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1Local Induction Approximation In The Theory Of Superfluid Turbulence. Numerical Consideration
By M. V. Nedoboiko
The local induction approximation (LIA) of the Biot-Savart law is often used for numerical and analytical investigations of vortex dynamics in the theory of superfluid turbulence. In this paper, using numerical simulation, some features of the LIA is considered. The temporal evolution of vortex loop spectrum is studied numerically.
“Local Induction Approximation In The Theory Of Superfluid Turbulence. Numerical Consideration” Metadata:
- Title: ➤ Local Induction Approximation In The Theory Of Superfluid Turbulence. Numerical Consideration
- Author: M. V. Nedoboiko
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-cond-mat0303631
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2Unconstrained SU(2) Yang-Mills Theory With Topological Term In The Long-Wavelength Approximation
By A. M. Khvedelidze, D. M. Mladenov, H. -P. Pavel and G. Röpke
The Hamiltonian reduction of SU(2) Yang-Mills theory for an arbitrary \theta angle to an unconstrained nonlocal theory of a self-interacting positive definite symmetric 3 \times 3 matrix field S(x) is performed. It is shown that, after exact projection to a reduced phase space, the density of the Pontryagin index remains a pure divergence, proving the \theta independence of the unconstrained theory obtained. An expansion of the nonlocal kinetic part of the Hamiltonian in powers of the inverse coupling constant and truncation to lowest order, however, lead to violation of the \theta independence of the theory. In order to maintain this property on the level of the local approximate theory, a modified expansion in the inverse coupling constant is suggested, which for a vanishing \theta angle coincides with the original expansion. The corresponding approximate Lagrangian up to second order in derivatives is obtained, and the explicit form of the unconstrained analogue of the Chern-Simons current linear in derivatives is given. Finally, for the case of degenerate field configurations S(x) with rank|S| = 1, a nonlinear \sigma-type model is obtained, with the Pontryagin topological term reducing to the Hopf invariant of the mapping from the three-sphere S^3 to the unit two-sphere S^2 in the Whitehead form.
“Unconstrained SU(2) Yang-Mills Theory With Topological Term In The Long-Wavelength Approximation” Metadata:
- Title: ➤ Unconstrained SU(2) Yang-Mills Theory With Topological Term In The Long-Wavelength Approximation
- Authors: A. M. KhvedelidzeD. M. MladenovH. -P. PavelG. Röpke
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-hep-th0202145
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3Pairing Correlations And The Pseudo-Gap State: Application Of The Pairing Approximation Theory
By Jiri Maly, Boldizsar Janko and K. Levin
We investigate the pseudogap onset temperature $T^*$, the superconducting transition temperature $T_c$ and the general nature of the pseudogap phase using a diagrammatic BCS-Bose Einstein crossover theory. This decoupling scheme is based on the pairing approximation of Kadanoff and Martin, further extended by Patton (KMP). Our consideration of the KMP pairing approximation is driven by the objective to obtain BCS like behavior at weak coupling, (which does not necessarily follow for other diagrammatic schemes). The breakdown of the Fermi liquid state at $T^*$ is investigated within the lowest order theory and is associated with intermediate values of the coupling. The superconducting instability $T_c$ is evaluated by introducing mode coupling effects, in which the long lived pairs are affected by the single particle pseudogap states and vice versa. Our $T_c$ equations, which turn out to be rather simple as a result of the KMP scheme, reveal a rich structure as a function of $g$ in which the pseudogap is found to compete with superconductivity. Our results are compared with alternate theories in the literature.
“Pairing Correlations And The Pseudo-Gap State: Application Of The Pairing Approximation Theory” Metadata:
- Title: ➤ Pairing Correlations And The Pseudo-Gap State: Application Of The Pairing Approximation Theory
- Authors: Jiri MalyBoldizsar JankoK. Levin
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-cond-mat9805018
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4Asymptotic Theory For Statistics Of The Poisson--Voronoi Approximation
By Christoph Thäle and J. E. Yukich
This paper establishes expectation and variance asymptotics for statistics of the Poisson--Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to infinity. Statistics of interest include volume, surface area, Hausdorff measure, and the number of faces of lower-dimensional skeletons. We also consider the complexity of the so-called Voronoi zone and the iterated Voronoi approximation. Our results are consequences of general limit theorems proved with an abstract Steiner-type formula applicable in the setting of sums of stabilizing functionals.
“Asymptotic Theory For Statistics Of The Poisson--Voronoi Approximation” Metadata:
- Title: ➤ Asymptotic Theory For Statistics Of The Poisson--Voronoi Approximation
- Authors: Christoph ThäleJ. E. Yukich
- Language: English
“Asymptotic Theory For Statistics Of The Poisson--Voronoi Approximation” Subjects and Themes:
- Subjects: Probability - Mathematics
Edition Identifiers:
- Internet Archive ID: arxiv-1503.08963
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5DTIC ADA122925: An Approximation Theory For Nonlinear Partial Differential Equations With Applications To Identification And Control,
By Defense Technical Information Center
This paper establishes expectation and variance asymptotics for statistics of the Poisson--Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to infinity. Statistics of interest include volume, surface area, Hausdorff measure, and the number of faces of lower-dimensional skeletons. We also consider the complexity of the so-called Voronoi zone and the iterated Voronoi approximation. Our results are consequences of general limit theorems proved with an abstract Steiner-type formula applicable in the setting of sums of stabilizing functionals.
“DTIC ADA122925: An Approximation Theory For Nonlinear Partial Differential Equations With Applications To Identification And Control,” Metadata:
- Title: ➤ DTIC ADA122925: An Approximation Theory For Nonlinear Partial Differential Equations With Applications To Identification And Control,
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA122925: An Approximation Theory For Nonlinear Partial Differential Equations With Applications To Identification And Control,” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Banks,H T - BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS - *NONLINEAR DIFFERENTIAL EQUATIONS - *APPROXIMATION(MATHEMATICS) - *PARTIAL DIFFERENTIAL EQUATIONS - REPRINTS - CONTROL SYSTEMS - PARAMETERS - ESTIMATES - IDENTIFICATION - CONVERGENCE
Edition Identifiers:
- Internet Archive ID: DTIC_ADA122925
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6Revival Of Single-Particle Transport Theory For The Normal State Of High-Tc Superconductors: I. Relaxation-Time Approximation
By O. Narikiyo
A demonstration of the usefulness of a simple formula for the DC Hall conductivity based on the relaxation-time approximation is presented. The implementation of the formula on your PC can be completed within ten minutes. The formula is employed to explain the qualitative features of the measured DC Hall conductivity in the normal state of high-Tc superconductors.
