矩阵对策的两个注记

设(x*,y*)是以A=[aij]m×n为赢得矩阵G的对策解,则当局中人1,2各自独立地使用其最优策略x*=(x*1,x*2,…,xmn),y*=(y*1,y*2,…,y*n)时,局中人1的赢得期望为对策值v*=x*Ay*T.若局中人双方使用使得方差D(x*,y*)=∑∑(aij-v*)2x*iy*j达最小的对策解(x*,y*),则其赢得靠近v*的概率达到最大.以O记使方差达到最小的对策解的集合.若O满足(x(1),y(1)),(x(2),y(2))∈O蕴涵(x(1),y(2)),(x(2),y(1))∈O,则说O是可换的.本文首先证明了若矩阵对策G有纯解,则O是可换的.然后证明了如果限定局中人1在其混合扩充策略集的一个非空紧凸子集X中选取策略,那么存在X的一个非空紧子集O(X),它是有限个非空互不相交紧凸集之并,使得只要局中人1使用O(X)中的策略,那么在最坏的情况下可以取得最好的赢得.  

Jordan isomorphisms of upper triangular matrix rings

Let R be a 2-torsionfree ring with identity 1 and let T_n(R), n ? 2, be the ring of all upper triangular n × n matrices over R. We describe additive Jordan isomorphisms of T_n(R) onto an arbitrary ring and generalize several results on this line.  

On stability for a class of semilinear stochastic evolution equations

Sufficient conditions for almost surely asymptotic stability with a certain decay function of sample paths, which are given by mild solutions to a class of semilinear stochastic evolution equations, are presented. The analysis is based on introducing approximating system with strong solution and using a limiting argument to pass on some properties of strong solution to our purposes. Several examples are studied to illustrate our theory. In particular, by means of the derived results we lose conditions of certain stochastic evolution systems from Haussmann (1978) to obtain the pathwise stability for mild solution with probability one.  

A Class of generalized Lévy Laplacians in infinite dimensional calculus

A class of generalized Lévy Laplacians which contain as a special case the ordinary Lévy Laplacian are considered. Topics such as limit average of the second order functional derivative with respect to a certain equally dense (uniformly bounded) orthonormal base, the relations with Kuo’s Fourier transform and other infinite dimensional Laplacians are studied.  

ERKN methods for long-term integration of multidimensional orbital problems

This paper is devoted to introducing ERKN methods for long-term integration of multidimensional orbital problems. For the general multidimensional perturbed oscillators y^″+My=f(t,y)$y^{″}+\mathit{My}=f(t\text{,}y)$ with M∈R^m×m$M\in {\mathbb{R}}^{m\times m}$, the extended Runge–Kutta–Nyström (ERKN) methods are proposed by Wu et al. [X. Wu, X. You, W. Shi, B. Wang, ERKN integrators for systems of oscillatory second-order differential equations, Comput. Phys. Commun. 181 (2010) 1873–1887]. These methods exactly integrate the multidimensional unperturbed oscillators and are highly efficient when the perturbing forces are small. In this paper, we pay attention to the applications of ERKN methods to multidimensional orbital problems. Numerical experiments accompanied demonstrate that for long-term integration of multidimensional orbital problems the multidimensional ERKN methods are more efficient compared with high-quality codes proposed in the scientific literature. In particular, when an orbital problem under consideration is a Hamiltonian system, the symplectic ERKN methods preserve the Hamiltonian very well, and has better accuracy than the high-quality codes with the same computational cost.  

On Skew Derivations in Semiprime Rings

We investigate the commutativity in a (semi-)prime ring R which admits skew derivations δ ₁, δ ₂ satisfying [δ ₁(x), δ ₂(y)]?=?[x, y] for all x, y in a nonzero right ideal of R. This result is a natural generalization of Bell and Daif’s theorem on strong commutativity preserving derivations and a recent result by Ali and Huang.  

Strong commutativity preserving generalized derivations on right ideals

We characterize a prime ring R which admits a generalized derivation g and a map f : ρ → R such that [ f (x), g(y)]?=?[x, y] for all ${x,y\in \rho}$ , where ρ is a nonzero right ideal of R. With this, several known results can be either deduced or generalized.  

On Regularity Property of Retarded Ornstein–Uhlenbeck Processes in Hilbert Spaces

In this work, some regularity properties of mild solutions for a class of stochastic linear functional differential equations driven by infinite-dimensional Wiener processes are considered. In terms of retarded fundamental solutions, we introduce a class of stochastic convolutions which naturally arise in the solutions and investigate their Yosida approximants. By means of the retarded fundamental solutions, we find conditions under which each mild solution permits a continuous modification. With the aid of Yosida approximation, we study two kinds of regularity properties, temporal and spatial ones, for the retarded solution processes. By employing a factorization method, we establish a retarded version of the Burkholder–Davis–Gundy inequality for stochastic convolutions.  

买方抗衡势力对上游企业质量创新的影响--基于零售商Stackelberg竞争的分析

通过构建一个三阶段的完全信息动态博弈模型，考察了零售商买方抗衡势力对上游制造商质量创新的影响，结果表明：当领导者零售商具有买方抗衡势力时，抗衡势力增强抑制了制造商的质量创新，进而导致市场均衡价格下降，均衡产量增加，而零售商销量呈非单调变化；此外，随着抗衡势力持续的增强，消费者福利水平先上升后下降，最后，文章证明了零售商批发价格在一定条件下存在“水床效应”。  

Some results on zeros and uniqueness of difference-differential polynomials

We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions.We also investigate the uniqueness problems of difference...