A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal...

In this article, we discuss the numerical solution of Bingham-Bratu-Gelfand (BBG) problem, a non-smooth nonlinear eigenvalue problem associated with total variation integral and an exponential nonlinearity. Using fact that one can view as possible Lagrange multiplier constrained minimization from Calculus Variations, associate BBG initial value (dynamical flow), well suited to time-discretizati...

Let F be a local field of characteristic zero. D quaternion algebra over F. E quadratic extension μ character E×. We study the distinction problem for pair (GLn(D);GLn(E)) and we prove that any bi-(GLn(E); μ)-equivariant tempered generalized function on GLn(D) is invariant with respect to an anti-involution. Then it implies dimHomGLn(E)(π; μ) ≤ 1 by Gelfand-Kazhdan criterion. Thus give new proo...

Assembling a gene from candidate exons is an important problem in computational biology. Among the most successful approaches to this problem is spliced alignment, proposed by Gelfand et al., which scores different candidate exon chains within a DNA sequence of length m by comparing them to a known related gene sequence of length n, m = Θ(n). Gelfand et al. gave an algorithm for spliced alignme...

We construct a four-parameter family of Markov processes on infinite Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary of the Gelfand-Tsetlin graph or, equivalently, the space of extreme characters of the infinite-dimensional unitary group U(∞). The process has a unique inva...

Abstract We compute projective dimension of translated simple modules in the regular block Bernstein–Gelfand–Gelfand category $\mathcal{O}$ terms Kazhdan–Lusztig combinatorics. This allows us to determine which projectives can appear at last step a minimal resolution for module, confirming conjecture by Johan Kåhrström. also derive some inequalities, Lusztig’s $\textbf{a}$-function, possible de...

The Harish-Chandra homomorphism is due to [Harish-Chandra 1951]. Attention to universal modules with highest weights is in ]Harish-Chandra 1951], [Cartier 1955], as well as [Verma 1968], [BernsteinGelfand-Gelfand 1971a], [Bernstein-Gelfand-Gelfand 1971b], [Bernstein-Gelfand-Gelfand 1975]. See also [Jantzen 1979]. [1] We treat sl(2) in as simple a style as possible, to highlight ideas. Then sl(3...