凸函数的双参数平均不等式

凸函数的双参数平均不等式孙明保（岳阳大学基础课部，湖南４１４０００）关键词双参数平均，不等式．分类号ＡＭＳ（１９９１）２６Ｄ／ＣＣＬＯ１７４．１３设ｆ（ｘ）在［ａ，ｂ］上可积且下界为正，则ｆ（ｘ）在［ａ，ｂ］上的双参数平均定义为Ｍｐ，ｑ（ｆ）＝∫ｂ...     

共形平坦黎曼流形M~n到常曲率黎曼流形Sn+1(c)的等距浸入

<正> §1 引言设Mn和（?）n+1分别是n维和n+1维的黎曼流形,i:Mn→（?）n+1是等距浸入（见[1]第七章）,我们把Mn和像i（Mn）,点P∈Mn和像点i（P）∈i（Mn）（?）n+1看成一样,即把Mn看作（?）n+1里的浸入曲超面i（Mn）。在每个坐标邻域内,浸入i的方程可写成     

透过“教材”关注“向量”

自新课程改革以来,向量正式从"幕后"走向"前台",成交衔接代数、几何与三角的纽带,把向量和向量法穿插、渗透和融合到其他知识点中,已成为数学试题中一道亮丽的风景.现在笔者通过对人教A版的教材例题或习题来谈谈向量与向量法的广泛应用.     

Control and Nash Games with Mean Field Effect

Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007, of Gueant-Lasry-Lions in 2011, of Huang-Caines-Malham in 2007 and many others). There are a lot of applications. In general, the applications concern approximating an infinite number of players with common behavior by a representative agent. This agent has to solve a control problem perturbed by a field equation, representing in some way the behavior of the average infinite number of agents. This approach does not lead easily to the problems of Nash equilibrium for a finite number of players, perturbed by field equations, unless one considers averaging within different groups, which has not been done in the literature, and seems quite challenging. In this paper, the authors approach similar problems with a different motivation which makes sense for control and also for differential games. Thus the systems of nonlinear partial differential equations with mean field terms, which have not been addressed in the literature so far, are considered here.     

参数弱向量平衡问题解集的似Holder性和相依导数

本文研究了一类参数弱向量平衡问题解集的似Hölder性和相依导数. 首先, 讨论了该问题的一类实值间隙函数的Lipschitz连续性和Hadamard方向可微性. 然后, 借助这些性质, 建立了该问题解集的似Hölder性和Hölder连续性以及相依导数的具体表达式.     

关于地球健康的双层耦合网络模型

建立了一个基于平均场动力学的微分方程组和反应—扩散模型的双层耦合网络模型,用来分析、预测及评价地球生物与环境的健康问题。在双层耦合网络模型中,根据地球地理和气候分布,将全球划分为九块区域,并以此作为全球网络的节点;同时,七个具有代表性的反映地球健康状况的元素,如人口密度、森林、空气质量、生物多样性等,被挑选出作为元素网络的节点。再通过平均场动力学微分方程,建立并描述了各个元素间的联系与相互作用;利用数据确定模型参数,从而完善模型,最后,以此模型完成寻找临界点、灵敏度分析、网络结构分析、引入不确定性等工作。     

局部传输信息不等式和曲率维数条件的等价性

本文得到了曲率维数条件CD(ρ,∞) 和CD(0, n)与相应的局部传输信息不等式的等价性.     

加权线性支持向量分类机的数据扰动分析

加权线性支持向量分类机是数据挖掘的新方法.它对应于一个优化问题.针对加权线性支持向量分类机优化问题建立了数据扰动分析理论方法.具体地针对加权线性支持向量分类机的原始问题建立了数据扰动分析基本定理,定理可以得到加权线性支持向量分类机问题的解及决策函数对数据参数的偏导数,同时可以定量分析输入数据的误差以及数据各种变化对其解以及决策函数值的定量影响,可以回答加权线性支持向量分类机问题的稳定性问题和灵敏度分析问题.     

基于区间效率的贷款定价研究

以存款利息支出率、费用支出率、预期违约损失率、目标利润率等4个定价指标作为输入,以贷款利率作为输出,采用支持向量机回归算法建立基于区间效率的贷款定价模型.创新与特色一是通过区间数形式来反映预期违约损失率、目标利润率、费用支出率等,改变了现有研究将目标利润、贷款费用、违约损失等变量看作确定性数值来定价的现状.使贷款利率更具有竞争性.二是通过比较不同核函数、核参数下的训练样本的贷款效率区间与合理的贷款效率区间的匹配程度,确定贷款定价模型最优的核函数和核参数,进而建立了贷款定价模型.间接解决了在考虑贷款价格能否被银行、客户接受情况下贷款利率确定的问题.     

METHOD OF CENTERS ALGORITHM FOR MULTI-OBJECTIVE PROGRAMMING PROBLEMS

In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is defined so that the sub-problems that must be solved during its execution may be solved by finite-step procedures. Conditions are given under which the algorithm generates sequences of feasible points and constraint multiplier vectors that have accumulation points satisfying the KKT conditions. Finally, we establish convergence of the proposed method of centers algorithm for solving multiobjective programming problems.