Necessary and Sufficient Conditions for Viability for Nonlinear Evolution Inclusions

We consider the viability problem for nonlinear evolutions inclusions of the form u′(t)?∈?Au(t)?+?F(u(t)), where A is an m-dissipative (possible nonlinear and multi-valued) operator acting in a Banach space X, K?X is a nonempty, locally closed set and $F:K{\user1{ \rightsquigarrow }}X$ is with nonempty, convex, closed and bounded values. We define the concept of A-quasi-tangent set to K at a given point ξ?∈?K and we prove a necessary condition for C ⁰-viability expressed in terms of this new tangency concept. We next show that, under various natural extra-assumptions, the necessary condition is also sufficient. We extend the results to the quasi-autonomous case, we deal with the existence of noncontinuable or even global C ⁰-solutions and, as applications, we deduce a comparison result and a sufficient condition for null controllability.     

Necessary and Sufficient Conditions for Zero-stiffness Postbuckling

In the course of sensitivity analysis of the initial postbuckling behavior of elastic structures, a special case may occur which is referred to as zero-stiffness postbuckling. The purpose of this paper is to present sufficient and necessary conditions for this special case which is associated with a favorable form of transition from imperfection sensitivity to imperfection insensitivity in the course of sensitivity analysis of the initial postbuckling path. Koiter's initial postbuckling analysis is chosen as the vehicle for quantification of the initial postbuckling behavior. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

幂幺矩阵的充要条件

研究幂幺矩阵的充要条件,利用矩阵的秩和齐次线性方程组解空间的维数.将m=2时幂幺矩阵的充要条件推广到一般幂幺矩阵的充要条件,得出了幂幺矩阵可对角化的结果,并将幂幺矩阵的充要条件平行地推广到幂幺线性变换.     

Two Suficient and Necesary Conditions for Quasidisks

ＴｗｏＳｕｆｉｃｉｅｎｔａｎｄＮｅｃｅｓａｒｙＣｏｎｄｉｔｉｏｎｓｆｏｒＱｕａｓｉｄｉｓｋｓ＊）ＣｈｕＹｕｍｉｎｇ（褚玉明）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｓｈａ，４１００８２）...     

一类二阶非线性微分系统有界性与收敛性的充分必要条件

本文给出了如下一类二阶非线性微分系统 解的有界性的一些新的充分条件,获得了（Ｓ’）的所有解有界或收敛到零的充分必要 条件．所获的结果能够应用于Ｌｉｅｎａｒｄ类型方程 它改进与扩展了［１,２］等文献关于同样问题的一些重要结果．     

二阶非线性差分方程有界解振动的充分必要条件

在本文中,我们给出了非线性二阶差分方程△（p_n△y_n）+q_nf（y_n-r_n）=0有界解振动的充分必要条件和比较定理,所得结果推广了文[3,6,7]的相应定理。     

Necessary and Sufficient Conditions for the Lipschitzian Invertibility of the Nonlinear Differential Mapping d/dt − f in the Spaces LP(ℝ,ℝ), 1≤p≤ ∞

Mathematical Notes - We obtain necessary and sufficient conditions for the Lipschitzian invertibility of the differential mapping d/dt ? f, where $\user1{f}\user2{:}\mathbb{R} \to...     

Necessary and Sufficient Conditions for Efficiency Via Convexificators

Based on the extended Ljusternik Theorem by Jiménez-Novo, necessary conditions for weak Pareto minimum of multiobjective programming problems involving inequality, equality and set constraints in terms of convexificators are established. Under assumptions on generalized convexity, necessary conditions for weak Pareto minimum become sufficient conditions.     

Necessary and Sufficient Conditions for Minimax Fractional Programming

We establish the necessary and sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems solving generalized convex functions. Subsequently, we apply the optimality conditions to formulate one parametric dual problem and we prove weak duality, strong duality, and strict converse duality theorems.     

E—matrices and Several Necessary and Sufficient Conditions

AER-x.,Aiscalledanonnegative(nonPositive)matrixifau>O(a,jO(aiirtO),markedA>O(AO(i#j),auO,wecallp(A)=max{IA,l,lA,l'.-.,lAnl},(whereA,,A2,..',A"areeigenva1ueofA)asspectralradiusofA.LemmalIfAe7'.,thenareanonnegativesquarematrxBandapositivenumberksuchthatA=B-kI(whereIistheidentitymatrixofordern).ProofLetbti=…     

Necessary and Sufficient Conditions for Solving Infinite-Dimensional Linear Inequalities

The existence of a feasible solution to a system of infinite-dimensional linear inequalities is characterized by a topological generalization of the Farkas Condition. If this result is specialized to a finite-dimensional vector space with finite positive cone, then a geometric proof of the classic Minkowski-Farkas Lemma is obtained. A dual version leads to an infinite-dimensional extension of the Theorem of the Alternative.     

Error Bounds: Necessary and Sufficient Conditions

The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space.     

Necessary and Sufficient Conditions for Existence and Uniqueness of Bounded and Almost-Periodic Solutions of Nonlinear Differential Equations

Necessary and sufficient conditions of the existence and uniqueness of bounded and almost-periodic solutions of nonlinear dif ferential equation dx/dt+f(x)=h(t), tR, are obtained. Here f: RR is continuous, h: RR is continuous and bounded.     

一类奇异非线性方程的正整体解存在的充分必要条件

本文研究形如Δ^nu=f(|x|,u,|Δ↓u|u^-β，x∈R^N的奇异非线性多调和方程在R^N(N≥3)上的正整体解，给出了该方程具有无穷多个其渐进阶刚好为|x|^2n-2的正整体解的充分与必要条件。     

Necessary and Sufficient Convexity Conditions for the Ranges of Vector Measures

The absence of atoms in Lyapunov's Convexity Theorem is a sufficient, but not a necessary condition for the convexity of the range of an n - dimensional vector measure. In this paper algebraic and topological convexity conditions generalizing Lyapunov's Theorem are developed which are sufficient and necessary as well. From these results the converse of Lyapunov's Theorem is derived in the form of a nonconvexity statement which gives insight into the geometric structure of the ranges of vector measures with atoms. Further, a characterization of the one-dimensional faces of a zonoid Z_μ, is given with respect to the generating spherical Borel measure μ. As an application, it is shown that the absence of μ - atoms is a necessary and sufficient convexity condition for the range of the indefinite integral ∫ x dμ where x denotes the identical function on S^n-1.     

跳过程随机可比的充要条件

本文研究跳过程的随机可比性·基于文献［２］和［３］,证明两个跳过程随机可比的充要条件是其ｑ对可比·同时,改进了［６］中唯一性问题的结果     

Necessary and Sufficient Conditions for Internal Stability of Linear Formations

Doklady Mathematics - Necessary and sufficient conditions for the internal stability of formations whose dynamics are defined by linear differential equations have been obtained. The classes of...     

幻方的几个充要条件

建立等重方阵的概念,并运用它阐述幻方、2次幻方、3次幻方及中心对称互补幻方的充要条件,根据这些结论构作出一些8阶、9阶2次中心对称互补幻方.     

Sufficient and Necessary Conditions for Stochastic Comparability of Jump Processes

Abstract This note is devoted to the study of the stochastic comparability of jump processes. On the basis of [2] and [3], it is proved that two jump processes are stochatically comparable if and only if their q-pairs are comparable. Meanwhile, the result concerning the uniqueness given in [6] is also improved upon. Research supported in part by DPFIHE(Grant No.96002704), NNSFC(Grant No.19771008), MCSEC, Ying-Tung Fok Educational Foundation and Youth Science Foundation of BNU