# Mathematics

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**Mathematics**Let $pounds$ be the category of all locally compact abelian (LCA) groups. In this paper, the groups $G$ in $pounds$ are determined such that every extension $0to Xto Yto Gto 0$ with divisible, $sigma-$compact $X$ in $pounds$... more

Computing driving directions has motivated many shortest path algorithms based on preprocessing. Given a graph, the preprocessing stage computes a modest amount of auxiliary data, which is then used to speed up online queries. In... more

Critical‐band spectrum is known to represent the redundancies of the human auditory system. Vector quantization constitutes a minimal redundant code set for a given signal source. In this study, these techniques are combined in a low‐rate... more

The additive (s1, s2)–functional inequality of the form ‖f(x + 2y + 3z)− f(x + z)− 2f(y + z)‖ ≤ ‖s1(f(x + 2y − 3z)− f(x− z)− 2f(y − z))‖ + ∥∥∥∥s2 (f(x + z) + 2f(y + z)− 2f (x + 2y + 3z 2 ))∥∥∥∥ is solved without any regularity... more

For a fixed positive integer \kappa, the functional equation \kappa f(m^2 + n^2) = f(\kappa m^2) + \kappa f(n^2), (m,n\in\mathbb{N}) is solved for multiplicative functions f. This complements a 1996 result of Chung [2] which deals with... more

ABSTRACT The characterization of distributions is well known in the field of statistics and reliability. This paper characterizes a few distributions with the help of failure rate, mean residual, log-odds rate, and aging intensity... more

We give a new separability criterion, a necessary condition for separability of N-partite quantum states. The criterion is based on the Bloch representation of a N-partite quantum state and makes use of multilinear algebra, in particular,... more

In developing modern logic, Frege aims to substantiate the logicist view of arithmetic. In this view, arithmetic is reducible to logic: one can define all arithmetical notions using only logical notions, and prove all arithmetic truths... more

One of characteristics of the traffic intensity in M/M/1 queue is the expected queue length. In this article, the problem of Bayes, E-Bayes, and robust Bayes estimation of the expected length in a ...

This paper presents a technique for the optimization of bound queries over disjunctive deductive databases with constraints. The proposed approach is an extension of the well-known Magic-Set technique and is well-suited for being... more

ABSTRACT The aim of this note is to give an extension of a result by McShane to a general stochastic integral operator with a non-Lipschitz condition on the coefficient functions.

We consider a class of stochatic dieren tial equations with non- Lipschitz coecien t functions which modeling the evolution of the price of stocks on the nancial market. We study the existence and uniqueness of so- lution processes as... more

ABSTRACT Very high-order transverse mode selection using intra-cavity phase elements in passive Q-switched Nd:YAG and Er:glass lasers is reported. Stable operation of pure high-order modes is achieved (TEM44), resulting in considerable... more