in this paper we will generalize  some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .

The behavior of various types of noncompact covering properties such as paracompactness, metacompactness, subparacompactness, submetacompactness, etc., are studied under various types of fuzzy mappings such as open map, closed map, perfect map, etc. Moreover the concept of para-Lindelof space is introduced in L-topological spaces and its properties and behavior under maps are obtained.

As is well known the category of paracompact spaces is important in algebraic topology and the theory of fiber spaces. The following question arises naturally. If a space (Hausdorff space) B is paracompact, is the space of paths B1 (I = [0, l]), with, of course, the compact-open topology, also paracompact? The following simple example answers the question in the negative. Let X denote the set o...

This paper deals with some questions that have received a lot of attention since they were raised by Hejhal and Rackner in their 1992 numerical computations of Maass forms. We establish sharp upper and lower bounds for the L2-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex L∞-bounds are applied to pro...

Let G be a fixed graph with largest (adjacency matrix) eigenvalue λ0 and with its universal cover having spectral radius ρ. We show that a random cover of large degree over G has its “new” eigenvalues bounded in absolute value by roughly √ λ0ρ. This gives a positive result about finite quotients of certain trees having “small” eigenvalues, provided we ignore the “old” eigenvalues. This positive...

where <£fc(X)=2w=i dk(ri)e^ +residue term. Hopefully, one could expand the k integral and estimate the resulting infinite series. This does not seem feasible, however, unless k{z) satisfies a certain approximate functional equation (AFE); see [5, p. 147] and [6, p. 42]. This is one reason why only k=l, k=2 are known. However, Bellman [2] has shown that, if the e~ in k(z) are replaced b...