半平面上的随机Dirichlet级数

研究右半平面上的随机Dirichlet级数．为此需要给定一个系数条件,有的文章对此有专门研究．这里首先给出一个较宽的系数条件,并证明在一定意义上是最好的．通常随机级数研究的是同分布随机变量序列,这里通过推广Paley－Zygmund引理,把随机级数的研究引向一般得多的不要求同分布的情况．由于这些是研究随机级数的基础内容．因此应用该文的结论及方法,可以推广和改良一系列定理,并使得有关问题的研究变得方便简洁．     

Qualitative Properties of Eigenvectors Related to Multivalued Operators and some Existence Results

In this work, we study a class of nonlinear eigenvalue problems related to fully discontinuous operators. In particular, we prove the existence of a critical point for two distinct problems. Connected with this problem, we also study a minimization problem with constraint, and we investigate the existence of solutions for a resonant case near zero. Moreover, we give some estimates and qualitative properties of solutions by using the relative rearrangement theory.     

A generalization of local divergence measures

In this paper we propose a generalization of the concept of the local property for divergence measures. These new measures will be called g-local divergence measures, and we study some of their properties. Once this family is defined, a characterization based on Ling’s theorem is given. From this result, we obtain the general form of g-local divergence measures as a function of the divergence in each element of the reference set; this study is divided in three parts according to the cardinality of the reference set: finite, infinite countable or non-countable. Finally, we study the problem of componible divergence measures as a dual concept of g-local divergence measures.     

On nonlinear Fredholm integral equations with non-differentiable Nemystkii operator

From decomposition method for operators, we consider a Newton-Steffensen iterative scheme for approximating a solution of nonlinear Fredholm integral equations with non-differentiable Nemystkii operator. By means of a convergence study of the iterative scheme applied to this type of nonlinear Fredholm integral equations, we obtain domains of existence and uniqueness of solution for these equations. In addition, we illustrate this study with a numerical experiment.     

与Gauss测度有关的椭圆方程比较结果中等号成立的条件

In this paper, we deal with a Dirichlet problem for linear elliptic equations related to Gauss measure. For this problem, we study the converse of some inequalities proved by other authors, in the sense that we study the case of equalities and show that equalities are achieved only in the ＂symmetrized＂ situations. In addition, under other assumptions, we give a different form of comparison results and discuss the corresponding case of equalities.     

The explicit solution of the profit maximization problem with box-constrained inputs

In this paper we study the profit-maximization problem, considering maximum constraints for the general case of m-inputs and using the Cobb-Douglas model for the production function. To do so, we previously study the firm’s cost minimization problem, proposing an equivalent infimal convolution problem for exponential-type functions. This study provides an analytical expression of the production cost function, which is found to be a piece-wise potential. Moreover, we prove that this solution belongs to class C¹. Using this cost function, we obtain the explicit expression of maximum profit. Finally, we illustrate the results obtained in this paper with an example.     

Relative asymptotics for orthogonal matrix polynomials

In this paper we study sequences of matrix polynomials that satisfy a non-symmetric recurrence relation. To study this kind of sequences we use a vector interpretation of the matrix orthogonality. In the context of these sequences of matrix polynomials we introduce the concept of the generalized matrix Nevai class and we give the ratio asymptotics between two consecutive polynomials belonging to this class. We study the generalized matrix Chebyshev polynomials and we deduce its explicit expression as well as we show some illustrative examples. The concept of a Dirac delta functional is introduced. We show how the vector model that includes a Dirac delta functional is a representation of a discrete Sobolev inner product. It also allows to reinterpret such perturbations in the usual matrix Nevai class. Finally, the relative asymptotics between a polynomial in the generalized matrix Nevai class and a polynomial that is orthogonal to a modification of the corresponding matrix measure by the addition of a Dirac delta functional is deduced.     

The Cauchy‐Kowalewski product for bicomplex holomorphic functions

In this paper we study the Cauchy‐Kowalewski extension of real analytic functions satisfying a system of differential equations connected to bicomplex analysis, and we use this extension to study the product in the space of bicomplex holomorphic functions. We also show how these ideas can be used to define a Fourier transform for bicomplex holomorphic functions.     

The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation

In this paper we study the confluence of two regular singular points of the hypergeometric equation into an irregular one. We study the consequence of the divergence of solutions at the irregular singular point for the unfolded system. Our study covers a full neighborhood of the origin in the confluence parameter space. In particular, we show how the divergence of solutions at the irregular singular point explains the presence of logarithmic terms in the solutions at a regular singular point of the unfolded system. For this study, we consider values of the confluence parameter taken in two sectors covering the complex plane. In each sector, we study the monodromy of a first integral of a Riccati system related to the hypergeometric equation. Then, on each sector, we include the presence of logarithmic terms into a continuous phenomenon and view a Stokes multiplier related to a 1-summable solution as the limit of an obstruction that prevents a pair of eigenvectors of the monodromy operators, one at each singular point, to coincide.     

A comparison of ratios and fractions and their roles as tools in proportional reasoning

In an attempt to develop our shared understanding of the relationship between ratios and fractions, we began a phenomenological study to gather evidence from teachers and textbooks and to collect evidence from our own experiences. In this article, we present five possible models for this relationship and a summary of evidence to support each. We also present the model that we developed to represent our shared understanding and provide the results of a study for which we have used our model to help us analyze students’ uses of ratios and fractions in their solutions to proportion-related problems.     