“Revival Of Single-Particle Transport Theory For The Normal State Of High-Tc Superconductors: I. Relaxation-Time Approximation” Metadata:
- Title: ➤ Revival Of Single-Particle Transport Theory For The Normal State Of High-Tc Superconductors: I. Relaxation-Time Approximation
- Author: O. Narikiyo
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-1204.5300
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7Covariant Approximation Schemes For Calculation Of The Heat Kernel In Quantum Field Theory
By Ivan G. Avramidi
This paper is an overview on our recent results in the calculation of the heat kernel in quantum field theory and quantum gravity. We introduce a deformation of the background fields (including the metric of a curved spacetime manifold) and study various asymptotic expansions of the heat kernel diagonal associated with this deformation. Especial attention is payed to the low-energy approximation corresponding to the strong slowly varying background fields. We develop a new covariant purely algebraic approach for calculating the heat kernel diagonal in low-energy approximation by taking into account a finite number of low-order covariant derivatives of the background fields, and neglecting all covariant derivatives of higher orders. Then there exist a set of covariant differential operators that together with the background fields and their low-order derivatives generate a finite dimensional Lie algebra. In the zeroth order of the low-energy perturbation theory, determined by covariantly constant background, we use this algebraic structure to present the heat operator in the form of an average over the corresponding Lie group. This simplifies considerably the calculations and allows to obtain closed explicitly covariant formulas for the heat kernel diagonal. These formulas serve as the generating functions for the whole sequence of the Hadamard-Minakshisundaram- De Witt-Seeley coefficients in the low-energy approximation.
“Covariant Approximation Schemes For Calculation Of The Heat Kernel In Quantum Field Theory” Metadata:
- Title: ➤ Covariant Approximation Schemes For Calculation Of The Heat Kernel In Quantum Field Theory
- Author: Ivan G. Avramidi
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-hep-th9509075
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8DTIC ADA220864: An Approximation Theory For The Identification Of Linear Thermoelastic Systems
By Defense Technical Information Center
An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well- posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions, and convergence solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme is discussed and numerical results indicating how our approach might be used in a study of damping mechanisms in flexible structures are presented.
“DTIC ADA220864: An Approximation Theory For The Identification Of Linear Thermoelastic Systems” Metadata:
- Title: ➤ DTIC ADA220864: An Approximation Theory For The Identification Of Linear Thermoelastic Systems
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA220864: An Approximation Theory For The Identification Of Linear Thermoelastic Systems” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Rosen, I G - INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA - *THERMOELASTICITY - *LINEAR SYSTEMS - *APPROXIMATION(MATHEMATICS) - FORMULATIONS - THEORY - NUMERICAL ANALYSIS - ELASTIC PROPERTIES - DAMPING - ABSTRACTS - ESTIMATES - SOLUTIONS(GENERAL) - THERMAL CONDUCTIVITY - IDENTIFICATION SYSTEMS - PARABOLAS - CONVERGENCE - INVERSION - EQUATIONS - OPERATORS(PERSONNEL) - FLEXIBLE STRUCTURES - HILBERT SPACE - ONE DIMENSIONAL - PARAMETERS - SPLINES - SIZES(DIMENSIONS)
Edition Identifiers:
- Internet Archive ID: DTIC_ADA220864
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9The Strong-Coupling Expansion And The Ultra-local Approximation In Field Theory
By N. F. Svaiter
We discuss the strong-coupling expansion in Euclidean field theory. In a formal representation for the Schwinger functional, we treat the off-diagonal terms of the Gaussian factor as a perturbation about the remaining terms of the functional integral. We first study the strong-coupling expansion in the \phi^4 theory and also quantum electrodynamics. Assuming the ultra-local approximation, we examine the analytic structure of the zero-dimensional generating functions in the complex coupling constants plane. Second, we discuss the ultra-local generating functional in two idealized field theory models. To control the divergences of the strong-coupling perturbative expansion two different steps are used. First, we introduce a lattice structure to give meaning to the ultra-local generating functional. Using an analytic regularization procedure we discuss briefly how it is possible to obtain a renormalized Schwinger functional associated with these scalar models, going beyond the ultra-local approximation. Using the strong-coupling perturbative expansion we show how it is possible to compute the renormalized vacuum energy of a self-interacting scalar field, going beyond the one-loop level.
“The Strong-Coupling Expansion And The Ultra-local Approximation In Field Theory” Metadata:
- Title: ➤ The Strong-Coupling Expansion And The Ultra-local Approximation In Field Theory
- Author: N. F. Svaiter
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-hep-th0404070
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10Logarithmic Potential Theory With Applications To Approximation Theory
By E. B. Saff
We provide an introduction to logarithmic potential theory in the complex plane that particularly emphasizes its usefulness in the theory of polynomial and rational approximation. The reader is invited to explore the notions of Fekete points, logarithmic capacity, and Chebyshev constant through a variety of examples and exercises. Many of the fundamental theorems of potential theory, such as Frostman's theorem, the Riesz Decomposition Theorem, the Principle of Domination, etc., are given along with essential ideas for their proofs. Equilibrium measures and potentials and their connections with Green functions and conformal mappings are presented. Moreover, we discuss extensions of the classical potential theoretic results to the case when an external field is present.
“Logarithmic Potential Theory With Applications To Approximation Theory” Metadata:
- Title: ➤ Logarithmic Potential Theory With Applications To Approximation Theory
- Author: E. B. Saff
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-1010.3760
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11Strong Approximation Of Black--Scholes Theory Based On Simple Random Walks
By Zsolt Nika and Tamás Szabados
A basic model in financial mathematics was introduced by Black, Scholes and Merton in 1973 (BSM model). A classical discrete approximation in distribution is the binomial model given by Cox, Ross and Rubinstein in 1979 (CRR model). The BSM and the CRR models have been used for example to price European call and put options. Our aim in this work is to give a strong (almost sure, pathwise) discrete approximation of the BSM model using a suitable nested sequence of simple, symmetric random walks. The approximation extends to the stock price process, the value process, the replicating portfolio, and the greeks. An important tool in the approximation is a discrete version of the Feynman--Kac formula as well. It is hoped that such a discrete pathwise approximation can be useful for example when teaching students whose mathematical background is limited, e.g. does not contain measure theory or stochastic analysis.
“Strong Approximation Of Black--Scholes Theory Based On Simple Random Walks” Metadata:
- Title: ➤ Strong Approximation Of Black--Scholes Theory Based On Simple Random Walks
- Authors: Zsolt NikaTamás Szabados
“Strong Approximation Of Black--Scholes Theory Based On Simple Random Walks” Subjects and Themes:
- Subjects: Probability - Mathematics
Edition Identifiers:
- Internet Archive ID: arxiv-1411.0501
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12Diophantine Approximation On Manifolds And The Distribution Of Rational Points: Contributions To The Convergence Theory
By Victor Beresnevich, Robert C. Vaughan, Sanju Velani and Evgeniy Zorin
In this paper we develop the convergence theory of simultaneous, inhomogeneous Diophantine approximation on manifolds. A consequence of our main result is that if the manifold $M \subset \mathbb{R}^n$ is of dimension strictly greater than $(n+1)/2$ and satisfies a natural non-degeneracy condition, then $M$ is of Khintchine type for convergence. The key lies in obtaining essentially the best possible upper bound regarding the distribution of rational points near manifolds.
