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A two-density approach to the general many-body problem and a proof of principle for small atoms and molecules

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Frontiers of physics 2019年第2期14卷 89-96页

作者： thomas Pope Werner Hofer School of Natural and Environmental Sciences Newcastle UniversityNewcastle NE1 7RUUnited Kingdom Institute of Physics & University of Chinese Academy of Sciences Chinese Academy of SciencesBeijing 100190China

An extended electron model fully recovers many of the experimental results of quantum mechanics while it avoids many of the pitfalls and remains generally free of paradoxes. The formulation of the manybody electronic problem here resembles the Kohn Sham formulation of standard density functional theory. However, rather than referring electronic properties to a large set of single electron orbitals, the extended electron model uses only mass density and field components, leading to a substantial increase in computational efficiency. To date, the Hohenberg-Kohn theorems have not been proved for a model of this type, nor has a universal energy functional been presented. In this paper, we address these problems and show that the Hohenberg Kohn theorems do also hold for a density model of this type. We then present a proof^of^concept practical implementation of this method and show that it reproduces the accuracy of more widely used methods on a test-set of small atomic systems, thus paving the way for the development of fast, efficient and accurate codes on this basis.

关键词： many-body condensed matter Hartree-Fock density functional theory extended electrons

JAMES GLIMM:MATHEMATICIAN,FRIEND,MENTOR

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Acta Mathematica Scientia 2010年第2期30卷 369-376页

作者： Arthur Jaffe thomas Spencer Department of Mathematics Harvard University School of Mathematics Institute for Advanced Study

A description of Jim＇s contributions to mathematics would take us far beyond our expertise. Jim was never content to spend too long in any one area of mathematics. Operator algebras, hyperbolic systems of conservation laws, fluid dynamics, quantum field theory and statistical mechanics and the computational aspects of applied mathematics are just a few of the areas to which Jim has contributed. Here we relate a few impressionistic recollections of personal interactions, together with some ideas about his work in quantum field theory and statistical mechanics. In spite of the non-technical character of these observations, we hope nevertheless that they will provide pleasure for our dear friend and for other readers as well.

关键词： JAMES GLIMM work

Evolution of gustatory reflex systems in the brainstems of fishes

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Integrative Zoology 2009年第1期4卷 53-63页

作者： thomas E.FINGER Department of Cell and Developmental Biology University of Colorado DenverAuroraUSA

The great number of species of teleosts permits highly specialized forms to evolve to occupy particular *** diversity allows for extreme variations in brain structure according to particular sensory or motor *** the case of the taste system,goldfish(Carassius auratus L.,1758)and some carps have evolved a specialized in-traoral food-sorting apparatus along with corresponding specializations of gustatory centers in the brainstem.A comparison of circuitry within the complex vagal lobe of goldfish,and of the simpler gustatory lobes in catfish(Ictalurus punctatus Rafinesque,1818)shows numerous similarities in organization and *** labeling studies using horseradish peroxidase and biotinylated dextran amine in catfish shows a direct projection from the vagal lobe to the motoneurons of nucleus ambiguus which innervate oropharyngeal ***,a three neuron reflex arc connects gustatory input to motor *** the vagal lobe of goldfish,a similar three neuron arc can be identified:from primary gustatory afferent,to vagal lobe interneuron,thence to dendrites of the vagal motoneurons that innervate the pharyngeal ***,despite large differences in the gross appearance of the vagal gustatory systems in the brains of catfish and goldfish,the essential connectivity and circuitry is *** suggests that evolutionary change in the central nervous system largely proceeds by rearrangement and elaboration of existing systems,rather than by addition of new structures or circuits.

关键词： evolution medulla nucleus of the solitary tract taste vagus nerve.

WEAK APPROXIMATION OF OBLIQUELY REFLECTED DIFFUSIONS IN TIME-DEPENDENT DOMAINS

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Journal of Computational Mathematics 2010年第5期28卷 579-605页

作者： Kaj Nystroem thomas Oenskog Department of Mathematics and Mathematical Statistics Umeae University SE-901 87 Umed Sweden

In an earlier paper, we proved the existence of solutions to the Skorohod problem with oblique reflection in time-dependent domains and, subsequently, applied this result to the problem of constructing solutions, in time-dependent domains, to stochastic differential equations with oblique reflection. In this paper we use these results to construct weak approximations of solutions to stochastic differential equations with oblique reflection, in time-dependent domains in Rd, by means of a projected Euler scheme. We prove that the constructed method has, as is the case for normal reflection and time-independent domains, an order of convergence equal to 1/2 and we evaluate the method empirically by means of two numerical examples. Furthermore, using a well-known extension of the Feynman-Kac formula, to stochastic differential equations with reflection, our method gives, in addition, a Monte Carlo method for solving second order parabolic partial differential equations with Robin boundary conditions in time-dependent domains.

关键词： Stochastic differential equations Oblique reflection Robin boundary condi-tions Skorohod problem Time-dependent domain Weak approximation Monte Carlomethod Parabolic partial differential equations Projected Euler scheme.

