golfjes over het algemeen gericht in lijn met de windrichting. Aldus bestaat er een verband tussen de hoeveelheid teruggestrooide energie en de windsterkte en -richting op enige hoogte. Een scatterometer instrument wordt zo ontworpen dat uit diverse metingen van het teruggestrooide vermogen, windsterkte en -richting afgeleid kunnen worden. Deze metingen kunnen dan eenvoudig vergeleken worden met bestaande windgegevens van boeien, schepen en weermodellen ter calibratie en validatie.?SAMENVATTING viii Overzicht In de loop der jaren zijn scatterometer instrumenten aan boord van verscheidene satellieten gelanceerd. De scatterometers op de ERS-1 en ERS-2 ("European Remote-sensing Satellite") hebben de langste staat van dienst en zijn sinds 1991 operationeel. Deze scatterometers (die identiek zijn) hebben ieder drie antennes, waarmee het oceaanoppervlak in drie verschillende richtingen bemeten wordt. Een punt op het aardoppervlak wordt eerst door de naar voren gerichte bundel belicht, dan door de naar opzij gerichte bundel, en als laatste door de naar achteren gerichte bundel. De drie metingen, verder kortweg aangeduid als trits, kunnen tegen elkaar worden uitgezet, hetgeen resulteert in een ruimtelijk (3D) plaatje. Door uitgekiende doorsneden te maken van deze ruimte kan de samenhang van de drie metingen kwalitatief worden bestudeerd. De drie metingen blijken dan inderdaad een sterke samenhang te vertonen die verklaard kan worden uit twee geofysische parameters. De drie metingen liggen namelijk in het algemeen dichtbij een hoornvormig (2D) oppervlak. De lengterichting van de hoorn blijkt voornamelijk te corresponderen met een variërende windsterkte (of ruwheid van de zee), en de kortste omtrek van de hoorn met een variërende windrichting (ofwel oriëntatie van de capillaire golfjes). De karakterisatie en modellering van dit oppervlak heeft geleid tot een aanzienlijke verbetering in de interpretatie van de scatterometer, zoals beschreven is in dit proefschrift. Hierboven is een uiterst simplistisch beeld gegeven van de fysica die van belang is bij de interpretatie van de scatterometer. Het eerste hoofdstuk van dit proefschrift beschrijft in meer detail de fysische modellering van belang bij de interpretatie van de scatterometer metingen. Ten eerste, de topografie van het zeeoppervlak is uitermate gecompliceerd en niet nauwkeurig te beschrijven met eenvoudige mathematische vergelijkingen. De capillaire golven hebben een andere fasesnelheid dan de langere golven en beide hebben hiermee een ingewikkelde dynamische interactie. Bij hogere windsnelheid breken de golven en ontstaan er schuimkoppen, hetgeen de fysische beschrijving verder compliceert. Ten tweede, de interactie van een schuin invallende microgolfbundel met dit gecompliceerde oppervlak is evenmin nauwkeurig te beschrijven. Zowel verstrooiing als reflectie kunnen een rol spelen. Ten derde, over de relatie tussen de amplitude van de capillaire golven en de wind op enige hoogte, laten we veronderstellen 10 m, is in de literatuur niet de overeenstemming tot in het gewenste detail. Bij lage windsnelheid zouden de oppervlaktespanning of variaties in de wind variabiliteit een rol kunnen spelen. Gezien de fysische complexiteit, is het niet verwonderlijk dat voor de interpretatie van scatterometer metingen statistische methoden hun opgang gevonden hebben. Dit proefschrift gaat met name in op deze methoden, en geeft, aan de hand van vijf wetenschappelijke publicaties, een tamelijk volledig beeld van de "state-of-the-art", zoals die bereikt is met de?SAMENVATTING ix ERS scatterometers (ERS-1 vanaf 17 juli 1991 en later ERS-2 vanaf 22 november 1995). Het derde hoofdstuk behandelt de visualisatie van de gemeten tritsen in de 3D meetruimte, de bepaling van de spreiding van de metingen rond het hoornvormige oppervlak, en de schatting van de meest waarschijnlijke "werkelijke" (of ruisvrije) trits bij het hoornvormige oppervlak gegeven de metingen en hun nauwkeurigheid (inversie). De perceptie dat de metingen met grote waarschijnlijkheid dichtbij een hoornvormig oppervlak liggen, vormt essentiële a priori informatie van belang voor de inversie. Een inversieprocedure gestoeld op waarschijnlijkheidstheorie is afgeleid. Verder worden aan de hand van de structuur van het hoornvormige oppervlak indicatoren bepaald, van belang voor de kwaliteitscontrole, instrumentbewaking, en de verdere verwerking van de gegevens. In de appendix wordt een methode besproken die beschrijft hoe, aan de hand van geselecteerde windgegevens en een goed wind-microgolf verband, ofwel transfer functie, de scatterometer verstrooiingsmetingen gecalibreerd kunnen worden boven de oceaan. Het blijkt dat deze calibratie, die per antenne wordt uitgevoerd, uiterst nauwkeurig is, en, wanneer toegepast, in de 3D meetruimte de verdeling van gemeten tritsen gemiddeld dichterbij de door de transfer functie gemodelleerde hoorn brengt. Dit levert een verbetert scatterometer wind product op. De methode was met name van groot belang voor de validatie en calibratie van de ERS-2 scatterometer, voordat de instrumentele calibratie was voltooid. Met behulp van een set windgegevens uit een weermodel en hun geschatte nauwkeurigheden, passend in locatie en tijd bij een set van scatterometer metingen en hun geschatte nauwkeurigheden, kan met quasi-lineaire schattingstheorie ("Maximum Likelihood Estimation") de meest waarschijnlijke wind-microgolf transfer functie worden afgeleid. De niet-lineariteit en onnauwkeurige formulering van de transfer functie, een niet-uniforme verdeling van invoergegevens, en een inaccurate formulering van de geschatte nauwkeurigheid kunnen hier een goed resultaat in de weg staan. Een nieuwe functie, genoemd CMOD4, wordt afgeleid in hoofdstuk IV. Een eerste eis die gesteld wordt aan een transfer functie, is dat het in de 3D meetruimte nauwkeurig bij de gemeten tritsen past. Wanneer de "fit" optimaal is zal het gecombineerde effect van meetonnauwkeurigheid en inversiefout kleiner zijn dan 0.5 m s -1 in de wind vector. CMOD4 blijkt binnen deze fout bij de metingen te passen. Een tweede eis is, dat voor een onafhankelijke gegevensset, het verschil tussen de geïnverteerde scatterometer wind en de bijpassende wind van bijvoorbeeld een weermodel zo klein mogelijk is. In de praktijk blijkt dat deze tweede eis impliciet volgt uit de eerste, maar ook dat de onnauwkeurigheid van de scatterometer wind met name wordt bepaald door de associatie van een locatie op de hoorn met een wind vector. De onnauwkeurigheid in de scatterometer wind kan dan ook goed beschreven worden in het wind domein.?SAMENVATTING x In hoofdstuk V wordt dit laatste verder uitgewerkt, en wordt gestreefd naar een gedetailleerde wind calibratie met behulp van in situ gegevens. Windgegevens bevatten doorgaans een relatief grote onnauwkeurigheid. Het wordt aangetoond dat ijking of regressie van zulke gegevens niet mogelijk is in een vergelijking van twee meetsystemen, tenzij de nauwkeurigheid van één van de twee meetsystemen bekend is. In de praktijk is dit meestal niet zo. Voor deze gevallen wordt een methode voorgesteld die uitgaat van de simultane vergelijking van drie meetsystemen. In dit geval kan zowel de ijking als een foutenmodel voor de drie meetsystemen worden opgelost. Toepassing van de methode laat zien dat de scatterometer wind afgeleid met behulp van CMOD4 ruwweg 5 % te laag is, en de oppervlaktewind van het gebruikte weermodel ongeveer 5 % te hoog. Het hoornvormige oppervlak blijkt te bestaan uit twee nauw samenvallende laagjes. Wanneer de wind een component heeft in de kijkrichting van de middelste microgolfbundel wordt de ene hoorn beschreven, en wanneer de wind een component heeft tegengesteld hieraan, de andere. Uit een trits metingen (met ruis) kan dus in het algemeen niet een unieke windvector worden bepaald. Twee ongeveer tegengestelde oplossingen resulteren. Deze dubbelzinnigheid in de windrichting kan in de praktijk worden opgelost door die oplossing te kiezen die het dichtst bij een korte termijn weervoorspelling ligt. Daarna kunnen eisen worden gesteld aan de ruimtelijke consistentie van het gevonden windvector veld. Zoals beschreven in hoofdstuk V levert zo'n methode de goede oplossing in meer dan 99 % van de gevallen. Zo kan een in het algemeen kwalitatief goed windproduct worden afgeleid uit de ERS scatterometermetingen. In het tweede gedeelte van hoofdstuk V wordt ingegaan op de assimilatie van scatterometergegevens in weermodellen. Voor variationele gegevensassimilatie wordt een methode voorgesteld, waarbij de dubbelzinnige scatterometerwinden worden geassimileerd, en niet direct de terugstrooiingsmetingen. Dit vanwege het feit dat de onzekerheid in de interpretatie van de scatterometer, het best is uit te drukken als een fout in de wind. De projectie van deze fout op de microgolfmetingen is niet-lineair, en daarmee tamelijk moeilijk te verwerken binnen de context van meteorologische variationele gegevensassimilatie. Assimilatie van de dubbelzinnige wind daarentegen is tamelijk recht toe recht aan. De scatterometermetingen leiden tot een duidelijk betere analyse en korte-termijn voorspelling van het windveld boven zee. De bedekking is echter zodanig dat andere windwaarnemingen nog lang een zeer welkome aanvulling zullen zijn. Nieuwe Amerikaanse scatterometers met een grotere bedekking zijn in ontwikkeling (met name QuikSCAT en SeaWinds). Vanwege hun andere geometrie en golflengte is echter eerst ontwikkelwerk nodig om tot een gedegen interpretatie te komen. De in dit proefschrift beschreven methodologie kan een belangrijke rol spelen in de interpretatie van de gegevens van deze scatterometers. De volgende generatie Europese scatterometers (ASCAT genoemd) heeft een?SAMENVATTING xi grote bedekking en de microgolflengte en meetgeometrie van de ERS scatterometers. Hiermee zijn we op termijn verzekerd van een goed scatterometer wind product.?SAMENVATTING xii

The sensitivity of catchment hypsometry and hypsometric properties to DEM resolution and polynomial order

NASA Astrophysics Data System (ADS)

Liffner, Joel W.; Hewa, Guna A.; Peel, Murray C.

2018-05-01

Derivation of the hypsometric curve of a catchment, and properties relating to that curve, requires both use of topographical data (commonly in the form of a Digital Elevation Model - DEM), and the estimation of a functional representation of that curve. An early investigation into catchment hypsometry concluded 3rd order polynomials sufficiently describe the hypsometric curve, without the consideration of higher order polynomials, or the sensitivity of hypsometric properties relating to the curve. Another study concluded the hypsometric integral (HI) is robust against changes in DEM resolution, a conclusion drawn from a very limited sample size. Conclusions from these earlier studies have resulted in the adoption of methods deemed to be "sufficient" in subsequent studies, in addition to assumptions that the robustness of the HI extends to other hypsometric properties. This study investigates and demonstrates the sensitivity of hypsometric properties to DEM resolution, DEM type and polynomial order through assessing differences in hypsometric properties derived from 417 catchments and sub-catchments within South Australia. The sensitivity of hypsometric properties across DEM types and polynomial orders is found to be significant, which suggests careful consideration of the methods chosen to derive catchment hypsometric information is required.

