A demand adjustment process

The aspiration approach to cooperative games, which has been studied by a number of authors, including Cross, Turbay, Albers, Selten and Bennett, presumes that players in a game bargain over their reservation prices, or aspirations. A number of aspiration-based solution concepts have been put forth, and aspiration solutions have been connected to non-cooperative bargaining models. Missing in this approach has been theory of how aspirations themselves arise. The present paper is an attempt to fill this gap. It describes a very general demand adjustment process, using the framework of set-valued dynamical systems developed by Maschler and Peleg. This demand adjustment process always converges; sufficient conditions are given in order that it converge to an aspiration, and that it converge in a finite number of steps.     

A DUAL NON-LINEAR PROGRAM

In the paper a dual of a nonlinear fractional functional programming problem has beenformulated.This problem can be used to obtain a solution of the mixed 0—1 integer linearprogramming problem.Some properties related to the primal and dual have been given.     

A new coefficient of association

Summary In this paper, a coefficient of association has been suggested and its properties have also been investigated in the light of Renyi's demands for a coefficient of association. Also, a test of association has been proposed on the basis of a sample counterpart of this coefficient of association, calculated fromr×s contingency tables. This is thus an alternative to the usual Chi-square.     

由主子阵和缺损特征对构造Jacobi矩阵

１．引言设ｎ阶Ｊａｃｏｂｉ矩阵为 Ｊａｃｏｂｉ矩阵逆特征值问题的研究在振动工程、结构设计和系统参数识别等领域有重要应用．由主子阵和谱数据构造Ｊａｃｏｂｉ阵Ｊｎ,戴华首次得到ｎ为偶数时有解的充要条件,并给出了一个数值算法 ［１］;［２］对 ｎ为任意正整数时给出了一个新算法,此算法在计算过程中可自动判断解的存在性．由缺损特征对和谱数据构造三对角对称阵,［３］给出了有解的充要条件,本文研究由主子阵和缺损特征对构造Ｊａｃｏｂｉ矩阵,其问题如下： 问题Ａ．给定ｋ阶Ｊａｃｏｂｉ阵又给定和求和阶 Ｊａｃｏｂｉ阵使…     

A new index for measuring seasonality: A transportation cost approach

Seasonal fluctuations characterize many natural and social phenomena. Although the causes and impacts of seasonality are generally well documented in different study contexts, and many methods for isolating the seasonal component have been developed, considerably less attention has been paid to the measurement of the degree of seasonality. After reviewing the main indices used for measuring seasonality in different study contexts, we will propose a new approach in which seasonality is evaluated on the basis of the solution of a transportation problem. By considering the interdisciplinary nature of seasonal phenomena, the topic of measuring seasonality merits attention from a wide variety of perspectives.     

概率型数据模糊化方法研究

在实际中用一个精确量很难描述一个比较模糊的概念，如好坏、高低等，而用模糊数学方法往往能很好地解决这类问题。在模糊评估和模糊控制中，常常碰到隶属度如何确定或将精确数据如何模糊化的问题。本文采用正态分布模型对概率型数据进行模糊化，并针对正态分布模型存在边缘非单调性的缺陷，对模型进行了改进，最终建立了改进型正态分布模糊化模型，通过模糊化实例计算，证明这种方法是有效可行的。     

A Survey of Manor Road

Manor Road is a private road. The residents, responsible for its maintenance, had been concerned that the deterioration of its surface had been caused by non-residential traffic using it as a throughway and thereby infringing their privacy. Several schemes had been proposed to restrict non-resident usage but each would cause some degree of inconvenience to the residents. Before adopting one of the proposals, a survey was conducted to determine the ratio of the number of resident to non-resident vehicles using the road. The results suggested that there was far less non-residential usage than had been supposed. Further analysis indicated that the damage to the road was being caused by weathering and poor construction when it was first built. Furthermore, the pot-holes in the road tended to inhibit unwanted traffic and hence contributed to safeguarding the privacy of the residents without more specific action being taken.     

A dual decomposition algorithm

Suppose that a large-scale block-diagonal linear programming problem has been solved by the Dantzig—Wolfe decomposition algorithm and that an optimal solution has been attained. Suppose further that it is desired to perform a post-optimality analysis or a complete parametric analysis on the cost-coefficients or the RHS of the linking constraints. Efficient techniques for performing these analyses for the ordinary simplex case have not been easily applied to this case as one operation involves doing a minimizing ratio between all columns of two rows of the tableau. As the columns are not readily known in Dantzig—Wolfe decomposition, other techniques must be used. To date, suggested methods involve solving small linear programs to find these minimizing ratios. In this paper a method is presented which requires solving no linear programs (except possibly in the case of degeneracy of a subproblem) using and utilizing only the information typically stored for Dantzig—Wolfe decomposition.     

一类非线性椭圆问题的schwarz算法

其中考虑下述泛函最小问题:求u∈W01,α(Ω),使F(u)=     

A Hypergeometric Inequality

A sequence of coefficients that appeared in the evaluation of a rational integral has been shown to be unimodal. The original proof is based on a inequality for hypergeometric functions. A generalization is presented.     

A collocation method to fit geophysical survey data

A self adaptive collocation method has been applied to the quantitative interpretation of geophysical survey data. Examples of interpretation of vertical electrical soundings (VES) and magneto-telluric soundings (MTS) have been chosen for this work due to the high nonlinearity of the response functions and to the high degree of correlation of the parameters involved. In both cases horizontally isotropic multi-layered models have been adopted.For comparison two different computing algorithms have been considered. In the first, using a generalized inverse formulation a new different decomposition into characteristic values has been used. In the second the Marquardt procedure has been modified in an original way to give a faster convergence using a strategy based on the contemporary adjustment of the step length and the direction of the regression. The confidence limits of the results have been evaluated.Results are given for interpretation of both MTS and VES curves using the two different algorithms. Model data and field data have been considered for an effective comparison of speed of convergence and accuracy.     

