布尔矩阵的指标格的性质

介绍了布尔矩阵的行零元、列零元和相容子矩阵的定义并讨论了它们的性质,给出了布尔矩阵的指标格分别为分配格、半分配格和半模格的等价条件.     

形式三角矩阵环的零因子图

本文研究了形式三角矩阵环的零因子结构与零因子图的问题.利用零因子的性质及交换环零因子图的有关结论及分类讨论的方法,获得了形式三角矩阵环的零因子图直径为2的充要条件,推广了有限交换环的零因子图的相关结果.     

零积决定的三角代数

本文研究了三角代数是否是零积决定的代数的问题.利用零积决定的代数的等价条件和代数方法,获得了三角代数是零积决定的代数的条件,推广了矩阵代数是零积决定的代数的结果.作为应用,得到零积决定的代数的零积导子一定是准导子.     

零截断及零调整离散模型的计数数据分析方法的新进展之综述研究

在社会学、心理学、生态学、保险学、医学、流行病学等领域,人们经常收集到各种各样的计数资料以研究它们的规律和特征.往往会出现计数数据不包含零观测值或零观测值过多的情形.一系列零截断和零膨胀离散模型也由此提出用于分析这一类数据,如零截断/零膨胀泊松分布、零截断/零膨胀负二项分布等.在利用这一类模型进行拟合时,对未知参数进行统计推断是必要的.已有的文献仅局限于解决单一模型的参数推断问题.本文基于近几年提出的零截断分布和零膨胀分布的随机表示,在统一的模型框架下,建立了计算参数极大似然估计的一般方法并应用于常见的离散型分布.进一步提出更一般的零调整模型,扩大了模型的适用范围,为研究人员进行零调整计数数据分析提供合适和便捷的方法与选择.我们通过随机模拟和两个实例分析来说明这些方法的实用性.     

计算对称群Sn的所有幂零子群

本文研究了对称群Sn的所有幂零子群的计算方法.利用添加生成元的方法,获得了S7的全部5119个幂零子群.结果表明此方法是有效的.     

一类非线性微分代数系统的零动态

控制系统的零动态是系统一种内部动态品质,其行为与系统的许多性质相联系,如系统的稳定性,反馈镇定与输出跟踪等.针对一类非线性微分代数系统,提出了输出零子流形和零动态的概念.利用M-导数方法,探讨了此类系统的输出零子流形的性质,并给出了此类系统的输出零子流形和零动态算法,也讨论了该算法的一些性质.最后,给出一个例子说明如何利用系统的零动态来讨论系统的反馈稳定化问题.     

模糊二人零和对策的纳什均衡求解

用三角模糊数刻画二人零和对策支付值的不确定性,提出了计算模糊二人零和对策纳什均衡解的多目标规划方法.给出了一种基于区间数比较的三角形模糊数排序方法,根据该方法将模糊二人零和对策转化为多目标线性规划.通过一个数值实例说明了该方法的有效性和实用性.     

扰动色谱方程黎曼解的极限-delta激波的行成和转换

本文主要讨论扰动色谱方程delta激波解的行成和转换,并讨论上述方程的黎曼问题.当扰动参数趋于零时,通过研究黎曼解的极限,我们可以观察到如下两个重要现象:激波和接触间断重合行成delta激波,一类激波(一个变量含有delta函数).     

2012年高考北京卷理科数学压轴题的一般情形解析

题目设A是由m×n个实数组成的m行n列的数表,满足:每个数的绝对值不大于1,且所有数的和为零.记S(m,n)为所有这样的数表构成的集合.对于A∈S(m,n),记ri(A)为A的第i行各数之和     

Morita Context环的幂零性

设(A,B,V,W,(),[])是一个Morita Context,C=A VW B是对应的Morita Context环.用基本环论方法,给出了C与A,B,V,W之间关于环的诣零性,幂零性,局部幂零性,N—诣零性,P—性等性质的关系.     

On the Least Number of Fixed Points of an Equivariant Map

The problem on the least number of fixed points of an equivariant map of a compact polyhedron on which a finite group acts is considered. For such a map, the least number of fixed points and the least number of fixed orbits are estimated in terms of invariants of the type of Nielsen numbers. The estimates obtained are sharp. The results are similar to those of P. Wong, but their assumptions are essentially weaker. Some notations are refined. The proofs are constructive.     

Trajectory Modeling of Robot Manipulators in the Presence of Obstacles

This paper presents two different strategies for the problem of the optimal trajectory planning of robot manipulators in the presence of fixed obstacles. The first strategy is related to the situation where the trajectory must pass through a given number of points. The second strategy corresponds to the case where only the initial and final points are given. The optimal traveling time and the minimum mechanical energy of the actuators are considered together to build a multiobjective function. The trajectories are defined using spline functions and are obtained through offline computation for online operation. Sequential unconstrained minimization techniques (SUMT) have been used for the optimization. The obstacles are considered as three-dimensional objects sharing the same workspace performed by the robot. The obstacle avoidance is expressed in terms of the distances between potentially colliding parts. Simulation results are presented and show the efficiency of the general methodology used in this paper.     