Strong stabilization servo controller with optimization of performance criteria.

PubMed

Sarjaš, Andrej; Svečko, Rajko; Chowdhury, Amor

2011-07-01

Synthesis of a simple robust controller with a pole placement technique and a H(∞) metrics is the method used for control of a servo mechanism with BLDC and BDC electric motors. The method includes solving a polynomial equation on the basis of the chosen characteristic polynomial using the Manabe standard polynomial form and parametric solutions. Parametric solutions are introduced directly into the structure of the servo controller. On the basis of the chosen parametric solutions the robustness of a closed-loop system is assessed through uncertainty models and assessment of the norm ‖•‖(∞). The design procedure and the optimization are performed with a genetic algorithm differential evolution - DE. The DE optimization method determines a suboptimal solution throughout the optimization on the basis of a spectrally square polynomial and Šiljak's absolute stability test. The stability of the designed controller during the optimization is being checked with Lipatov's stability condition. Both utilized approaches: Šiljak's test and Lipatov's condition, check the robustness and stability characteristics on the basis of the polynomial's coefficients, and are very convenient for automated design of closed-loop control and for application in optimization algorithms such as DE. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Polynomial expressions of electron depth dose as a function of energy in various materials: application to thermoluminescence (TL) dosimetry

NASA Astrophysics Data System (ADS)

Deogracias, E. C.; Wood, J. L.; Wagner, E. C.; Kearfott, K. J.

1999-02-01

The CEPXS/ONEDANT code package was used to produce a library of depth-dose profiles for monoenergetic electrons in various materials for energies ranging from 500 keV to 5 MeV in 10 keV increments. The various materials for which depth-dose functions were derived include: lithium fluoride (LiF), aluminum oxide (Al 2O 3), beryllium oxide (BeO), calcium sulfate (CaSO 4), calcium fluoride (CaF 2), lithium boron oxide (LiBO), soft tissue, lens of the eye, adiopose, muscle, skin, glass and water. All materials data sets were fit to five polynomials, each covering a different range of electron energies, using a least squares method. The resultant three dimensional, fifth-order polynomials give the dose as a function of depth and energy for the monoenergetic electrons in each material. The polynomials can be used to describe an energy spectrum by summing the doses at a given depth for each energy, weighted by the spectral intensity for that energy. An application of the polynomial is demonstrated by explaining the energy dependence of thermoluminescent detectors (TLDs) and illustrating the relationship between TLD signal and actual shallow dose due to beta particles.

Investigating and Modelling Effects of Climatically and Hydrologically Indicators on the Urmia Lake Coastline Changes Using Time Series Analysis

NASA Astrophysics Data System (ADS)

Ahmadijamal, M.; Hasanlou, M.

2017-09-01

Study of hydrological parameters of lakes and examine the variation of water level to operate management on water resources are important. The purpose of this study is to investigate and model the Urmia Lake water level changes due to changes in climatically and hydrological indicators that affects in the process of level variation and area of this lake. For this purpose, Landsat satellite images, hydrological data, the daily precipitation, the daily surface evaporation and the daily discharge in total of the lake basin during the period of 2010-2016 have been used. Based on time-series analysis that is conducted on individual data independently with same procedure, to model variation of Urmia Lake level, we used polynomial regression technique and combined polynomial with periodic behavior. In the first scenario, we fit a multivariate linear polynomial to our datasets and determining RMSE, NRSME and R² value. We found that fourth degree polynomial can better fit to our datasets with lowest RMSE value about 9 cm. In the second scenario, we combine polynomial with periodic behavior for modeling. The second scenario has superiority comparing to the first one, by RMSE value about 3 cm.

Volumetric calibration of a plenoptic camera.

PubMed

Hall, Elise Munz; Fahringer, Timothy W; Guildenbecher, Daniel R; Thurow, Brian S

2018-02-01

The volumetric calibration of a plenoptic camera is explored to correct for inaccuracies due to real-world lens distortions and thin-lens assumptions in current processing methods. Two methods of volumetric calibration based on a polynomial mapping function that does not require knowledge of specific lens parameters are presented and compared to a calibration based on thin-lens assumptions. The first method, volumetric dewarping, is executed by creation of a volumetric representation of a scene using the thin-lens assumptions, which is then corrected in post-processing using a polynomial mapping function. The second method, direct light-field calibration, uses the polynomial mapping in creation of the initial volumetric representation to relate locations in object space directly to image sensor locations. The accuracy and feasibility of these methods is examined experimentally by capturing images of a known dot card at a variety of depths. Results suggest that use of a 3D polynomial mapping function provides a significant increase in reconstruction accuracy and that the achievable accuracy is similar using either polynomial-mapping-based method. Additionally, direct light-field calibration provides significant computational benefits by eliminating some intermediate processing steps found in other methods. Finally, the flexibility of this method is shown for a nonplanar calibration.

Functional Form of the Radiometric Equation for the SNPP VIIRS Reflective Solar Bands: An Initial Study

NASA Technical Reports Server (NTRS)

Lei, Ning; Xiong, Xiaoxiong

2016-01-01

The Visible Infrared Imaging Radiometer Suite (VIIRS) aboard the Suomi National Polar-orbiting Partnership (SNPP) satellite is a passive scanning radiometer and an imager, observing radiative energy from the Earth in 22 spectral bands from 0.41 to 12 microns which include 14 reflective solar bands (RSBs). Extending the formula used by the Moderate Resolution Imaging Spectroradiometer instruments, currently the VIIRS determines the sensor aperture spectral radiance through a quadratic polynomial of its detector digital count. It has been known that for the RSBs the quadratic polynomial is not adequate in the design specified spectral radiance region and using a quadratic polynomial could drastically increase the errors in the polynomial coefficients, leading to possible large errors in the determined aperture spectral radiance. In addition, it is very desirable to be able to extend the radiance calculation formula to correctly retrieve the aperture spectral radiance with the level beyond the design specified range. In order to more accurately determine the aperture spectral radiance from the observed digital count, we examine a few polynomials of the detector digital count to calculate the sensor aperture spectral radiance.

Study of Randomness in AES Ciphertexts Produced by Randomly Generated S-Boxes and S-Boxes with Various Modulus and Additive Constant Polynomials

NASA Astrophysics Data System (ADS)

Das, Suman; Sadique Uz Zaman, J. K. M.; Ghosh, Ranjan

2016-06-01

In Advanced Encryption Standard (AES), the standard S-Box is conventionally generated by using a particular irreducible polynomial {11B} in GF(28) as the modulus and a particular additive constant polynomial {63} in GF(2), though it can be generated by many other polynomials. In this paper, it has been shown that it is possible to generate secured AES S-Boxes by using some other selected modulus and additive polynomials and also can be generated randomly, using a PRNG like BBS. A comparative study has been made on the randomness of corresponding AES ciphertexts generated, using these S-Boxes, by the NIST Test Suite coded for this paper. It has been found that besides using the standard one, other moduli and additive constants are also able to generate equally or better random ciphertexts; the same is true for random S-Boxes also. As these new types of S-Boxes are user-defined, hence unknown, they are able to prevent linear and differential cryptanalysis. Moreover, they act as additional key-inputs to AES, thus increasing the key-space.

Generalized neurofuzzy network modeling algorithms using Bézier-Bernstein polynomial functions and additive decomposition.

PubMed

Hong, X; Harris, C J

2000-01-01

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bézier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bézier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bézier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bézier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

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.

A revision of the tribe Planitorini van Achterberg (Hymenoptera, Braconidae, Euphorinae), with description of a new genus from Australia.

PubMed

van Achterberg, Cornelis; Quicke, Donald L J; Boring, C Andrew

2017-01-01

The tribe Planitorini van Achterberg (Hymenoptera: Braconidae: Euphorinae) is revised. One new genus Paramannokeraia gen. n. (type species: P. gibsoni sp. n. ) and five new species from Australia are described and illustrated: Mannokeraia albipalpis van Achterberg, sp. n. , M. nigrita van Achterberg, sp. n. , M. punctata van Achterberg, sp. n. , Paramannokeraia gibsoni van Achterberg & Quicke, sp. n. and P. juliae van Achterberg, sp. n. The tribe Mannokeraiini van Achterberg, 1995, is synonymized with the tribe Planitorini ( syn. n. ).

A revision of the tribe Planitorini van Achterberg (Hymenoptera, Braconidae, Euphorinae), with description of a new genus from Australia

PubMed Central

van Achterberg, Cornelis; Quicke, Donald L.J.; Boring, C. Andrew

2017-01-01

Abstract The tribe Planitorini van Achterberg (Hymenoptera: Braconidae: Euphorinae) is revised. One new genus Paramannokeraia gen. n. (type species: P. gibsoni sp. n.) and five new species from Australia are described and illustrated: Mannokeraia albipalpis van Achterberg, sp. n., M. nigrita van Achterberg, sp. n., M. punctata van Achterberg, sp. n., Paramannokeraia gibsoni van Achterberg & Quicke, sp. n. and P. juliae van Achterberg, sp. n. The tribe Mannokeraiini van Achterberg, 1995, is synonymized with the tribe Planitorini (syn. n.). PMID:29290713

Consequences of the Introduction of Insensitive Munitions on Safety, Collateral Damage and Operations (consequenties van de invoering van mkm-munitie op veiligheid, gevolgschade en (internationaal) opereren

DTIC Science & Technology

2006-06-01

van de werkzaamheden In dit rapport worden de gevolgen van initiatie van munitie door een ongewilde externe stimulus beschouwd aan de hand van reele...operationele scenario’s. Dit wordt vergeleken met de gevolgen in dezelfde scenario’s, waarin gebruik is gemaakt van Minder Kwetsbare Munitie (MKM). Naast...de historie van MKM wordt uitgelegd wat Inleiding of terroristische activiteiten, maar ook door MKM is. Vervolgens worden de gevolgen Munitie en de

Genomic and expression analysis of the vanG-like gene cluster of Clostridium difficile.

PubMed

Peltier, Johann; Courtin, Pascal; El Meouche, Imane; Catel-Ferreira, Manuella; Chapot-Chartier, Marie-Pierre; Lemée, Ludovic; Pons, Jean-Louis

2013-07-01

Primary antibiotic treatment of Clostridium difficile intestinal diseases requires metronidazole or vancomycin therapy. A cluster of genes homologous to enterococcal glycopeptides resistance vanG genes was found in the genome of C. difficile 630, although this strain remains sensitive to vancomycin. This vanG-like gene cluster was found to consist of five ORFs: the regulatory region consisting of vanR and vanS and the effector region consisting of vanG, vanXY and vanT. We found that 57 out of 83 C. difficile strains, representative of the main lineages of the species, harbour this vanG-like cluster. The cluster is expressed as an operon and, when present, is found at the same genomic location in all strains. The vanG, vanXY and vanT homologues in C. difficile 630 are co-transcribed and expressed to a low level throughout the growth phases in the absence of vancomycin. Conversely, the expression of these genes is strongly induced in the presence of subinhibitory concentrations of vancomycin, indicating that the vanG-like operon is functional at the transcriptional level in C. difficile. Hydrophilic interaction liquid chromatography (HILIC-HPLC) and MS analysis of cytoplasmic peptidoglycan precursors of C. difficile 630 grown without vancomycin revealed the exclusive presence of a UDP-MurNAc-pentapeptide with an alanine at the C terminus. UDP-MurNAc-pentapeptide [d-Ala] was also the only peptidoglycan precursor detected in C. difficile grown in the presence of vancomycin, corroborating the lack of vancomycin resistance. Peptidoglycan structures of a vanG-like mutant strain and of a strain lacking the vanG-like cluster did not differ from the C. difficile 630 strain, indicating that the vanG-like cluster also has no impact on cell-wall composition.

Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics

NASA Astrophysics Data System (ADS)

Engliš, Miroslav; Ali, S. Twareque

2015-07-01

Continuing our earlier investigation of the Hermite case [S. T. Ali and M. Engliš, J. Math. Phys. 55, 042102 (2014)], we study an unorthodox variant of the Berezin-Toeplitz quantization scheme associated with Laguerre polynomials. In particular, we describe a "Laguerre analogue" of the classical Fock (Segal-Bargmann) space and the relevant semi-classical asymptotics of its Toeplitz operators; the former actually turns out to coincide with the Hilbert space appearing in the construction of the well-known Barut-Girardello coherent states. Further extension to the case of Legendre polynomials is likewise discussed.

Simulation of Shallow Water Jets with a Unified Element-based Continuous/Discontinuous Galerkin Model with Grid Flexibility on the Sphere

DTIC Science & Technology

2013-01-01

is the derivative of the N th-order Legendre polynomial . Given these definitions, the one-dimensional Lagrange polynomials hi(ξ) are hi(ξ) = − 1 N(N...2. Detail of one interface patch in the northern hemisphere. The high-order Legendre -Gauss-Lobatto (LGL) points are added to the linear grid by...smaller ones by a Lagrange polynomial of order nI . The number of quadrilateral elements and grid points of the final grid are then given by Np = 6(N

Analysis of Adaptive Mesh Refinement for IMEX Discontinuous Galerkin Solutions of the Compressible Euler Equations with Application to Atmospheric Simulations

DTIC Science & Technology

2013-01-01

ξi be the Legendre -Gauss-Lobatto (LGL) points defined as the roots of (1 − ξ2)P ′N (ξ) = 0, where PN (ξ) is the N th order Legendre polynomial . The...mesh refinement. By expanding the solution in a basis of high order polynomials in each element, one can dynamically adjust the order of these basis...on refining the mesh while keeping the polynomial order constant across the elements. If we choose to allow non-conforming elements, the challenge in

Polynomial approximation of the Lense-Thirring rigid precession frequency

NASA Astrophysics Data System (ADS)

De Falco, Vittorio; Motta, Sara

2018-05-01

We propose a polynomial approximation of the global Lense-Thirring rigid precession frequency to study low-frequency quasi-periodic oscillations around spinning black holes. This high-performing approximation allows to determine the expected frequencies of a precessing thick accretion disc with fixed inner radius and variable outer radius around a black hole with given mass and spin. We discuss the accuracy and the applicability regions of our polynomial approximation, showing that the computational times are reduced by a factor of ≈70 in the range of minutes.

Causality and a -theorem constraints on Ricci polynomial and Riemann cubic gravities

NASA Astrophysics Data System (ADS)

Li, Yue-Zhou; Lü, H.; Wu, Jun-Bao

2018-01-01

In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost-free, exhibiting an a -theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost-free and a -theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gravities.

Local zeta factors and geometries under Spec Z

NASA Astrophysics Data System (ADS)

Manin, Yu I.

2016-08-01

The first part of this note shows that the odd-period polynomial of each Hecke cusp eigenform for the full modular group produces via the Rodriguez-Villegas transform ([1]) a polynomial satisfying the functional equation of zeta type and having non-trivial zeros only in the middle line of its critical strip. The second part discusses the Chebyshev lambda-structure of the polynomial ring as Borger's descent data to \\mathbf{F}_1 and suggests its role in a possible relation of the Γ\\mathbf{R}-factor to 'real geometry over \\mathbf{F}_1' (cf. [2]).

The neighbourhood polynomial of some families of dendrimers

NASA Astrophysics Data System (ADS)

Nazri Husin, Mohamad; Hasni, Roslan

2018-04-01

The neighbourhood polynomial N(G,x) is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph and it is defined as (G,x)={\\sum }U\\in N(G){x}|U|, where N(G) is neighbourhood complex of a graph, whose vertices of the graph and faces are subsets of vertices that have a common neighbour. A dendrimers is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, we compute this polynomial for some families of dendrimer.

Polynomial asymptotes of the second kind

NASA Astrophysics Data System (ADS)

Dobbs, David E.

2011-03-01

This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and conics. Prerequisites include the division algorithm for polynomials with coefficients in the field of real numbers and elementary facts about limits from calculus. This note could be used as enrichment material in courses ranging from Calculus to Real Analysis to Abstract Algebra.

Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials

DOE PAGES

Kent, Stephen M.

2018-02-15

If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike polynomials. Methodologies are presented to derive these polynomials to arbitrary order. This methodology is applied to aberration patterns produced by a misaligned Ritchey Chretian telescope and to distortion patterns at the focal plane of the DESI optical corrector, where it is shown to provide a more efficient description of distortion than conventional expansions.

Chebyshev polynomials in the spectral Tau method and applications to Eigenvalue problems

NASA Technical Reports Server (NTRS)

Johnson, Duane

1996-01-01

Chebyshev Spectral methods have received much attention recently as a technique for the rapid solution of ordinary differential equations. This technique also works well for solving linear eigenvalue problems. Specific detail is given to the properties and algebra of chebyshev polynomials; the use of chebyshev polynomials in spectral methods; and the recurrence relationships that are developed. These formula and equations are then applied to several examples which are worked out in detail. The appendix contains an example FORTRAN program used in solving an eigenvalue problem.

The discrete Toda equation revisited: dual β-Grothendieck polynomials, ultradiscretization, and static solitons

NASA Astrophysics Data System (ADS)

Iwao, Shinsuke; Nagai, Hidetomo

2018-04-01

This paper presents a study of the discrete Toda equation that was introduced in 1977. In this paper, it is proved that the determinantal solution of the discrete Toda equation, obtained via the Lax formalism, is naturally related to the dual Grothendieck polynomials, a K-theoretic generalization of the Schur polynomials. A tropical permanent solution to the ultradiscrete Toda equation is also derived. The proposed method gives a tropical algebraic representation of the static solitons. Lastly, a new cellular automaton realization of the ultradiscrete Toda equation is proposed.

Flat bases of invariant polynomials and P-matrices of E{sub 7} and E{sub 8}

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

Talamini, Vittorino

2010-02-15

Let G be a compact group of linear transformations of a Euclidean space V. The G-invariant C{sup {infinity}} functions can be expressed as C{sup {infinity}} functions of a finite basic set of G-invariant homogeneous polynomials, sometimes called an integrity basis. The mathematical description of the orbit space V/G depends on the integrity basis too: it is realized through polynomial equations and inequalities expressing rank and positive semidefiniteness conditions of the P-matrix, a real symmetric matrix determined by the integrity basis. The choice of the basic set of G-invariant homogeneous polynomials forming an integrity basis is not unique, so it ismore » not unique the mathematical description of the orbit space too. If G is an irreducible finite reflection group, Saito et al. [Commun. Algebra 8, 373 (1980)] characterized some special basic sets of G-invariant homogeneous polynomials that they called flat. They also found explicitly the flat basic sets of invariant homogeneous polynomials of all the irreducible finite reflection groups except of the two largest groups E{sub 7} and E{sub 8}. In this paper the flat basic sets of invariant homogeneous polynomials of E{sub 7} and E{sub 8} and the corresponding P-matrices are determined explicitly. Using the results here reported one is able to determine easily the P-matrices corresponding to any other integrity basis of E{sub 7} or E{sub 8}. From the P-matrices one may then write down the equations and inequalities defining the orbit spaces of E{sub 7} and E{sub 8} relatively to a flat basis or to any other integrity basis. The results here obtained may be employed concretely to study analytically the symmetry breaking in all theories where the symmetry group is one of the finite reflection groups E{sub 7} and E{sub 8} or one of the Lie groups E{sub 7} and E{sub 8} in their adjoint representations.« less

The expression and comparison of healthy and ptotic upper eyelid contours using a polynomial mathematical function.

PubMed

Mocan, Mehmet C; Ilhan, Hacer; Gurcay, Hasmet; Dikmetas, Ozlem; Karabulut, Erdem; Erdener, Ugur; Irkec, Murat

2014-06-01

To derive a mathematical expression for the healthy upper eyelid (UE) contour and to use this expression to differentiate the normal UE curve from its abnormal configuration in the setting of blepharoptosis. The study was designed as a cross-sectional study. Fifty healthy subjects (26M/24F) and 50 patients with blepharoptosis (28M/22F) with a margin-reflex distance (MRD1) of ≤2.5 mm were recruited. A polynomial interpolation was used to approximate UE curve. The polynomial coefficients were calculated from digital eyelid images of all participants using a set of operator defined points along the UE curve. Coefficients up to the fourth-order polynomial, iris area covered by the UE, iris area covered by the lower eyelid and total iris area covered by both the upper and the lower eyelids were defined using the polynomial function and used in statistical comparisons. The t-test, Mann-Whitney U test and the Spearman's correlation test were used for statistical comparisons. The mathematical expression derived from the data of 50 healthy subjects aged 24.1 ± 2.6 years was defined as y = 22.0915 + (-1.3213)x + 0.0318x(2 )+ (-0.0005x)(3). The fifth and the consecutive coefficients were <0.00001 in all cases and were not included in the polynomial function. None of the first fourth-order coefficients of the equation were found to be significantly different in male versus female subjects. In normal subjects, the percentage of the iris area covered by upper and lower lids was 6.46 ± 5.17% and 0.66% ± 1.62%, respectively. All coefficients and mean iris area covered by the UE were significantly different between healthy and ptotic eyelids. The healthy and abnormal eyelid contour can be defined and differentiated using a polynomial mathematical function.

Interpolation Hermite Polynomials For Finite Element Method

NASA Astrophysics Data System (ADS)

Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel

2018-02-01

We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle element, to be built in high accuracy finite element schemes, is given.

Venus radar mapper attitude reference quaternion

NASA Technical Reports Server (NTRS)

Lyons, D. T.

1986-01-01

Polynomial functions of time are used to specify the components of the quaternion which represents the nominal attitude of the Venus Radar mapper spacecraft during mapping. The following constraints must be satisfied in order to obtain acceptable synthetic array radar data: the nominal attitude function must have a large dynamic range, the sensor orientation must be known very accurately, the attitude reference function must use as little memory as possible, and the spacecraft must operate autonomously. Fitting polynomials to the components of the desired quaternion function is a straightforward method for providing a very dynamic nominal attitude using a minimum amount of on-board computer resources. Although the attitude from the polynomials may not be exactly the one requested by the radar designers, the polynomial coefficients are known, so they do not contribute to the attitude uncertainty. Frequent coefficient updates are not required, so the spacecraft can operate autonomously.

On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.