DOES WATER DISINFECTANT PLAY A SUPPORTIVE ROLE IN THE SPREAD OF INFECTIOUS DISEASE? A MATHEMATICAL STUDY

The waterborne diseases cause millions of deaths across the globe. It was a preconceived notion since years that ingestion of contaminated water is the only possible way for the spread of waterborne infectious diseases. But some recent studies have shown that waterborne disease can also spread as a result of human to human transmission. The use of disinfectants is a common practice to prevent a waterborne disease. We assume that the inclusion of the disinfectant, although helpful in prevention of disease, caused negative effect on individuals. In this paper, a nonlinear mathematical model has been proposed to analyze the negative effects caused by disinfectant of water on individuals. Our study shows that if the mixing of disinfectant has not been performed in a controlled manner, then it results in an increase in human to human transmission of disease. The equilibrium and stability analysis have been performed to study the nature of the model system. An extensive numerical experiment has been performed to support the analytical findings.     

一类递推关系式的解的计算公式

文献[1]给出了一个三项单指标的常系数齐次递推式的一般解公式。本文一类带双指标的变系数非齐次递推关系的解的结构。其结果，对双指标的相应递推关系式的解的求出，亦或在其有关理论的研究方面，皆有其作用。     

A Public Key Cryptosystem Based On A Subgroup Membership Problem

We present a novel public key encryption scheme semantically secure in the standard model under the intractability assumption of a subgroup membership problem related to the factorization problem.Parts of this paper have already been published by the authors [13]AMS classification: 94A60     

A generalization of frames in Banach spaces

Fusion Banach frames satisfying property S have been studied. A sufficient condition for the existence of a fusion Banach frame satisfying property S in weakly compactly generated Banach spaces has been given. Also, a necessary and sufficient condition for a fusion Banach frame to satisfy property S has been given. Finally, fusion Banach frames satisfying property S have been characterized in terms of closedness of certain subspaces of the dual spaces in the weak*-topology.     

A novel chaotic attractor

In this letter, a novel chaotic attractor is reported. Some basic dynamical properties, such as Lyapunov exponents, fractal dimension, Poincare mapping, the continuous spectrum and chaotic behavior of this new transverse butterfly attractor are studied. Meanwhile, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed numerical as well as theoretical analysis. Furthermore, the complex chaotic dynamical behavior of the system has been also proofed by experimental simulation of a designed electronic oscillator based on EWB.     

A note on weighing designs

Summary Banerjee [1], [2] has shown that the arrangements afforded by a Balanced Incomplete Block Design can be used as an efficient spring balance design. Such designs suffer from one drawback viz., there are only a few or no degrees of freedom left for the estimation of error-variance,σ ². To overcome this difficulty, it has been suggested that the whole design may be repeated a certain number of times to get an estimate of the error variance. In the present note an attempt has been made to give an alternative design where there is no necessity of such repetition. It has been also shown that these designs give a lesser variance of the estimated weights than the repeated design. Institute of Agricultural Research Statistics     

A Trivariate Box Macroelement

Given a rectangular box which has been split into 24 tetrahedra, we show how to construct a C¹ macroelement using polynomial pieces of degree 6.     

A survey of school timetabling research

Although there has been a fair amount of research in the area of school timetabling, this domain has not developed as well as other fields of educational timetabling such as university course and examination timetabling. This can possibly be attributed to the fact that the studies in this domain have generally been conducted in isolation of each other and have addressed different school timetabling problems. Furthermore, there have been no comparative studies on the success of different methodologies on a variety of school timetabling problems. As a way forward this paper provides an overview of the research conducted in this domain, details of problem sets which are publicly available and proposes areas for further research in school timetabling.     

A RIEMANN-HILBERT PROBLEM IN A RIEMANN SURFACE

One of the inspirations behind Peter Lax’s interest in dispersive integrable systems, as the small dispersion parameter goes to zero, comes from systems of ODEs discretizing 1-dimensional compressible gas dynamics [17]. For example, an understanding of the asymptotic behavior of the Toda lattice in different regimes has been able to shed light on some of von Neumann’s conjectures concerning the validity of the approximation of PDEs by dispersive systems of ODEs. Back in the 1990s several authors have worked on the long time asymptotics of the Toda lattice [2, 7, 8, 19]. Initially the method used was the method of Lax and Levermore [16], reducing the asymptotic problem to the solution of a minimization problem with constraints (an "equilibrium measure" problem). Later, it was found that the asymptotic method of Deift and Zhou (analysis of the associated Riemann-Hilbert factorization problem in the complex plane) could apply to previously intractable problems and also produce more detailed information. Recently, together with Gerald Teschl, we have revisited the Toda lattice; instead of solutions in a constant or steplike constant background that were considered in the 1990s we have been able to study solutions in a periodic background. Two features are worth noting here. First, the associated Riemann-Hilbert factorization problem naturally lies in a hyperelliptic Riemann surface. We thus generalize the Deift-Zhou "nonlinear stationary phase method" to surfaces of nonzero genus. Second, we illustrate the important fact that very often even when applying the powerful Riemann-Hilbert method, a Lax-Levermore problem is still underlying and understanding it is crucial in the analysis and the proofs of the Deift-Zhou method!