Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let g I be the corresponding semi-simple subalgebra of g. Denote by W I the Weyl group of g I and let w • and w I • be the longest elements of W and W I , respectively. In this paper we show that the answer to Kostant's problem, i.e. whether the universal enveloping algebra surjec...

Every simple module having character height at most one for a restricted Cartantype Lie algebra g can be realized as a quotient of a module obtained by starting with a simple module S for the homogeneous component of degree zero in the natural grading of g, extending the action trivially to positive components and inducing up to g. It is shown that if S is not restricted, or if it is restricted...

â a model is developed for separation of multicomponent gas mixtures in a countercurrent hollow fiber membrane module. while the model’s solution in countercurrent module usually involves in a time consuming iterative procedure, a proper initial guess is proposed for beginning the calculation and a simple procedure is introduced for correcting the guesses, hereby the cpu time is decreased ess...

Let $M_R$ be a non-zero‎ ‎module and ${mathcal F}‎: ‎sigma[M_R]times sigma[M_R]‎ ‎rightarrow$ Mod-$Bbb{Z}$ a bifunctor‎. ‎The‎ ‎$mathcal{F}$-reversibility of $M$ is defined by ${mathcal‎ ‎F}(X,Y)=0 Rightarrow {mathcal F}(Y,X)=0$ for all non-zero $X,Y$‎ ‎in $sigma[M_R]$‎. ‎Hom (resp‎. ‎Rej)-reversibility of $M$ is‎ ‎characterized in different ways‎. ‎Among other things‎, ‎it is shown‎ ‎th...

 A model is developed for separation of multicomponent gas mixtures in a countercurrent hollow fiber membrane module. While the model’s solution in countercurrent module usually involves in a time consuming iterative procedure, a proper initial guess is proposed for beginning the calculation and a simple procedure is introduced for correcting the guesses, hereby the CPU time is decreased ess...

There are well-known constructions of the exceptional simple Lie algebras of type E8 and F4 which go back to Witt [Wit41], as Z2-graded algebras g = g0̄⊕g1̄ with even part the orthogonal Lie algebras so16 and so9 respectively, and odd part given by their spin representations (see [Ada96]). Brown [Bro82] found a new simple finite dimensional Lie algebra over fields of characteristic 3 which presen...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

Let A be an associative algebra over a field K such that the dimension, [A:P], of A over K is finite. Following the terminology of [8], we shall say that A is of bounded module type if there exists an integer re such that for every indecomposable left A-module M, the inequality [M: K] zí re holds. The algebra A is of finite module type if A has only a finite number of nonisomorphic indecomposab...