一类非线性椭圆组很弱解的正则性

本文在可控增长条件（1．2）－（14）下,对一类非线性椭圆方程组（1．1）改进其很弱解偏微商的可积性,使其为经典意义下的弱解．     

医学随访研究设计表及其使用方法

本文由过去提出的医学随访研究基础方法和应用模型设计出３２０个常用临床试验方案，制成设计供临床应用．与以往设计相比，其优点是１．便于限定失访水平，２．没有来自信息性终检的偏性，３．便于限定终末终检率在其阈值之下，避免设计错误，保证结果的可靠性，４．设计灵活，无Ｍｏｒｇａｎ误差．利用这些表可简化设计过程．附工作实例描述其使用方法．     

弹性力学问题的最小二乘混合有限元法

该文给出弹性力学问题的混合有限元法及其整体估计．该方法不受经典的B．一B．条件约束．因此,其有限元空间可以自由地选择,并得到最优的误差估计．     

一个求总极值的实现算法及其收敛性

1978年,郑权等首先提出了一种用积分─水平集求总极值的方法及用Monte－Carlo随机投点实现的实现其法,其实现算法是否收敛未解决的问题．本文提出一种用数论方法实现的实现算法,并证明了该实现其法是收敛的．初步的数值结果表明,该实现其法是较有效的．     

一类多目标广义分式规划问题的最优性条件和对偶

研究了一类不可微多目标广义分式规划问题．首先,在广义Abadie约束品性条件下,给出了其真有效解的Kuhn—Tucker型必要条件．随后,在（C,a,P,d）一凸性假设下给出其真有效解的充分条件．最后,在此基础上建立了一种对偶模型,证明了对偶定理．得到的结果改进了相关文献中的相应结论．     

非对称开采时矿柱失稳的尖点突变模型

针对非对称开采时矿柱稳定性问题建立了一个简化的力学模型．基于势能原理,应用尖点突变理论对矿柱成为非稳定系统进行了探讨,导出了失稳的充要条件、矿柱变形突跳量和能量释放表达式,为定量研究其失稳问题奠定了基础．结果表明:系统的失稳不仅与其所受载荷有关,而且与其内部刚度分配有关,当相对刚度值越大,所承受的临界载荷也越大,越不容易失稳．反之,越容易失稳,且失稳时所释放的能量越大,危害也越大．给出了算例,其计算结果可为安排开采顺序、合理布置采场等提供依据．     

完备格中的成分理论

在完备格中引入了元素的成分概念．基于此,引入了元素的宽度的概念．在分配格的情形证明了元素的成分集对有限并运算封闭且有某种遗传性．证明了元素的有限宽度的成分之集是定向集．称没有非平凡成分的元素为颗粒．称每个非零元素都可表示为其颗粒成分之并的完备格为颗粒表示格．证明了拓扑空间是局部连通的充要条件是其开集格为颗粒表示格．     

给一组高考题“卸妆”

审视很多高考试题,往往是对某些简单的问题的有意“妆饰”,一旦对其卸了“妆”,便还原了问题的本来面目,使其水落而石出,不难求解．本文对一组高考题卸妆还原,重现其原貌．     

解函数复合最值问题的常用策略

在数学竞赛和高考题中,常常会遇到一些在一类最大值中求其最小值或在一类最小值中求其最大值的复合最值问题．它是函数最值中的一种特殊类型,解决这类问题的方法也比较特殊．本文介绍解决此类问题的一些常用策略．     

让数学课堂“活”起来——谈一道习题启发性教学的体会

启发式教育思想源于我国古代伟大的教育家孔子,他主张“不愤不启,不悱不发”．《学记》中也明确指出启发式教学过程应当是“道而弗牵,强而弗抑,开而弗达”,好的教师应当是“善歌者,使人继其声;善教者,使人继其志”．实际上,启发式教学作为我国传统教学思想的瑰宝,其对教学实践的指导作用是不言而喻的．正如有的学者所指出的“启发式教学是教师在演讲时永远应该坚持的传统,不能忘记．教师的这种基本功的启发示范是双基教学的一部分,永远不会过时．本文中笔者从一例习题教学的实践谈一些体会．     

一种非单调滤子信赖域算法解线性不等式约束优化

本文给出了一种新的多维滤子算法结合非单调信赖域策略解线性约束优化.目标函数及其投影梯度的分量组成了新的多维滤子，并且与信赖域半径有关.当信赖域半径充分小时，新的滤子能接受试探点，避免算法无限循环.非单调信赖域策略保证了新算法的整体收敛性.目前为止，多维滤子算法局部收敛性分析仍然没有解决，在合理假设下，我们分析了新算法的局部超线性收敛性.数值结果验证了算法的有效性.     

