Detecting all evolutionarily stable strategies

In evolutionary game theory, the central solution concept is the evolutionarily stable state, which also can be interpreted as an evolutionarily stable population strategy (ESS). As such, this notion is a refinement of the Nash equilibrium concept in that it requires an additional stability property. In the present paper, an algorithm for detectingall ESSs of a given evolutionary game consisting of pairwise conflicts is presented which both is efficient and complete, since it involves a procedure avoiding the search for unstable equilibria to a considerable extent, and also has a finite, exact routine to check evolutionary stability of a given equilibrium. The article also contains the generalization of these results to the playing-the-field setting, where the payoff is nonlinear.     

Sobolev空间中与非齐次细分方程相关的细分格式的收敛阶

研究如下形式的非齐次细分方程,其中向量值函数是未知的,g是给定的紧支集向量值函数,a 是一个具有有限长的r×r矩阵值序列,称为细分面具,M是一个s×s整数矩阵, 并且满足limn→∞M-n=0.我们在Sobolev空间(Wpk(Rs))r(1≤p≤∞)中研究与非齐次细分方程相关的细分格式的收敛性和收敛阶.选择具有紧支集向量值函数,定义n=1,2,….这个叠代过程称为细分格式(详见文献[1-29]).     

On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation

Numerical solution of hyperbolic partial differential equation with an integral condition continues to be a major research area with widespread applications in modern physics and technology. Many physical phenomena are modeled by nonclassical hyperbolic boundary value problems with nonlocal boundary conditions. In place of the classical specification of boundary data, we impose a nonlocal boundary condition. Partial differential equations with nonlocal boundary specifications have received much attention in last 20 years. However, most of the articles were directed to the second‐order parabolic equation, particularly to heat conduction equation. We will deal here with new type of nonlocal boundary value problem that is the solution of hyperbolic partial differential equations with nonlocal boundary specifications. These nonlocal conditions arise mainly when the data on the boundary can not be measured directly. Several finite difference methods have been proposed for the numerical solution of this one‐dimensional nonclassic boundary value problem. These computational techniques are compared using the largest error terms in the resulting modified equivalent partial differential equation. Numerical results supporting theoretical expectations are given. Restrictions on using higher order computational techniques for the studied problem are discussed. Suitable references on various physical applications and the theoretical aspects of solutions are introduced at the end of this article. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

一类正定复矩阵的谱特征

本文给出了一类正定复矩阵的特征值的分布，同时建立了稳定矩阵与正定矩阵之间的内在联系，确立了稳定矩阵的若干判定方法。     

双参数六点细分法

提出了一类包含两个形状参数的双参数六点细分法,可以构造光滑插值曲线和光滑逼近曲线,并且可以通过对两个参数取值的调整使得曲线达到一致收敛,C1或C2.讨论了形状参数对细分法的收敛性及连续性的影响,给出了细分法一致收敛、C1连续、C2连续的充分条件,并给出了一些数值算例.     

The classification of two-component Cuntz-Krieger algebras

Cuntz-Krieger algebras with exactly one nontrivial closed ideal are classified up to stable isomorphism by the Cuntz invariant. The proof relies on Rørdam's classification of simple Cuntz-Krieger algebras up to stable isomorphism and the author's classification of two-component reducible topological Markov chains up to flow equivalence.

     

Faithful and unfaithful students in time series learning

A model neuron with delay line feedback connections can learna time series generated by another neuron. In the case thatboth neurons have identical transfer functions, a model neuron(student) is capable of reproducing the instruction sequencegenerated by another neuron (teacher), but the parameters arenot uniquely determined by learning a quasi-periodic time series.A student that has completed the learning can be either faithfulor unfaithful, depending on whether it continues mimicking theteacher's time series over a long interval after the learningor whether it departs from the teacher and eventually generatesa time series that bears no resemblance to the teacher's. Inthe case that both neurons have different transfer functions,a student is generally incapable of reproducing the instructionsequence. Each student readjusts its parameters so as to minimizethe mean-squared deviation between the instruction signal andits own output, but this parameter set is not uniquely determined.In this unrealizable learning, the degeneracy among faithfulstudents is lifted and there is no more distinction betweenfaithful and unfaithful students.     

Properties of operator stable distributions in infinite-dimensional Banach spaces

The results of this paper concern the connections between different characterizations of operator stable distributions in infinite-dimensional separable Banach spaces. Such assertions are closely related with the strong and uniform operator topology. In particular, the new motions of strongly and uniformlyG-stable distributions are discussed.     

Convergence and Application of a Decomposition Method Using Duality Bounds for Nonconvex Global Optimization

The subject of this article is a class of global optimization problems, in which the variables can be divided into two groups such that, in each group, the functions involved have the same structure (e.g. linear, convex or concave, etc.). Based on the decomposition idea of Benders (Ref. 1), a corresponding master problem is defined on the space of one of the two groups of variables. The objective function of this master problem is in fact the optimal value function of a nonlinear parametric optimization problem. To solve the resulting master problem, a branch-and-bound scheme is proposed, in which the estimation of the lower bounds is performed by applying the well-known weak duality theorem in Lagrange duality. The results of this article concentrate on two subjects: investigating the convergence of the general algorithm and solving dual problems of some special classes of nonconvex optimization problems. Based on results in sensitivity and stability theory and in parametric optimization, conditions for the convergence are established by investigating the so-called dual properness property and the upper semicontinuity of the objective function of the master problem. The general algorithm is then discussed in detail for some nonconvex problems including concave minimization problems with a special structure, general quadratic problems, optimization problems on the efficient set, and linear multiplicative programming problems.