Georgescu模糊选择函数伪传递合理性的研究

本文研究模糊选择函数伪传递合理性。对普通选择函数伪传递合理的两个充要条件进行了模糊化,讨论了它们的独立性;证明了对Georgescu模糊选择函数而言,这两个条件仍是伪传递合理的充分条件,但不再是必要条件。     

IM分担一个或两个小函数的亚纯函数的唯一性

In this paper, the uniqueness problems of two meromorphic functions sharing one or two small functions IM are studied. By imposing certain conditions on the counting functions of four or three other small functions and constructing auxiliary function, some general uniqueness results are obtained.     

Complete monotonicity of a function involving the divided difference of digamma functions

In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.     

Strict inequality of Robin eigenvalues for elliptic differential operators on Lipschitz domains

On a bounded Lipschitz domain we consider two selfadjoint operator realizations of the same second order elliptic differential expression subject to Robin boundary conditions, where the coefficients in the boundary conditions are functions. We prove that inequality between these functions on the boundary implies strict inequality between the eigenvalues of the two operators, provided that the inequality of the functions in the boundary conditions is strict on an arbitrarily small nonempty, open set.     

A note on pair-formation functions

In this paper, we take a closer look at two harmonic mean functions [1, 2] and two minimum functions (moving dominance function [3] and group-specific minimum function), in two sex multigroup populations. Comparisons between these functions are focused on proportionate mixing. We show that under some special conditions, the two harmonic mean functions are identical; and under the mixing framework of Castillo-Chavez and Busenberg [4], the two minimum functions are also identical (for both proportionate and nonproportionate mixing). Simulations of a simple demographic model with the four functions are also performed to confirm the above mentioned identity and to illustrate the behavior of these functions.     

Reducing subspaces of compressed analytic Toeplitz operators on the Hardy space

In this paper we discuss necessary conditions and sufficient conditions for the compression of an analytic Toeplitz operator onto a shift coinvariant subspace to have nontrivial reducing subspaces. We give necessary and sufficient conditions for the kernel of a Toeplitz operator whose symbol is the quotient of two inner functions to be nontrivial and obtain examples of reducing subspaces from these kernels. Motivated by this result we give necessary conditions and sufficient conditions for the kernel of a Toeplitz operator whose symbol is the quotient of two inner functions to be nontrivial in terms of the supports of the two inner functions. By studying the commutant of a compression, we are able to give a necessary condition for the existence of reducing subspaces on certain shift coinvariant subspaces.     

Conditions Characterizing Minima of the Difference of Functions

 Optimization problems involving differences of functions arouse interest as generalizations of so-called d.c. problems, i.e. problems involving the difference of two convex functions. The class of d.c. functions is very rich, so d.c. problems are rather general optimization problems. Several global optimality conditions for these d.c. problems have been proposed in the optimization literature. We provide a survey of these conditions and try to detect their common basis. This enables us to give generalizations of the conditions to situations when the objective function is no longer a difference of convex functions, but the difference of two functions which are representable as the upper envelope of an arbitrary family of functions. (Received 6 February 2001; in revised form 11 October 2001)     

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

<正>In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.     

Ups and Downs of First Order Sentences on Random Graphs

whenever is a fixed positive irrational. This raises the question what zero-one valued functions on the positive irrationals arise as the limit probability of a first order sentence on these graphs. Here we prove two necessary conditions on these functions, a number-theoretic and a complexity condition. We hope to prove in a subsequent paper that these conditions together with two simpler and previously proved conditions are also sufficient and thus they constitute a characterization. Received October 2, 1998     

Two-dimensional Green’s functions for semi-infinite isotropic thermoelastic plane

Based on the two-dimensional steady-state governing equations of isotropic thermoelastic material and the compact general solution expressed in three harmonic functions, the corresponding three harmonic functions contain nine undetermined constants are constructed for a line heat source applied in the interior of a semi-infinite thermoelastic plane. All components of thermoelastic field in the semi-infinite plane can be derived by substituting the harmonic functions into the general solution. And the undetermined constants can be obtained by the compatibility conditions, equilibrium conditions and the different boundary conditions for extended Mindlin problem and extended Lorentz problem. Thus, the Green’s functions in above two cases are obtained, and the numerical results are given graphically by contours.     

