L—fuzzy Ring and L—fuzzy Module

Ｌ－ｆｕｚｚｙＲｉｎｇａｎｄＬ－ｆｕｚｚｙＭｏｄｕｌｅＬ－ｆｕｚｚｙＲｉｎｇａｎｄＬ－ｆｕｚｚｙＭｏｄｕｌｅ￥ＳｕｎＲｏｎｇｇｕａｎｇＪｉａｎｇＢａｏｑｉｎｇ（ＨｕｍａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ，４７５００１）ＲｅｎＸｕｅｊｕｎ（Ｍｉｎｑ...     

Calorimetric study of Diepoxide Chain-Extended Poly(Ethylene Terephthalate)

A series of chain-extended PET samples were obtained by the use of different amounts of a diepoxide as chain extender, which was prepared for this purpose. These samples exhibited different intrinsic viscosities and degrees of branching or cross-linking. The effects of this differentiation on the thermal properties were studied by differential scanning calorimetry. The thermal parameters studied were the glass transition temperature (T_g), the cold-crystallization temperature (T_cc), the melting temperature (T_m), the enthalpy (ΔH_m) and the degree of crystallinity. The data revealed that, the higher the quantity of chain extender or the chain extension time, the higher T_gand T_cc, but the lower T_mand ΔH_m, i.e. the more amorphous the chain-extended samples, as also shown by density measurements. This revised version was published online in July 2006 with corrections to the Cover Date.     

聚对苯二甲酸乙二醇酯和聚对苯二甲酸丁二醇酯化学扩链反应

综述了用于聚对苯二甲酸乙二醇酯（ＰＥＴ）、聚对苯二甲酸丁二醇酯（ＰＢＴ）化学扩链反应的羧基加成型和羟基加成型扩链剂，以及缩合型扩链反应、羧基加成型扩链反应和羟基加成型扩链反应、羧羟基同时加成型扩链反应。讨论了扩链反应、反应特性和扩链产物的性能，并简要介绍了国内研究概况。参考文献２０篇。     

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.     

Convergence in Conformal Field Theory

Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. The author reviews some main convergence results, conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras. He also reviews the related analytic extension results, conjectures and problems. He discusses the convergence and analytic extensions of products of intertwining operators (chiral conformal fields) and of q-traces and pseudo-q-traces of products of intertwining operators. He also discusses the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result. He then explains conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.     

Left invariant special Kähler structures

We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial 1-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples.     

An existence result for linear partial differential equations with coefficients in an algebra of generalized functions

We prove the existence of solutions for essentially all linear partial differential equations with -coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy's equation has solutions whenever its right-hand side is a classical -function.

     

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.

     

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.