复模糊函数与模糊复函数的微分及其性质

已有的复模糊函数的微分是由复区间值函数的微分和扩张原理给出的,本文利用模糊结构元理论及模糊数的广义限定运算给出与已有的复模糊函数微分等价的定义,同时给出模糊复函数微分的定义,并讨论其解析性质,给出模糊复函数解析的充要条件.     

Differential Equations of Fractional Order: Methods,Results and Problems. II

The article, being a continuation of the first one [A.A. Kilbas and J.J. Trujillo (2001). Differential equations of fractional order. Methods, results and problems, I. Applicable Analysis , 78 (1-2), 153-192.], deals with the so-called differential equations of fractional order in which an unknown function is contained under the operation of a derivative of fractional order. The methods and the results in the theory of such fractional differential equations are presented including the Dirichlet-type problem for ordinary fractional differential equations, studying such equations in spaces of generalized functions, partial fractional differential equations and more general abstract equations, and treatment of numerical methods for ordinary and partial fractional differential equations. Problems and new trends of research are discussed.     

Determinant Forms for Extended Heat Functions and Expansions of Solutions of Associated Cauchy Problems

We briefly review series solutions of differential equations problems of the second order that lead to coefficients expressed in terms of determinants. Derivative type formulas involving a generating function with several parameters are developed for these determinant coefficients in first order problems. These permit constructing determinant forms for the heat polynomials and their Appell transforms. Hadamard's theorem for bounding determinants and conical regions are used to deduce simplified versions of expansion theorems involving these polynomials and associated Appell transforms. Extended versions of the heat equation are also considered.     

临界情况下模糊矩阵对策的性质

讨论临界情况下模糊矩阵对策的性抽,对模型问题各种情况给出了临界值c*的定义,证明了当d(f1,f2)＜ε≤c*时,模糊矩阵对策模型问题关于价值函数f1(x)、f2(x)具有连续依赖性和可调和性。     

牛顿插值级数与解析函数惟一性定理

将插补基点为ｚ＝ｎ的牛顿插值级数的一些性质推广到一般的基点ｚ＝λｎ,并建立起半平面内的一条解析函数惟一性定理。     

Maps on Ultrametric Spaces,Hensel's Lemma,and Differential Equations Over Valued Fields

We give a criterion for maps on ultrametric spaces to be surjective and to preserve spherical completeness. We show how Hensel's Lemma and the multidimensional Hensel's Lemma follow from our result. We give an easy proof that the latter holds in every henselian field. We also prove a basic infinite-dimensional Implicit Function Theorem. Further, we apply the criterion to deduce various versions of Hensel's Lemma for polynomials in several additive operators, and to give a criterion for the existence of integration and solutions of certain differential equations on spherically complete valued differential fields, for both valued D-fields in the sense of Scanlon, and differentially valued fields in the sense of Rosenlicht. We modify the approach so that it also covers logarithmic-exponential power series fields. Finally, we give a criterion for a sum of spherically complete subgroups of a valued abelian group to be spherically complete. This in turn can be used to determine elementary properties of power series fields in positive characteristic.     

Lexical Scope and Statistical Computing

Abstract

Programming environments such as S and Lisp-Stat have languages for performing computations, data storage mechanisms, and a graphical interface. These languages provide an interactive interface to data analysis that is invaluable. To take full advantage of these programming environments, statisticians must understand the differences between them. Ihaka and Gentleman introduced R, a version of S which uses a different scoping regimen. In some ways this makes R behave more like Lisp-Stat. This article discusses the concept of scoping rules and shows how lexical scope can enhance the functionality of a language.     

On partial sums of a gaussian sequence with stationary increments

We establish large increment properties for a Gaussian sequence with stationary increments under global conditions. Limit theorems for partial sums of the sequence with nonpositive correlation functions or the correlation functions on their speed of convergence to zero are proved via estimating a probability inequality on the supremum of Gaussian processes     

On Perturbed Discrete Boundary Value Problems

In this paper, we study nonlinear discrete boundary value problems of the form x ( t +1)= A ( t ) x ( t )+ h ( t )+ k f ( t , x ( t ), k ) subject to Bx (0)+ Dx ( J )= u + k g ( x (0), x ( J ), k ) where k is a "small" parameter. Our main concern is the case of resonance, that is, the situation where the associated linear homogeneous boundary value problem x ( t +1)= A ( t ) x ( t ), Bx (0)+ Dx ( J )=0 admits nontrivial solutions. We establish conditions for the solvability of the nonlinear boundary value problem when k is "small". We also establish qualitative properties of these solutions.