in this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.

In this article, we have shown, for the add-point monad T, thepartial morphism category Set*is isomorphic to the Kleisli category SetT. Alsowe have proved that the category, SetT, of T-algebras is isomorphic to thecategory Set of pointed sets. Finally we have established commutative squaresinvolving these categories.

∗This research was supported by funding from the Robert Wood Johnson Foundation. Iain Cockburn, Rebecca Eisenberg, Bronwyn Hall, Mark Lemley, Douglas Lichtman, Jean Lanjouw, David Mowery, Richard R. Nelson, Arti Rai, Mark Schankerman, Scott Stern, and Rosemarie Ziedonis provided helpful comments on an earlier draft of this paper. I also benefitted from feedback from participants at the 2004 NBE...

and Applied Analysis 3 For given nonlinear operators T, g, h, we consider the problem of finding u ∈ H : h u ∈ K such that 〈 Tu, g v − h u 〉 ≥ 0, ∀v ∈ H : g v ∈ K, 2.1 which is called the extended general variational inequality. Noor 13–16 has shown that the minimum of a class of differentiable nonconvex functions on hg-convex set K in H can be characterized by extended general variational ineq...

The article includes schemes of deening by structural induction, and deenitions and theorems related to: the set of variables which have free occurrences in a ZF-formula, the set of all valuations of variables in a model, the set of all valuations which satisfy a ZF-formula in a model, the satissability of a ZF-formula in a model by a valuation, the validity of a ZF-formula in a model, the axio...

Revised 2006 (see the various sections for authors). In this section we give various parameters for common detector components. The quoted numbers are usually based on typical devices, and should be regarded only as rough approximations for new designs. More detailed discussions of detectors and their underlying physics can be found in books by Ferbel [1], Grupen [2], Kleinknecht [3], Knoll [4]...

This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$

in this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. we establishthe orthogonality relations for square integrable representationsof homogeneous spaces which give rise to the existence of aunique self adjoint positive operator on the set of admissiblewavelets. finally, we show that this operator is a constant multiple of identity operator...