席位分配的最大概率法

文章对席位公平分配问题进行了探索 ,提出了用最大概率作为公平分配的原则 ,给出了简单算法 ,并由此给出了一类组合数乘积最大值的计算方法 .     

拟序下收入分配的不公平度量研究

收入分配的不公平度量是福利经济学研究的一个主要问题.Alain和Patrick在收入分配的不公平度量方法中引入了拟序下的绝对差异、绝对剥夺和绝对满足的概念,对它们之间的关系有过讨论,但并没有给出证明.本文在此基础之上,详细地探讨了它们三者、Lorenz准则、累进性转移、T-转移之间的关系,同时给出了完整的证明.     

席位分配问题的有界整数变量规划模型及其应用

对席位分配问题进行再研究,以公平分摊性公理为基础,分别从议员公平性、公民公平性和州公平性的角度出发建立了三个相应的数学模型,它们都可归结为有界整数变量非线性规划模型.给出三个席位分配模型的一个统一算法,算法简单有效.最后给出了模型应用实例.     

基于分类的资源公平分配决策方法

针对资源分配问题,本文提出了基于分类的决策方法以实现效率与公平的权衡。首先,研究了效率最优分配与完全均等分配过程,阐明了边际效用对分配结果的影响,指出个体间边际效用相差越小,两种分配的结果越接近。其次,构建0-1整数规划模型求解分类结果,目标是使类与类之间边际效用相差尽可能小。然后,按类对资源进行分配,类间采用完全均等分配,类中采用效率最优分配。通过选择分类数量可以实现不同程度的公平。最后,运用算例验证方法的有效性,说明分类数量对效率与公平的影响。     

资源公平分配的遗传算法研究

文章对决策优化的经典问题席位公平分配进行了研究，提出应用遗传算法对该模型进行求解。两例资源公平分配决策实例研究表明，遗传算法优化结果较其它方法都更合理。     

一个公平分配席位的新方案

提出了公平累加分配席位的方法,并证明了该方法在一定条件下满足公平分摊原则和席位单调性原则.并进一步指出该方法具备更多的公平性质.     

优势分析在组织行为学研究中的应用——组织公平与工作倦怠关系的实证研究

在组织行为学研究过程中经常需要确定各自变量的相对重要性,而优势分析则是提示不同自变量重要性的有效方法。本研究以程序公平、分配公平与工作倦怠的关系为例,详细介绍了如何采用优势分析来确定各自变量的相对重要性。结果表明,预测玩世不恭时,程序公平相对来说更重要,贡献了已解释方差的56.07%;预测情绪衰竭时,分配公平相对来说更重要,贡献了已解释方差的59.09%;预测成就感低落时,程序公平相对来说更重要,贡献了已解释方差的93.55%。     

席位分配的平均公平度方法

定义个体相对于总体的公平程度,即个体公平度与总体绝对公平度的比值,当比值趋于1时,就说明分配方案使该个体满意.利用方差的概念定义平均公平度,使个体公平程度相对于总体的公平程度的差距最小,等价于每一个个体公平度都很接近,并且趋于1,每个个体的公平程度达到最大,此时座位分配最为公平.     

改进的收入空间法及其在中等收入人口度量中的应用

提出了衡量社会分配公平的局部公平指数D(p)=((L'(p))/((L"(p))),给出了其确切的经济学解释.同时定义了分别对应穷人和富人的Gini指数G_1,G_2,在此基础上建立了改进的收入空间法,用于确定中等收入人口范围:[(1-1/2D(1-G_1))m,(1+1/2D(1-G_2))m],其中m为中位收入.模型对2013全国研究生数学建模竞赛E题的收入分配数据进行定量研究,得出的结论与经济学的原理"两极分化时中等收入人口降低,中问隆起时中等收入人口升高"相符合,这体现了模型的准确性与可靠性.     

考虑实体店公平关切的制造商线上渠道模式选择研究

通过构建双渠道供应链的博弈模型,研究实体店的纵向分配公平关切和横向同行公平关切对制造商线上渠道模式选择的影响。在理论研究的基础上,通过数值仿真得到的研究结果表明,当实体店纵向分配公平关切程度较低时,制造商应该选择线上直销模式;当实体店纵向分配公平关切程度较高时,若电商要求的租金比例较小,制造商会选择线上代销模式;如果电商要求的租金比例较大,制造商会选择线上直销模式。当满足一定的市场条件时,制造商和实体店将同时偏好线上直销模式或线上代销模式。     

超高强度钢形变与断裂规律研究

运用先进的物理方法,测出了超高强度钢负荷-伸长曲线新的形状,建立了一种由负荷-伸长全曲线计算真应力-真应变的方法,计算结果指出:在整个变形阶段中,不论是在最大负荷前或最大负荷后都是分段幂乘硬化的,最后研究硬化指数的计算方法,供讨论.     