“Diophantine Approximation On Manifolds And The Distribution Of Rational Points: Contributions To The Convergence Theory” Metadata:
- Title: ➤ Diophantine Approximation On Manifolds And The Distribution Of Rational Points: Contributions To The Convergence Theory
- Authors: Victor BeresnevichRobert C. VaughanSanju VelaniEvgeniy Zorin
- Language: English
“Diophantine Approximation On Manifolds And The Distribution Of Rational Points: Contributions To The Convergence Theory” Subjects and Themes:
- Subjects: Number Theory - Mathematics
Edition Identifiers:
- Internet Archive ID: arxiv-1506.09049
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13The Generalized Minkowski Functional With Applications In Approximation Theory
By Szilard Gy. Revesz
We give a systematic and thorough study of geometric notions and results connected to Minkowski's measure of symmetry and the extension of the well-known Minkowski functional to arbitrary, not necessarily symmetric convex bodies K on any (real) normed space X. Although many of the notions and results we treat in this paper can be found elsewhere in the literature, they are scattered and possibly hard to find. Further, we are not aware of a systematic study of this kind and we feel that several features, connections and properties - e.g. the connections between many equivalent formulations - are new, more general and they are put in a better perspective now. In particular, we prove a number of fundamental properties of the extended Minkowski functional, including convexity, global Lipschitz boundedness, linear growth and approximation of the classical Minkowski functional of the central symmetrization of the body K. Our aim is to present how in the recent years these notions proved to be surprisingly relevant and effective in problems of approximation theory.
“The Generalized Minkowski Functional With Applications In Approximation Theory” Metadata:
- Title: ➤ The Generalized Minkowski Functional With Applications In Approximation Theory
- Author: Szilard Gy. Revesz
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-math0703388
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14DTIC ADA058542: Diffusion Theory Of Reaction Rates. II. Ornstein - Uhlenbeck Approximation.
By Defense Technical Information Center
The diffusion theory of reaction rates is considered in the Ornstein--Uhlenbeck approximation. The rate constant is calculated by using a modified Kramers (eigenvalue) method and by using the expected time formulation. The transmission coefficient is calculated. It is shown how correlation functions can be calculated. In the last section, a model problem is considered. (Author)
“DTIC ADA058542: Diffusion Theory Of Reaction Rates. II. Ornstein - Uhlenbeck Approximation.” Metadata:
- Title: ➤ DTIC ADA058542: Diffusion Theory Of Reaction Rates. II. Ornstein - Uhlenbeck Approximation.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA058542: Diffusion Theory Of Reaction Rates. II. Ornstein - Uhlenbeck Approximation.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Mangel,Marc - CENTER FOR NAVAL ANALYSES ARLINGTON VA - *REACTION KINETICS - *DIFFUSION THEORY - FOURIER TRANSFORMATION - EIGENVALUES - CORRELATION TECHNIQUES - MOLECULAR PROPERTIES - METHOD OF CHARACTERISTICS - TRANSMISSIVITY - STEEPEST DESCENT METHOD
Edition Identifiers:
- Internet Archive ID: DTIC_ADA058542
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15On Banachic Kernels And Approximation Theory
By Marc Atteia
In this paper, I generalize a previous one about hilbertian kernels and approximation theory
“On Banachic Kernels And Approximation Theory” Metadata:
- Title: ➤ On Banachic Kernels And Approximation Theory
- Author: Marc Atteia
“On Banachic Kernels And Approximation Theory” Subjects and Themes:
- Subjects: Functional Analysis - Numerical Analysis - Mathematics
Edition Identifiers:
- Internet Archive ID: arxiv-1606.08728
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The book is available for download in "texts" format, the size of the file-s is: 0.14 Mbs, the file-s for this book were downloaded 20 times, the file-s went public at Fri Jun 29 2018.
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16Quantum Mechanics From General Relativity : An Approximation For A Theory Of Inertia
By Sachs, Mendel
In this paper, I generalize a previous one about hilbertian kernels and approximation theory
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- Author: Sachs, Mendel
- Language: English
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- Subjects: Quantum theory - Relativity (Physics) - Particles (Nuclear physics)
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17DTIC ADA146927: Numerical Methods And Approximation And Modelling Problems In Stochastic Control Theory.
By Defense Technical Information Center
Research during this period continued in the following topic areas: (1) Nonlinear filtering; (2) Large deviations problems; (3) Stochastic control of piecewise-deterministic processes; (4) Stochastic variational calculus; (5) Approximating multiple Ito integrals with band-limited processes; (6) Large deviations methods and asymptotic properties of recursive algorithms; and (7) Approximation and modelling for distributed stochastic systems. Progress is summarized and a list of publications supported by the grant is included in the report. (Author)
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- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA146927: Numerical Methods And Approximation And Modelling Problems In Stochastic Control Theory.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Fleming,W H - BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS - *MATHEMATICAL MODELS - *CONTROL THEORY - *NUMERICAL METHODS AND PROCEDURES - *STOCHASTIC CONTROL - INTEGRALS - MATHEMATICAL FILTERS - NONLINEAR SYSTEMS - APPROXIMATION(MATHEMATICS) - ASYMPTOTIC SERIES - RECURSIVE FUNCTIONS
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18DTIC ADA078288: Numerical Methods And Approximation And Modelling Problems In Stochastic Control Theory.
By Defense Technical Information Center
Many areas of stochastic control were studied in this period. Monte-Carlo algorithms of type appearing in adaptive systems were studied and stability, convergence and rate of convergence results obtained. The analytical techniques developed for this purpose have a wide applicability in the study of similar algorithms. Robust computationally oriented approximations to optimal non-linear filters were developed. A deep study of how to find the Markov system that best approximates a given non-linear system with a wide band-width input was undertaken and very good results obtained. The problem is important in control and communication theory because it is usually desired to use the many available methods for analyzing Markov systems. The results obtained seem to be the best available so far and application to control and communication theory are being pursued. Optimal stochastic control problems under the condition of partial information on the system state were studied and a new formulation, similar to that of the non-linear filtering problem, developed. The approach seems promising in providing qualitative information on this difficult class of problems. Part of the technique uses measure-valued processes in a way which has wider applicability to problems involving distributed states or information. (Author)
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- Author: ➤ Defense Technical Information Center
- Language: English
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- Subjects: ➤ DTIC Archive - Fleming ,Wendell H - BROWN UNIV PROVIDENCE R I LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS - *MATHEMATICAL MODELS - *STOCHASTIC CONTROL - ADAPTIVE CONTROL SYSTEMS - MONTE CARLO METHOD - NONLINEAR SYSTEMS - APPROXIMATION(MATHEMATICS) - RECURSIVE FUNCTIONS - CONVERGENCE - ADAPTIVE FILTERS - NUMERICAL METHODS AND PROCEDURES - APPLIED MATHEMATICS - MARKOV PROCESSES - DIFFUSION THEORY
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19Theory Of Thermoelectric Effects When The Temperature Approximation Is Incorrect
Many areas of stochastic control were studied in this period. Monte-Carlo algorithms of type appearing in adaptive systems were studied and stability, convergence and rate of convergence results obtained. The analytical techniques developed for this purpose have a wide applicability in the study of similar algorithms. Robust computationally oriented approximations to optimal non-linear filters were developed. A deep study of how to find the Markov system that best approximates a given non-linear system with a wide band-width input was undertaken and very good results obtained. The problem is important in control and communication theory because it is usually desired to use the many available methods for analyzing Markov systems. The results obtained seem to be the best available so far and application to control and communication theory are being pursued. Optimal stochastic control problems under the condition of partial information on the system state were studied and a new formulation, similar to that of the non-linear filtering problem, developed. The approach seems promising in providing qualitative information on this difficult class of problems. Part of the technique uses measure-valued processes in a way which has wider applicability to problems involving distributed states or information. (Author)
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20Local Charge Distributions In Metallic Alloys: A Local Field Coherent Potential Approximation Theory
By Ezio Bruno, Leon Zingales and Antonio Milici
Electronic structure calculations performed on very large supercells have shown that the local charge excesses in metallic alloys are related through simple linear relations to the local electrostatic field resulting from distribution of charges in the whole crystal. By including local external fields in the single site Coherent Potential Approximation theory, we develop a novel theoretical scheme in which the local charge excesses for random alloys can be obtained as the responses to local external fields. Our model maintains all the computational advantages of a single site theory but allows for full charge relaxation at the impurity sites. Through applications to CuPd and CuZn alloys, we find that, as a general rule, non linear charge rearrangements occur at the impurity site as a consequence of the complex phenomena related with the electronic screening of the external potential. This nothwithstanding, we observe that linear relations hold between charge excesses and external potentials, in quantitative agreement with the mentioned supercell calculations, and well beyond the limits of linearity for any other site property.