Enlisting excel--again

In Volume 26, Number 2, we reported on a group case study runfor level 3 mathematics students at the University of Brighton.At the core of the study was a quadratic assignment problem,and we reported on attempts by students to use Excel to solvethe problem, and on the attendant difficulties. We providedan elegant solution. In this article, we report on another interestingcase study, this time developed for level 2 mathematics students.Again Excel is used to achieve a solution. We report on ourefforts—and on how student answers led to improvements.     

Difference method of increased order of accuracy for the Poisson equation with nonlocal conditions

In a rectangular domain, we consider the two-dimensional Poisson equation with nonlocal boundary conditions in one of the directions. For this problem, we construct a difference scheme of fourth-order approximation, study its solvability, and justify an iteration method for solving the corresponding system of difference equations. We give a detailed study of the spectrum of the matrix representing this system. In particular, we obtain a criterion for the nondegeneracy of this matrix and conditions for its eigenvalues to be positive.     

ENVIRONMENTAL POLLUTION AND UNILATERAL CONTROL IN AN OPEN ECONOMY

In this paper we study two questions in environmental economics. First, within the context of a simple 2 × 2 × 2 static general equilibrium model, we seek to determine the conditions under which environmental policy, pursued unilaterally by a large country will make that country worse off. The empirical dimension of this question is stressed, and the key parameters which are germane to any policy discussion regarding this issue are identified. Second, we study—once again from the perspective of a large country—the possibility of using the domestic tax structure optimally to attain environmental policy objectives. Keeping the empirical dimension of the question in mind, we show how to compute optimal externality correcting taxes. We then briefly focus on the links between our stylized analytical model and the applied general equilibrium models currently being developed to study the effects of environmental policy quantitatively.     

Hopf-Cole transformation to some systems of partial differential equations

In this paper we study a system of nonlinear partial differential equations which we write as a Burgers equation for matrix and use the Hopf-Cole transformation to linearize it. Using this method we solve initial value problem and initial boundary value problems for some systems of parabolic partial differential equations. Also we study an initial value problem for a system of nonlinear partial differential equations of first order which does not have solution in the standard distribution sense and construct an explicit solution in the algebra of generalized functions of Colombeau. Received November 1999     

A generalization of local divergence measures

In this paper we propose a generalization of the concept of the local property for divergence measures. These new measures will be called g-local divergence measures, and we study some of their properties. Once this family is defined, a characterization based on Ling’s theorem is given. From this result, we obtain the general form of g-local divergence measures as a function of the divergence in each element of the reference set; this study is divided in three parts according to the cardinality of the reference set: finite, infinite countable or non-countable. Finally, we study the problem of componible divergence measures as a dual concept of g-local divergence measures.     

A novel computer virus model and its dynamics

In this paper, we propose a novel computer virus propagation model and study its dynamic behaviors; to our knowledge, this is the first time the effect of anti-virus ability has been taken into account in this way. In this context, we give the threshold for determining whether the virus dies out completely. Then, we study the existence of equilibria, and analyze their local and global asymptotic stability. Next, we find that, depending on the anti-virus ability, a backward bifurcation or a Hopf bifurcation may occur. Finally, we show that under appropriate conditions, bistable states may be around. Numerical results illustrate some typical phenomena that may occur in the virus propagation over computer network.     

Convergence Theorem for Variational Inequality in Hilbert Spaces with Applications

In this paper, we study variational inequality over the set of the common fixed points of a countable family of quasi-nonexpansive mappings. To tackle this problem, we propose an algorithm and use it to prove a strong convergence theorem under suitable conditions. As applications, we study variational inequality over the solution set of different nonlinear or linear problems, like minimization problems, split feasibility problems, convexly pseudoinverse problems, convex linear inverse problems, etc.     

The algebraic structure of left semi-trusses

The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative “distributive” laws were defined. In an effort to study these “left distributive” laws and the interaction they entail on the algebraic structures, Brzeziński introduced skew left trusses and left semi-trusses. In particular the class of left semi-trusses is very wide, since it contains all rings, associative algebras and distributive lattices. In this paper, we investigate the subclass of left semi-trusses that behave like the algebraic structures that came up in the study of the Yang-Baxter equation. We study the interaction of the operations and what this interaction entails on their respective semigroups. In particular, we prove that in the finite case the additive structure is a completely regular semigroup. Secondly, we apply our results on a particular instance of a left semi-truss called an almost left semi-brace, introduced by Miccoli to study its algebraic structure. In particular, we show that one can associate a left semi-brace to any almost left semi-brace. Furthermore, we show that the set-theoretic solutions of the Yang-Baxter equation originating from almost left semi-braces arise from this correspondence.     

A molecular method applied to a non-local PDE in stratified Lie groups

In this article we study a transport-diffusion equation in the framework of the stratified Lie groups. For this equation we will study the existence of the solutions, a maximum principle, a positivity principle and Hölder regularity.     

Perturbation des Resolvantes Triangulaires et Balayage des Couples Excessifs

In this work, we start by developing an elementary potential theory associated to a triangular kernel. Then we study the perturbation of triangular resolvent, which enable us to characterize, with an elementary way, the excessive couples relatively to a triangular resolvent U. Finally, we study the balayage of U-surmedians couples and the triangular resolvents in duality.