纯弯曲矩形截面梁Ⅰ型单边裂纹端部的应力应变场及裂纹失稳扩展临界应力的计算

本文应用文[1]的分析方法,研究了纯弯曲矩形载面梁Ⅰ型单边裂纹端部的应力应变场,给出了裂纹尖端的应力应变分量和计算裂纹端部弹性变形区和变形强化区宽度的公式以及计算裂纹失稳扩展临界应力的方程组。最后用计算实例对裂纹失稳扩展临界应力方程组进行了验证,最大误差不超过0.18%.     

Numerical pseudodifferential operator and Fourier regularization

The concept of numerical pseudodifferential operator, which is an extension of numerical differentiation, is suggested. Numerical pseudodifferential operator just is calculating the value of the pseudodifferential operator with unbounded symbol. Many ill-posed problems can lead to numerical pseudodifferential operators. Fourier regularization is a very simple and effective method for recovering the stability of numerical pseudodifferential operators. A systematically theoretical analysis and some concrete examples are provided.     

黄金分割算法在简支桥梁设计计算中的应用

移动荷载作用下,简支桥梁横截面上弯矩的变化为二元函数Z=f(x,y),本文给出了绝对最大弯矩Zm ax的极值点x*、y*的判别方法:利用数学中的黄金分割算法搜索梁的绝对最大弯矩对应的最危险横截面位置x*;利用力学中的影响线理论判别该截面发生最大弯矩时的最危险荷载位置y*,计算该横截面的最大弯矩得到梁的绝对最大弯矩.该算法易于编写计算程序,以计算机为工具,适用于任意有限多个平行移动荷载在桥梁上移动,对于桥梁的设计计算与安全评估,有一定的实用价值.     

CALCULATING AN ELEMENT OF B-DIFFERENTIAL FOR A VECTOR-VALUED MAXIMUM FUNCTION*

In this paper, we propose a method of calculating an element of B-differential, also an element of Clarke generalized Jacobian, for a vector-valued maximum function. This calculation is required in many existing numerical methods for the solution of nonsmooth equations and for the nonsmooth optimization. The generalization of our method to a vector-valued smooth composition of maximum functions is also discussed. Particularly, we propose a method of obtaining the set of B-differential for a vector-valued maximum of affine functions.

     

An adaptive cellular updating scheme for the continuous–discontinuous cellular automaton method

The updating scheme is very important for cellular automata, which costs the vast majority of CPU time of the whole calculating process and dramatically influences the convergence rate, and the traditional node sequence scheme is often ineffective. Aimed at this issue, based on the unbalanced nodal force, an adaptive updating scheme for continuous–discontinuous cellular automaton method is proposed in this paper. The cell whose unbalanced force is maximum is the first updating cell, and the next one is its neighbors whose unbalanced force is also maximum in all remain neighbors, and do the updating operation according to this scheme until the updating for all cells is finished. Theory and convergence of the present scheme is studied, then we can get the maximum calculating efficiency, and the computational expanse can be greatly improved. Some examples by different iteration schemes are shown to demonstrate that the present scheme is efficient and time saving.     

A Note on the Calculation of Step-Lengths in Interior-Point Methods for Semidefinite Programming

In each iteration of an interior-point method for semidefinite programming, the maximum step-length that can be taken by the iterate while maintaining the positive semidefiniteness constraint needs to be estimated. In this note, we show how the maximum step-length can be estimated via the Lanczos iteration, a standard iterative method for estimating the extremal eigenvalues of a matrix. We also give a posteriori error bounds for the estimate. Numerical results on the performance of the proposed method against two commonly used methods for calculating step-lengths (backtracking via Cholesky factorizations and exact eigenvalues computations) are included.     

Allocating Doctors to Shifts in an Accident and Emergency Department

A method is proposed for allocating doctors to weekly shifts in an accident and emergency department of a hospital. Two models, solved by dynamic programming, are used. The first finds the optimal solution to the problem of allocating doctors per hour of the week proportionally to the corresponding patient arrival-rate; and the second uses this solution to smooth out the hourly discrepancies in the number of doctors within a shift. The solution is then assessed by computer simulation.