非光滑非凸多目标规划的Wolfe型对偶性

本文利用作者提出的某些非凸概念,讨论了非光滑非凸多目标规划的Wolfe型对偶性.     

非自治非光滑系统的Matrosov稳定性定理

本文在一般Filippov解意义下研究了一类非自治非光滑切换系统的Matrosov稳定性定理,并作为推论,修正了相关文献中关于非光滑系统稳定性的一个结果,最后给出了在一类带有不连续摩擦项的力学系统的跟踪问题中的应用．     

非参数理论综述

对非参数理论进行了系统地综述.非参数理论中一个比较重要的内容是估计方法,常见的非参数估计方法有核估计、局部多项式估计、近邻估计等.光滑参数的选取、"维数灾难"与边界点问题也是与非参数理论有关的重要内容,也对这些方面进行综述.最后,文章还综述了非参数技术在时间序列模型中的有关应用问题.     

一类特殊非齐次树上非齐次马尔可夫链的强律

极限定理一直是国际概率论界研究的中心课题之一.本文通过构造适当的辅助非负鞅而给出了一类特殊非齐次树上可列非齐次马尔可夫链场的若干强律.     

非均匀调和函数的两类边值问题与积分表达式

本文给出非均匀指数函数的定义及性质,并且进一步引入了非均匀三角函数、非均匀双曲函数和非均匀对数函数.最后利用非均匀指数函数表达形式和非均匀解析函数的Cauchy积分理论,建立了非均匀泊松积分公式和非均匀施瓦茨积分公式,获得了非均匀调和函数在两类特殊边界上的狄利克雷问题和诺伊曼问题解的显示表达式.     

非单特征值引出的非线性方程分歧问题

本文讨论非线性方程f(x,λ)=θ的分歧问题,这里f:x×R→Y为非线性可微映射, x,Y为Banaclh空间.利用偏导算子A=fx(x0,λ0)的广义逆A ,研究了一类由非单特征值引出的分歧问题,给出了刻划分歧性的定理,推广了Crandall M G与Robinowitz P H的由单特征值引出的分歧性定理.     

基于非单调线搜索非拟牛顿法的全局收敛性

本文就非拟牛顿法在无约束最优化问题上，对采用非单调线搜索的情况下是否具有全局收敛性进行了研究，在目标函数满足一致凸的条件下，证明了非拟牛顿族是全局收敛的．     

Hilbert空间中拟非扩张非自映像的不动点的粘滞迭代方法

针对Hilbert空间中拟非扩张非自映像引入了三种新的粘滞方法,并证明了所提出的三种算法的强收敛,改进和推广了相关的结果.     

渐进非扩张非自映像新的迭代的强收敛

研究了渐进非扩张非自映像新的迭代的强收敛问题.利用保核收缩映像的基本性质,定义了一种新的Ishikawa型迭代序列,并在一致凸的Banach空间里,证明了该迭代序列在适当条件下强收敛到T的不动点.结果改进和推广了一些最新成果.     

两个非单调点PM函数的非单调高度

众所周知,单调函数的非单调高度都为0,而对于非单调的函数,情况将变得非常复杂.由于非单调高度的变化影响迭代根的构造,因此在动力系统的研究中具有重要的意义.将在之前N型PM函数的非单调高度研究的基础上,继续讨论两个非单调点PM函数的非单调高度分类,得到此类函数高度的完整分析,并以此研究其动力学性质.     

Qualities of goods in the models of production

In this paper the models of production in which the qualities of goods are considered are presented. Such models are completely described by the families of matrices or by a function which has some properties which are natural from the economic point of view. The special cases of the models are the well known linear model of production and the van Neumann-Gale's model.     

直觉模糊关系的截集性质

定义了直觉模糊关系的截集以及并给出了它们的基本性质,同时分别讨论了自反、对称、传递直觉模糊关系与经典二元关系之间的等价刻画;其次,提出直觉模糊关系的定义域与值域的概念;最后,分析了直觉模糊关系合成的截集性质.     