非可微分二层Lipschitz规划的广义微分和广义方向导数

本文对构成函数为Ｌｉｐｓｃｈｉｔｚ函数的二层规划问题,利用非光滑分析工具,讨论了下层极值函数和上层复合目标函数的Ｌｉｐｓｃｈｉｔｚ连续性,给出了这些函数的广义微分和广义方向导数的估计式。本文得到的结果为进一步研究非可微二层Ｌｉｐｓｃｈｉｔｚ规划的最优性条件和有效算法等理论和方法问题奠定了基础。     

二元函数的可微性研究

研究二元函数的可微性,得到两个充分条件,它们与已有的判别二元函数可微性的充分条件相比更为简单,因而使得应用更为简便.     

Multifunctions and the fixed point property for products of ordered sets

Sufficient conditions for the fixed point property for products of two partially ordered sets are proved. These conditions are formulated in terms of multifunctions (functions with non-empty sets as values).     

The optimality conditions for optimization problems with convex constraints and multiple fuzzy-valued objective functions

The optimality conditions for multiobjective programming problems with fuzzy-valued objective functions are derived in this paper. The solution concepts for these kinds of problems will follow the concept of nondominated solution adopted in the multiobjective programming problems. In order to consider the differentiation of fuzzy-valued functions, we invoke the Hausdorff metric to define the distance between two fuzzy numbers and the Hukuhara difference to define the difference of two fuzzy numbers. Under these settings, the optimality conditions for obtaining the (strongly, weakly) Pareto optimal solutions are elicited naturally by introducing the Lagrange multipliers.     

Necessary conditions without differentiability assumptions in unilateral control problems

We derive two theorems combining existence with necessary conditions for the relaxed unilateral problem of the optimal control of ordinary differential equations in which the functions that define the problem are Lipschitz-continuous in the state variables. These theorems generalize the results presented in a previous paper [8] by the addition of unilateral constraints on the state and control functions. As in that paper, the new necessary conditions have a canonical form obtained by replacing, in the “customary” conditions, the partial derivatives with respect to the state variables by finite difference quotients at neighboring arguments, and then applying limiting processes and convexification. More general necessary conditions are also obtained in terms of the representations of the Lipschitz-continuous functions as compositions.     

Two Classes of Merit Functions for Infinite-Dimensional Second Order Complimentary Problems

In this article, we extend two classes of merit functions for the second-order complementarity problem (SOCP) to infinite-dimensional SOCP. These two classes of merit functions include several popular merit functions, which are used in nonlinear complementarity problem, (NCP)/(SDCP) semidefinite complementarity problem, and SOCP, as special cases. We give conditions under which the infinite-dimensional SOCP has a unique solution and show that all these merit functions provide an error bound for infinite-dimensional SOCP and have bounded level sets. These results are very useful for designing solution methods for infinite-dimensional SOCP.     

On jet-convex functions and their tensor products

In this article, we introduce necessary and sufficient conditions for the tensor product of two convex functions to be convex. For our analysis we introduce the notions of true convexity, jet-convexity, true jet-convexity as well as true log-convexity. The links between jet-convex and log-convex functions are elaborated. As an algebraic tool, we introduce the jet product of two symmetric matrices and study some of its properties. We illustrate our results by an application from global optimization, where a convex underestimator for the tensor product of two functions is constructed as the tensor product of convex underestimators of the single functions.     

Total Defect of a Meromorphic Function and All its Derivatives (II)

This paper is concerned with an extremal problem for meromorphic functions. The necessary and sufficient conditions for a meromorphic function and all its derivatives with maximum defect two are obtained and the behavior of such functions is investigated in detail.     

Two-dimensional steady-state general solution for isotropic thermoelastic materials with applications. II. Green’s function for two-phase infinite plane

Green’s function for isotropic thermoelastic two-phase infinite plane under a line heat source is established in this paper. By virtue of the fourth compact general solutions in Part I which is expressed in three harmonic functions, six new suitable harmonic functions with undetermined constants are constructed for the two semi-infinite planes of the two-phase infinite plane, respectively. The corresponding thermoelastic field can be obtained by substituting these harmonic functions into the general solution, and the undetermined constants can be determined by compatibility conditions and the equilibrium conditions. Numerical results are given graphically by contours.     

Hadamard well-posed vector optimization problems

In this paper, two kinds of Hadamard well-posedness for vector-valued optimization problems are introduced. By virtue of scalarization functions, the scalarization theorems of convergence for sequences of vector-valued functions are established. Then, sufficient conditions of Hadamard well-posedness for vector optimization problems are obtained by using the scalarization theorems.