Discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings

In this paper, we consider the implicit quasi-variational inequality without continuity assumptions of data mappings. Our approach here is completely different from the one based on KKM theorem in the literature. Interesting applications to generalized quasi-variational inequalities for both discontinuous mappings and discontinuous fuzzy mappings are given.This paper was partially supported by the NSC grant no. 86-2115-M-110-004.     

渐近正则映射对的不动点

本文在P一致凸Banach空间中证明了浙近正则映射对的若干不动点定理．在Hilbert空间，Lp空间，Hardy空间Hp和Sobolev空间Hp，k中，1＜P＜＋∞，k≥0，也建立了这些映射的若干不动点定理．本文推广了Gornicki[9，10]，Kruppel[11,12]和其他作者的结果。     

Some Remarks On Vector Optimization Problems

We prove the existence of a weak minimum for vector optimization problems by means of a vector variational-like inequality and preinvex mappings.     

Images of locally compact metric spaces

We establish relationships between locally compact-metric spaces and all kinds of spaces with mk-system (compact k-network) by means of compact-covering mappings, quotient mapping and closed mappings. This revised version was published online in June 2006 with corrections to the Cover Date.     

完美非线性映射的一类构造

在分组密码中 ,为了抗差分攻击 ,需要完美非线性映射 .利用有限域 Zp上的广义 Bent函数和不可约多项式 ,给出了完美非线性映射的一类构造 .     

Generalized Variational-Like Inequalities with Nonmonotone Set-Valued Mappings

In this paper, we introduce a new class of generalized variational-like inequalities involving a nonmonotone-type set-valued mapping which is more general than those in the known literature. By applying a KKM-type theorem established by the author, some existence theorems for the solutions to the class of generalized variational-like inequalities are proved in Hausdorff locally convex topological vector spaces.     

Generalized convexity and concavity of the optimal value function in nonlinear programming

In this paper we consider generalized convexity and concavity properties of the optimal value functionf ^* for the general parametric optimization problemP(_ε) of the form min _x f(x, ε) s.t.x∈R(ε). Many results on convexity and concavity characterizations off ^* were presented by the authors in a previous paper. Such properties off ^* and the solution set mapS ^* form an important part of the theoretical basis for sensitivity, stability and parametric analysis in mathematical optimization. We give sufficient conditions for several types of generalized convexity and concavity off ^*, in terms of respective generalized convexity and concavity assumptions onf and convexity and concavity assumptions on the feasible region point-to-set mapR. Specializations of these results to the parametric inequality-equality constrained nonlinear programming problem are provided. Research supported by Grant ECS-8619859, National Science Foundation and Contract N00014-86-K-0052, Office of Naval Research.     

On weak-open π-images of metric spaces

In this paper, we give some characterizations of metric spaces under weak-open π-mappings, which prove that a space is g-developable (or Cauchy) if and only if it is a weak-open π-image of a metric space.     

The nature of the bufferness phenomenon in weakly dissipative systems

We propose a mechanism for accumulating attractors in finite-dimensional weakly dissipative systems. The essence of this mechanism is that if a Hamiltonian or a conservative system with one and a half or more degrees of freedom is perturbed by small additional terms ensuring that it is dissipative, then under certain conditions, the number of its attractors appearing in small neighborhoods of different elliptic equilibriums or cycles of the nonperturbed system can increase without bound as the perturbations tend to zero. We consider meaningful examples from mechanics and radio physics: models of the bouncing ball dynamics, Fermi accelerations, the linear oscillator with impacts, and the self-excited oscillator with a discrete sequence of RLC circuits in the feedback circuit. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 447–466, March, 2006.