Haisheng Li showed that given a module (W,YW (·, x)) for a vertex algebra (V, Y (·, x)), one can obtain a new V -module W = (W,YW (Δ(x)·, x)) if Δ(x) satisfies certain natural conditions. Li presented a collection of such Δ-operators for V = L(k, 0) (a vertex operator algebra associated with an affine Lie algebra, k a positive integer). In this paper, for each irreducible L(k, 0)-module W , we ...

comIn the present study, CO2 removal from natural gas stream has been studied using a flat sheet membrane contactor. A three dimensional mathematical model is developed to describe the process. The model considers the transport of a gas mixture containing carbon dioxide and methane through a flat sheet membrane contactor module. The model is based on the non-wetted mode of operation, in which t...

Let G be a simple algebraic group over C with the Weyl group W . For a unipotent element u ∈ G, let Bu be the variety of Borel subgroups of G containing u. Let L be a Levi subgroup of a parabolic subgroup of G with the Weyl subgroup WL of W . Assume that u ∈ L and let B L u be a similar variety as Bu for L. We describe, for a certain choice of u ∈ L and e ≥ 1, the W -module ⊕ n≡k mod e H2n(Bu) ...

Suppose R and S are local rings and (R,m) → (S,n) is a flat local homomorphism. Given a finitely generated S-module N , we say N is extended (from R) provided there is an R-module M such that S ⊗R M is isomorphic to N as an S-module. If such a module M exists, it is unique up to isomorphism (cf. [EGA, (2.5.8)], and it is necessarily finitely generated. The m-adic completion R → R̂ and the Hensel...

The energy resources of nature are limited. According to the report from the International Energy Agency (IEA), there is 19% of the energy used for illumination. It's well known that LED is an excellent choice to instead the incandescent lamp for saving energy. But the other question comes out while the high power LED is applied. There is only about 20% of the input power converts to light ener...

Our aim in the present article is to introduce and study new types of retractions of closed flat Robertson-Walker W model. Types of the deformation retract of closed flat Robertson-Walker W model are obtained. The relations between the retraction and the deformation retract of curves in W model are deduced. Types of minimal retractions of curves in W model are also presented. Also, the isometri...

Let A d be the complex polynomial ring in d variables. A contractive A d-module is Hilbert space H equipped with an A d action such that for any ξ 1 , ξ 2 ,. Such objects have been shown to be useful for modeling d-tuples of mutually commuting operators acting on a Hilbert space. An example is given by H 2 d , which is the Hilbert space of holomorphic functions on B d = {z ∈ C d : |z| ≤ 1} gene...

Let A be a Z-graded associative algebra and let ρ be an irreducible N-graded representation of A on W with finite-dimensional homogeneous subspaces. Then it is proved that ρ(Ã) = glJ (W ), where à is the completion of A with respect to a certain topology and glJ (W ) is the subalgebra of EndW , generated by homogeneous endomorphisms. It is also proved that an N-graded vector space W with finite...

1.1. Setup. In this talk k is a field of characteristic 0. Let (W,S) be a Coxeter group with |S| = n < ∞. Also we let V = ∑ s∈S kes be the reflection representation of W , and R = k[V ]. R is a graded algebra with V ∗ in degree 2. We abbreviate M ⊗R N = MN for a right R-module M and a left R-module N . We let {αs}s∈S be the dual basis of {es}s∈S , which can be considered as elements in V ∗ ⊂ R....

Let Y denote a D-class symmetric association scheme with D ≥ 3, and suppose Y is almostbipartite Pand Q-polynomial. Let x denote a vertex of Y and let T = T (x) denote the corresponding Terwilliger algebra. We prove that any irreducible T -module W is both thin and dual thin in the sense of Terwilliger. We produce two bases for W and describe the action of T on these bases. We prove that the is...