Musielak-Orlicz序列空间的一致Gateaux可微性

利用Musielak-Orlicz函数列的某些性质,给出了赋Luxemburg范数的Musielak-Orlicz序列空间是有一致Gateaux可微性的充要条件及赋Orlicz范数的Musielak-Orlicz序列空间是弱一致凸的判别准则.     

无限参与人市场博弈中可传递效用核的存在性

文章考虑一个具有无限多参与人与无限维商品空间的生产经济.在这样的生产经济中,构建一类具有无限参与人的市场博弈,并定义出其中可传递效用核.结合过去有限参与人合作均衡存在性定理,文章主要证明了市场博弈中可传递效用核的存在性.具有无限维商品空间和无限多参与人市场博弈的构建,与市场博弈中的可传递效用核的存在性证明为文章的两个主要贡献.     

B值鞅的一致可积条件与Banach空间的几何特性

在子σ-代数列(B_n)正规情形下,本文研究了B值鞅(f_N,B_n)的一致可积性与条件 (?)λP(S~2(f)>λ)=0之间的关系,证明了当值空间同构于g凸或p光滑空间时,两者可互推。特别当值空间同构于Hilbert空间时,两者为等价。     

赋Orlicz范数Musielak-Orlicz序列空间的一致Gateaux可微性

给出赋Orlicz范数的Musielak-Orlicz序列空间具有一致Gateaux可微性的充分必要条件.     

基于复杂网络的能源互联网信息物理融合系统跨空间风险传递研究

能源互联网呈现物理信息深度融合的趋势,为电力系统管理研究定义了新的研究框架。作为一个先进的复杂系统,能源互联网信息物理系统(Energy Internet Cyber-Physical System,ECPS)在其发展过程中面临着一些新的挑战,其中一个就是耦合结构下的风险管理。本文结合复杂网络理论和风险传递理论,着重在拓扑层面分析了ECPS跨空间交互机理,并在此基础上定义了交互路径和交互系数;接着建立了ECPS跨空间风险传递模型,量化描述了风险的传递和演化过程,并进行了风险影响评估;最后,通过仿真实验分析了三种不同交互系数节点故障的风险传递过程和不同攻击模式下系统的崩溃过程。对仿真结果的讨论阐述了能源互联网风险跨空间传递的特点,为更深入地研究ECPS的风险管理提供了参考。     

可拓扑生成的L-fuzzy保序算子空间的权、特征及稠密度

在可拓扑生成的L-fuzzy保序算子空间中研究权,特征及稠密度这三种基数函数,讨论它们与相应的生成底空间的ω-权、ω-特征及ω-稠密度的关系。     

局部凸空间上锥映象拓扑度的计算

本文给出了局部凸空间上锥映象拓扑度计算的一个结果，并举例说明了它的应用．     

K-非常凸空间

本文引入了一种新的K凸空间K-非常凸空间,及其对偶空间K-非常光滑空间,它们分别是非常凸空间和非常光滑空间的推广但又严格弱于非常凸空间和非常光滑空间,因此它们又有许多独特的性质.本文讨论了它们的一些特性及与其它K凸性和K光滑性的关系,推广了[3]、[6]、[7]、[8]中的一些结果.     

一类三维神经元模型的分支研究

考虑一类三维神经元模型的分支问题.利用常微分方程的定性与分支理论的知识,讨论了模型的平衡点个数及其稳定性,主要分析了平衡点的Hopf分支和Bogdanov-Takens分支,并得到了相应的鞍结点分支曲线,Hopf分支曲线与同宿分支曲线.     

Finding Mixed Cells in the Mixed Volume Computation

In practice, finding mixed cells in certain polyhedral subdivisions plays a dominating role when a polyhedral homotopy is employed to approximate all isolated zeros of polynomial systems. This paper gives a new algorithm for the mixed cell computation via a new formulation of the underlying linear programming problems. Numerical results show that the algorithm provides a major advance in the speed of computation with much less memory requirements. March 17, 2000. Final version received: November 2, 2000. Online publication: February 20, 2001.     

Extension of M-Convexity and L-Convexity to Polyhedral Convex Functions

The concepts of M-convex and L-convex functions were proposed by Murota in 1996 as two mutually conjugate classes of discrete functions over integer lattice points. M/L-convex functions are deeply connected with the well-solvability in nonlinear combinatorial optimization with integer variables. In this paper, we extend the concept of M-convexity and L-convexity to polyhedral convex functions, aiming at clarifying the well-behaved structure in well-solved nonlinear combinatorial optimization problems in real variables. The extended M/L-convexity often appears in nonlinear combinatorial optimization problems with piecewise-linear convex cost. We investigate the structure of polyhedral M-convex and L-convex functions from the dual viewpoint of analysis and combinatorics and provide some properties and characterizations. It is also shown that polyhedral M/L-convex functions have nice conjugacy relationships.     

Mean Curvature and Volume of Extrinsic Spheres in Hypersurfaces of Real Space Forms

Given a hypersurface P^n-1 in a real space form of constantcurvature b, , we have obtained a lower bound for the norm of the mean curvature normal vector field of extrinsicspheres in P^n-1 in terms of the mean curvature of the geodesic spheres in , with the same radius, and the meancurvature of P^n-1, characterizing too the equality.     

k-Drop凸空间的特征

通过研究局部k-drop凸空间的一些性质,得出了k-drop凸性质与自反且k-严格凸是等价的,同时k-drop凸空间具有商遗传性.     

确定线性规划全部最优解的方法

使用凸多面体的表示定理 ,导出了标准型线性规划最优解的一般表达式 ,并基于单纯形法 ,给出最优解唯一性条件以及当唯一性条件不满足时求出全部最优解的计算步骤 ,同时附有数值例子 .     

一类特殊的Fuzzy局部凸空间

文中给出了Ｆｕｚｙ有界型空间的定义，在此基础上，讨论了Ｆｕｚｙ有界型空间的等价定理，最后证明了Ｑ－Ｃ_ＩＦｕｚｙ局部凸空间是有界型的．     

Calculus of convex polyhedra and polyhedral convex functions by utilizing a multiple objective linear programming solver

ABSTRACT

The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed convex hull of the union are considered. Basic operations for one convex polyhedron are, for example, the polar, the conical hull and the image under affine transformation. The concept of a P-representation of a convex polyhedron is introduced. It is shown that many polyhedral calculus operations can be expressed explicitly in terms of P-representations. We point out that all the relevant computational effort for polyhedral calculus consists in computing projections of convex polyhedra. In order to compute projections we use a recent result saying that multiple objective linear programming (MOLP) is equivalent to the polyhedral projection problem. Based on the MOLP solver bensolve a polyhedral calculus toolbox for Matlab and GNU Octave is developed. Some numerical experiments are discussed.