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- Authors: Ezio BrunoLeon ZingalesAntonio Milici
- Language: English
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21Optimal Estimation In Approximation Theory : [proceedings Of An International Symposium On Optimal Estimation In Approximation Theory Held In Freudenstadt, Federal Republic Of Germany, September 27-29, C1976]
By International Symposium on Optimal Estimation in Approximation Theory, Freudenstadt, Ger., 1976
Electronic structure calculations performed on very large supercells have shown that the local charge excesses in metallic alloys are related through simple linear relations to the local electrostatic field resulting from distribution of charges in the whole crystal. By including local external fields in the single site Coherent Potential Approximation theory, we develop a novel theoretical scheme in which the local charge excesses for random alloys can be obtained as the responses to local external fields. Our model maintains all the computational advantages of a single site theory but allows for full charge relaxation at the impurity sites. Through applications to CuPd and CuZn alloys, we find that, as a general rule, non linear charge rearrangements occur at the impurity site as a consequence of the complex phenomena related with the electronic screening of the external potential. This nothwithstanding, we observe that linear relations hold between charge excesses and external potentials, in quantitative agreement with the mentioned supercell calculations, and well beyond the limits of linearity for any other site property.
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- Title: ➤ Optimal Estimation In Approximation Theory : [proceedings Of An International Symposium On Optimal Estimation In Approximation Theory Held In Freudenstadt, Federal Republic Of Germany, September 27-29, C1976]
- Author: ➤ International Symposium on Optimal Estimation in Approximation Theory, Freudenstadt, Ger., 1976
- Language: English
“Optimal Estimation In Approximation Theory : [proceedings Of An International Symposium On Optimal Estimation In Approximation Theory Held In Freudenstadt, Federal Republic Of Germany, September 27-29, C1976]” Subjects and Themes:
- Subjects: ➤ Approximation theory -- Congresses - Mathematical optimization -- Congresses - Computational complexity -- Congresses
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- Internet Archive ID: optimalestimatio0000inte
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22Diffuse Approximation To The Kinetic Theory In A Fermi System
By V. M. Kolomietz and S. V. Lukyanov
We suggest the diffuse approach to the relaxation processes within the kinetic theory for the Wigner distribution function. The diffusion and drift coefficients are evaluated taking into consideration the interparticle collisions on the distorted Fermi surface. Using the finite range interaction, we show that the momentum dependence of the diffuse coefficient $D_{p}(p)$ has a maximum at Fermi momentum $p=p_{F}$ whereas the drift coefficient $K_{p}(p)$ is negative and reaches a minimum at $p\approx p_{F}$. For a cold Fermi system the diffusion coefficient takes the non-zero value which is caused by the relaxation on the distorted Fermi-surface at temperature $T=0$. The numerical solution of the diffusion equation was performed for the particle-hole excitation in a nucleus with $A=16$. The evaluated relaxation time $\tau_{r}\approx 8.3\cdot 10^{-23}\mathrm{s}$ is close to the corresponding result in a nuclear Fermi-liquid obtained within the kinetic theory.
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- Authors: V. M. KolomietzS. V. Lukyanov
- Language: English
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23NASA Technical Reports Server (NTRS) 19960001203: Relaxation Approximation In The Theory Of Shear Turbulence
By NASA Technical Reports Server (NTRS)
Leslie's perturbative treatment of the direct interaction approximation for shear turbulence (Modern Developments in the Theory of Turbulence, 1972) is applied to derive a time dependent model for the Reynolds stresses. The stresses are decomposed into tensor components which satisfy coupled linear relaxation equations; the present theory therefore differs from phenomenological Reynolds stress closures in which the time derivatives of the stresses are expressed in terms of the stresses themselves. The theory accounts naturally for the time dependence of the Reynolds normal stress ratios in simple shear flow. The distortion of wavenumber space by the mean shear plays a crucial role in this theory.
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- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
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- Subjects: ➤ NASA Technical Reports Server (NTRS) - RELAXATION (MECHANICS) - REYNOLDS STRESS - SHEAR FLOW - TURBULENCE - TURBULENCE MODELS - LINEAR EQUATIONS - STRESS RATIO - TIME DEPENDENCE - Rubinstein, Robert
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24Methods Of Approximation Theory In Complex Analysis And Mathematical Physics : Leningrad, May 13-24, 1991
Leslie's perturbative treatment of the direct interaction approximation for shear turbulence (Modern Developments in the Theory of Turbulence, 1972) is applied to derive a time dependent model for the Reynolds stresses. The stresses are decomposed into tensor components which satisfy coupled linear relaxation equations; the present theory therefore differs from phenomenological Reynolds stress closures in which the time derivatives of the stresses are expressed in terms of the stresses themselves. The theory accounts naturally for the time dependence of the Reynolds normal stress ratios in simple shear flow. The distortion of wavenumber space by the mean shear plays a crucial role in this theory.