Differential sensitivity of solutions of convex constrained optimal control problems for discrete systems

A family of optimal control problems for discrete systems that depend on a real parameter is considered. The problems are strongly convex and subject to state and control constraints. Some regularity conditions are imposed on the constraints.The control problems are reformulated as mathematical programming problems. It is shown that both the primal and dual optimal variables for these problems are right-differentiable functions of a parameter. The right-derivatives are characterized as solutions to auxiliary quadratic control problems. Conditions of continuous differentiability are discussed, and some estimates of the rate of convergence of the difference quotients to the respective derivatives are given.     

Digital computation of transient characteristics of an induction motor on switched supply

A novel method of computing the nonlinear differential equations relating to the transient behaviour of an induction motor using a polynomial series, is presented. The stator and rotor currents and the angle of rotation are expressed as polynomial series dependent on time. These are then substituted into the differential equations of the induction motor to compute the polynomial coefficients and, consequently, the transient quantities. Since the equations are nonlinear, the computations are carried out using the step-by-step method. The stator and rotor currents, speed and torque are calculated for acceleration and braking conditions. The results are compared both analytically and experimentally.     

Integrability of the discretization of the controlled Euler Top

The Euler equations with two controls are discretized by using the bilinear transformation method. The discrete equations are explicit and exhibit a sufficient number of conserved quantities for integrability. The explicit solution to the discrete controlled Euler top are deduced in terms of elliptic functions.     

Linearized stability analysis of two-dimension Burnett equations

The linearized stability analyses of two-dimension Burnett equations were studied in present paper for the first time. The characteristic stability equation of two-dimension original Burnett equation was first derived and the characteristic curve was achieved. The material derivatives in original Burnett equations are then replaced with the Euler and Navier-Stokes equations. The stabilities of these two alternative Burnett equations are then analyzed. The linearized stability analyses show that the two-dimension original Burnett and Euler-based Burnett equations are not stable while the Navier-Stokes-based Burnett equations are stable. The critical Knudsen number for the original Burnett and Euler-based Burnett equations are 0.074 and 0.353, respectively. These critical Knudsen number are smaller than those of corresponding one-dimension equations. The two-dimension Burnett equations are more unstable than one-dimension equations.     

Subinverses of fuzzy matrices

A matrix operation is examined for fuzzy matrices and interesting properties of fuzzy matrices are obtained using the operation. Particularly some properties concerning subinverses and regularity of fuzzy matrices are given and the largest subinverse is shown by the properties. The properties are closely related to inverses of fuzzy matrices and fuzzy equations. Moreover fuzzy preorders are examined using the matrix operation and basic properties are obtained. The results are considered to be useful for the theory of fuzzy matrices.     

Optimization of technology parameters for the plane-strain component in the process of gas quenching

The paper introduces an optimization method for the technology parameters of the plane-strain component in the process of gas quenching. Distortion, residual stress, average surface hardness and standard deviation of surface hardness are regarded as the optimization objectives. A new heat transfer coefficient model is presented, five distinct heat transfer coefficients are used at various regions of the model. The five heat transfer coefficients are regarded as the design variables, and four regressive equations are established by using response surface method. The four equations, respectively represent the relations between the four optimization objectives and the design variables. A multi-objectives optimization model is established, and the multi-objectives optimization model is optimized by the non-linear method. The optimized technology parameters are used to simulate the gas quenching process by FEM software. The quenching results after optimization are compared with those before optimization. The comparison shows that the quenching quality after optimization is better than that before optimization. After optimization, the four optimization objectives are all improved.     

Fuzzy理论在工程环境灾害预测中的应用

针对矿山大型排土场所出现的滑坡等工程环境灾害的预测与防治问题,着重探讨排土场边坡失稳破坏预测问题.文中采用Fuzzy数学中的Fuzzy概率测度理论建立理论预测分析模型,并对大型排土场边坡失稳破坏的Fuzzy概率测度进行具体的预测分析,所获结果与已有的经典分析方法所获理论结果一致.针对矿山大型排土场所出现的滑坡等工程环境灾害防治问题,提出了具体的防治技术措施.     

Mathematical model of the pipeline with angular joint of elements

A mathematical model of the pipeline as a Koiter-Vlasov moment shell with kink lines of the surface at the junctions of the pipe segments was constructed and substantiated. The following tasks are solved: The geometric parameters of the mechanical system as a three-dimensional elastic body and as a shell are found; force factors of the shell are expressed in terms of displacements of the middle surface of the wall, taking into account the presence of a kink line; equations of pipe equilibrium are derived as Koiter-Vlasov shells with an edge along the line; forces on oblique sections are expressed as functions of shell movements; the conjugation conditions on the pipe joint line for displacements and the angle of rotation of the normal are imposed and justified; conjugation conditions for bending moments, shear forces, transverse and normal forces are imposed and justified. The presence of the solution singularity at points on the connection line of the pipe segments is theoretically established and illustrated by the numerical example.