关于某些多边形积的剩余有限性

讨论嵌入子群是循环群的有限p-群的多边形积,得到了多边形积为剩余有限的一个充分条件.     

非定常对流扩散方程保正格式解的存在性

本文发展了非定常对流扩散方程的非线性保正格式.该格式为单元中心型有限体积格式,保持局部通量的守恒性,适用于任意星形多边形网格,本文证明了该离散格式解的存在性,并给出数值结果,表明该格式具有二阶精度.     

多边形外角和定理应用举例

<正>我们知道,"多边形的外角和等于360°."它反映了多边形的本质特征(与边数无关).据此,我们可以解决一些与多边形的内角及外角有关的问题,举例说明.例1一个多边形的每一个内角均为150°,求它的边数.解由多边形的每一个内角均为150°,得该多边形的每一个外角均为30°.根据"多边形的外角和等于360°",可知该多边形的边数为     

非定常扩散方程的单元中心型有限体积格式

本文基于调和平均点建立了一种新的单元中心型有限体积格式,用以求解非定常扩散方程.在网格边上离散法向流时,选择该网格边两端点和该边上的一个调和平均点作为辅助插值点,并将这些辅助插值点上的未知量用网格单元中心点的未知量进行替换,最终得到一个只含网格单元中心未知量的有限体积格式.该格式满足线性精确性质和局部守恒性,且适用于任意多边形网格.在六种不同的多边形网格上进行四个数值实验,分别考虑扩散系数是连续的和间断的以及非线性的情况,数值结果表明:本文所构造的格式在六种网格上的L2误差均可达到二阶收敛精度,对于不同类型的扩散系数,该格式保持良好的鲁棒性,并且从编程实现的角度来说,该格式更易于向三维情况推广.     

多边形与多面体的几何特性计算

本文推导了几个积分公式,以计算任意多边形与任意多面体的几何特性。其结果可用于有限单元法的分析计算中,以确定各种高阶单元的劲度矩阵与广义力;也可用于各种动力机械基础的计算中,以确定基础的形心,惯矩等。     

折线基本性质初探

为了从整体上掌握众多直线形的特征,应对折线的结构性质作一般考查,本文着重探讨平面折线的若干基本性质 1 折线的一般性质平面上一些线段顺次首尾相接构成的图形称为平面折线,我们约定,任何端点不在另外的线段上,构成折线的线段称为边,线段的端点称为顶点,共顶点的两边称为邻边,共边二顶点称为邻顶点,如果折线每条边都有两条邻边,就称为封闭折线,否则为开折线。定理1 n边封闭折线有n个顶点;n边开折线有n 1个顶点。边不相交的折线称为简单折线,简单封闭折线称为多边形,多边形划分平面的两部分,其中有限部分称为多边形内部,不难证明。定理2 n边形内部可用不相交的对角线划分为     

正多边形的一种扩展及扩展后的面积求解

<正>《中学生数学》2007年7月(上)25页刊登的《多边形扩展后的面积问题》一文中介绍了一种将一个三角形扩展而成新的三角形的办法,该文把这种办法推广到多边形的情况,求解得到新的多边形与原多边形的面积关系.笔者受其启发,在下面给出一种正多边形的扩展方式,求解扩展前后多边形的面积关系问题.     

探求凸多边形的外角和

凸多边形的一边与另一边的延长线所组成的角,叫做多边形的外角,我们知道任意多边形的外角和等于360°.这个结论说明多边形的外角和与多边形的边数n无关,是一个固定不变的量360°.就让我们从不同的角度一起回顾和感受其探索的过程吧.     

多边形外角和定理的妙用

多边形的内角和与边数的多少有密切的关系,而多边形的外角和恒等于360°,与边数无关才更好地反映了多边形的深层特征.解题时,若能把多边形的“内角”问题与多边形的“外角”问题结合起来,则可达到“化难为易、化繁为简”的效果.     

关于圆和椭圆逼近显示的最优算法(英文)

本文给出了一个逼近显示圆的新算法。该算法是通过相交多边形而不是内接多边形逼近圆。由于构造相交多边形时其面积等于圆面积 ,因此新算法是最优逼近。同时还推广到椭圆     

模糊有限自动机的乘积覆盖性

推广模糊有限自动机的有限积,包括direct infinite乘积、cascade infinite乘积和wreath infinite 来积.进而讨论它们之间的关系,得到乘积覆盖性等代数性质.     

关于Brauer指标乘积的一个注记

给出在一定条件下不可约Brauer指标乘积的分解形式,并与不可约常指标乘积相比较,由此说明Brauer指标乘积的不可约分解有其自身的特点.     

The distribution function inequality for a finite sum of finite products of Toeplitz operators

A generalized area function associated with a finite sum of finite products of Toeplitz operators is introduced. A distribution function inequality is established for the generalized area function. By using the distribution function inequality, we characterize when a finite sum of finite products of Toeplitz operators on the Hardy space is a compact perturbation of a Toeplitz operator.     

Reaching the minimum ideal in a finite semigroup

We introduce the depth parameters of a finite semigroup, which measure how hard it is to produce an element in the minimum ideal when we consider generating sets satisfying some minimality conditions. We estimate such parameters for some families of finite semigroups, and we obtain an upper bound for wreath products and direct products of two finite (transformation) monoids.     

Subdirect products of finitely presented metabelian groups

There has been substantial investigation in recent years of subdirect products of limit groups and their finite presentability and homological finiteness properties. To contrast the results obtained for limit groups, Baumslag, Bridson, Holt and Miller investigated subdirect products (fibre products) of finitely presented metabelian groups. They showed that, in contrast to the case for limit groups, such subdirect products could have diverse behaviour with respect to finite presentability.We show that, in a sense that can be made precise, ‘most’ subdirect products of a finite set of finitely presented metabelian groups are again finitely presented. To be a little more precise, we assign to each subdirect product a point of an algebraic variety and show that, in most cases, those points which correspond to non-finitely presented subdirect products form a subvariety of smaller dimension.     

套代数上Lie同态的一个局部刻画（英文）

In this paper,linear maps preserving Lie products at zero points on nest algebras are studied.It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism.As an application,the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained.     

Finite products are biproducts in a compact closed category

If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.     

Bicrossed Products for Finite Groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.     

Inventory decisions for a finite horizon problem with product substitution options and time varying demand

The inventory control of substitutable products has been recognized as a problem worthy of study in the operations management literature. Product substitution provides flexibility in supply chain management and enhances response time in production control. This paper proposes a finite horizon inventory control problem for two substitutable products, which are ordered jointly in each replenishment epoch. Demand for the products are assumed to be time–varying. In case of a stock–out for one of the products, its demand is satisfied by using the stock of the other product. The optimal ordering schedule, for both products, that minimizes the total cost over a finite planning horizon is derived. Numerical examples along with sensitivity analyses are also presented.