A note on -bases of rings

Let be a tower of rings of characteristic . Suppose that is a finitely presented -module. We give necessary and sufficient conditions for the existence of -bases of over . Next, let be a polynomial ring where is a perfect field of characteristic , and let be a regular noetherian subring of containing such that . Suppose that is a free -module. Then, applying the above result to a tower of rings, we shall show that a polynomial of minimal degree in is a -basis of over .

     

Completely continuous multilinear operators on spaces

Given a -linear operator from a product of spaces into a Banach space , our main result proves the equivalence between being completely continuous, having an -valued separately continuous extension to the product of the biduals and having a regular associated polymeasure. It is well known that, in the linear case, these are also equivalent to being weakly compact, and that, for , being weakly compact implies the conditions above but the converse fails.

     

新工科视域下物理化学实验的延展性探索*——以二组分固-液相图绘制实验为例

以物理化学实验中二组分固-液相图绘制实验为例,通过科学设计,充分利用实验中步冷曲线数据自动采集的时间,引入大型仪器差示扫描量热仪(DSC)绘制相图的拓展实验。在不显著增加教学课时的前提下,有效促进了科研资源参与人才培养,实现了课堂内容的拓展与延伸,提高了学生的学习热情和实践能力,助力新时代需求的创新型工科人才培养。     

Preparation and properties of aniline chain-extended thermoplastic epoxy resin using triphenylphosphine as catalyst

Thermoplastic resins have been widely used in fiber reinforced polymer composites because of its recyclability and short cycle times. However, the high viscosity after heating and melting restricts its infiltration on the surface of fiber. In this study, a series of thermoplastic epoxy resins were prepared via the chain extension reaction of epoxy groups with liquid aniline using triphenylphosphine (TPP) as catalyst. The relationship between polymer network structure and performance was comprehensively investigated. The solubility tests indicated that excessive aniline or TPP facilitated the crosslinking of resins. Besides, on the premise of thermoplasticity, appropriate TPP could increase the degree of chain extension, molecular weight, and glass transition temperature of resins. Furthermore, the in-situ polymerization process facilitated infiltration between epoxy resin and the fibers before chain extension reaction. The bending test showed that the flexural performance of the sample with 2 phr of TPP was improved by 38.8%. Therefore, this work provides a feasible method to prepare the thermoplastic epoxy resins and its fiber-reinforced composites with good mechanical properties.     

Derivations and Automorphisms of the Positive Part of the Two-parameter Quantum Group Ur,s(B3)

We compute the derivations of the positive part of the two-parameter quantum group U_(r,s)(B_3) and show that the Hochschild cohomology group of degree 1 of this algebra is a threedimensional vector space over the base field C. We also compute the groups of(Hopf) algebra automorphisms of the augmented two-parameter quantized enveloping algebra ?_(r,s)~(≥0)(B_3).     

Edge proximity and matching extension in punctured planar triangulations

A matching $M$ in a graph $G$ is said to be extendable if there exists a perfect matching of $G$ containing $M$. In 1989, it was shown that every connected planar graph with at least $8$ vertices has a matching of size three which is not extendable. In contrast, the study of extending certain matchings of size three or more has made progress in the past decade when the given graph is $5$-connected planar triangulation or $5$-connected plane graphs with few non-triangular faces.In this paper, we prove that if $G$ is a $5$-connected plane graph of even order in which at most two faces are not triangular and $M$ is a matching of size four in which the edges lie pairwise distance at least three apart, then $M$ is extendable. A related result concerning perfect matching with proscribed edges is shown as well.     

基于单元的子区间摄动有限元方法研究

针对区间相关性导致区间扩张的问题,探讨了区间数之间的相关性并给出了降低区间扩张的子区间摄动方法。文中给出了基于单元的子区间摄动有限元计算公式和子区间划分数目的近似计算公式,同时文中讨论了区间有限元计算精度问题,给出了可提高计算效率的一些措施。对桁架结构和平面应力问题梁结构算例分析结果表明文中方法可以达到一定的计算精度,并且是合理可行的。     

SET-VALUED EXTENSION OF OPERATORS VIA STEINER SELECTIONS (Ⅰ)-THEORETICAL RESULTS

A way to extend operators in spaces of continuous functions to spaces of continuous set-valued functions is proposed. This extension is developed through the Steiner selections of the set-valued functions. Their properties and characteristics of the convergence of sequences of operators of this class are studied. In Part Ⅱ of this series some applications to approximation theory will be shown.     

Large-deformation properties of wheat dough in uni- and biaxial extension. Part I. Flour dough

Rheological and fracture properties of optimally mixed flour doughs from three wheat cultivars which perform differently in cereal products were studied in uniaxial and biaxial extension. Doughs were also tested in small angle sinusoidal oscillation. In accordance with previously published results the linear region was found to be very small. The rheological properties at small deformations hardly depended on the cultivar. A higher water content of the dough resulted in a lower value for the storage modulus and a slightly higher value for tan . For both uniaxial and biaxial extension a more than proportional increase in stress was found with increasing strain, a phenomenon called strain hardening. In uniaxial extension (i) stresses at a certain strain were higher and (ii) the stress was less dependent on the strain rate than in biaxial extension. This indicates that in elongational flow orientational effects are of large importance for the mechanical properties of flour dough. This conclusion is consistent with published data on birefringence of stretched gluten. Fracture stress and strain increased with increasing deformation rate. The observed time-dependency of fracture properties can best be explained by inefficient transport of energy to the crack tip. Presumably, this is caused by energy dissipation due to inhomogeneous deformation because of friction between structural elements, e.g. between dispersed particles and the network. Differences in the rheological properties at large deformations between the cultivars were observed with respect to (i) stress, (ii) strain hardening, (iii) strain rate dependency of the stress, (iv) fracture properties and (v) the stress difference between uniaxial and biaxial extension.