紧致交换矩阵半群

通过将矩阵同时对角化或同时上三角化的方法,给出有关紧致Abel矩阵半群以及紧致Hermite矩阵半群中矩阵的特征值的一些很好的刻画,证明了由可逆的Hermite矩阵构成的紧致矩阵半群中每个矩阵的特征值都是±1,Hermite矩阵单半群相似于对角矩阵半群,紧致交换矩阵半群的谱半径不超过1,等等.     

The k‐piece packing problem

A k‐piece of a graph G is a connected subgraph of G all of whose nodes have degree at most k and at least one node has degree equal to k. We consider the problem of covering the maximum number of nodes of a graph by node disjoint k‐pieces. When k = 1 this is the maximum matching problem, and when k = 2 this is the problem, recently studied by Kaneko [ 19 [, of covering the maximum number of nodes by disjoint paths of length greater than 1. We present a polynomial time algorithm for the problem as well as a Tutte‐type existence theorem and a Berge‐type min‐max formula. We also solve the problem in the more general situation where the “pieces” are defined in terms of lower and upper bounds on the degrees. © 2006 Wiley Periodicals, Inc. J Graph Theory     

Projective Representations and Pure Pseudorepresentations of Hermitian Symmetric Simple Lie Groups

It is shown that an arbitrary irreducible continuous unitary projective representation of a simple Hermitian symmetric Lie group is generated by a strongly continuous pure unitary pseudorepresentation of the adjoint group of the Lie group.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 140–146.Original Russian Text Copyright © 2005 by A. I. Shtern.     

Towards the Actual Relationship Between NP and Exponential Time

We consider the relationship between the computational complexity classes NP and EL (deterministic exponential linear time). Taking into account the inclusion or incomparability of these classes, the existence or nonexistence of immune sets in their differences, and the existence or nonexistence of sparse sets in the differences, there are exactly 24 different cases for their relationship. We show that 16 cases are impossible in the real nonrelativized world as well as in any relativized world. Each of the remaining 8 cases is realizable in appropriate relativized worlds. Further we examine which of the 8 cases is most probably for a random oracle.     

影响单摆振动周期的参数研究

应用振动分析的方法,研究了单摆的周期受摆角、摆球的线度、地球纬度、摆球离地面的高度、介质黏度和介质密度参数的影响;作出了周期比随参数变化的曲线.结果表明:单摆的周期随摆角、摆球的线度、摆球离地面的高度、介质黏度和介质密度的增大而增大,随地球纬度的增大而减小.     

An information-based traffic control in a public conveyance system: Reduced clustering and enhanced efficiency

A new public conveyance model applicable to buses and trains is proposed in this paper by using stochastic cellular automaton. We have found the optimal density of vehicles, at which the average velocity becomes maximum, significantly depends on the number of stops and passengers behavior of getting on a vehicle at stops. The efficiency of the hail-and-ride system is also discussed by comparing the different behavior of passengers. Moreover, we have found that a big cluster of vehicles is divided into small clusters, by incorporating information of the number of vehicles between successive stops.     

建筑工程中混凝土质量控制系统的应用

建设项目混凝土质量控制是一个庞大的系统工程.为提高施工阶段混凝土质量控制效果,详细地分析并分解了混凝土施工过程中可能遇到的各种影响质量的因素,采用VFp 6.0研制了对这些因素进行综合控制的软件.软件采用五个子系统,力求操作简便,结合生产实际,以适于领导者指挥生产总结提高和工程技术人员计算与控制之用.     

A sense-making approach to proof: Strategies of students in traditional and problem-based number theory courses

This paper reports the results of an exploratory study of the perceptions of and approaches to mathematical proof of undergraduates enrolled in lecture-based and problem-based “transition to proof” courses. While the students in the lecture-based course demonstrated conceptions of proof that reflect those reported in the research literature as insufficient and typical of undergraduates, the students in the problem-based course were found to hold conceptions of and approach the construction of proofs in ways that demonstrated efforts to make sense of mathematical ideas. This sense-making manifested itself in the ways in which students employed initial strategies, notation, prior knowledge and experiences, and concrete examples in the proof construction process. These differences were also seen when students were asked to determine the validity of completed proofs. These results suggest that such a problem-based course may provide opportunities for students to develop conceptions of proof that are more meaningful and robust than does a traditional lecture-based course.     

Optimization problems for general simple population with n-impulsive harvest

In this paper, n-impulsive harvest problems of general simple population are discussed by models with Dirac function. The optimal impulsive harvest policies to protect the renewable resource better are obtained under conditions of fixed quantity per impulsive harvest. Then, a concept of the sequence for ?-optimal harvest moments for general simple population is presented which is beneficial to protect resource better and sustainable development. Finally, we apply the conclusions to some special models.     

经济数学基础精品课程的建设与教学实践

介绍了安徽省精品课程《经济数学基础》课程建设的主要成果.其中包括教学内容的改革,教材和教辅材料的建设,教学方法和教学手段的改革以及实践性教学环节和教学科研的成果.