‎Let $G$ be a locally compact abelian group‎. ‎The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$‎. ‎Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level‎. ‎Also‎, ‎the construction of affine frames for $L^2(G)$ bas...

Let $G$ be a compact Lie group. In this article, we investigate the Cauchy problem for nonlinear wave equation with viscoelastic damping on . More precisely, some $L^2$ -estimates solution to homogeneous damped utilizing group Fourier transform We also prove that there is no improvement of any decay rate norm $\|u(t,\,\cdot )\|_{L^2(G)}$ by further assuming $L^1(G)$ -regularity initial data. Fi...

By studying Cameron’s operator in terms of determinants, two kinds “integer” sequences incomplete numbers were introduced. One was the sequence restricted numbers, including s-step Fibonacci sequences. Another associated Lamé higher order. classical Trudi’s formula and inverse relation, more expressions able to be obtained. These relations identities can extended those negative integers or rati...

A 2−2| log 2|−α (α = 2 if d ≥ 3, α = 3 if d = 2) result is obtained for the existence time of solutions of semilinear different speed Klein-Gordon system with weakly decaying Cauchy data, of size 2, in certain circumstances of nonlinearity. keywords: Weakly decaying Cauchy data, Existence time, Klein-Gordon equations with different speeds. Subject class: 35L70 1 Statement of the Main Result We ...

A novel trust region method for solving linearly constrained nonlinear programs is presented. The proposed technique is amenable to a distributed implementation, as its salient ingredient is an alternating projected gradient sweep in place of the Cauchy point computation. It is proven that the algorithm yields a sequence that globally converges to a critical point. As a result of some changes t...

n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem. 

Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations. A logic for convergent infinite computations is proposed by extending first order theories using Cauchy sequences, which has stronger expressive power than the first order logic. A class of fixed points characte...

We identify certain general geometric conditions on a foliation of spacetime (M,g) by timelike curves that will impede the existence null geodesic lines, especially if possesses compact Cauchy hypersurface. The absence such in turn, yields well-known restrictions geometry cosmological spacetimes, context Bartnik's splitting conjecture. Since (non)existence lines is actually conformally invarian...

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

This is the last article in a series of three initiated by the second author. We elaborate on the concepts and theorems constructed in the previous articles. In particular, we prove that the GH and the GGH uniformities previously introduced on the moduli space of isometry classes of globally hyperbolic spacetimes are different, but the Cauchy sequences which give rise to well-defined limit spac...