Laser cut hole matrices in novel armour plate steel for appliqué battlefield vehicle protection

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Defence Technology（防务技术） 2016年第5期12卷 351-359页

作者： Daniel J. thomas Engineering Manufacturing Centre College of Engineering Swansea University Swansea UK

During this research, experimental rolled homogeneous armour steel was cast, annealed and laser cut to form an appliqué plate. This Martensitic–Bainitic microstructure steel grade was used to test a novel means of engineering lightweight armour. It was determined that a laser cutting speed of 1200 mm/min produced optimum hole formations with limited distortion. The array of holes acts as a double-edged solution, in that they provide weight saving of 45%, providing a protective advantage and increasing the surface area. Data collected were used to generate laser cut-edge hole projections in order to identify the optimum cutting speed, edge condition, cost and deformation performance. These parameters resulted in the generation of a surface, with less stress raising features. This can result in a distribution of stress across the wider surface. Provided that appropriate process parameters are used to generate laser cut edges, then the hardness properties of the surface can be controlled. This is due to compressive residual stresses produced in the near edge region as a result of metallurgical transformations. This way the traverse cutting speed parameter can be adjusted to alter critical surface characteristics and microstructural properties in close proximity to the cut-edge. A relationship was identified between the width of the laser HAZ and the hardness of the cut edge. It is the thickness of the HAZ that is affected by the laser process parameters which can be manipulated with adjusting the traverse cutting speed.

关键词： Armour steels Defence systems Steel processing Armour engineering

MIXED INTERIOR PENALTY DISCONTINUOUS GALERKIN METHODS FOR ONE-DIMENSIONAL FULLY NONLINEAR SECOND ORDER ELLIPTIC AND PARABOLIC EQUATIONS

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Journal of Computational Mathematics 2014年第2期32卷 107-135页

作者： Xiaobing Feng thomas Lewis Department of Mathematics The University of Tennessee Knoxville TN 37996 U.S.A. Department of Mathematics and Statistics The University of North Carolina at Greensboro NC 27402 U.S.A.

This paper is concerned with developing accurate and efficient numerical methods for one-dimensional fully nonlinear second order elliptic and parabolic partial differential equations （PDEs）. In the paper we present a general framework for constructing high order interior penalty discontinuous Galerkin （IP-DG） methods for approximating viscosity solutions of these fully nonlinear PDEs. In order to capture discontinuities of the second order derivative uxx of the solution u, three independent functions p1,p2 and p3 are introduced to represent numerical derivatives using various one-sided limits. The proposed DG frame- work, which is based on a nonstandard mixed formulation of the underlying PDE, embeds a nonlinear problem into a mostly linear system of equations where the nonlinearity has been modified to include multiple values of the second order derivative uxz. The proposed framework extends a companion finite difference framework developed by the authors in [9] and allows for the approximation of fully nonlinear PDEs using high order polynomials and non-uniform meshes. In addition to the nonstandard mixed formulation setting, another main idea is to replace the fully nonlinear differential operator by a numerical operator which is consistent with the differential operator and satisfies certain monotonicity （called g-monotonicity） properties. To ensure such a g-monotonicity, the crux of the construction is to introduce the numerical moment, which plays a critical role in the proposed DG frame- work. The g-monotonicity gives the DG methods the ability to select the mathematically ＂correct＂ solution （i.e., the viscosity solution） among all possible solutions. Moreover, the g-monotonicity allows for the possible development of more efficient nonlinear solvers as the special nonlinearity of the algebraic systems can be explored to decouple the equations. This paper also presents and analyzes numerical results for several numerical test problems which are used to guage

关键词： Fully nonlinear PDEs Viscosity solutions Discontinuous Galerkin methods.

Rationally connected varieties -On a conjecture of Mumford

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Science China Mathematics 2017年第6期60卷 1019-1028页

作者： LAZIC Vladimir PETERNELL thomas Mathematisches Institut Universitat Bonn Bonn 53115 Germany Mathematisches Institut Universitat Bayreuth Bayreuth 95440 Germany

We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.

关键词： rationally connected varieties Mumford conjecture non vanishing conjecture abundance

Analysis of Metamaterial Cloaks Using Circular Split Ring Resonator Structures

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Computers, Materials & Continua 2016年第6期52卷 133-141页

作者： Susan thomas Balamati Choudhury REVA University Bengaluru NAL Bengaluru.

A novel microwave cloak using circular split ring resonator(SRR)based metamaterial structure has been proposed in this *** cloak which operates at a frequency of 10.6 GHz is composed of cylindrical dielectric sheets printed with circular split ring resonators of spatially varying and anisotropic material *** article also focuses on the phenomenon of resonant splitting in circular SRR microwave cloak.A detailed analysis of various linear metamaterial arrays and their response has also been elucidated.

关键词： Cloaking metamaterial circular split ring resonator.

THERE IS NO MATHEMATICAL VALIDITY FOR USING FUZZY NUMBER CRUNCHING IN THE ANALYTIC HIERARCHY PROCESS

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Journal of Systems Science and Systems Engineering 2006年第4期15卷 457-464页

作者： thomas L. SAATY University of Pittsburgh Pittsburgh PA 15260

Fuzzy logic has difficulty producing valid answers in decision-making. Absent are theorems to prove that it works to produce results already known that are being estimated with judgments by transforming such judgments numerically. The numerical representation of judgments in the AHP is already fuzzy. Making fuzzy judgments more fuzzy does not lead to a better more valid outcome and it often leads to a worse one. The compatibility index of the AHP is used to illustrate how the answers obtained by fuzzifying AHP judgments do not produce better results than direct derivation of the principal eigenvector. Other authors who did experiments with given data in decision making quoted in the conclusions section of the paper, have observed that fuzzy sets gives the poorest answers among all methods used to derive best decisions.

关键词： Analytic Hierarchy Process fuzzy logic compatibility index validity