1998-01-01

Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions

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

Lüchow, Arne, E-mail: luechow@rwth-aachen.de; Jülich Aachen Research Alliance; Sturm, Alexander

2015-02-28

Jastrow correlation factors play an important role in quantum Monte Carlo calculations. Together with an orbital based antisymmetric function, they allow the construction of highly accurate correlation wave functions. In this paper, a generic expansion of the Jastrow correlation function in terms of polynomials that satisfy both the electron exchange symmetry constraint and the cusp conditions is presented. In particular, an expansion of the three-body electron-electron-nucleus contribution in terms of cuspless homogeneous symmetric polynomials is proposed. The polynomials can be expressed in fairly arbitrary scaling function allowing a generic implementation of the Jastrow factor. It is demonstrated with a fewmore » examples that the new Jastrow factor achieves 85%–90% of the total correlation energy in a variational quantum Monte Carlo calculation and more than 90% of the diffusion Monte Carlo correlation energy.« less

Polynomial equations for science orbits around Europa

NASA Astrophysics Data System (ADS)

Cinelli, Marco; Circi, Christian; Ortore, Emiliano

2015-07-01

In this paper, the design of science orbits for the observation of a celestial body has been carried out using polynomial equations. The effects related to the main zonal harmonics of the celestial body and the perturbation deriving from the presence of a third celestial body have been taken into account. The third body describes a circular and equatorial orbit with respect to the primary body and, for its disturbing potential, an expansion in Legendre polynomials up to the second order has been considered. These polynomial equations allow the determination of science orbits around Jupiter's satellite Europa, where the third body gravitational attraction represents one of the main forces influencing the motion of an orbiting probe. Thus, the retrieved relationships have been applied to this moon and periodic sun-synchronous and multi-sun-synchronous orbits have been determined. Finally, numerical simulations have been carried out to validate the analytical results.

A general method for computing Tutte polynomials of self-similar graphs

NASA Astrophysics Data System (ADS)

Gong, Helin; Jin, Xian'an

2017-10-01

Self-similar graphs were widely studied in both combinatorics and statistical physics. Motivated by the construction of the well-known 3-dimensional Sierpiński gasket graphs, in this paper we introduce a family of recursively constructed self-similar graphs whose inner duals are of the self-similar property. By combining the dual property of the Tutte polynomial and the subgraph-decomposition trick, we show that the Tutte polynomial of this family of graphs can be computed in an iterative way and in particular the exact expression of the formula of the number of their spanning trees is derived. Furthermore, we show our method is a general one that is easily extended to compute Tutte polynomials for other families of self-similar graphs such as Farey graphs, 2-dimensional Sierpiński gasket graphs, Hanoi graphs, modified Koch graphs, Apollonian graphs, pseudofractal scale-free web, fractal scale-free network, etc.

a Unified Matrix Polynomial Approach to Modal Identification

NASA Astrophysics Data System (ADS)

Allemang, R. J.; Brown, D. L.

1998-04-01

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.

Derivatives of random matrix characteristic polynomials with applications to elliptic curves

NASA Astrophysics Data System (ADS)

Snaith, N. C.

2005-12-01

The value distribution of derivatives of characteristic polynomials of matrices from SO(N) is calculated at the point 1, the symmetry point on the unit circle of the eigenvalues of these matrices. We consider subsets of matrices from SO(N) that are constrained to have at least n eigenvalues equal to 1 and investigate the first non-zero derivative of the characteristic polynomial at that point. The connection between the values of random matrix characteristic polynomials and values of L-functions in families has been well established. The motivation for this work is the expectation that through this connection with L-functions derived from families of elliptic curves, and using the Birch and Swinnerton-Dyer conjecture to relate values of the L-functions to the rank of elliptic curves, random matrix theory will be useful in probing important questions concerning these ranks.

Pseudo spectral collocation with Maxwell polynomials for kinetic equations with energy diffusion

NASA Astrophysics Data System (ADS)

Sánchez-Vizuet, Tonatiuh; Cerfon, Antoine J.

2018-02-01

We study the approximation and stability properties of a recently popularized discretization strategy for the speed variable in kinetic equations, based on pseudo-spectral collocation on a grid defined by the zeros of a non-standard family of orthogonal polynomials called Maxwell polynomials. Taking a one-dimensional equation describing energy diffusion due to Fokker-Planck collisions with a Maxwell-Boltzmann background distribution as the test bench for the performance of the scheme, we find that Maxwell based discretizations outperform other commonly used schemes in most situations, often by orders of magnitude. This provides a strong motivation for their use in high-dimensional gyrokinetic simulations. However, we also show that Maxwell based schemes are subject to a non-modal time stepping instability in their most straightforward implementation, so that special care must be given to the discrete representation of the linear operators in order to benefit from the advantages provided by Maxwell polynomials.

Planar harmonic polynomials of type B

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

1999-11-01

The hyperoctahedral group acting on icons/Journals/Common/BbbR" ALT="BbbR" ALIGN="TOP"/>N is the Weyl group of type B and is associated with a two-parameter family of differential-difference operators {Ti:1icons/Journals/Common/leq" ALT="leq" ALIGN="TOP"/> iicons/Journals/Common/leq" ALT="leq" ALIGN="TOP"/> N}. These operators are analogous to partial derivative operators. This paper finds all the polynomials h on icons/Journals/Common/BbbR" ALT="BbbR" ALIGN="TOP"/>N which are harmonic, icons/Journals/Common/Delta" ALT="Delta" ALIGN="TOP"/>Bh = 0 and annihilated by Ti for i>2, where the Laplacian 0305-4470/32/46/308/img1" ALT="(sum). They are given explicitly in terms of a novel basis of polynomials, defined by generating functions. The harmonic polynomials can be used to find wavefunctions for the quantum many-body spin Calogero model.

LMI-based stability analysis of fuzzy-model-based control systems using approximated polynomial membership functions.

PubMed

Narimani, Mohammand; Lam, H K; Dilmaghani, R; Wolfe, Charles

2011-06-01

Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S-procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.

Polynomial chaos expansion with random and fuzzy variables

NASA Astrophysics Data System (ADS)

Jacquelin, E.; Friswell, M. I.; Adhikari, S.; Dessombz, O.; Sinou, J.-J.

2016-06-01

A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.

Fast beampattern evaluation by polynomial rooting

NASA Astrophysics Data System (ADS)

Häcker, P.; Uhlich, S.; Yang, B.

2011-07-01

Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. The direction estimation capabilities of a sensor array depend on its beampattern. To find the array configuration leading to the best angle estimation by a global optimization algorithm, a huge amount of beampatterns have to be calculated to detect their maxima. In this paper, a novel algorithm is proposed to find all maxima of an array's beampattern fast and reliably, leading to accelerated array optimizations. The algorithm works for arrays having the sensors on a uniformly spaced grid. We use a general version of the gcd (greatest common divisor) function in order to write the problem as a polynomial. We differentiate and root the polynomial to get the extrema of the beampattern. In addition, we show a method to reduce the computational burden even more by decreasing the order of the polynomial.

Ligand Shaping in Induced Fit Docking of MraY Inhibitors. Polynomial Discriminant and Laplacian Operator as Biological Activity Descriptors.

PubMed

Lungu, Claudiu N; Diudea, Mircea V; Putz, Mihai V

2017-06-27

Docking-i.e., interaction of a small molecule (ligand) with a proteic structure (receptor)-represents the ground of drug action mechanism of the vast majority of bioactive chemicals. Ligand and receptor accommodate their geometry and energy, within this interaction, in the benefit of receptor-ligand complex. In an induced fit docking, the structure of ligand is most susceptible to changes in topology and energy, comparative to the receptor. These changes can be described by manifold hypersurfaces, in terms of polynomial discriminant and Laplacian operator. Such topological surfaces were represented for each MraY (phospho-MurNAc-pentapeptide translocase) inhibitor, studied before and after docking with MraY. Binding affinities of all ligands were calculated by this procedure. For each ligand, Laplacian and polynomial discriminant were correlated with the ligand minimum inhibitory concentration (MIC) retrieved from literature. It was observed that MIC is correlated with Laplacian and polynomial discriminant.

Automatic differentiation for Fourier series and the radii polynomial approach

NASA Astrophysics Data System (ADS)

Lessard, Jean-Philippe; Mireles James, J. D.; Ransford, Julian

2016-11-01

In this work we develop a computer-assisted technique for proving existence of periodic solutions of nonlinear differential equations with non-polynomial nonlinearities. We exploit ideas from the theory of automatic differentiation in order to formulate an augmented polynomial system. We compute a numerical Fourier expansion of the periodic orbit for the augmented system, and prove the existence of a true solution nearby using an a-posteriori validation scheme (the radii polynomial approach). The problems considered here are given in terms of locally analytic vector fields (i.e. the field is analytic in a neighborhood of the periodic orbit) hence the computer-assisted proofs are formulated in a Banach space of sequences satisfying a geometric decay condition. In order to illustrate the use and utility of these ideas we implement a number of computer-assisted existence proofs for periodic orbits of the Planar Circular Restricted Three-Body Problem (PCRTBP).

A Formally Verified Conflict Detection Algorithm for Polynomial Trajectories

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony; Munoz, Cesar

2015-01-01

In air traffic management, conflict detection algorithms are used to determine whether or not aircraft are predicted to lose horizontal and vertical separation minima within a time interval assuming a trajectory model. In the case of linear trajectories, conflict detection algorithms have been proposed that are both sound, i.e., they detect all conflicts, and complete, i.e., they do not present false alarms. In general, for arbitrary nonlinear trajectory models, it is possible to define detection algorithms that are either sound or complete, but not both. This paper considers the case of nonlinear aircraft trajectory models based on polynomial functions. In particular, it proposes a conflict detection algorithm that precisely determines whether, given a lookahead time, two aircraft flying polynomial trajectories are in conflict. That is, it has been formally verified that, assuming that the aircraft trajectories are modeled as polynomial functions, the proposed algorithm is both sound and complete.

Polynomial algebra of discrete models in systems biology.

PubMed

Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard

2010-07-01

An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.

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.

Hilbert's 17th Problem and the Quantumness of States

NASA Astrophysics Data System (ADS)

Korbicz, J. K.; Cirac, J. I.; Wehr, Jan; Lewenstein, M.

2005-04-01

A state of a quantum system can be regarded as classical (quantum) with respect to measurements of a set of canonical observables if and only if there exists (does not exist) a well defined, positive phase-space distribution, the so called Glauber-Sudarshan P representation. We derive a family of classicality criteria that requires that the averages of positive functions calculated using P representation must be positive. For polynomial functions, these criteria are related to Hilbert’s 17th problem, and have physical meaning of generalized squeezing conditions; alternatively, they may be interpreted as nonclassicality witnesses. We show that every generic nonclassical state can be detected by a polynomial that is a sum-of-squares of other polynomials. We introduce a very natural hierarchy of states regarding their degree of quantumness, which we relate to the minimal degree of a sum-of-squares polynomial that detects them.

