An interior-point affine-scaling trust-region method for semismooth equations with box constraints

An algorithm for the solution of a semismooth system of equations with box constraints is described. The method is an affine-scaling trust-region method. All iterates generated by this method are strictly feasible. In this way, possible domain violations outside or on the boundary of the box are avoided. The method is shown to have strong global and local convergence properties under suitable assumptions, in particular, when the method is used with a special scaling matrix. Numerical results are presented for a number of problems arising from different areas.     

单位复超球上多复变解析函数的边值问题

讨论了二元复变解析函数在单位复超球区域上的某些边值问题,包括Dirichlet问题和Riemann-Hilbert问题,利用Cauchy公式、Plemelj公式以及级数展开的方法,我们对不同标数的情形,给出了所提问题可解的充分必要条件.     

On the choice of approximations in direct problems of nozzle design

Two problems are considered: the design of a supersonic nozzle with a uniform exit characteristic and the design of a subsonic nozzle part with a plane (straight) sonic line in the minimum cross section. It is shown how the choice of a nozzle profile approximation affects the direct solutions to variational gas dynamics problems. The nozzle profile is described by polynomials or splines (quadratic, cubic, rational). The varied variables are the profile’s expansion coefficients in terms of basis functions or the parameters to be interpolated. It is shown that a priori information on the monotonicity of the desired profile improves the efficiency of the solution.     

核属于H函数类的多维Fredholm积分方程类近似解的计算复杂性

给出了在 Lp,2 p<∞ ,范意义下 ,核下自由项均属于 H函数类的多维 Fredholm积分方程类近似解的ε-计算复杂性估计 .     

Properties of an exact crystalline many-body ground state

A new quantum many-body Hamiltonian is introduced, for which the exact ground state is a Jastrow-type product. This Hamiltonian is interpreted as a one-component |x|-potential Coulomb system in free boundary conditions, and by explicit calculation it is shown that the ground state is crystalline. The generaln-body density matrix is calculated, and is related to then-body density matrix calculated in periodic boundary conditions.     

对称函数各完备集展开系数之间的转换

本文从三种构成完备集的对称函数的定义及有关性质出发，讨论了对称函数在各完备集中展开系数之间的转换，给出了相应的变换矩阵，从而建立了各完备集之间的相互联系.     

ON THE PERSISTENCE AND POSITIVE PERIODIC SOLUTION FOR PLANAR COMPETING LOTKA-VOLTERRA SYSTEMS

1IntroductionLetusa;onsi~~l'tile2-(1llTlellsiollalco'ttipetit;ion1,of-,ha--\./O]1,'lrra,s:\,s(t()lcfl.r]=.r,(l)j(t)--a,1(-t)xl--a,,(lt)x,),,.(II)ac=ac(6~(t-)--a21(t)x,--a22(t);rZ),xvhere(J:,.:x'2)eR;,~{(;t:l,.xZ)la:l20,IZ.20},l),(l),ail(t)fi{~j:lar(>conti…     

Geometry of optimal value functions with applications to redundancy in linear programming

In 1967, Wets and Witzgall (Ref. 1) made, in passing, a connection between frames of polyhedral cones and redundancy in linear programming. The present work elaborates and formalizes the theoretical details needed to establish this relation. We study the properties of optimal value functions in order to derive the correspondence between problems in redundancy and the frame of a polyhedral cone. The insights obtained lead to schemes to improve the efficiency of procedures to detect redundancy in the areas of linear programming, stochastic programming, and computational geometry.The author is indebted to G. Dewan for his review and discussions.     

Theory of discharge sectionalized along a gas flow

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The equivalence of ensembles for lattice systems: Some examples and a counterexample

We describe the problem of the equivalence of ensembles at the level of states for classical lattice systems. We discuss circumstances where the vanishing of the specific information gain of a sequence of microcanonical measures with respect to a sequence of grand canonical measures implies the equivalence of ensembles. We give a simple derivation of a criterion for the vanishing of the specific information gain in terms of thermodynamic functions. The proof uses ideas from the theory of large deviations but is self-contained. We show how the criterion works in a simple model of a paramagnet and in the Ising model of a ferromagnet in any dimension but fails in the case of the Curie-Weiss mean-field model.