一种新的集合序列收敛性

本我们引进了无穷维Ｂａｎａｃｈ空间中的一种新的集合序列收敛性概念,讨论了它与其它收敛性概念的关系。另外,我们还研究了集合序列根限的Ｍｉｎｋｏｗｓｋｉ和。     

A new trust region method for unconstrained optimization

In this paper, we propose a new trust region method for unconstrained optimization problems. The new trust region method can automatically adjust the trust region radius of related subproblems at each iteration and has strong global convergence under some mild conditions. We also analyze the global linear convergence, local superlinear and quadratic convergence rate of the new method. Numerical results show that the new trust region method is available and efficient in practical computation.     

Normalized convergence in stochastic optimization

A new concept of (normalized) convergence of random variables is introduced. This convergence is preserved under Lipschitz transformations, follows from convergence in mean and itself implies convergence in probability. If a sequence of random variables satisfies a limit theorem then it is a normalized convergent sequence. The introduced concept is applied to the convergence rate study of a statistical approach in stochastic optimization.     

Projection-Splitting Algorithms for General Monotone Variational Inequalities

We suggest and analyze some new splitting type projection methods for solving general variational inequalities by using the updating technique of the solution. The convergence analysis of these new methods is considered and the proof of convergence is very simple. These new methods are versatile.     

补偿随机规划的一种新数值方法

本文给出解决两阶段求援随机规划的一种新的数值方法.由于引进了新的逼近技术,该方法具有全局收敛性和局部超线性收敛性.     

交错级数的对数判别法

从正项级数的Raabe对数判别法入手,给出了交错级数的一个新的审敛方法.与文[1],[2]所给的审敛法相比,当交错级数的一般项含有幂指项时,利用该审敛法判断其敛散性显得尤为简便.     

A gradient-related algorithm with inexact line searches

In this paper, a new gradient-related algorithm for solving large-scale unconstrained optimization problems is proposed. The new algorithm is a kind of line search method. The basic idea is to choose a combination of the current gradient and some previous search directions as a new search direction and to find a step-size by using various inexact line searches. Using more information at the current iterative step may improve the performance of the algorithm. This motivates us to find some new gradient algorithms which may be more effective than standard conjugate gradient methods. Uniformly gradient-related conception is useful and it can be used to analyze global convergence of the new algorithm. The global convergence and linear convergence rate of the new algorithm are investigated under diverse weak conditions. Numerical experiments show that the new algorithm seems to converge more stably and is superior to other similar methods in many situations.     

A new application of Lagrange-Bürmann expansions. I. General principle

A new scheme is developed for improving the convergence of slowly convergent series solutions. The method is based on a transformation of variables of similarity form whereby the resulting composite function is constructed by its Lagrange-Bürmann expansion. It is the improved convergence of the new expansion that we take most advantage of in this method. The convergence of the Lagrange-Bürmann expansion as well as its inversion scheme is proved for analytic (object) functions. The inversion is required to recover from the Lagrange-Bürmann expansion the object function which is imbedded in the mapping functions. Several numerical examples demonstrate the improved convergence of the new method. The improvement owes much to the invariance properties of the mapping function under a group and the “built-in” feature of analytic continuation of the method. These features are elucidated in detail.     

A new simultaneous method of fourth order for finding complex zeros in circular interval arithmetic

Starting from disjoint disks which contain polynomial complex zeros, the new iterative interval method for simultaneous finding of inclusive disks for complex zeros is formulated. The convergence theorem and the conditions for convergence are considered, and the convergence is shown to be fourth. Numerical examples are included.