Inelastic processes in atomic collisions involving ground state and laser-prepared atoms

NASA Astrophysics Data System (ADS)

Planje, Willem Gilles

1999-11-01

In dit proefschrift worden experimenten beschreven waarbij ionen of atomen met een bepaalde snelheid op een ensemble van doelwitatomen worden gericht. Wanneer twee deeltjes elkaar voldoende genaderd hebben, vindt er wissel- werking plaats waarbij allerlei processen kunnen optreden. Deze processen resulteren in specieke eindproducten. Kennis over de interactie tussen twee botsingspartners wordt verkregen door te bekijken welke eindproducten ontstaan, en in welke mate. Een belangrijke grootheid die van invloed is op mogelijke processen is de onderlinge snelheid van de twee kernen, oftewel de botsingssnelheid. Wanneer de botsingssnelheid voldoende klein is dan kunnen de verschillende reactiemechanismen zowel kwalitatief als kwanti- tatief vaak goed voorspeld worden door het systeem te beschouwen als een kort-stondig molecuul, opgebouwd uit de twee botsende deeltjes. De ver- schillende processen die kunnen optreden worden gekwaliceerd afhankelijk van de vorming van bepaalde eindproducten. Ruwweg de volgende indeling kan gemaakt worden: 1. de interne structuur van de eindproducten zijn identiek aan die van de beginproducten. We spreken dan van een elastische botsing. 2. e en van de deeltjes of beiden worden in een aangeslagen toestand ge- bracht (of ge¨oniseerd). Dit zijn processen waarbij de herschikte elek- tronen zich bij de oorspronkelijke kern bevinden. We spreken dan van excitatie of ionisatie. 3. e en of meerdere elektronen bevinden zich bij de andere kern na de botsing (eventueel in aangeslagen toestand). We spreken dan van elek- tronenoverdracht. In het eerste deel van deze dissertatie worden botsingsexperimenten tussen heliumionen en natriumatomen beschreven waarbij het proces van elek- tronenoverdracht wordt onderzocht. Bij dit mechanisme is het buitenste 117?Samenvatting natriumelektron betrokken. Deze kan relatief gemakkelijk `overspringen' naar het heliumion wanneer deze zich dicht in de buurt van het natrium- atoom bevindt. Het elektron kan hierbij een bepaalde (aangeslagen) toe- stand bezetten. Wij meten de bezetting van de heliumtoestanden die onder uitzending van XUV licht ( ? 58 nm) vervallen naar de heliumgrondtoe- stand. Door de lichtintensiteit te meten onderzoeken we de mate van elek- tronenoverdracht naar een selecte groep van singlet helium`eind'toestanden, namelijk He(1s2p), He(1s3s), He(1s3p) en He(1s3d). In een reactie- vergelijking ziet het mechanisme er als volgt uit: He + (1s) + ( Na(3s) Na(3p) e- -! He + Na + -! He(1s 2 ) +h(58 nm) + Na + Het experiment kent een extra dimensie door het feit dat het, in beginsel bol- symmetrische, natriumatoom een bepaalde ruimtelijk uitlijning kan worden meegegeven. Met behulp van laserlicht van een specieke frequentie en po- larisatie, wordt het buitenste natriumelektron in een aangeslagen p toestand gebracht. Het aanslaan naar deze toestand heeft als gevolg dat het valentie- elektron zich op grotere afstand van zijn kern bevindt dan voorheen. Daar- naast kan, afhankelijk van de gebruikte laserpolarisatie, het buitenste elek- tron zich nu rond de natriumkern bewegen volgens een bepaalde anisotrope verdeling, de bolsymmetrie is doorbroken. De eecten van de excitatie en ruimtelijk verdeling van dit natriumelektron op het proces van elektronen- overdracht zijn onderzocht voor botsingsenergie¨en vari¨erend van 0.5 keV tot 6.0 keV. De metingen laten zien dat het eect van laserexcitatie een bezettingstoe- name van de beschouwde singlet heliumtoestanden betekent, ongeacht de uitlijning van het natrium 3p elektron. Dit is simpelweg te begrijpen uit het feit dat het 3p natrium elektron minder sterk gebonden is en elektro- nenoverdracht makkelijker gaat. Daarnaast is de uitlijning van het aanges- lagen elektron van invloed op de elektronenoverdracht. De resultaten zijn vergeleken met berekeningen van S.E. Nielsen en T.H. Rod [13], die de elek- tronoverdracht beschrijven in een model waarbij het betrokken elektron zich beweegt in bepaalde eectieve potentiaalvelden. De goede overeenkomsten van onze metingen met de berekeningen rechtvaardigen de theoretische be- nadering van Nielsen en Rod. 118?Samenvatting In het tweede gedeelte van het proefschrift worden botsingen beschouwd tussen helium- en neonatomen. Hierbij wordt nu niet gekeken naar bots- ingsproducten die zich manifesteren door bepaald licht uit te zenden, maar een elektron emitteren met een bepaalde energie. Verschillende soorten `eind'producten kunnen elektronen uitzenden, waaronder de negatieve ion- toestanden. Het elektronenspectrum, gemeten voor dit botsingssysteem, vertoont twee pieken die het spectrum domineren bij 16.2 eV en 19.4 eV voor verschillende botsingsenergie¨en tussen de 0.35 keV en 6.0 keV. Deze piekstructuren wijzen op de vorming van de kort-levende, negatieve iontoe- standen Ne-(2p 5 3s 2 ) en He-(1s2s 2 ) ten gevolge van de overdracht van e en elektron: He 0 + Ne 0 -! He-(1s2s 2 ) +Ne + (2p 5 ) 3 10- 14 s -! He 0 (1s 2 ) +Ne + + e- (19.37 eV) He 0 + Ne 0 -! He + (1s) +Ne-(2p 5 3s 2 ) 2:5 10- 13 s -! He + (1s) +Ne 0 (2p 6 ) +e- (16.15 eV) De meetresultaten vertonen een fenomeen waarbij de bezettingen van de negatieve iontoestanden een oscillerend gedrag vertonen als functie van de botsingssnelheid. Dit duidt op interferentie tussen de twee bijna-ontaarde moleculaire toestanden [He- + Ne + ] en[He + + Ne-]. Het is echter zeer op- merkelijk dat deze oscillatie wordt waargenomen in een experiment als deze, waarin de uitgezonden elektronen worden gemeten ongeacht de afbuighoek van het heliumatoom. Dit impliceert een speciek aanslagmechanisme van de moleculaire negatieve iontoestanden. Nader beschouwing van het bots- ingssysteem laat zien dat het instantane molecuul twee overgangen moet ondergaan voordat de negatieve iontoestanden gevormd worden. Als gevolg hiervan is de snelheid waarmee het negatieve en positieve ion uit elkaar be- wegen nagenoeg onafhankelijk van de afbuighoek van het helium projectiel en is oscillatie mogelijk waarneembaar. De wisselwerking tussen de twee beschouwde moleculaire toestanden impliceert gecorreleerde overdracht van twee elektronen: He- + Ne + 2e- ! He + + Ne- Door het quasi-resonante systeem als resonant te beschouwen kan het fenomeen kwalitatief goed verklaard worden. 119?Samenvatting Inhet laatstedeelwordt de bevolkingvanauto¨oniserende natriumtoestanden bekeken in He +=0 + Na botsingen. In tegenstelling tot de voorgaande exper- imenten waarin elektronenoverdracht beschouwd werd, betreft het hier een excitatiemechanisme. De beschouwde `eind'producten, i.e. de auto¨oniserende natriumtoestanden, bestaan in het algemeen kort en gaan over naar een stabiele iontoestand onder uitzending van een elektron met een toestands- karakteristieke kinetische energie. Door de elektronenspectra te meten bij verschillende botsingsenergie¨en, wordt de bezetting van de auto¨oniserende toestanden onderzocht. Ook hier wordt het eect van laserexcitatie en laser- polarisatie van het natriumatoom op de vorming van deze toestanden, en de mate waarin, bekeken. De metingen laten zien dat zowel in He + -Na als in He 0 -Na botsingen de invloed van de ruimtelijk uitlijning van het buitenste natriumelektron op de elektronenspectra nihil is. Dit impliceert dat het betrokken 3p elektron hoofdzakelijk een passieve rol speelt in de vorming van auto¨oniserende toe- standen: het blijft hoofdzakelijk de 3p toestand bezetten als een `toeschouwer' zonder een overgang te maken naar een andere toestand. Dit wordt boven- dien bevestigd door het feit dat wanneer een fractie natriumatomen aange- slagen wordt naar de p toestand dit een even grote reductie betekent van onder meer de populatie van de auto¨oniserende toestand Na(2p 5 3s 2 ). De verwachte grote toename van Na(2p 5 3p 2 ) toestanden, in geval van Na(3p) doelwitten, is niet waargenomen. 120?121?122

Testing of next-generation nonlinear calibration based non-uniformity correction techniques using SWIR devices

NASA Astrophysics Data System (ADS)

Lovejoy, McKenna R.; Wickert, Mark A.

2017-05-01

A known problem with infrared imaging devices is their non-uniformity. This non-uniformity is the result of dark current, amplifier mismatch as well as the individual photo response of the detectors. To improve performance, non-uniformity correction (NUC) techniques are applied. Standard calibration techniques use linear, or piecewise linear models to approximate the non-uniform gain and off set characteristics as well as the nonlinear response. Piecewise linear models perform better than the one and two-point models, but in many cases require storing an unmanageable number of correction coefficients. Most nonlinear NUC algorithms use a second order polynomial to improve performance and allow for a minimal number of stored coefficients. However, advances in technology now make higher order polynomial NUC algorithms feasible. This study comprehensively tests higher order polynomial NUC algorithms targeted at short wave infrared (SWIR) imagers. Using data collected from actual SWIR cameras, the nonlinear techniques and corresponding performance metrics are compared with current linear methods including the standard one and two-point algorithms. Machine learning, including principal component analysis, is explored for identifying and replacing bad pixels. The data sets are analyzed and the impact of hardware implementation is discussed. Average floating point results show 30% less non-uniformity, in post-corrected data, when using a third order polynomial correction algorithm rather than a second order algorithm. To maximize overall performance, a trade off analysis on polynomial order and coefficient precision is performed. Comprehensive testing, across multiple data sets, provides next generation model validation and performance benchmarks for higher order polynomial NUC methods.

Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential

NASA Astrophysics Data System (ADS)

Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.

1995-08-01

The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.

Transfer matrix computation of generalized critical polynomials in percolation

DOE PAGES

Scullard, Christian R.; Jacobsen, Jesper Lykke

2012-09-27

Percolation thresholds have recently been studied by means of a graph polynomial PB(p), henceforth referred to as the critical polynomial, that may be defined on any periodic lattice. The polynomial depends on a finite subgraph B, called the basis, and the way in which the basis is tiled to form the lattice. The unique root of P B(p) in [0, 1] either gives the exact percolation threshold for the lattice, or provides an approximation that becomes more accurate with appropriately increasing size of B. Initially P B(p) was defined by a contraction-deletion identity, similar to that satisfied by the Tuttemore » polynomial. Here, we give an alternative probabilistic definition of P B(p), which allows for much more efficient computations, by using the transfer matrix, than was previously possible with contraction-deletion. We present bond percolation polynomials for the (4, 82), kagome, and (3, 122) lattices for bases of up to respectively 96, 162, and 243 edges, much larger than the previous limit of 36 edges using contraction-deletion. We discuss in detail the role of the symmetries and the embedding of B. For the largest bases, we obtain the thresholds p c(4, 82) = 0.676 803 329 · · ·, p c(kagome) = 0.524 404 998 · · ·, p c(3, 122) = 0.740 420 798 · · ·, comparable to the best simulation results. We also show that the alternative definition of P B(p) can be applied to study site percolation problems.« less

The first report of the vanC₁ gene in Enterococcus faecium isolated from a human clinical specimen.

