Length two extensions of modules for the Witt algebra

In this paper, we establish an explicit classification of length two extensions of tensor modules for the Witt algebra using the cohomology of the Witt algebra with coe?cients in the module of the space of homomorphisms between the two modules of interest. To do this we extended our module to a module that has a compatible action of the commutative algebra of Laurent polynomials in one variable. In this setting, we are be able to directly compute all possible 1-cocycles.     

Regular Substructures of Hom

Extending the notion of von Neumann regular elements in a ring R, a homomorphism f:A→M between R-modules is said to be regular if there exists some g:M → A such that fgf = f. In this paper we report about the use of this term in module theory.      

Fractionation of human plasma proteins by hydrophobic interaction membrane chromatography

This paper discusses the fractionation of human plasma proteins HSA and HIgG by hydrophobic interaction membrane chromatography. A type of microporous polyvinylidine fluoride (PVDF) membrane having 0.1 μm pore size was identified as being suitable for carrying out this separation. This membrane bound HIgG at 1.5 M ammonium sulphate concentration, a condition at which HSA did not. Based on this selective binding resulting from the selective pressure induced by the high anti-chaotropic salt concentration, these human plasma proteins were fractionated. The HIgG binding capacity of the PVDF membrane examined in this study was 42.8 mg/ml at a feed concentration of 0.45 mg/ml. Separation of simulated HSA/HIgG mixtures were carried out in the pulse and step input modes and the HSA and HIgG fractions thus obtained were analysed for purity using affinity chromatography and SDS-PAGE. HSA and HIgG purities were typically in excess of 97–98%.     

On the generalized Hyers-Ulam stability of module left derivations

Let A be a unital normed algebra and let M be a unitary Banach left A-module. If f:A→M is an approximate module left derivation, then f:A→M is a module left derivation. Moreover, if M=A is a semiprime unital Banach algebra and f(tx) is continuous in t∈R for each fixed x in A, then every approximately linear left derivation f:A→A is a linear derivation which maps A into the intersection of its center Z(A) and its Jacobson radical rad(A). In particular, if A is semisimple, then f is identically zero.     

Smoothness and differentials in positive characteristic

Let u: A → B be a morphism of noetherian local rings. It is known that if u is formally smooth, then Ω _B|A is formally projective. We give several cases in which the converse is true, in the case of rings containing a field of positive characteristic. Work supported by the CEEX program of the Romanian Ministry of Education and Research, Contract 2-CEx06-11-20/2006.     

On the spectrum of almost periodic solution of second order scalar functional differential equations with piecewise constant argument

We study the spectrum containment of almost periodic solution to neutral delay differential equations with piecewise constant argument (EPCA, for short). We find an important property, which is different from that given by Cartwright for ordinary differential equations (ODE). Some known (periodic solution) results would be expanded. As a corollary, it is shown that EPCA with periodic perturbations possess a quasi-periodic solution and no periodic solution. This new phenomenon is due to the piecewise constant argument and illustrates a crucial difference between ODE and EPCA.     

三维正交机织复合材料的力学性能研究

利用材料试验机装置开展了三维正交机织Kevlar/乙烯基树脂复合材料力学实验,实验表明面内经向拉伸和厚度z方向压缩时,材料具有一定的应变率效应,厚度z方向压缩强度远大于面内压缩强度,而面内经向和纬向的拉伸强度则相当.结合纤维的编织方式,对这些现象做了必要的定性分析.最后,本文基于三维正交机织复合材料的结构特点,推导了一组可用于估算三维正交机织复合材料弹性模量的公式,估算结果和实验值接近.     

K[X]~m中模的生成基及其应用

本文研究了多项式环上的素模中的生成基理论和方法．通过建立新的约化准则,得到了模中生成基的结构和机械化计算方法．对于低维情形给出了素模中生成基的充分必要条件．文中的方法本质地简化了传统的模中Ｇｒｏｂｎｅｒ基方法．文中同时介绍了该方法在样条理论研究中的应用,并给出了一些计算例子．     

系数在模李超代数~$W(m,3,\underline{1})$ 上的~$\frak{gl}(2,\mathbb{F})$ 的一维上同调

研究了系数在模李超代数~$W(m,3,\underline{1})$ 上的~$\frak{gl}(2,\mathbb{F})$ 的一维上同调, 其中~$\mathbb{F}$ 是一个素特征的代数闭域且~$\frak{gl}(2,\mathbb{F})$ 是系数在~$\mathbb{F}$ 上的~$2\times 2$ 阶矩阵李代数. 计算出所有~$\frak{gl}(2,\mathbb{F})$ 到模李超代数~$W(m,3,\underline{1})$ 的子模的导子和内导子. 从而一维上同调~$\textrm{H}^{1}(\frak{gl}(2,\mathbb{F}),W(m,3,\underline{1}))$ 可以完全用矩阵的形式表示.     

Module Homomorphisms on Random Normed Modules

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