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- Language: English
“Methods Of Approximation Theory In Complex Analysis And Mathematical Physics : Leningrad, May 13-24, 1991” Subjects and Themes:
- Subjects: ➤ Approximation theory -- Congresses - Functions of complex variables -- Congresses - Mathematical analysis -- Congresses - Mathematical physics -- Congresses - Théorie de l'approximation - Physique mathématique - Approximation theory - Functions of complex variables - Mathematical analysis - Mathematical physics - Approximation - Mathematische fysica - Benaderingen (wiskunde)
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25Exact Constants In Approximation Theory
By Korneĭchuk, Nikolaĭ Pavlovich
Leslie's perturbative treatment of the direct interaction approximation for shear turbulence (Modern Developments in the Theory of Turbulence, 1972) is applied to derive a time dependent model for the Reynolds stresses. The stresses are decomposed into tensor components which satisfy coupled linear relaxation equations; the present theory therefore differs from phenomenological Reynolds stress closures in which the time derivatives of the stresses are expressed in terms of the stresses themselves. The theory accounts naturally for the time dependence of the Reynolds normal stress ratios in simple shear flow. The distortion of wavenumber space by the mean shear plays a crucial role in this theory.
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- Author: ➤ Korneĭchuk, Nikolaĭ Pavlovich
- Language: English
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26Approximation And Exactness In Finite State Optimality Theory
By Dale Gerdemann and Gertjan van Noord
Previous work (Frank and Satta 1998; Karttunen, 1998) has shown that Optimality Theory with gradient constraints generally is not finite state. A new finite-state treatment of gradient constraints is presented which improves upon the approximation of Karttunen (1998). The method turns out to be exact, and very compact, for the syllabification analysis of Prince and Smolensky (1993).
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- Authors: Dale GerdemannGertjan van Noord
- Language: English
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27Hartree-Fock-Bogoliubov Theory Versus Local-density Approximation For Superfluid Trapped Fermionic Atoms
By Marcella Grasso and Michael Urban
We investigate a gas of superfluid fermionic atoms trapped in two hyperfine states by a spherical harmonic potential. We propose a new regularization method to remove the ultraviolet divergence in the Hartree-Fock-Bogoliubov equations caused by the use of a zero-range atom-atom interaction. Compared with a method used in the literature, our method is simpler and has improved convergence properties. Then we compare Hartree-Fock-Bogoliubov calculations with the semiclassical local-density approximation. We observe that for systems containing a small number of atoms shell effects, which cannot be reproduced by the semiclassical calculation, are very important. For systems with a large number of atoms at zero temperature the two calculations are in quite good agreement, which, however, is deteriorated at non-zero temperature, especially near the critical temperature. In this case the different behavior can be explained within the Ginzburg-Landau theory.
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- Title: ➤ Hartree-Fock-Bogoliubov Theory Versus Local-density Approximation For Superfluid Trapped Fermionic Atoms
- Authors: Marcella GrassoMichael Urban
- Language: English
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- Internet Archive ID: arxiv-cond-mat0305588
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28Theory Of Electronic Transport In Random Alloys With Short-range Order: Korringa-Kohn-Rostoker Non-local Coherent Potential Approximation
By P. R. Tulip, J. B. Staunton, S. Lowitzer, D. Ködderitzsch and H. Ebert
We present an ab-initio formalism for the calculation of transport properties in compositionally disordered systems within the framework of the Korringa-Kohn-Rostoker non-local coherent potential approximation. Our formalism is based upon the single-particle Kubo-Greenwood linear response and provides a natural means of incorporating the effects of short-range order upon the transport properties. We demonstrate the efficacy of the formalism by examining the effects of short-range order and clustering upon the transport properties of disordered $AgPd$ and $CuZn$ alloys.
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- Title: ➤ Theory Of Electronic Transport In Random Alloys With Short-range Order: Korringa-Kohn-Rostoker Non-local Coherent Potential Approximation
- Authors: P. R. TulipJ. B. StauntonS. LowitzerD. KödderitzschH. Ebert
- Language: English
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- Internet Archive ID: arxiv-0712.2388
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29Local Density Approximation For Exchange In Excited-state Density Functional Theory
By Manoj K. Harbola and Prasanjit Samal
Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate excitation energies.
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- Title: ➤ Local Density Approximation For Exchange In Excited-state Density Functional Theory
- Authors: Manoj K. HarbolaPrasanjit Samal
- Language: English
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- Internet Archive ID: arxiv-cond-mat0407099
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30An Ocean Medium Pulse Propagation Model Based On Linear Systems Theory And The WKB Approximation
By Campbell, Peter R. M.
A general, modular, pulse propagation model for underwater acoustics that is based on linear systems theory for sound-speed profiles as a function of depth is presented. The development and computer implementation of the model, together with results from preliminary computer simulation studies involving the transmission of CW and LFM pulses from a planar array of complex weighted point sources is reported. The studies examined free-space propagation problems (i.e., no boundaries) in homogeneous and inhomogeneous media using a transfer function of the ocean medium based on the WKB approximation. The two main outputs from the model are the predicted complex acoustic field as a function of frequency and spatial location and the time-domain output electrical signal from each element in a receive planar array.
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- Author: Campbell, Peter R. M.
- Language: English
“An Ocean Medium Pulse Propagation Model Based On Linear Systems Theory And The WKB Approximation” Subjects and Themes:
- Subjects: ➤ Linear systems - WKB - Underwater acoustics - Pulse propagation - Planar array - CW - LFM - Computer simulation - Complex acoustic field - Output electrical signal - Beamsteering
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- Internet Archive ID: anocemediumpulse1094527177
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31NASA Technical Reports Server (NTRS) 19880014126: An Approximation Theory For The Identification Of Nonlinear Distributed Parameter Systems
By NASA Technical Reports Server (NTRS)
An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.
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- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 19880014126: An Approximation Theory For The Identification Of Nonlinear Distributed Parameter Systems” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - APPROXIMATION - DISTRIBUTED PARAMETER SYSTEMS - IDENTIFYING - NONLINEAR SYSTEMS - ANALOGS - CONVERGENCE - ELLIPTIC FUNCTIONS - GALERKIN METHOD - OPERATORS (MATHEMATICS) - PARABOLIC DIFFERENTIAL EQUATIONS - PARTIAL DIFFERENTIAL EQUATIONS - Banks, H. T. - Reich, Simeon - Rosen, I. G.