PubMed

Sun, Mingyue; Wang, Yue; Chen, Zhongju; Zhu, Xuhui; Tian, Lei; Sun, Ziyong

2014-09-01

The vanC₁ gene, which is chromosomally located, confers resistance to vancomycin and serves as a species marker for Enterococcus gallinarum. Enterococcus faecium TJ4031 was isolated from a blood culture and harbours the vanC₁gene. Polymerase chain reaction (PCR) assays were performed to detect vanXYc and vanTc genes. Only the vanXYc gene was found in the E. faecium TJ4031 isolate. The minimum inhibitory concentrations of vancomycin and teicoplanin were 2 µg/mL and 1 µg/mL, respectively. Real-time reverse transcription-PCR results revealed that the vanC₁ and vanXYc genes were not expressed. Pulsed-field gel electrophoresis and southern hybridisation results showed that the vanC₁ gene was encoded in the chromosome. E. faecalis isolated from animals has been reported to harbour vanC₁gene. However, this study is the first to report the presence of the vanC₁gene in E. faecium of human origin. Additionally, our research showed the vanC₁gene cannot serve as a species-specific gene of E. gallinarum and that it is able to be transferred between bacteria. Although the resistance marker is not expressed in the strain, our results showed that E. faecium could acquire the vanC₁gene from different species.

High-pressure high-temperature crystal growth of equiatomic rare earth stannides RENiSn and REPdSn

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

Heymann, Gunter; Heying, Birgit; Rodewald, Ute Ch.

2016-04-15

The two series of equiatomic rare earth (RE) stannides RENiSn and REPdSn were systematically studied with respect to high-pressure modifications. The normal-pressure (NP) low-temperature (LT) modifications were synthesized by arc-melting and subsequently treated under high-pressure (P{sub max}=11.5 GPa) and high-temperature (T{sub max}=1570 K) conditions in a Walker-type multi-anvil press. The pressure and temperature conditions were systematically varied in order to improve the crystallization conditions. The new ZrNiAl-type high-pressure modifications HP-RENiSn (RE=Sc, Y, La, Gd–Lu) and HP-REPdSn (RE=Y, Sm–Dy) were obtained in 80 mg quantities, several of them in X-ray pure form. Some of the REPdSn stannides with the heavy raremore » earth elements show high-temperature (HT) modifications. The structures of HP-ScNiSn, HP-GdNiSn, HP-DyNiSn (both ZrNiAl-type), NP-YbNiSn, and HT-ErPdSn (both TiNiSi-type) were refined from single crystal diffractometer data, indicating full ordering of the transition metal and tin sites. TiNiSi-type NP-EuPdSn transforms to MgZn{sub 2}-type HP-EuPdSn: P6{sub 3}/mmc, a=588.5(2), c=917.0(3) pm, wR2=0.0769, 211 F{sup 2} values, 11 variables. The structure refinement indicated statistical occupancy of the palladium and tin sites on the tetrahedral network. The X-ray pure high-pressure phases were studied with respect to their magnetic properties. HP-YPdSn is a Pauli paramagnet. The susceptibility data of HP-TbNiSn, HP-DyNiSn, HP-GdPdSn, and HP-TbPdSn show experimental magnetic moments close to the free ion values of RE{sup 3+} and antiferromagnetic ordering at low temperature with the highest Néel temperature of 15.8 K for HP-TbPdSn. HP-SmPdSn shows the typical Van Vleck type behavior along with antiferromagnetic ordering at T{sub N}=5.1 K. HP-EuPdSn shows divalent europium and antiferromagnetic ordering at 8.9 K followed by a spin reorientation at 5.7 K. - Graphical abstract: Packing of the polyhedra in the high-pressure phase of EuPdSn. - Highlights: • High-pressure phases of the stannides RENiSn and REPdSn. • Crystal growth conditions. • Pressure- and temperature-driven phase transitions. • Magnetic properties.« less

Tweede Serie Ergonomietests Lichtgewicht Bommenpakken (Second Series of Ergonomic Tests on Lightweight Bomb Disposal Suits)

DTIC Science & Technology

2007-12-01

warmtebelastingtests vast te stellen en (sit-and-reach, stand-and-reach. abductie referentiewaarden te bepalen door het van de arnen, anteflexie van de armen ...volgende, bewegingbeperkingtests: sit-and-reach, stand-and-reach. abductie van de armen , anteflexie van de armen en beperking van zicht. Bij de sit-and...gebogen op de rand van een tafel en houdt de armen zo ver mogeijk gestrekt naar voren op tafel. Daarbij wordt de afstand vanaf de rand van de tafel tot

Molecular Characterization of Enterococcus faecalis N06-0364 with Low-Level Vancomycin Resistance Harboring a Novel d-Ala-d-Ser Gene Cluster, vanL▿

PubMed Central

Boyd, David A.; Willey, Barbara M.; Fawcett, Darlene; Gillani, Nazira; Mulvey, Michael R.

2008-01-01

Enterococcus faecalis N06-0364, exhibiting a vancomycin MIC of 8 μg/ml, was found to harbor a novel d-Ala-d-Ser gene cluster, designated vanL. The vanL gene cluster was similar in organization to the vanC operon, but the VanT serine racemase was encoded by two separate genes, vanTmL (membrane binding) and vanTrL (racemase). PMID:18458129

The Maximums and Minimums of a Polnomial or Maximizing Profits and Minimizing Aircraft Losses.

ERIC Educational Resources Information Center

Groves, Brenton R.

1984-01-01

Plotting a polynomial over the range of real numbers when its derivative contains complex roots is discussed. The polynomials are graphed by calculating the minimums, maximums, and zeros of the function. (MNS)

19 CFR 10.41a - Lift vans, cargo vans, shipping tanks, skids, pallets, and similar instruments of international...

Code of Federal Regulations, 2014 CFR

2014-04-01

... for inspection by Customs officials upon reasonable notice. (3) If the container does not exit the U.S... 19 Customs Duties 1 2014-04-01 2014-04-01 false Lift vans, cargo vans, shipping tanks, skids... Traffic § 10.41a Lift vans, cargo vans, shipping tanks, skids, pallets, and similar instruments of...

19 CFR 10.41a - Lift vans, cargo vans, shipping tanks, skids, pallets, and similar instruments of international...

Code of Federal Regulations, 2012 CFR

2012-04-01

... for inspection by Customs officials upon reasonable notice. (3) If the container does not exit the U.S... 19 Customs Duties 1 2012-04-01 2012-04-01 false Lift vans, cargo vans, shipping tanks, skids... Traffic § 10.41a Lift vans, cargo vans, shipping tanks, skids, pallets, and similar instruments of...

19 CFR 10.41a - Lift vans, cargo vans, shipping tanks, skids, pallets, and similar instruments of international...

Code of Federal Regulations, 2013 CFR

2013-04-01

... for inspection by Customs officials upon reasonable notice. (3) If the container does not exit the U.S... 19 Customs Duties 1 2013-04-01 2013-04-01 false Lift vans, cargo vans, shipping tanks, skids... Traffic § 10.41a Lift vans, cargo vans, shipping tanks, skids, pallets, and similar instruments of...

First and Second Order Stokes Generation by SRS in Methane: Influence of Rep-Rate, Beam Quality and Astigmatism (Opwekking van Eerste en Tweede Orde Stokes d.m.v. SRS in Methaan: Invloed van de Pulsfrequentie, de Bundelkwaliteit en Astigmatisme)

DTIC Science & Technology

1992-09-01

omzettings rendementen van circa 75% gehaad bij een ingangs- energie van 280 mJ. De mogelijkheden tot bet halen van een hoger rendement lijken...of rep-rate, beam quality and astigmatism DImi-Thu-B~mO ITA1EiM-tT-h lF I~~ ~~’ IAPR2 8 1993~ I ~Xtbai Uiitdw FJ.M. van Putten J.C. van den Heuvel RJ.L...Influence of rep-rate. beam quality and astigmatism author(s) : F.J.M. van Putten, I.C. van den Heuvel, R.J.L. Lerou institute : TNO Physics and

Sylow p-groups of polynomial permutations on the integers mod pn☆

PubMed Central

Frisch, Sophie; Krenn, Daniel

2013-01-01

We enumerate and describe the Sylow p-groups of the groups of polynomial permutations of the integers mod pn for n⩾1 and of the pro-finite group which is the projective limit of these groups. PMID:26869732

Cubic Polynomials, Their Roots and the Perron-Frobenius Theorem

ERIC Educational Resources Information Center

Dealba, Luz Maria

2002-01-01

In this note several cubic polynomials and their roots are examined, in particular, how these roots move as some of the coefficients are modified. The results obtained are applied to eigenvalues of matrices. (Contains 8 figures and 1 footnote.)

Faulhaber's Triangle

ERIC Educational Resources Information Center

Torabi-Dashti, Mohammad

2011-01-01

Like Pascal's triangle, Faulhaber's triangle is easy to draw: all you need is a little recursion. The rows are the coefficients of polynomials representing sums of integer powers. Such polynomials are often called Faulhaber formulae, after Johann Faulhaber (1580-1635); hence we dub the triangle Faulhaber's triangle.

Social Security Polynomials.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

1992-01-01

Demonstrates how the uniqueness and anonymity of a student's Social Security number can be utilized to create individualized polynomial equations that students can investigate using computers or graphing calculators. Students write reports of their efforts to find and classify all real roots of their equation. (MDH)

Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials

NASA Astrophysics Data System (ADS)

Kent, Stephen M.

2018-04-01

If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike polynomials. Methodologies are presented to derive these polynomials to arbitrary order. This methodology is applied to aberration patterns produced by a misaligned Ritchey–Chrétien telescope and to distortion patterns at the focal plane of the DESI optical corrector, where it is shown to provide a more efficient description of distortion than conventional expansions.

Explicit analytical expression for the condition number of polynomials in power form

NASA Astrophysics Data System (ADS)

Rack, Heinz-Joachim

2017-07-01

In his influential papers [1-3] W. Gautschi has defined and reshaped the condition number κ∞ of polynomials Pn of degree ≤ n which are represented in power form on a zero-symmetric interval [-ω, ω]. Basically, κ∞ is expressed as the product of two operator norms: an explicit factor times an implicit one (the l∞-norm of the coefficient vector of the n-th Chebyshev polynomial of the first kind relative to [-ω, ω]). We provide a new proof, economize the second factor and express it by an explicit analytical formula.

How many invariant polynomials are needed to decide local unitary equivalence of qubit states?

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

Maciążek, Tomasz; Faculty of Physics, University of Warsaw, ul. Hoża 69, 00-681 Warszawa; Oszmaniec, Michał

2013-09-15

Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e., by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure.

Positivity-preserving High Order Finite Difference WENO Schemes for Compressible Euler Equations

DTIC Science & Technology

2011-07-15

the WENO reconstruction. We assume that there is a polynomial vector qi(x) = (ρi(x), mi(x), Ei(x)) T with degree k which are (k + 1)-th order accurate...i+ 1 2 = qi(xi+ 1 2 ). The existence of such polynomials can be established by interpolation for WENO schemes. For example, for the fifth or- der...WENO scheme, there is a unique vector of polynomials of degree four qi(x) satisfying qi(xi− 1 2 ) = w+ i− 1 2 , qi(xi+ 1 2 ) = w− i+ 1 2 and 1 ∆x ∫ Ij qi

Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems

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

Lu, Fei; Department of Mathematics, University of California, Berkeley; Morzfeld, Matthias, E-mail: mmo@math.lbl.gov

2015-02-01

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior.

Colored knot polynomials for arbitrary pretzel knots and links

DOE PAGES

Galakhov, D.; Melnikov, D.; Mironov, A.; ...

