关于拟AP内射模的一些研究

Let R be a ring. R is called right AP-injective if, for any a ∈ R, there exists a left ideal of R such that lr(a) = Ra (?) Xa. We extend this notion to modules. A right .R-module M with 5 = End(MR) is called quasi AP-injective if, for any s ∈ S, there exists a left ideal Xs of S such that ls(Ker(s)) = Ss (?) Xs. In this paper, we give some characterizations and properties of quasi AP-injective modules which generalize results of Page and Zhou.     

L—fuzzy Ring and L—fuzzy Module

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High performance polyethersulfone UF membrane for manufacturing spiral wound module: preparation,morphology, performance,and chemical cleaning

Large sheet asymmetric polyethersulfone (PES) ultrafiltration membranes were prepared via phase inversion process in a continuous conveyor system with addition of PVP to the casting solution. Dimethylacetamide (DMAc) and mixture of water and isopropyl alcohol (70/30 v%) were used as solvent and non‐solvent respectively. The prepared membrane was 0.96 m wide and 3 m long. The pieces of the membrane were selected randomly for characterization in terms of performance using cross flow filtration for milk concentration, image analysis, scanning electron microscopy (SEM), and cleaning procedures. It was found that the prepared membrane has high porosity and high water flux during milk filtration. In addition, cleaning experiments indicated that NaOH/HCl/NaOH sequence is an effective procedure for cleaning the fouled membrane during milk concentration. Copyright © 2007 John Wiley & Sons, Ltd.     

Mass transfer and benzene removal from air using latex rubber tubing and a hollow-fiber membrane module

A dense-phase latex rubber tube and a polyporous propylene hollow-fiber membrane module (HFMM) were investigated for control of benzene-contaminated gas streams. The abiotic mass flux observed through the latex tube was 3.9–13 mg/(min·m²) for 150 ppm of benzene at various gas and liquid flow rates, while a 100-fold lower mass flux was observed in the HFMM. After seeding with an aromatic-degrading culture enriched from activated sludge, the observed removal was 80% of 150 ppm, corresponding toa mass flux of 45 mg/(min·m²). The observed mass flux through the HFMM during biofiltration also rose, to 0.4 mg/(min·m²). Because the HFMM had a 50-fold higher surface area than the latex tube, the observed ben zene removal was 99.8%. Compared to conventional biofilters, the two reactors had modest elimination capacities, 2.5–18 g/(m³·h) in the latex tube membrane bioreactor and 4.8–58 g/(m³·h) in the HFMM. Although the HFMM had a higher elimination capacity, the gas-phase pressure drop was much greater.     

Axiomatizing subcategories of Abelian categories

We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated.     

Gorenstein AC亏范畴*

作者定义了Gorenstein AC导出范畴 D^b_gac(R)并且和导出范畴作了一些比较.作者定义了Gorenstein AC奇点范畴 D^b_gacsg(R),在这个范畴中具有有限Gorenstein AC- 投射维数的模都是零对象.同时, 作者给出了由Gorenstein AC- 投射模构成的稳定范畴到奇点范畴的三角嵌入 F : GAC → D^b_sg(R) .通过作函子 F 的商引入Gorenstein AC亏范畴 D^b_gacd(R),并且给出三角等价 D^b_gacd(R) = D^b_gacsg(R)     

Tensor products over abelian Walgebras

Tensor products of Calgebras over an abelian Walgebra are studied. The minimal Cnorm on is shown to be just the quotient of the minimal Cnorm on if or is exact.

     

Generalized logic and the representation of rings

Following the progression towards weaker logics, a number of authors have considered the notion of a sheaf over a quantale or, equivalently, a quantale valued set. In this paper, we use ideas from enriched category theory to motivate the definition of a quantic sheaf. Given a localic subquantale of Q, a quantic sheaf over Q gives a sheaf in the usual sense. As an application, we derive a series of sheaf representations for commutative rings including the familiar Pierce representation.     

A closed model category for ()-connected spaces

For each integer , we give a distinct closed model category structure to the category of pointed spaces such that the corresponding localized category is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to is based on maps which induce isomorphisms on all homotopy group functors and for any choice of base point. For each , the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on for .

     

Fractional Power Series and Pairings on Drinfeld Modules

Let be an algebraically closed field containing which is complete with respect to an absolute value . We prove that under suitable constraints on the coefficients, the series converges to a surjective, open, continuous -linear homomorphism whose kernel is locally compact. We characterize the locally compact sub--vector spaces of which occur as kernels of such series, and describe the extent to which determines the series. We develop a theory of Newton polygons for these series which lets us compute the Haar measure of the set of zeros of of a given valuation, given the valuations of the coefficients. The ``adjoint' series converges everywhere if and only if does, and in this case there is a natural bilinear pairing

which exhibits as the Pontryagin dual of . Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module.