Some relations on completely regular semigroups

A semigroup S is called a Clifford semigroup if it is completely regular and inverse. In this paper, some relations related to the least Clifford semigroup congruences on completely regular semigroups are characterized. We give the relation between Y and ξ on completely regular semigroups and get that Y ^* is contained in the least Clifford congruence on completely regular semigroups generally. Further, we consider the relation Y ^*, Y, ν and ε on completely simple semigroups and completely regular semigroups. This work is supported by Leading Academic Discipline Project of Shanghai Normal University, Project Number: DZL803 and General Scientific Research Project of Shanghai Normal University, No. SK200707.     

Reflections, Rotations, and Pythagorean Numbers

In this article, simple reflections, rotations and the Cartan theorem are handled using Clifford algebras. With this tool we provide a constructive proof of the Cartan theorem and the relationship with Pythagorean numbers is discussed.      

SYMBOLIC VERSOR COMPRESSION ALGORITHM

In an inner-product space, an invertible vector generates a reflection with respect to a hyperplane, and the Clifford product of several invertible vectors, called a versor in Clifford algebra, generates the composition of the corresponding reflections, which is an orthogonal transformation. Given a versor in a Clifford algebra, finding another sequence of invertible vectors of strictly shorter length but whose Clifford product still equals the input versor, is called versor compression. Geometrically, versor compression is equivalent to decomposing an orthogonal transformation into a shorter sequence of reflections. This paper proposes a simple algorithm of compressing versors of symbolic form in Clifford algebra. The algorithm is based on computing the intersections of lines with planes in the corresponding Grassmann-Cayley algebra, and is complete in the case of Euclidean or Minkowski inner-product space.     

基于复眼透镜的大面积均匀照明方案研究

为了实现大面积矩形均匀光斑,提出一种基于双排复眼透镜的设计方案。使用TracePro软件对该照明系统方案的效果进行建模仿真,分析了复眼透镜组的间距、后工作距离等参数对光斑面积和均匀性的影响。结果表明,复眼透镜间距越小、后工作距离越大,得到的光斑面积越大;而当间距控制在微透镜焦距附近时,光斑均匀性最佳。利用该设计方案,可在1 m的后工作距离得到尺寸350 mm200 mm的光斑,光斑中心280 mm160 mm范围内光照度均匀性＞0.85,该部分面积超过光斑整体面积的60%。该匀光方案有望在医用光疗、路灯照明等大面积均匀光照明领域得到广泛应用。     

The approximate solution of Riemann type problems for Dirac equations by Newton embedding method

We study an existence and uniqueness for the nonlinear Riemann type problem and also give an error estimation for the approximate solutions in the Newton embedding procedure in higher dimensional spaces. Clifford analysis plays a key role in our approach.     

A block‐centered finite difference method for fractional Cattaneo equation

In this article, a block‐centered finite difference method for fractional Cattaneo equation is introduced and analyzed. The unconditional stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norm with optimal order of convergence both for pressure and velocity are established on nonuniform rectangular grids. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.     

乘法半群为正规纯整群的半环

乘法半群为正规纯整群[矩形群]的半环类记为NBG(eG).本文主要研究了NBG中半环的一些性质和它的坚固框架结构.     

E-自反逆半群上的Clifford同余

研究E-自反逆半群上的Clifford同余.本文中的结果是James[1],McAlister[2],Petrich[3]和Reilly[4]等人关于E-酉逆半群上的相应同余定理在E-自反逆半群上的自然推广.     

高斯光束照射下与矩孔相关的孔径衍射

依据基尔霍夫衍射理论,利用幂级数展开的方法,推导出傍轴条件下高斯光束的矩孔及单缝衍射的近似计算公式,并通过数值计算、数值模拟等方法对衍射场的基本特性进行了讨论。     

长方腔自然对流第一次分岔突变现象的数值分析

在对网格密度作用进行详细分析的基础上,采用二阶全展开 Euler-Taylor-Galerkin分裂步有限元方法,对封闭水平矩形腔体内流体 (Pr=0.71)自然对流的第一次分岔过程进行了数值预报. 计算结果表明,第一次分岔相应的流动拓扑及临界Rayleigh ($Ra$)数随矩形腔体长宽比(W/B)取值的不同时会发生较大变化. 在所计算的长宽比取值范围内,封闭矩形腔内,流体自然对流第一次分岔拓扑的变化对应两种大的类型: 在较小的长宽比取值范围内(W/B\le 2.5),临界Ra数两侧,流动从单一涡核的定常流动突变成为具有不对称结构的定常双涡核运动, 在此范围内临界Ra数的取值随W/B取值的增加而减小;当对应长宽比取值2.6 \le W/B \le 4.0时,第一次分岔拓扑结构的变化呈现出更加复杂的特性,临界Ra数两侧流动从定常双涡核突变为定常非对称的三涡核流动,相应的临界Ra 数也随W/B的增加而减少. 而在区间[2.5,2.6]两端,临界Ra数的取值发生一次阶跃式突增,将该长宽比取值的区间定义为长方腔内该流体第一次分岔的突变区间.