Partial Orderings in the Category of Matrices over the Quaternion Field

ＰａｒｔｉａｌＯｒｄｅｒｉｎｇｓｉｎｔｈｅＣａｔｅｇｏｒｙｏｆＭａｔｒｉｃｅｓｏｖｅｒｔｈｅＱｕａｔｅｒｎｉｏｎＦｉｅｌｄＺｈｕａｎｇＷａｊｉｎ（庄瓦金）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈａｎｇＮｏｒｍａｌＣｏｌｌｅｇｅ，Ｆｕｊｉ...     

一类模糊逻辑系统幺半群与同态映射

首先利用代数中幺半群的概念给出了模糊逻辑系统专业领域的概念, 建立专业领域概念的目的是为了规范模糊逻辑系统中语言变量的取值范围, 从而将模糊逻辑系统看作是某个笛卡儿乘积幺半群的有限子集. 然后利用这个笛卡儿乘积幺半群的乘积运算构造了模糊逻辑系统幺半群. 最后, 在一定的约定条件下证明了通常使用的一类Mamdani形模糊逻辑系统的输出可以看作是从模糊逻辑系统幺半群到连续函数域的同态映射.     

代数构造及在Ramsey理论中的应用

这篇文章在伽罗瓦域上的代数构造和关于一些特定类型图的Ramsey数之间建立了一个关系. 研究了关于伽罗瓦域上的代数构造的方程及方程组的解. 我们得到了一些关于二部图的Ramsey数的新的下界和上界.     

On the field of definition for modularity of CM elliptic curves

The purpose of this paper is to decide the conditions under which a CM elliptic curve is modular over its field of definition.     

A multidirectional shear rheometer for polymer melts

A parallel plate shear rheometer for polymer melts was built for superposed shear tests in two orthogonal directions. To examine its performance, a standard test was developed, including a change of the shear direction by angles between 0° and 180°. The results were analyzed to obtain preliminary information on the multidirectional shear behavior of a low-density polyethylene melt. The measured orthogonal components of the shear force were added and then split again into components of the original and of the changed shear direction. It was found, within the range of error, that these components depend only on time and on the shear rate, but not on the angle by which the shear direction is changed. The total shear rate was 0.56 s^–1.Dedicated to Prof. Dr. Joachim Meissner on the occasion of his 60th birthday.     

Singular Functions and Characterizations of Field Concentrations: a Survey

In the presence of closely located inclusions of the extreme material property, the physical fields, such as the electric field and the stress tensor, may be concentrated and arbitrarily large in the narrow region between two inclusions. Recently there has been significant progress on the quantitative characterization of the field concentration in the contexts of electrostatics(Laplace equation), linear elasticity(Lamé system), and viscous flow(Stokes system). This paper is to review such progress in a coherent way.     

A single theory for some quasi-static,supersonic, atomic,and tectonic scale applications of dislocations

We describe a model based on continuum mechanics that reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity. As applications, we explore the questions of the existence of a Peierls stress in a continuum theory, dislocation annihilation, dislocation dissociation, finite-speed-of-propagation effects of elastic waves vis-a-vis dynamic dislocation fields, supersonic dislocation motion, and short-slip duration in rupture dynamics.     

Dynamics of the infinitely-thin kink

We consider the dynamics of the domain-wall kink soliton, in particular we study the zero mode of translation. In the infinitely-thin kink limit, we show that the zero mode is almost completely frozen out, the only remnant being a dynamically constrained four-dimensional mode of a single but arbitrary frequency. In relation to this result, we show that the usual mode expansion for dealing with zero modes - implicit collective coordinates - is not in fact a completely general expansion, and that one must use instead a traditional generalised Fourier analysis.