It is proved that an irreducible quasifinite W∞-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight W∞module is a module of the intermediate series. For a nondegenerate additive subgroup Γ of F, where F is a field of characteristic zero, there is a simple Lie or associative algebra W(Γ, n)(1) spanned by differential opera...

Let R be a right GF -closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorenstein ring R, the G...

We prove various extensions of the Local Flatness Criterion over a Noetherian local ring R with residue field k. For instance, if Ω is a complete R-module of finite projective dimension, then Ω is flat if and only if Torn (Ω, k) = 0 for all n = 1, . . . , depth(R). In low dimensions, we have the following criteria. If R is onedimensional and reduced, then Ω is flat if and only if Tor1 (Ω, k) = ...

Background and Objectives: Pomegranate juice (PJ) contains large particles that stick to evaporator walls causing off flavors in the concentrate due to burning. Microfiltration is used to clarify PJ. Fouling is a limiting phenomenon that can prevent the industrialization of membrane clarification. Changes in the geometry of the membrane module such as using baffles are useful to decrease this p...

This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay the foundation for this study. For any vector space W , we study what we call quasi compatible subsets of Hom(W,W ((x))) and we prove that any maximal quasi compatible subspace has a natural nonlocal (namely noncom...

For a nondegenerate additive subgroup Γ of the n-dimensional vector space IF over an algebraically closed field IF of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type W(Γ, n) spanned by all differential operators uD1 1 · · ·D mn n for u ∈ IF [Γ] (the group algebra), and m1, ...,mn ≥ 0, where D1, ...,Dn are degree operators. In this paper, it is proved that an ...

The lamination of OPV modules to corrugated roof cladding has been undertaken. The 3-dimensional form of the cladding provides three advantages for outdoor OPV deployment; firstly the ‘footprint’ of the solar cell is reduced, which leads to B10% improved power conversion (PCE) efficiency per unit area. Secondly, the oblique angle performance is enhanced, leading to increased output in the early...

Let R be a ring. A right R-module is said to C-flat if the kernel of any epimorphism B → C-pure in B, i.e. induced map Hom(C,B) Hom(C,A) surjective for cyclic C. Projective modules are and weakly-flat neat-flat. In this article, it discussed connections between C-flat, weakly-flat, neat-flat singly flat modules. It shown that coincide with singly-projective over arbitrary rings. Next, several c...

We define and study generalized nil-Coxeter algebras associated to Coxeter groups. Motivated by a question of Coxeter (1957), we construct the first examples of such finite-dimensional algebras that are not the ‘usual’ nil-Coxeter algebras: a novel 2-parameter type A family that we call NCA(n, d). We explore several combinatorial properties of NCA(n, d), including its Coxeter word basis, length...