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...

Let $H$ be a weak Hopf algebra that is finitely generated module over its affine center. We show has finite self-injective dimension and so the Brown--Goodearl Conjecture holds in this special setting.

Let X be a complex manifold. We prove that direct images of principal value and residue currents on are smooth outside sets small in certain sense. also the sheaf such is stalkwise injective OX-module.

The purpose of this paper is to give a constructive algorithm for the computation of bases of finitely presented free modules over the Weyl algebras of differential operators with polynomial or rational coefficients. In particular, we show how to use these results in order to recognize when a multidimensional linear system defined by partial differential equations with polynomial or rational co...

Let φ : (R, m)→ (S, n) be a local homomorphism of commutative noetherian local rings. Suppose that M is a finitely generated S-module. A generalization of Grothendieck’s non-vanishing theorem is proved for M (i.e. the Krull dimension of M over R is the greatest integer i for which the ith local cohomology module of M with respect to m, Hi m(M), is non-zero). It is also proved that the Gorenstei...

Let be a left and right noetherian ring and mod the category of finitely generated left -modules. In this article, we show the following results. 1 For a positive integer k, the condition that the subcategory of mod consisting of i-torsionfree modules coincides with the subcategory of mod consisting of i-syzygy modules for any 1 ≤ i ≤ k is left-right symmetric. 2 If is an -Gorenstein ring and N...

Let Λ be a left and right noetherian ring and modΛ the category of finitely generated left Λ-modules. In this paper we show the following results: (1) For a positive integer k, the condition that the subcategory of modΛ consisting of i-torsionfree modules coincides with the subcategory of modΛ consisting of i-syzygy modules for any 1 ≤ i ≤ k is left-right symmetric. (2) If Λ is an Auslander rin...