广义可加Fuzzy测度

本文首先引入Fuzzy集类上（广义）可加Fuzzy测度的有关概念,然后给出Fuzzy集上关于可加Fuzzy测度的Fuaay积分及有关定理,最后在一定条件下给出广义可加Fuzzy测度的一系列分解定理。     

多复变中一个带Haseman位移及共轭值的非线性边值问题

研究多复变中一个带Haseman位移及共轭值的非线性边值问题.利用积分方程方法和Schauder不动点原理给出问题解的存在性和积分表示,并用压缩映象原理证明了线性问题解的唯一性.     

A bound for Wilson''''s general theorem

Given any set K of positive integers and positive integer λ, let c(K,λ) denote the smallest integer such that v∈B(K,λ) for every integer v≥c(K,λ) that satisfies the congruences λv(v-1)≡0 (mod β(K) and λ(v-1)≡0 (mod α(K)). Let K0 be an equivalent set of K, k and k* be the smallest and the largest integers in K0. We prove that c(K,λ)≤exp exp{Q0}Qo=max{2(2p(ko)2-k2kk)p(ko)4,(Kk242y-k-2)(y2)}, whereand y=k*+k(k-1)+1.     

Komlós Theorem for Unbounded Random Sets

We present the Komlós theorem for multivalued functions whose values are closed (possibly unbounded) convex subsets of a separable Banach space. Komlós theorem can be seen as a generalization of the SLLN for it deals with a sequence of integrable multivalued functions that do not have to be identically distributed nor independent. The Artstein–Hart SLLN for random sets with values in Euclidean spaces is derived from the main result. Finally, since the main theorem concerns multifunctions whose values are allowed to be unbounded, we can restate it in terms of normal integrands (random lower semicontinuous functions).     

Algebraic independence of the values ofE-functions at singular points and Siegel’s conjecture

We prove a generalization of Shidlovskii’s theorem on the algebraic independence of the values ofE-functions satisfying a system of linear differential equations that is well known in the theory of transcendental numbers. We consider the case in which the values ofE-functions are taken at singular points of these systems. Using the obtained results, we prove Siegel’s conjecture that, for the case of first-order differential equations, anyE-function satisfying a linear differential equation is representable as a polynomial in hypergeometricE-functions. Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 174–190, February, 2000.     

Set Systems with L‐Intersections and k‐Wise L‐Intersecting Families

In this paper, by employing linear algebra methods we obtain the following main results:

• (i) Let and be two disjoint subsets of such that Suppose that is a family of subsets of such that for every pair and for every i. Then Furthermore, we extend this theorem to k‐wise L‐intersecting and obtain the corresponding result on two cross L‐intersecting families. These results show that Snevily's conjectures proposed by Snevily (2003) are true under some restricted conditions. This result also gets an improvement of a theorem of Liu and Hwang (2013).
• (ii) Let p be a prime and let and be two subsets of such that or and Suppose that is a family of subsets of [n] such that (1) for every pair (2) for every i. Then This result improves the existing upper bound substantially.

     

Periodicity and non‐negativity of solutions for nonlinear neutral differential equations with variable delay via fixed point theorems

We use a modification of Krasnoselskii's fixed point theorem introduced by Burton to show the periodicity and non‐negativity of solutions for the nonlinear neutral differential equation with variable delay We invert this equation to construct the sum of a compact map and a large contraction, which is suitable for applying the modification of Krasnoselskii's theorem. Copyright © 2015 John Wiley & Sons, Ltd.     

Symmetry analysis of the charged squashed Kaluza–Klein black hole metric

In this research article, a complete analysis of symmetries and conservation laws for the charged squashed Kaluza–Klein black hole space‐time in a Riemannian space is discussed. First, a comprehensive group analysis of the underlying space‐time metric using Lie point symmetries is presented, and then the n‐dimensional optimal system of this space‐time metric, for n = 1,…,4, are computed. It is shown that there is no any n‐dimensional optimal system of Lie symmetry subalgebra associated to the system of geodesic for n≥5. Then the point symmetries of the one‐parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian that means Noether symmetries are found, and then the conservation laws associated to the system of geodesic equations are calculated via Noether's theorem. Copyright © 2015 John Wiley & Sons, Ltd.     

Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays

This paper is concerned with interval general bidirectional associative memory (BAM) neural networks with proportional delays. Using appropriate nonlinear variable transformations, the interval general BAM neural networks with proportional delays can be equivalently transformed into the interval general BAM neural networks with constant delays. The sufficient condition for the existence and uniqueness of equilibrium point of the model is established by applying Brouwer's fixed point theorem. By constructing suitable delay differential inequalities, some sufficient conditions for the global exponential stability of the model are obtained. Two examples are given to illustrate the effectiveness of the obtained results. This paper ends with a brief conclusion. Copyright © 2016 John Wiley & Sons, Ltd.     

一类拟线性椭圆方程的非平凡解

运用环绕理论和对称型山路理论对一类具有次临界多项式增长和次临界指数增长的$p$-Laplacian方程建立一个非平凡解(无穷多个非平凡解)的存在性结果.