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...

A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...

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...

A new method is presented for numerically capturing a moving interface of arbitrary dimension and codimension. The method is named the ‘local level set method’, since it localizes the level set method near the interface to significantly reduce the computational expense of the level set method. Following the framework of the level set method, an interface is implicitly represented as the zero le...

abstract level of groundwater is decreased which is mainly because, withdrawal of groundwater is increased, because of lack of right management. economics of rural based farming and farming is dependent of water so decreasing of groundwater effects social welfare. in this study decrease of welfare measure by reason of reduction of groundwater level considered. this study investigated the impact...

We present a simple semi-supervised relation extraction system with large-scale word clustering. We focus on systematically exploring the effectiveness of different cluster-based features. We also propose several statistical methods for selecting clusters at an appropriate level of granularity. When training on different sizes of data, our semi-supervised approach consistently outperformed a st...

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...