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- Internet Archive ID: NASA_NTRS_Archive_19880014126
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32Microsoft Research Video 147087: Probabilistic Approximation Theorems In Game Theory And Stochastic Optimization/The Theory Of Crowdsourcing
By Microsoft Research
Talk 1: 3:30 to 4:15 Title: Probabilistic Approximation Theorems in Game Theory and Stochastic Optimization Speaker: Costis Daskalakis, MIT Abstract: In Economics, reliability theory and other domains, uncertainty is often modeled assuming Bayesian knowledge about unknown parameters. This assumption enables important results, e.g. Nash's theorem on the existence of equilibria in randomized strategies in games, and Myerson's theorem on revenue-optimal auctions. On the other hand, stochastic uncertainty may introduce computational complexity, in the form of PPAD-completeness for computing Nash equilibria, and more generally non-linearity in the resulting optimization problems. In this talk, we explore probabilistic approximation theorems that alleviate the computational complexity, drawing examples from Game Theory and Stochastic optimization. In particular, we present finitary central limit theorems and extreme value theorems and apply those to obtain polynomial time approximation schemes for Nash equilibria in anonymous games, multi-dimensional pricing, and network reliability problems. (based on joint work with Christos Papadimitriou, Yang Cai, and Ankur Moitra) Talk 2: 4:25 PM to 4:55 PM Title: The Theory of Crowdsourcing Speaker: Jason Hartline, Northwestern Crowdsourcing contests have been popularized by the Netflix challenge and websites like TopCoder and Taskcn. What is crowdsourcing? Imagine you are designing a new web service, you have it all coded up, but the site looks bad because you haven't got any graphic design skills. You could hire an artist to design your logo, or you could post the design task as a competition to crowdsourcing website Taskcn with a monetary reward of 100. Contestants on Taskcn would then compete to produce the best logo. You then select your favorite logo and award that contestant the 100 prize. In this talk, I discuss the theory of crowdsourcing contests. First, I will show how to model crowdsourcing contests using auction theory. Second, I will discuss how to solve for contestant strategies. I.e., suppose you were entering such a programming contest on TopCoder, how much work should you do on your entry to optimize your gains from winning less the cost of doing the work? Finally, I will discuss inefficiency from the fact that the effort of losing contestants is wasted (e.g., every contestant has to do work to design a logo, but you only value your favorite logo). I will show that this wasted effort is at most half of the total amount of effort. A consequence is that crowdsourcing is approximately as efficient a means of procurement as conventional methods (e.g., auctions or negotiations). Joint work with Shuchi Chawla and Balu Sivan
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- Author: Microsoft Research
- Language: English
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- Subjects: ➤ Microsoft Research - Microsoft Research Video Archive - Yuval Peres - Costis Daskalakis and Jason Hartline
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- Internet Archive ID: ➤ Microsoft_Research_Video_147087
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33Enskog Theory For Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
By V. Garzo, C. M. Hrenya and J. W. Dufty
The linear integral equations defining the Navier-Stokes (NS) transport coefficients for polydisperse granular mixtures of smooth inelastic hard disks or spheres are solved by using the leading terms in a Sonine polynomial expansion. Explicit expressions for all the NS transport coefficients are given in terms of the sizes, masses, compositions, density and restitution coefficients. In addition, the cooling rate is also evaluated to first order in the gradients. The results hold for arbitrary degree of inelasticity and are not limited to specific values of the parameters of the mixture. Finally, a detailed comparison between the derivation of the current theory and previous theories for mixtures is made, with attention paid to the implication of the various treatments employed to date.
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- Authors: V. GarzoC. M. HrenyaJ. W. Dufty
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- Internet Archive ID: arxiv-cond-mat0702110
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34DTIC ADA196306: An Approximation Theory For The Identification Of Nonlinear Distributed Parameter Systems
By Defense Technical Information Center
An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators(satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified)are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original infinite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed. Keywords: Nonlinear distributed systems; Numerical analysis; Inverse problems; Approximation.
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- Author: ➤ Defense Technical Information Center
- Language: English
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- Subjects: ➤ DTIC Archive - Banks, H T - INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA - *MONOTONE FUNCTIONS - *APPROXIMATION(MATHEMATICS) - DISTRIBUTION - PARAMETERS - THEORY - NUMERICAL ANALYSIS - ABSTRACTS - PROBLEM SOLVING - IDENTIFICATION - NONLINEAR SYSTEMS - LINEARITY - MASS TRANSFER - THERMAL CONDUCTIVITY - EVOLUTION(GENERAL) - INVERSION - OPERATORS(MATHEMATICS) - ANALOG SYSTEMS - MODELS - LINEAR SYSTEMS - SIZES(DIMENSIONS)
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- Internet Archive ID: DTIC_ADA196306
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35Analysis Of The Spin Hall Effect In CuIr Alloys: Combined Approach Of Density Functional Theory And Hartree-Fock Approximation
By Zhuo Xu, Bo Gu, Michiyasu Mori, Timothy Ziman and Sadamichi Maekawa
We analyze the spin Hall effect in CuIr alloys in theory by the combined approach of the density functional theory (DFT) and Hartree-Fock (HF) approximation. The SHA is obtained to be negative without the local correlation effects. After including the local correlation effects of the 5d orbitals of Ir impurities, the SHA becomes positive with realistic correlation parameters, and consistent with experiment [Niimi et al., Phys. Rev. Lett. 106, 126601 (2011)]. Moreover, our analysis shows that the DFT+HF approach is a convenient and general method to study the influence of local correlation effects on the spin Hall effect.
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- Authors: Zhuo XuBo GuMichiyasu MoriTimothy ZimanSadamichi Maekawa
“Analysis Of The Spin Hall Effect In CuIr Alloys: Combined Approach Of Density Functional Theory And Hartree-Fock Approximation” Subjects and Themes:
- Subjects: Strongly Correlated Electrons - Condensed Matter
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- Internet Archive ID: arxiv-1411.7733
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36New Interpretation For Energy Gap $Δ$ Of The Cut-off Approximation In The BCS Theory Of Superconductivity
By Zhidong Hao
This paper concerns the solution of the self-consistency equation for energy gap parameter $\Delta_{\bf k}$ in the BCS theory of superconductivity. We show that there exists a well-defined relation between the solution for energy gap parameter amplitude $|\Delta_{\bf k}|$ for a general interaction $V_{{\bf k},{\bf k}'}$ and energy gap $\Delta$ obtained by using the cut-off approximation. The relation between $|\Delta_{\bf k}|$ and $\Delta$ indicates that $\Delta$ is a weighted average over $|\Delta_{\bf k}|$ of electronic states within cut-off energy $\xi_c$ around the Fermi surface. In this interpretation for $\Delta$, $\xi_c$ is not a property of $V_{{\bf k},{\bf k}'}$, but a parameter specifying the energy range within which the weighted average over $|\Delta_{\bf k}|$ is taken. We show that the proper choice for the value of $\xi_c$ is only a few $k_BT_c$ (i.e., $\xi_c/k_BT_c$ is about 3 or 4). We also show that the cut-off approximation, even with $\xi_c/k_BT_c=\infty$, is a good approximation when it is used to calculate quantities such as the condensation energy and the specific heat, but it leads to significant overestimation for the Josephson critical current density of a Josephson junction if $\xi_c/k_BT_c \gg 1$ is assumed.
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- Title: ➤ New Interpretation For Energy Gap $Δ$ Of The Cut-off Approximation In The BCS Theory Of Superconductivity
- Author: Zhidong Hao
- Language: English
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- Internet Archive ID: arxiv-0706.2392
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37Eulerian Perturbation Theory In Non-Flat Universes: Second-Order Approximation
By Paolo Catelan, Francesco Lucchin, Sabino Matarrese and Lauro Moscardini
The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be solved {\it exactly}, rather than approximately, even for cosmological models with arbitrary density parameter $\Omega$. The Eulerian approach we present here allows to calculate the higher-order moments of the initially Gaussian density and velocity fields: in particular, we compute the gravitationally induced skewness of the density and velocity-divergence fields for any value of $\Omega$, confirming the extremely weak $\Omega$-dependence of the skewness previously obtained via Lagrangian perturbation theory. Our results show that the separability assumption of higher-order Eulerian perturbative solutions is restricted to the Einstein-de Sitter case only.