2015-04-01

A very simple expression is conjectured for arbitrary colored Jones and HOMFLY polynomials of a rich (g+1)-parametric family of pretzel knots and links. The answer for the Jones and HOMFLY is fully and explicitly expressed through the Racah matrix of Uq(SU N), and looks related to a modular transformation of toric conformal block. Knot polynomials are among the hottest topics in modern theory. They are supposed to summarize nicely representation theory of quantum algebras and modular properties of conformal blocks. The result reported in the present letter, provides a spectacular illustration and support to this general expectation.

Fitness Probability Distribution of Bit-Flip Mutation.

PubMed

Chicano, Francisco; Sutton, Andrew M; Whitley, L Darrell; Alba, Enrique

2015-01-01

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.

A Study on Gröbner Basis with Inexact Input

NASA Astrophysics Data System (ADS)

Nagasaka, Kosaku

Gröbner basis is one of the most important tools in recent symbolic algebraic computations. However, computing a Gröbner basis for the given polynomial ideal is not easy and it is not numerically stable if polynomials have inexact coefficients. In this paper, we study what we should get for computing a Gröbner basis with inexact coefficients and introduce a naive method to compute a Gröbner basis by reduced row echelon form, for the ideal generated by the given polynomial set having a priori errors on their coefficients.

Transform Decoding of Reed-Solomon Codes. Volume II. Logical Design and Implementation.

DTIC Science & Technology

1982-11-01

i A. nE aib’ = a(bJ) ; j=0, 1, ... , n-l (2-8) i=01 Similarly, the inverse transform is obtained by interpolation of the polynomial a(z) from its n...with the transform so that either a forward or an inverse transform may be used to encode. The only requirement is that tie reverse of the encoding... inverse transform of the received sequence is the polynomial sum r(z) = e(z) + a(z), where e(z) is the inverse transform of the error polynomial E(z), and a

Comparative Analysis of Various Single-tone Frequency Estimation Techniques in High-order Instantaneous Moments Based Phase Estimation Method

NASA Astrophysics Data System (ADS)

Rajshekhar, G.; Gorthi, Sai Siva; Rastogi, Pramod

2010-04-01

For phase estimation in digital holographic interferometry, a high-order instantaneous moments (HIM) based method was recently developed which relies on piecewise polynomial approximation of phase and subsequent evaluation of the polynomial coefficients using the HIM operator. A crucial step in the method is mapping the polynomial coefficient estimation to single-tone frequency determination for which various techniques exist. The paper presents a comparative analysis of the performance of the HIM operator based method in using different single-tone frequency estimation techniques for phase estimation. The analysis is supplemented by simulation results.

Estimation of Phase in Fringe Projection Technique Using High-order Instantaneous Moments Based Method

NASA Astrophysics Data System (ADS)

Gorthi, Sai Siva; Rajshekhar, G.; Rastogi, Pramod

2010-04-01

For three-dimensional (3D) shape measurement using fringe projection techniques, the information about the 3D shape of an object is encoded in the phase of a recorded fringe pattern. The paper proposes a high-order instantaneous moments based method to estimate phase from a single fringe pattern in fringe projection. The proposed method works by approximating the phase as a piece-wise polynomial and subsequently determining the polynomial coefficients using high-order instantaneous moments to construct the polynomial phase. Simulation results are presented to show the method's potential.

High degree interpolation polynomial in Newton form

NASA Technical Reports Server (NTRS)

Tal-Ezer, Hillel

1988-01-01

Polynomial interpolation is an essential subject in numerical analysis. Dealing with a real interval, it is well known that even if f(x) is an analytic function, interpolating at equally spaced points can diverge. On the other hand, interpolating at the zeroes of the corresponding Chebyshev polynomial will converge. Using the Newton formula, this result of convergence is true only on the theoretical level. It is shown that the algorithm which computes the divided differences is numerically stable only if: (1) the interpolating points are arranged in a different order, and (2) the size of the interval is 4.

Analytical solution of tt¯ dilepton equations

NASA Astrophysics Data System (ADS)

Sonnenschein, Lars

2006-03-01

The top quark antiquark production system in the dilepton decay channel is described by a set of equations which is nonlinear in the unknown neutrino momenta. Its most precise and least time consuming solution is of major importance for measurements of top quark properties like the top quark mass and tt¯ spin correlations. The initial system of equations can be transformed into two polynomial equations with two unknowns by means of elementary algebraic operations. These two polynomials of multidegree two can be reduced to one univariate polynomial of degree four by means of resultants. The obtained quartic equation is solved analytically.

Polynomial approximation of Poincare maps for Hamiltonian system

NASA Technical Reports Server (NTRS)

Froeschle, Claude; Petit, Jean-Marc

1992-01-01

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Umbral Calculus and Holonomic Modules in Positive Characteristic

NASA Astrophysics Data System (ADS)

Kochubei, Anatoly N.

2006-03-01

In the framework of analysis over local fields of positive characteristic, we develop algebraic tools for introducing and investigating various polynomial systems. In this survey paper we describe a function field version of umbral calculus developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. We consider modules over the Weyl-Carlitz ring, a function field counterpart of the Weyl algebra. It is shown that some basic objects of function field arithmetic, like the Carlitz module, Thakur's hypergeometric polynomials, and analogs of binomial coefficients arising in the positive characteristic version of umbral calculus, generate holonomic modules.

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

PubMed

Khader, M M

2013-10-01

In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

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

PubMed

Chen, Minfeng; Gao, Zongsheng; Du, Yunfei

2017-01-01

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

On generalized Melvin solution for the Lie algebra E_6

NASA Astrophysics Data System (ADS)

Bolokhov, S. V.; Ivashchuk, V. D.

2017-10-01

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H_s(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H_s(z), s = 1,\\ldots ,6, for the Lie algebra E_6 are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q_s, s = 1,\\ldots ,6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E_6-polynomials at large z are governed by the integer-valued matrix ν = A^{-1} (I + P), where A^{-1} is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z_2-group of symmetry of the Dynkin diagram. The 2-form fluxes Φ ^s, s = 1,\\ldots ,6, are calculated.

Volumetric calibration of a plenoptic camera

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

Hall, Elise Munz; Fahringer, Timothy W.; Guildenbecher, Daniel Robert

Here, the volumetric calibration of a plenoptic camera is explored to correct for inaccuracies due to real-world lens distortions and thin-lens assumptions in current processing methods. Two methods of volumetric calibration based on a polynomial mapping function that does not require knowledge of specific lens parameters are presented and compared to a calibration based on thin-lens assumptions. The first method, volumetric dewarping, is executed by creation of a volumetric representation of a scene using the thin-lens assumptions, which is then corrected in post-processing using a polynomial mapping function. The second method, direct light-field calibration, uses the polynomial mapping in creationmore » of the initial volumetric representation to relate locations in object space directly to image sensor locations. The accuracy and feasibility of these methods is examined experimentally by capturing images of a known dot card at a variety of depths. Results suggest that use of a 3D polynomial mapping function provides a significant increase in reconstruction accuracy and that the achievable accuracy is similar using either polynomial-mapping-based method. Additionally, direct light-field calibration provides significant computational benefits by eliminating some intermediate processing steps found in other methods. Finally, the flexibility of this method is shown for a nonplanar calibration.« less

Volumetric calibration of a plenoptic camera

DOE PAGES

Hall, Elise Munz; Fahringer, Timothy W.; Guildenbecher, Daniel Robert; ...

2018-02-01

Here, the volumetric calibration of a plenoptic camera is explored to correct for inaccuracies due to real-world lens distortions and thin-lens assumptions in current processing methods. Two methods of volumetric calibration based on a polynomial mapping function that does not require knowledge of specific lens parameters are presented and compared to a calibration based on thin-lens assumptions. The first method, volumetric dewarping, is executed by creation of a volumetric representation of a scene using the thin-lens assumptions, which is then corrected in post-processing using a polynomial mapping function. The second method, direct light-field calibration, uses the polynomial mapping in creationmore » of the initial volumetric representation to relate locations in object space directly to image sensor locations. The accuracy and feasibility of these methods is examined experimentally by capturing images of a known dot card at a variety of depths. Results suggest that use of a 3D polynomial mapping function provides a significant increase in reconstruction accuracy and that the achievable accuracy is similar using either polynomial-mapping-based method. Additionally, direct light-field calibration provides significant computational benefits by eliminating some intermediate processing steps found in other methods. Finally, the flexibility of this method is shown for a nonplanar calibration.« less

Hydrodynamics of the VanA-type VanS histidine kinase: an extended solution conformation and first evidence for interactions with vancomycin

PubMed Central

Phillips-Jones, Mary K.; Channell, Guy; Kelsall, Claire J.; Hughes, Charlotte S.; Ashcroft, Alison E.; Patching, Simon G.; Dinu, Vlad; Gillis, Richard B.; Adams, Gary G.; Harding, Stephen E.

2017-01-01

VanA-type resistance to glycopeptide antibiotics in clinical enterococci is regulated by the VanSARA two-component signal transduction system. The nature of the molecular ligand that is recognised by the VanSA sensory component has not hitherto been identified. Here we employ purified, intact and active VanSA membrane protein (henceforth referred to as VanS) in analytical ultracentrifugation experiments to study VanS oligomeric state and conformation in the absence and presence of vancomycin. A combination of sedimentation velocity and sedimentation equilibrium in the analytical ultracentrifuge (SEDFIT, SEDFIT-MSTAR and MULTISIG analysis) showed that VanS in the absence of the ligand is almost entirely monomeric (molar mass M = 45.7 kDa) in dilute aqueous solution with a trace amount of high molar mass material (M ~ 200 kDa). The sedimentation coefficient s suggests the monomer adopts an extended conformation in aqueous solution with an equivalent aspect ratio of ~(12 ± 2). In the presence of vancomycin over a 33% increase in the sedimentation coefficient is observed with the appearance of additional higher s components, demonstrating an interaction, an observation consistent with our circular dichroism measurements. The two possible causes of this increase in s – either a ligand induced dimerization and/or compaction of the monomer are considered. PMID:28397853

In Vivo Fluorescence Confocal Microscopy to Investigate the Role of RhoC in Inflammatory Breast Cancer

DTIC Science & Technology

2005-04-01

5084. 6. Colpaert CG, Vermeulen PB, Benoy I, Soubry A, van Roy F, van Beest P, Goovaerts G, Dirix LY, van Dam P, Fox SB, Harris AL, van MarckEA...cancer. Cancer Res 1999, 59: 5079-5084. 17 14. Colpaert CG, Vermeulen PB, Benoy I, Soubry A, van Roy F, van Beest P, Goovaerts G, Dirix LY, van Dam P...Ohira S, Feng Y, Nikaido T, Konishi I: Up- regulation of small GTPases, RhoA and RhoC, is associated with tumor progression in ovarian carcinoma. Lab

Mentale Inzetbaarheid van Teams: Ontwikkeling van een Moden van Teamfunctioneren als Module voor SCOPE (Mental Readiness of Teams - Development of a Team Model as Module for SCOPE)

DTIC Science & Technology

2007-04-01

inzetbaarheid van teams: ontwikkeling van een model van teamfunctioneren als module voor SCOPE Datumn april 2007 Auteur (s) R. de B~ruin C’. Vervvijs A.J...Datum april 2007 Programmaleider Projectleider Auteur (s) dr. W.A. Lotens, TNO Defensie en A.]. van Vijet, TNO Defensie en R. de Bruin Veiligheid...Deelnemers verwachten wel, in lijn met de theorie , dat een lage cohesie samenhangt met een lage effectiviteit. Een hoge cohesie, daarentegen, zou

User Manual PIRATE Model, Release Beta 1.0. (Handleiding PIRATE model, versie Beta 1.0)

DTIC Science & Technology

1998-01-01

Beperkingen van PIRATE 40 9 . Conclusies en aanbevelingen 41 10. Referenties 42 11 . Ondertekening 43 TNO-rapport FEL-97-A285 Inleiding Bij maritieme...Inhoud Inleiding 7 1.1 Doel van PIRATE 7 1.2 Werking van PIRATE 8 1.3 Opbouw van de handleiding 8 2. Bediening van PIRATE 9 2.1 Systeemvereisten 10...2.2 Installatie 10 2.3 Bediening van de gebruikersinterface 11 2.4 Gebruiken van de figuren in andere programmes 15 3. Radars, radars in PIRATE

Molecular epidemiology of vancomycin resistant enterococci in a tertiary care hospital in Saudi Arabia.

