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.     

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.     

L－fuzzy集网的R－收敛性质

本文在ＬＦ拓扑空间中建立了Ｌ－ｆｕｚｚｙ集网的弱收敛（Ｒ－收敛）概念，应用文［４］中的Ｒ－闭包，系统讨论了它们的性质，证明了等式ＲｌｉｍＡ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ和ＲｌｉｍＡ＿ｎ＝Ａ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ并且给出了Ｌ－ｆｕｚｚｙ集网与其子网之间的关系。     

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.     

Simulation of nonlinear properties of ferroelectric and piezoceramicmaterials

Ferroelectric and piezoelectric materials are becoming a very significant part of smart materials that are used widely as actuators, sensors and most common applications such as vibration control, precision positioning, precision cutting and microelectromechanical systems (MEMS). Piezoceramic materials show nonlinear characteristics when they are under high electromechanical loading. In this study, nonlinear behaviour of tetragonal perovskite type piezoceramic materials is simulated using micromechanical model. In the simulations uni‐axial loading is applied. The calculations which are based on a linear constitutive model, nonlinear domain switching model and a model of probability to switch are performed at each grain. The different domain switching effects (900 or 1800 domain switching for tetragonal perovskite structure) due to energy differences, different probability functions, different statistical random generators and material parameters are analyzed. Finally, simulation results are compared with the data of experiments are giving in literature. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Enumeration of point-determining graphs

Point-determining graphs are graphs in which no two vertices have the same neighborhoods, co-point-determining graphs are those whose complements are point-determining, and bi-point-determining graphs are those both point-determining and co-point-determining. Bicolored point-determining graphs are point-determining graphs whose vertices are properly colored with white and black. We use the combinatorial theory of species to enumerate these graphs as well as the connected cases.     

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.     

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.     

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.     

Stability of oscillatory solutions of differential equations with general piecewise constant arguments of mixed type

We examine scalar differential equations with general piecewise constant arguments of mixed type, in short DEPCAG of mixed type, that is, the arguments are general step functions. Criteria of existence of the oscillatory and nonoscillatory solutions of such equations are proposed. Necessary and sufficient conditions for stability of the zero solution are obtained. Our results are new, extend and improve earlier publications. Several numerical examples and simulations are also given to show the feasibility of our results.     

Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of such functions are defined and investigated. Four criteria of a family to be normal are proved. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proved that they are finite-dimensional Lie groups for compact manifolds. Their examples are given. Many characteristic features are found in comparison with commutatiive geometry over R or C. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 18, Functional Analysis, 2006.     

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.     

随机向量的函数的独立性的一个问题

给出了随机变量 X1,X2 ,X3 ,X4 每三个相互独立 ,但 X1±X2 与 X3 ± X4 不相互独立的例子 ,以及 X1,X2 ,X3 每两个相互独立 ,但 X1± X2 与 X3 不相互独立的例子 .     

Analysis of asymptotic distributions of some profitability characteristics of trade algorithms

The asymptotic behavior of a model sequence of price increments and some probability characteristics of a trade algorithm are investigated. It is proved that characteristics such as the number of buy and sell transactions and the value of total profitability are asymptotically normal for a stationary m-dependent sequence of price increments. Approximate formulas are derived to calculate their mathematical expectations and variances as functions of parameters of the price series and the trade algorithm. Some results of numerical experiments are presented.     

A rate of approach to the steady state of solutions of second-order hyperbolic equations

In this paper projection methods based on expansions of solutions of retarded function differential equations in terms of generalized eigenfunctions are considered. It is first shown that the projection series developed earlier by Hale and Shimanov and those considered by Bellman and Cooke are actually the same. Using extensions of the residue-type arguments of Bellman and Cooke, convergence results are then established for a class of perturbed systems. These results are applied to obtain approximations to optimal controls for certain infinite dimensional variational problems. Numerical results are presented for several examples.     

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.     

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.     

直积的推广与正交函数系的生成

Two new kinds of direct product of matrices are defined. Their properties are investigated . Direct products of matrix and set of continuous functions are also defined. Many complete sets of orthogonal functions, such as those sets given by Walsh [2], Paley [3], Chrestenson[4 ], and Watari [ 5 ], may be generated by : these newkinds of direct product . Direct products are also applicable to the generation of sets of piecewise orthogonal functions .     

Controllability and stabilization of programmed motions of reversible mechanical and electromechanical systems

Problems of controllability and methods of stabilizing programmed motions of a large class of mechanical and electromechanical systems which are reversible with respect to the control are considered. Criteria of the controllability and stabilizability of reversible systems are obtained. Programmed motions and algorithms of programmed control are designed in analytical form and algorithms of programmed motions for non-linear reversible systems are synthesized.     

Effect of cubic nonlinearity on soliton solutions of the Benjamin-Bona-Mahony equation

Soliton solutions of the Benjamin-Bona-Mahony equation with quadratic and cubic nonlinear terms are numerically simulated. Solitons with limiting amplitudes are found, and their interactions with solitons of other types are examined. Estimates for inelastic effects are presented.