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- Title: ➤ Eulerian Perturbation Theory In Non-Flat Universes: Second-Order Approximation
- Authors: Paolo CatelanFrancesco LucchinSabino MatarreseLauro Moscardini
- Language: English
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- Internet Archive ID: arxiv-astro-ph9411066
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38Approximation Theory : Proceedings Of The International Dortmund Meeting, IDoMAT 95 Held In Witten, Germany, March 13-17, 1995
By International Dortmund Meeting (1st : 1995 : Witten, Germany)
The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be solved {\it exactly}, rather than approximately, even for cosmological models with arbitrary density parameter $\Omega$. The Eulerian approach we present here allows to calculate the higher-order moments of the initially Gaussian density and velocity fields: in particular, we compute the gravitationally induced skewness of the density and velocity-divergence fields for any value of $\Omega$, confirming the extremely weak $\Omega$-dependence of the skewness previously obtained via Lagrangian perturbation theory. Our results show that the separability assumption of higher-order Eulerian perturbative solutions is restricted to the Einstein-de Sitter case only.
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- Title: ➤ Approximation Theory : Proceedings Of The International Dortmund Meeting, IDoMAT 95 Held In Witten, Germany, March 13-17, 1995
- Author: ➤ International Dortmund Meeting (1st : 1995 : Witten, Germany)
- Language: English
“Approximation Theory : Proceedings Of The International Dortmund Meeting, IDoMAT 95 Held In Witten, Germany, March 13-17, 1995” Subjects and Themes:
- Subjects: ➤ Approximation theory - Approximation theory -- Congresses - Approximationstheorie - Witten
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- Internet Archive ID: approximationthe0000inte_l6s7
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39Linear Operators And Approximation Theory
By p.p. korovkin
The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be solved {\it exactly}, rather than approximately, even for cosmological models with arbitrary density parameter $\Omega$. The Eulerian approach we present here allows to calculate the higher-order moments of the initially Gaussian density and velocity fields: in particular, we compute the gravitationally induced skewness of the density and velocity-divergence fields for any value of $\Omega$, confirming the extremely weak $\Omega$-dependence of the skewness previously obtained via Lagrangian perturbation theory. Our results show that the separability assumption of higher-order Eulerian perturbative solutions is restricted to the Einstein-de Sitter case only.
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- Author: p.p. korovkin
- Language: English
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40Approximation Theory
The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be solved {\it exactly}, rather than approximately, even for cosmological models with arbitrary density parameter $\Omega$. The Eulerian approach we present here allows to calculate the higher-order moments of the initially Gaussian density and velocity fields: in particular, we compute the gravitationally induced skewness of the density and velocity-divergence fields for any value of $\Omega$, confirming the extremely weak $\Omega$-dependence of the skewness previously obtained via Lagrangian perturbation theory. Our results show that the separability assumption of higher-order Eulerian perturbative solutions is restricted to the Einstein-de Sitter case only.
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41Range-separated Density-functional Theory With Random Phase Approximation Applied To Noncovalent Intermolecular Interactions
By Wuming Zhu, Julien Toulouse, Andreas Savin and János G. Angyán
Range-separated methods combining a short-range density functional with long-range random phase approximations RPAs with or without exchange response kernel are tested on rare-gas dimers and the S22 benchmark set of weakly interacting complexes of Jurecka et al. [Phys. Chem. Chem. Phys. 8, 1985 (2006 )] . The methods are also compared to full-range RPA approaches. Both range separation and inclusion of the Hartree-Fock exchange kernel largely improve the accuracy of intermolecular interaction energies. The best results are obtained with the method called RSH+RPAx, which yields interaction energies for the S22 set with an estimated mean absolute error of about 0.5-0.6 kcal/mol, corresponding to a mean absolute percentage error of about 7%-9% depending on the reference interaction energies used. In particular, the RSH+RPAx method is found to be overall more accurate than the range-separated method based on long-range second-order M{\o}ller-Plesset MP2 perturbation theory RSH+MP2 .
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- Title: ➤ Range-separated Density-functional Theory With Random Phase Approximation Applied To Noncovalent Intermolecular Interactions
- Authors: Wuming ZhuJulien ToulouseAndreas SavinJános G. Angyán
“Range-separated Density-functional Theory With Random Phase Approximation Applied To Noncovalent Intermolecular Interactions” Subjects and Themes:
- Subjects: Physics - Chemical Physics - Computational Physics
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- Internet Archive ID: arxiv-1404.2585
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42Similitude And Approximation Theory
Range-separated methods combining a short-range density functional with long-range random phase approximations RPAs with or without exchange response kernel are tested on rare-gas dimers and the S22 benchmark set of weakly interacting complexes of Jurecka et al. [Phys. Chem. Chem. Phys. 8, 1985 (2006 )] . The methods are also compared to full-range RPA approaches. Both range separation and inclusion of the Hartree-Fock exchange kernel largely improve the accuracy of intermolecular interaction energies. The best results are obtained with the method called RSH+RPAx, which yields interaction energies for the S22 set with an estimated mean absolute error of about 0.5-0.6 kcal/mol, corresponding to a mean absolute percentage error of about 7%-9% depending on the reference interaction energies used. In particular, the RSH+RPAx method is found to be overall more accurate than the range-separated method based on long-range second-order M{\o}ller-Plesset MP2 perturbation theory RSH+MP2 .
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- Language: English
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43DTIC ADA107520: Approximation Of Processes And Applications To Control And Communication Theory,
By Defense Technical Information Center
Diffusion models are useful and of widespread use in many areas of control and communication theory. The models are frequently used for systems that are not quite diffusions but are, hopefully, close to a diffusion in some sense. E.g., the input noise might be 'wide-band'--but not 'white-Gaussian.' Many approximation techniques have been developed, under different sets of assumptions. The typical results are of a weak convergence nature. The physical process (x (to the epsilon power) (.)) is parameterized by the parameter epsilon, and one tries to show that (x (to the epsilon power) (.)) converges weakly to some diffusion x(.) as epsilon goes to 0. The limit process x(.) is then used to study various properties of x (to the epsilon power) (.) for small epsilon.
“DTIC ADA107520: Approximation Of Processes And Applications To Control And Communication Theory,” Metadata:
- Title: ➤ DTIC ADA107520: Approximation Of Processes And Applications To Control And Communication Theory,
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA107520: Approximation Of Processes And Applications To Control And Communication Theory,” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Kushner, Harold J - BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS - *COMMUNICATION AND RADIO SYSTEMS - *CONTROL THEORY - *DIFFUSION THEORY - DIGITAL SYSTEMS - GAUSSIAN NOISE - APPROXIMATION(MATHEMATICS) - LIMITERS - PHASE LOCKED SYSTEMS - WEAK CONVERGENCE - LYAPUNOV FUNCTIONS - VOLTAGE CONTROLLED OSCILLATORS
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- Internet Archive ID: DTIC_ADA107520
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44Exponential Approximation By Stein's Method And Spectral Graph Theory
By Sourav Chatterjee, Jason Fulman and Adrian Rollin
General Berry-Esseen bounds are developed for the exponential distribution using Stein's method. As an application, a sharp error term is obtained for Hora's result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is the first use of Stein's method to study the spectrum of a graph with a non-normal limit.
