Asymptotics of the Moment Generating Function for the Range of Random Walks

The range of random walks means the number of distinct sites visited at least once by the random walk before time n. We are interested in the free energy function of the range of simple symmetric random walks and determine the asymptotic behavior near the origin.     

Generating Functions for Computing the Myerson Value

The complexity of a computational problem is the order of computational resources which are necessary and sufficient to solve the problem. The algorithm complexity is the cost of a particular algorithm. We say that a problem has polynomial complexity if its computational complexity is a polynomial in the measure of input size. We introduce polynomial time algorithms based in generating functions for computing the Myerson value in weighted voting games restricted by a tree. Moreover, we apply the new generating algorithm for computing the Myerson value in the Council of Ministers of the European Union restricted by a communication structure.     

On Generating Functions of Waiting Time Problems for Sequence Patterns of Discrete Random Variables

Let X , X , ... be a sequence of independent and identically distributed random variables, which take values in a countable set S = {0, 1, 2, ...}. By a pattern we mean a finite sequence of elements in S. For every i = 0, 1, 2, ..., we denote by P = "a a ... a " the pattern of some length k , and E denotes the event that the pattern P occurs in the sequence X , X , .... In this paper, we have derived the generalized probability generating functions of the distributions of the waiting times until the r-th occurrence among the events . We also have derived the probability generating functions of the distributions of the number of occurrences of sub-patterns of length l(l < k) until the fiurrence of the pattern of length k in the higher order Markov chain.     

和式sum from k=o to n(μ~kf(k))的发生函数算法

利用普通幂级数发生函数方法,通过对发生函数进行xD算子,得到和式∑k=0μkf(k)的计算公式,并计算该类和式.     

论中值定理类命题证明中的辅助函数构造

借助实例分析的方法,讨论在证明微分与积分相结合的中值定理类命题时,关于辅助函数的构造技巧及其变形思想.     

p-adic Measures of Algebraic Independence for the Values of Ramanujan Functions and Klein Modular Functions

In this paper, we give the p-adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions at algebraic points.     

GA-凸函数的Hadamard型不等式的改进和应用

通过研究函数的凸性、单调性及相关理论,建立了关于GA-凸函数的一些新的Hadamard型不等式,这些不等式推广了最近文献中的有关结果.     

Mahler型函数值代数无关性的p-adic度量

本文给出Mahler型函数值代数无关性的p-adic度量.     

Koch曲线所围区域内的一类解析函数边值问题

在经典解析函数边值理论中,当L为复平面上逐段光滑封闭曲线时,在L所围的内部和外部,Cauchy型积分解析;通过对Cauchy主值积分的讨论,可得Cauchy型积分在L上的左、右边值,且边值满足Plemelj公式.基于Koch曲线的构造方法,对一系列Cauchy型积分取极限,并附加上一定的Hlder条件,可得在Koch曲线所围的内部和外部区域内都解析的Cauchy型积分函数,进一步得到与经典解析函数边值问题类似的结果.     

An axiomatization of the Banzhaf value for cooperative games on antimatroids

Cooperative games on antimatroids are cooperative games in which coalition formation is restricted by a combinatorial structure which generalizes permission structures. These games group several well-known families of games which have important applications in economics and politics. The current paper establishes axioms that determine the restricted Banzhaf value for cooperative games on antimatroids. The set of given axioms generalizes the axiomatizations given for the Banzhaf permission values. We also give an axomatization of the restricted Banzhaf value for the smaller class of poset antimatroids. Finally, we apply the above results to auction situations.     

密度函数垂直表示及在非均匀随机数生成中的应用

本文给出密度函数垂直表示法,以及利用该方法产生给定概率密度函数的随机向量的一般算法。     

New inversion formula for the solution to an inverse diffraction problem

For the solution to the basic problem of quantitative texture analysis, a new inversion formula is derived that makes use of the generating function for Legendre polynomials.     

