INTRODUCTION 4 Introduction Zeta functions encoding geometric information such as zeta functions of algebraic varieties over finite fields or zeta functions of finite graphs will loosely be called geometric zeta functions in the sequel. Sometimes the geometric situation gives one tools at hand to prove analytical continuation, functional equation and an adapted form of the Riemann hypothesis. T...

An effective technique to design compact low pass filter has been proposed in this paper. The proposed method is highly effective for L-band applications. Low impedance microstrip lines are arranged such that they work as open stubs to increase the selectivity of the filter. Using the proposed technique about 57% size reduction has been realized with sharper roll off characteristics. An empiric...

Let C(L) be the ring of real-valued continuous functions on a frame L. In this paper, strongly fixed ideals and characterization of maximal ideals of C(L) which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of C(L), is st...

We show that a strong form of the so called Lindstrr om's Theorem 4] fails to generalize to extensions of L ! and L : For weakly compact there is no strongest extension of L ! with the (;)-compactness property and the LL owenheim-Skolem theorem down to. With an additional set-theoretic assumption, there is no strongest extension of L with the (;)-compactness property and the LL owenheim-Skolem ...

We introduce a notion of L-Betti numbers for locally compact, second countable, unimodular groups. We study the relation to the standard notion of L-Betti numbers of countable discrete groups for lattices. In this way, several new computations are obtained for countable groups, including lattices in algebraic groups over local elds, and Kac-Moody lattices. We also extend the vanishing of reduce...

For any n-dimensional compact Riemannian manifold (M, g) without boundary and another compact Riemannian manifold (N,h), we establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0, T ),W ). For the hydrodynamic flow (u, d) of nematic liquid crystals in dimensions n = 2 or 3, we show the uniqueness holds for the class of weak solutions provided either (i) for n =...

Let L be a Lie group and A a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L and G---A = L. Let a~G be such that Ada is semisimple and not contained in a compact subgroup of Aut (Lie(G)). Consider the expanding horospherical subgroup of G associated to a defined as U + = {g~ G:a-"ga"~ e as n ~ oo}. Let f2 be a non-empty open subset of U § and nf-* ~ be ...

For any n-dimensional compact Riemannian manifold (M, g) without boundary and another compact Riemannian manifold (N,h), we establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0, T ),W ). For the hydrodynamic flow (u, d) of nematic liquid crystals in dimensions n = 2 or 3, we show the uniqueness holds for the class of weak solutions provided either (i) for n =...

pot marigold (calendula officinalis l.) is a medicinal and ornamental plant. the effect of different concentrations of chlormequat (cycocel), and daminozide, two plant growth retardant, on plant height, flowering, the content of essence and some other traits in pot marigold (calendula officinalis) was assessed. plant growth retardants are commonly applied to limit stem elongation and produce a ...