Let R be a d-dimensional local ring, with maximal ideal m, containing a field and let x1, . . . , xd be a system of parameters for R. If depthR ≥ d − 1 and the local cohomology module H m (R) is finitely generated, then there exists an integer n such that the modules R/(x 1 , . . . , x d ) have the same Betti numbers, for all i ≥ n.

Cofiniteness of the generalized local cohomology modules $H^{i}_{mathfrak{a}}(M,N)$ of two $R$-modules $M$ and $N$ with respect to an ideal $mathfrak{a}$ is studied for some $i^{,}s$ witha specified property. Furthermore, Artinianness of $H^{j}_{mathfrak{b}_{0}}(H_{mathfrak{a}}^{i}(M,N))$ is investigated by using the above result, in certain graded situations, where $mathfrak{b}_{0}$ is an idea...

  We consider the maximal covering location-allocation problem with multiple servers. The objective is to maximize the population covered, subject to constraints on the number of service centers, total number of servers in all centers, and the average waiting time at each center. Each center operates as an M/M/k queuing system with variable number of servers. The total costs of establishing cen...

Let A be an associative algebra over C and L an invariant linear functional on it (trace). Let ω be an involutive antiautomorphism of A such that L(ω(a)) = L(a) for any a ∈ A. Then A admits a symmetric invariant bilinear form 〈a, b〉 = L(aω(b)). For A = U(sl(2))/m, where m is any maximal ideal of U(sl(2)), Leites and I have constructed orthogonal basis whose elements turned out to be, essentiall...

‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

Abstract: Let m, n, a1, a2, . . . , ar, b1, b2, . . . , br be integers with 1 ≤ a1 < · · · < ar ≤ m and 1 ≤ b1 < · · · < br ≤ n. And let x be the universal m× n matrix with the property that i-minors of first ai − 1 rows and first bi − 1 columns are all zero, for i = 1, . . . , r+1 (ar+1 := m+1 and br+1 := n+1). For an integer u with 1 ≤ u ≤ m, we denote by U the u×n matrix consisting of the fi...

The backing of the fuzzy ideal is normal ideal in some ring and in same time there fuzzy set whose is not fuzzy ideal and it backing set is ideal, i.e., it crisp is normal ideal. Consequently, in this paper we constructing a fuzziness function which defined on fuzzy sets and assigns membership grade for every fuzzy set whose it backing set are crisp ideal. Now, Let  be collection of all fuzzy s...

A natural generalization of Cohen's set of forcing conditions (the t w ~ valued functions with domain a finite subset of w) is the set of twovalued functions with domain an element of an ideal J on ~. The I~roblem treated in this paper is to determine when such forcing yields a generic real of minimal degree of constructibility. A :;imple decomposition argument shows that the non-maximality of ...

We establish triviality of some holomorphic Banach vector bundles on the maximal ideal space M(H∞) of the Banach algebra H∞ of bounded holomorphic functions on the unit disk D ⊂ C with pointwise multiplication and supremum norm. We apply the result to the study of the Sz.-Nagy operator corona problem. 1. Formulation of Main Results 1.1. We continue our study started in [Br2] of analytic objects...

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...