“Exponential Approximation By Stein's Method And Spectral Graph Theory” Metadata:
- Title: ➤ Exponential Approximation By Stein's Method And Spectral Graph Theory
- Authors: Sourav ChatterjeeJason FulmanAdrian Rollin
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-math0605552
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45Quasi-Local Density Functional Theory And Its Application Within Extended Thomas-Fermi Approximation
By V. B. Soubbotin, V. I. Tselyaev and X. Vinas
A generalization of the Density Functional Theory is proposed. The theory developed leads to single-particle equations of motion with a quasi-local mean-field operator, which contains a quasi-particle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the Extended Thomas-Fermi approximation. Within the framework of this approach the ground-state properties of the doubly magic nuclei are considered. The calculations have been performed using the finite-range Gogny D1S force. The results are compared with the exact Hartree-Fock calculations.
“Quasi-Local Density Functional Theory And Its Application Within Extended Thomas-Fermi Approximation” Metadata:
- Title: ➤ Quasi-Local Density Functional Theory And Its Application Within Extended Thomas-Fermi Approximation
- Authors: V. B. SoubbotinV. I. TselyaevX. Vinas
- Language: English
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- Internet Archive ID: arxiv-nucl-th0207029
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46On The Approximation In The Hermitian Treatment Of Dyson Boson Expansion Theory
By Atsushi Kajiyama, Kimikazu Taniguchi and Yoshinao Miyanishi
We discuss about the Hermitian treatment of Dyson-type boson expansion theory. We show that the basic assumption of the conventional treatment does not hold in general and the method is only approximately valid. We also show that the approximation is the same order as that of truncation of the expansion usually done in the Hermitian type boson expansion theory.
“On The Approximation In The Hermitian Treatment Of Dyson Boson Expansion Theory” Metadata:
- Title: ➤ On The Approximation In The Hermitian Treatment Of Dyson Boson Expansion Theory
- Authors: Atsushi KajiyamaKimikazu TaniguchiYoshinao Miyanishi
- Language: English
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- Internet Archive ID: arxiv-nucl-th9806091
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47Inverse Theorems In The Theory Of Approximation Of Vectors In A Banach Space With Exponential Type Entire Vectors
By S. Torba
Arbitrary operator A on a Banach space X which is the generator of C_0-group with certain growth condition at infinity is considered. The relationship between its exponential type entire vectors and its spectral subspaces is found. Inverse theorems on connection between the degree of smoothness of vector $x\in X$ with respect to operator A, the rate of convergence to zero of the best approximation of x by exponential type entire vectors for operator A, and the k-module of continuity are established. Also, a generalization of the Bernstein-type inequality is obtained. The results allow to obtain Bernstein-type inequalities in weighted L_p spaces.
“Inverse Theorems In The Theory Of Approximation Of Vectors In A Banach Space With Exponential Type Entire Vectors” Metadata:
- Title: ➤ Inverse Theorems In The Theory Of Approximation Of Vectors In A Banach Space With Exponential Type Entire Vectors
- Author: S. Torba
- Language: English
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- Internet Archive ID: arxiv-0809.4030
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48The Application Of Continued Fractions And Their Generalizations To Problems In Approximation Theory
By Khovanskii, Alexei Nikolaevich
XII, 212 p. ; 23 cm
“The Application Of Continued Fractions And Their Generalizations To Problems In Approximation Theory” Metadata:
- Title: ➤ The Application Of Continued Fractions And Their Generalizations To Problems In Approximation Theory
- Author: Khovanskii, Alexei Nikolaevich
- Language: English
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- Internet Archive ID: applicationofcon0000unse
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49Pseudogap And Superconducting Fluctuation In High-Tc Cuprates: Theory Beyond 1-loop Approximation
By Youichi Yanase
The pseudogap phenomena induced by the SC fluctuation are investigated in details. We perform a calculation beyond the 1-loop approximation. The SC fluctuation is microscopically derived on the basis of the repulsive Hubbard model. The vertex corrections are collected in the infinite order with use of the quasi-static approximation. The single-particle excitations, NMR 1/T_{1}T, spin susceptibility and superconducting transition temperature are discussed. The important role of the vertex correction is pointed out for the single particle spectral function. On the other hand, the validity of the 1-loop order theory is confirmed for other quantities. We shed light on the essential nature of SC fluctuation leading to the pseudogap from the comparison with spin and charge fluctuations.
“Pseudogap And Superconducting Fluctuation In High-Tc Cuprates: Theory Beyond 1-loop Approximation” Metadata:
- Title: ➤ Pseudogap And Superconducting Fluctuation In High-Tc Cuprates: Theory Beyond 1-loop Approximation
- Author: Youichi Yanase
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-cond-mat0407605
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50Multiplier Ideal Sheaves, Nevanlinna Theory, And Diophantine Approximation
By Paul Vojta
This note states a conjecture for Nevanlinna theory or diophantine approximation, with a sheaf of ideals in place of the normal crossings divisor. This is done by using a correction term involving a multiplier ideal sheaf. This new conjecture trivially implies earlier conjectures in Nevanlinna theory or diophantine approximation, and in fact is equivalent to these conjectures. Although it does not provide anything new, it may be a more convenient formulation for some applications.
“Multiplier Ideal Sheaves, Nevanlinna Theory, And Diophantine Approximation” Metadata:
- Title: ➤ Multiplier Ideal Sheaves, Nevanlinna Theory, And Diophantine Approximation
- Author: Paul Vojta
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-0709.3322
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Source: The Open Library
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1Approximation theory
By Approximation Theory (International Symposium) (1969 Lancaster)

“Approximation theory” Metadata:
- Title: Approximation theory
- Author: ➤ Approximation Theory (International Symposium) (1969 Lancaster)
- Language: English
- Number of Pages: Median: 356
- Publisher: Academic Press - Academic P
- Publish Date: 1970
- Publish Location: New York - London
“Approximation theory” Subjects and Themes:
- Subjects: ➤ Approximation theory - Congresses - Aproximacao (Analise Numerica) - Congres - Approximations (Mathematiques) - Approximationstheorie - Kongress
Edition Identifiers:
- The Open Library ID: OL22385051M - OL4912909M
- Online Computer Library Center (OCLC) ID: 96837
- Library of Congress Control Number (LCCN): 76117118
- All ISBNs: 9780126822502 - 0126822506
Access and General Info:
- First Year Published: 1970
- Is Full Text Available: Yes
- Is The Book Public: No
- Access Status: Borrowable
Online Access
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