PubMed

Somily, Ali M; Al-Mohizea, Maha M; Absar, Muhammed M; Fatani, Amal J; Ridha, Afaaf M; Al-Ahdal, Mohammed N; Senok, Abiola C; Al-Qahtani, Ahmed A

2016-08-01

Vancomycin-resistant enterococci (VRE) are a major cause of nosocomial infections with high mortality and morbidity. There is limited data on the molecular characterization of VRE in Saudi Arabia. This study was carried out to investigate the premise that a shift in VRE epidemiology is occurring in our setting. Enterococcus species identification and susceptibility testing plus VRE phenotypic confirmation by vancomycin and teicoplanin E-test were carried out. Vancomycin resistance genes were detected by PCR. Strain typing was conducted using PFGE. Among the strains of Enterococcus spp. investigated in this study, 17 (4.5%) were VRE. With the exception of one isolate from rectal swab, all others were clinical specimens with blood being the commonest source (n = 11; 64.7%), followed by urine (n = 3; 17.6%). The 17 VRE isolates were Enterococcus faecium (n/N = 13/17) and Enterococcus gallinarum (n/N = 4/17). Among E. faecium isolates, vanA(+)/vanB(+) (n/N = 8/13; 62%) exhibiting VanB phenotype were predominant. One of the five vanA(+)E. faecium isolates exhibited a VanB phenotype indicative of vanA genotype-VanB phenotype incongruence. E. gallinarum isolates exhibited a Van C phenotype although two were vanA(+)/vanC1(+). PFGE revealed a polyclonal distribution with eight pulsotypes. These findings indicate an evolving VRE epidemiology with vanA(+)/vanB(+) isolates and vanA genotype-VanB phenotype incongruence isolates, which were previously described as colonizers, are now causing clinical infection. Copyright © 2016 Elsevier Ltd. All rights reserved.

An efficient algorithm for choosing the degree of a polynomial to approximate discrete nonoscillatory data

NASA Technical Reports Server (NTRS)

Hedgley, D. R.

1978-01-01

An efficient algorithm for selecting the degree of a polynomial that defines a curve that best approximates a data set was presented. This algorithm was applied to both oscillatory and nonoscillatory data without loss of generality.

Nodal-line dynamics via exact polynomial solutions for coherent waves traversing aberrated imaging systems.

PubMed

Paganin, David M; Beltran, Mario A; Petersen, Timothy C

2018-03-01

We obtain exact polynomial solutions for two-dimensional coherent complex scalar fields propagating through arbitrary aberrated shift-invariant linear imaging systems. These solutions are used to model nodal-line dynamics of coherent fields output by such systems.

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.

Power of one nonclean qubit

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki; Fujii, Keisuke; Nishimura, Harumichi

2017-04-01

The one-clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single qubit of the initial state is pure and others are maximally mixed. Although the model is not universal, it can efficiently solve several problems whose classical efficient solutions are not known. Furthermore, it was recently shown that if the one-clean qubit model is classically efficiently simulated, the polynomial hierarchy collapses to the second level. A disadvantage of the one-clean qubit model is, however, that the clean qubit is too clean: for example, in realistic NMR experiments, polarizations are not high enough to have the perfectly pure qubit. In this paper, we consider a more realistic one-clean qubit model, where the clean qubit is not clean, but depolarized. We first show that, for any polarization, a multiplicative-error calculation of the output probability distribution of the model is possible in a classical polynomial time if we take an appropriately large multiplicative error. The result is in strong contrast with that of the ideal one-clean qubit model where the classical efficient multiplicative-error calculation (or even the sampling) with the same amount of error causes the collapse of the polynomial hierarchy. We next show that, for any polarization lower-bounded by an inverse polynomial, a classical efficient sampling (in terms of a sufficiently small multiplicative error or an exponentially small additive error) of the output probability distribution of the model is impossible unless BQP (bounded error quantum polynomial time) is contained in the second level of the polynomial hierarchy, which suggests the hardness of the classical efficient simulation of the one nonclean qubit model.

RpoS induces expression of the Vibrio anguillarum quorum-sensing regulator VanT.

PubMed

Weber, Barbara; Croxatto, Antony; Chen, Chang; Milton, Debra L

2008-03-01

In vibrios, regulation of the Vibrio harveyi-like LuxR transcriptional activators occurs post-transcriptionally via small regulatory RNAs (sRNAs) that destabilize the luxR mRNA at a low cell population, eliminating expression of LuxR. Expression of the sRNAs is modulated by the vibrio quorum-sensing phosphorelay systems. However, vanT mRNA, which encodes a LuxR homologue in Vibrio anguillarum, is abundant at low and high cell density, indicating that VanT expression may be regulated via additional mechanisms. In this study, Western analyses showed that VanT was expressed throughout growth with a peak of expression during late exponential growth. VanO induced partial destabilization of vanT mRNA via activation of at least one Qrr sRNA. Interestingly, the sigma factor RpoS significantly stabilized vanT mRNA and induced VanT expression during late exponential growth. This induction was in part due to RpoS repressing expression of Hfq, an RNA chaperone. RpoS is not part of the quorum-sensing regulatory cascade since RpoS did not regulate expression or activity of VanO, and RpoS was not regulated by VanO or VanT. VanT and RpoS were needed for survival following UV irradiation and for pigment and metalloprotease production, suggesting that RpoS works with the quorum-sensing systems to modulate expression of VanT, which regulates survival and stress responses.

Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer

NASA Astrophysics Data System (ADS)

Vinet, Luc; Zhedanov, Alexei

2012-07-01

Analogues of Krawtchouk polynomials defined on a bi-lattice are introduced. They are shown to provide a (novel) spin chain with perfect transfer. Their characterization, as well as their connection to the quadratic Hahn algebra, is given.

A conforming spectral collocation strategy for Stokes flow through a channel contraction

NASA Technical Reports Server (NTRS)

Phillips, Timothy N.; Karageorghis, Andreas

1989-01-01

A formula expressing the coefficients of an expansion 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.

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

Evaluation of Piecewise Polynomial Equations for Two Types of Thermocouples

PubMed Central

Chen, Andrew; Chen, Chiachung

2013-01-01

Thermocouples are the most frequently used sensors for temperature measurement because of their wide applicability, long-term stability and high reliability. However, one of the major utilization problems is the linearization of the transfer relation between temperature and output voltage of thermocouples. The linear calibration equation and its modules could be improved by using regression analysis to help solve this problem. In this study, two types of thermocouple and five temperature ranges were selected to evaluate the fitting agreement of different-order polynomial equations. Two quantitative criteria, the average of the absolute error values |e|ave and the standard deviation of calibration equation estd, were used to evaluate the accuracy and precision of these calibrations equations. The optimal order of polynomial equations differed with the temperature range. The accuracy and precision of the calibration equation could be improved significantly with an adequate higher degree polynomial equation. The technique could be applied with hardware modules to serve as an intelligent sensor for temperature measurement. PMID:24351627

Equations on knot polynomials and 3d/5d duality

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

Mironov, A.; Morozov, A.; ITEP, Moscow

2012-09-24

We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as 'differential' and (quantum) A-polynomial structures. We pay a special attention to identity between the A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d- 5d generalization of the AGT relation. Themore » shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.« 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

Online Removal of Baseline Shift with a Polynomial Function for Hemodynamic Monitoring Using Near-Infrared Spectroscopy.

PubMed

Zhao, Ke; Ji, Yaoyao; Li, Yan; Li, Ting

2018-01-21

Near-infrared spectroscopy (NIRS) has become widely accepted as a valuable tool for noninvasively monitoring hemodynamics for clinical and diagnostic purposes. Baseline shift has attracted great attention in the field, but there has been little quantitative study on baseline removal. Here, we aimed to study the baseline characteristics of an in-house-built portable medical NIRS device over a long time (>3.5 h). We found that the measured baselines all formed perfect polynomial functions on phantom tests mimicking human bodies, which were identified by recent NIRS studies. More importantly, our study shows that the fourth-order polynomial function acted to distinguish performance with stable and low-computation-burden fitting calibration (R-square >0.99 for all probes) among second- to sixth-order polynomials, evaluated by the parameters R-square, sum of squares due to error, and residual. This study provides a straightforward, efficient, and quantitatively evaluated solution for online baseline removal for hemodynamic monitoring using NIRS devices.

An Online Gravity Modeling Method Applied for High Precision Free-INS

PubMed Central

Wang, Jing; Yang, Gongliu; Li, Jing; Zhou, Xiao

2016-01-01

For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS. PMID:27669261

Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations

NASA Astrophysics Data System (ADS)

Ariznabarreta, Gerardo; García-Ardila, Juan C.; Mañas, Manuel; Marcellán, Francisco

2018-05-01

In this paper, Geronimus–Uvarov perturbations for matrix orthogonal polynomials on the real line are studied and then applied to the analysis of non-Abelian integrable hierarchies. The orthogonality is understood in full generality, i.e. in terms of a nondegenerate continuous sesquilinear form, determined by a quasidefinite matrix of bivariate generalized functions with a well-defined support. We derive Christoffel-type formulas that give the perturbed matrix biorthogonal polynomials and their norms in terms of the original ones. The keystone for this finding is the Gauss–Borel factorization of the Gram matrix. Geronimus–Uvarov transformations are considered in the context of the 2D non-Abelian Toda lattice and noncommutative KP hierarchies. The interplay between transformations and integrable flows is discussed. Miwa shifts, τ-ratio matrix functions and Sato formulas are given. Bilinear identities, involving Geronimus–Uvarov transformations, first for the Baker functions, then secondly for the biorthogonal polynomials and its second kind functions, and finally for the τ-ratio matrix functions, are found.

Maximum likelihood decoding of Reed Solomon Codes

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

Sudan, M.

We present a randomized algorithm which takes as input n distinct points ((x{sub i}, y{sub i})){sup n}{sub i=1} from F x F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in at least t places (i.e., y{sub i} = f (x{sub i}) for at least t values of i), provided t = {Omega}({radical}nd). The running time is bounded by a polynomial in n. This immediately provides a maximum likelihoodmore » decoding algorithm for Reed Solomon Codes, which works in a setting with a larger number of errors than any previously known algorithm. To the best of our knowledge, this is the first efficient (i.e., polynomial time bounded) algorithm which provides some maximum likelihood decoding for any efficient (i.e., constant or even polynomial rate) code.« less