Singular and nonsingular first-order initial value problems

Under barrier strip type arguments we investigate the existence of global solutions to the initial value problem x^′=f(t,x,x^′), x(0)=A, where the scalar function f(t,x,p) may be singular at x=A.     

Positive solutions for boundary value problems of second order difference equations and their computation

We consider the following two classes of second order boundary value problems for difference equation:

     

On the occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function

We point out an interesting occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function along the critical line. We discuss rigorous results in this direction for the shifted second moment and for the shifted fourth moment. Furthermore, we conjecture that the sine kernel also occurs in connection with the higher (even) shifted moments and show that this conjecture is closely related to a recent conjecture by Conrey, Farmer, Keating, Rubinstein, and Snaith (2003, 2005) [CFKRS1] and [CFKRS2].     

Games on fuzzy communication structures with Choquet players

Myerson (1977) used graph-theoretic ideas to analyze cooperation structures in games. In his model, he considered the players in a cooperative game as vertices of a graph, which undirected edges defined their communication possibilities. He modified the initial games taking into account the graph and he established a fair allocation rule based on applying the Shapley value to the modified game. Now, we consider a fuzzy graph to introduce leveled communications. In this paper players play in a particular cooperative way: they are always interested first in the biggest feasible coalition and second in the greatest level (Choquet players). We propose a modified game for this situation and a rule of the Myerson kind.     

An adjustable approach to fuzzy soft set based decision making

Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. Recently, decision making based on (fuzzy) soft sets has found paramount importance. This paper aims to give deeper insights into decision making based on fuzzy soft sets. We discuss the validity of the Roy-Maji method and show its true limitations. We point out that the choice value designed for the crisp case is no longer fit to solve decision making problems involving fuzzy soft sets. By means of level soft sets, we present an adjustable approach to fuzzy soft set based decision making and give some illustrative examples. Moreover, the weighted fuzzy soft set is introduced and its application to decision making is also investigated.     

Boundary integral equation methods in the theory of elasticity of hemitropic materials: A brief review

The theory of elasticity of hemitropic materials has recently been the object of rigorous mathematical analysis. In particular, the potential method and the theory of pseudodifferential equations have been used in studying the solvability in various function spaces of the main boundary value and transmission problems, in smooth and in Lipschitz domains. The main features and results of this boundary integral equations approach are briefly reviewed here.     

The Shapley value for arbitrary families of coalitions

We address the problem of finding a suitable definition of a value similar to that of Shapley’s, when the games are defined on a subfamily of coalitions with no structure. We present two frameworks: one based on the familiar efficiency, linearity and null player axioms, and the other on linearity and the behavior on unanimity games. We give several properties and examples in each case, and give necessary and sufficient conditions on the family of coalitions for the approaches to coincide.     

Bartlett分解与多元正态总体均值的广义推断

对多个正态总体均值的统计推断是一个古老而令人感兴趣的问题.本文利用样本协方差矩阵的Bartlett分解和广义p-值的概念给出一些关于均值的精确检验.模拟显示这些检验比已有的检验有更高的功效.同时,还根据协方差矩阵的Bartlett分解和样本均值向量,得到一个分布和未知参数无关的统计量,用它可以对多个正态总体共同均值做精确检验.模拟显示,这些检验犯第一错误的概率小于显著性水平,而且有更高的检验功效.     

超线性奇异Neumann边值问题的非平凡解

利用拓扑度计算,研究了一类超线性奇异Neumann边值问题非平凡解的存在性,其中非线性项可变号且下方无界.