Ever since the introduction of fuzzy sets by L. A. Zadeh [14], the fuzzy concept has invaded almost all branches of Mathematics. The concept of fuzzy topological space was introduced and developed by C.L. Chang [3] and since then many fuzzy topologists [1,6-13] have extended various notions in classical topology to fuzzy topological spaces. The concept of somewhat continuous functions was intro...

In conclusion, I may point out that Theorem II may be generalized by a weakening of the hypothesis (d) . (1) In the first place, continuity of [a, g] f with respect to the pair of variables a, /3 may be replaced by upper semi-continuity . This generalization requires no change in the proof . (2) This continuity (or upper semi-continuity) with respect to (a, /3) is used only to show that the set...

In some past works by the author and collaborators, the notion of ageing function of an exchangeable survival model was introduced and several properties of it were analyzed. Generally, the ageing function turns out to be a semi-copula. Here we focus attention on the special class of survival models whose ageing function is actually a copula. For pairs of models in this class we define a notion...

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

This paper contains selected applications of the new tangential extremal principles and related results developed in [20] to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints.

Lecture notes concerning basic properties of the solutions to the semi-linear Schrödinger equation. Based on these notes a series of lectures were given at the summer school on Mathematical Physics in Sogang University, Seoul, July 20-23, 2010.

The solvability in Sobolev spaces is proved for divergence form second order elliptic equations in the whole space, a half space, and a bounded Lipschitz domain. For equations in the whole space or a half space, the leading coefficients a are assumed to be measurable in one direction and have small BMO semi-norms in the other directions. For equations in a bounded domain, additionally we assume...

In generalized semi-infinite programming the feasible set is known to be not closed in general. In this paper, under natural and generic assumptions, the closure of the feasible set is described in explicit terms.

Different from previous researches which mostly focused on linear response control of seismically excited high-rise buildings, this study aims to control nonlinear seismic response of high-rise buildings. To this end, a semi-active control strategy, in which H∞ control algorithm is used and magneto-rheological dampers are employed for an actuator, is presented to suppress the nonlinear vibratio...