Numerical Methods for Computing Plausibility and Belief Distributions of Consequences of a Subjective Model of Object of Research

Numerical methods for computing plausibility and belief distributions of consequences of a subjective model are considered. More precisely, related constrained optimization problems are studied. Error estimates of the proposed algorithms are obtained. Techniques for taking into account the information about the consequence available to the researcher for improving the accuracy of computations are discussed.     

Complexity of realization of functions from a class of three-valued logic by formulas of special type

A set of functions of the three-valued logic is considered and upper estimates for the Shannon function in the class of formulas of special form are obtained for this set. Some examples of sequences of functions from this set are considered and exponential lower estimates of complexity are obtained. In this case the values of the Shannon function are obtained for the considered class with the accuracy up to an additive constant.     

一类三阶牛顿变形方法

A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton's method,are given.Their convergence properties are proved.They are at least third order convergence near simple root and one order convergence near multiple roots.In the end,numerical tests are given and compared with other known Newton's methods.The results show that the proposed methods have some more advantages than others.They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.     

On the existence of solutions of nonlinear equations

Nonlinear equations in Banach spaces are considered. Solvability conditions are obtained for them. These results are a generalization of the Hadamard diffeomorphism theorem. Additionally, conditions for the existence of coincidence points of two mappings acting on metric spaces are obtained.     

Some fundamental problems of the theory of thermoviscoelasticity

Methods of solving quasistatic problems of the linear theory of thermoviscoelasticity are discussed. Special attention is given to the method of approximations. Modern methods of solving contact problems with a variable boundary and problems with a time-dependent boundary are briefly reviewed. Methods of solving problems with a nonuniform temperature field are outlined. The basic relations of the nonlinear theory of thermoviscoelasticity are given. Its various modifications and simplifications associated with the introduction of fairly general assumptions are examined. Methods of solving problems in certain nonlinear theories are noted. Nonisothermal (coupled) problems of thermoviscoelasticity and questions relating to the general theory with physical and geometric nonlinearity are discussed.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 41–58, January–February, 1971.     

Data Perturbations of Matrices of Pairwise Comparisons

This paper deals with data perturbations of pairwise comparison matrices (PCM). Transitive and symmetrically reciprocal (SR) matrices are defined. Characteristic polynomials and spectral properties of certain SR perturbations of transitive matrices are presented. The principal eigenvector components of some of these PCMs are given in explicit form. Results are applied to PCMs occurring in various fields of interest, such as in the analytic hierarchy process (AHP) to the paired comparison matrix entries of which are positive numbers, in the dynamic input–output analysis to the matrix of economic growth elements of which might become both positive and negative and in vehicle system dynamics to the input spectral density matrix whose entries are complex numbers.     

Estimation of means of multivariate normal populations with order restriction

Multivariate isotonic regression theory plays a key role in the field of statistical inference under order restriction for vector valued parameters. Two cases of estimating multivariate normal means under order restricted set are considered. One case is that covariance matrices are known, the other one is that covariance matrices are unknown but are restricted by partial order. This paper shows that when covariance matrices are known, the estimator given by this paper always dominates unrestricted maximum likelihood estimator uniformly, and when covariance matrices are unknown, the plug-in estimator dominates unrestricted maximum likelihood estimator under the order restricted set of covariance matrices. The isotonic regression estimators in this paper are the generalizations of plug-in estimators in unitary case.     

Asymptotic solutions of non-classical boundary-value problems of the natural vibrations of orthotropic shells

The natural vibrations of orthotropic shells are considered in a three-dimensional formulation for different versions of the boundary conditions on the faces: rigid clamping rigid clamping, rigid clamping free surface, and mixed conditions. Asymptotic solutions of the corresponding dynamic equations of the three-dimensional problem of the theory of elasticity are obtained. The principal values of the frequencies of natural vibrations are determined. It is shown that three types of natural vibrations occur in the shell: two shear vibrations and a longitudinal vibration, which are due solely to the boundary conditions on the faces. It is proved that each boundary layer has its own natural frequency. The boundary-layer functions are determined and the rates at which they decrease with distance from the faces inside the shell are established.