Utilization of mathematical programming for public systems: An application to effective formation of integrated regional information networks

This paper concerns a methodological reflection on the multiobjective approach to public systems which involve group decision processes. Particular attention is given to an integrated program of regional systems which include value trade-offs between multiple objectives. Our intention is to combine the judgmental processes with the optimization processes in the soft public systems. A two-layer approach is applied. At the first layer, each regional program is formulated in mathematical programming based on a utility assessment with different regional characteristics. Each subsystem independently reflects its particular concern as a single agent. The dual optimal solutions obtained for each subsystem are treated as an index, or the theoretical prices, representing the value trade-offs among the multiple objectives. At the second layer, an effective formation of interregional cooperation for compromising the conflicting regional interests is examined. Ann-person cooperative game in the characteristic function form is used to evaluate the effectiveness of the cooperation. The characteristic function for the game is derived on the incremental value of the regional benefit after the formation of a cooperation. The nucleolus and the augmented nucleolus as the solution concepts of the cooperative game are used for indicating the effectiveness of the cooperation. Finally using alternative criteria, the results in assessing the best decisions are examined comparatively.     

实轴上的双解析函数Riemann边值逆问题

提出了一类实轴上的双解析函数Riemann边值逆问题.先消去参变未知函数,再采用易于推广的矩阵形式记法,可把问题转化为两个实轴上的解析函数Riemann边值问题.利用经典的Riemann边值问题理论,讨论了该问题正则型情况的解法,得到了它的可解性定理.     

正定矩阵在函数极值问题中的应用

通过正定矩阵来处理多元函数的极值问题,通过一个简单的方法,证明了关于多元函数极值存在的一个充分条件.     

Matrix approach to dual similar associated consistency for the Shapley value

In terms of the similarity of matrices, by combining the dual operator and the linear mapping with respect to Hamiache’s associated game on the game space, the Shapley value for TU-games is axiomatized as the unique value verifying dual similar associated consistency, continuity, and the inessential game property.     

Infeasibility and Directional Distance Functions with?Application to the Determinateness of?the?Luenberger Productivity Indicator

The purpose of this contribution is to highlight an underexplored property of the directional distance function, a recently introduced generalization of the Shephard distance function. It diagnoses in detail the economic conditions under which infeasibilities may occur for the case of directional distance functions and explores whether there exist any solutions that remedy the problem in an economically meaningful way. This discussion is linked to determinateness as a property in index theory and is illustrated by analyzing the Luenberger total factor productivity indicator, based upon directional distance functions. This indicator turns out to be impossible to compute under certain weak conditions. A fortiori, the same problems can also occur for less general productivity indicators and indexes. We acknowledge the constructive comments of two referees.     

角函数方法在二阶微分方程边值问题中的应用

利用角函数的方法讨论了下列二阶微分方程x″+g(t,x,x′)=0(1)x″+δsin(x)+h(t)=0(2)x″+g(t,x′)=0(3)在边界条件x(a)=x(b)=0(4)下解的存在性或唯一性问题.得到了边值问题(1)(4)的存在性定理,边值问题(2)(4)和(3)(4)的存在唯一性定理.     

特殊类型函数高阶导数与原函数的统一公式

本文通过研究几种特殊类型函数的高阶导数与原函数的求法 ,获得了由该类函数自身及其一阶导数的特征 ,即可快速写出该类函数的 n阶导数 y( n) 与原函数 y( - 1 ) 的统一公式 y( n) ( n=-1 ,1 ,2 ,3 ,… ) .该公式可给实际运算带来许多简化与方便 .     

Zonal Functions for the Unitary Groups and Applications to Hermitian Lattices

We study the decomposition of the space L²(Sⁿ⁻¹) under the actions of the complex and quaternionic unitary groups. We give an explicit basis for the space of zonal functions, which in the second case takes account of the action of the group of quaternions of norm 1. We derive applications to hermitian lattices.