Projective equivalence of Finsler and Riemannian surfaces

In this paper we ask when a Finsler surface is projectively equivalent to a given Riemannian surface and when is a Finsler surface projectively equivalent to some Riemannian surface in general. We obtain a necessary and sufficient condition for projective equivalence in both cases. We then consider the latter condition in terms of the Christoffel symbols of the Riemannian metric and investigate when six functions of two variables are the Christoffel symbols of a Riemannian metric. We employ an exterior differential system to analyze when four functions of two variables are the four projective quantities of a Riemannian metric. We end the paper with a theorem which applies the necessary and sufficient condition to 2-dimensional Randers metrics.     

Pension fund investments and the valuation of liabilities under conditional indexation

This paper reviews the investment policy of collective pension plans. We focus on funds with a collective Defined Contribution character. We suggest two reasons to invest in equities: the lack of a well-developed market in index-linked bonds, and deliberate deviations from the Defined Benefit nature of the plan. Furthermore, this paper assesses the value of limited or conditional indexation options found in many plans.     

浅谈现代教学和传统教学的结合

浅谈使用电子教案进行教学的体会 .揭示了如何充分利用现代教学技术的优势 .重点论述了如何在日常教学活动中把现代教学和传统教学有机地结合起来 ,以充分体现现代教育思想 ,培养创新型人才     

A stochastic model of AIDS and condom use

In this paper we introduce stochasticity into a model of AIDS and condom use via the technique of parameter perturbation which is standard in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as desired in any population dynamics. We also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment. Our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system.     

广义V—环与torsion理论

本文从一个角度推广了V—环的概念.定义τ—V环为使一切R上的关于某个torsion理论τ的τ—cocritical模皆内射的环,并将它与[1]中提出的F—V环进行了比较,得出了这种环的刻划.     

多媒体教学与传统教学优势互补的探讨

浅析了高等数学多媒体教学的正负效应,传统教学的特点与不足.结合教学实践,对传统教学与多媒体教学优势互补进行初步探讨,重点论述了优势互补能最大地发挥各种教学方法的综合功能,取得较好的教学效果.     

Density analysis of non-Markovian BSDEs and applications to biology and finance

In this paper, we provide conditions which ensure that stochastic Lipschitz BSDEs admit Malliavin differentiable solutions. We investigate the problem of existence of densities for the first components of solutions to general path-dependent stochastic Lipschitz BSDEs and obtain results for the second components in particular cases. We apply these results to both the study of a gene expression model in biology and to the classical pricing problems in mathematical finance.     

Global minimization of difference of quadratic and convex functions over box or binary constraints

In this paper, we present necessary as well as sufficient conditions for a given feasible point to be a global minimizer of the difference of quadratic and convex functions subject to bounds on the variables. We show that the necessary conditions become necessary and sufficient for global minimizers in the case of a weighted sum of squares minimization problems. We obtain sufficient conditions for global optimality by first constructing quadratic underestimators and then by characterizing global minimizers of the underestimators. We also derive global optimality conditions for the minimization of the difference of quadratic and convex functions over binary constraints. We discuss several numerical examples to illustrate the significance of the optimality conditions. The authors are grateful to the referees for their helpful comments and valuable suggestions which have contributed to the final preparation of the paper.     

Cumulative measures of information and stochastic orders

In this paper we present some known results on cumulative measures of information, study their properties and relate these definitions to concepts of reliability theory. We give some relations of these measures of discrimination with some well-known stochastic orders and with the relative reversed hazard rate order. We investigate also a stochastic comparison among the empirical cumulative measures that can be related to the cumulative measures. Large part of this paper is a survey article; however, in the last section, we define a new measure of discrimination between residual lifetimes and study some of its properties.     

Homogenization and penalization of functional first-order PDE

In this paper we study the asymptotic behavior of viscosity solutions for a functional partial differential equation with a small parameter as the parameter tends to zero. We study simultaneous effects of homogenization and penalization in functional first-order PDE. We establish a convergence theorem in which the limit equation is identified with some first order PDE.     

单自由度及多自由度系统非平稳随机振动

在文[1]中,对如下所示的非平稳随机过程其中,这里W(t,τ)是系统的单位脉冲响应函数.本文是[1]的继续,我们对单自由度及多自由度系统给出若干结果.     

Hecke-symmetry and rational period functions

In this paper, we continue our work in the direction of a characterization of rational period functions on the Hecke groups. We examine the role that Hecke-symmetry of poles plays in this setting, and pay particular attention to non-symmetric irreducible systems of poles for a rational period function. This gives us a new expression for a class of rational period functions of any positive even integer weight on the Hecke groups. We illustrate these properties with examples of specific rational period functions. We also correct the wording of a theorem from an earlier paper.     

A stochastic model for interactions of hot gases with cloud droplets and raindrops

In this paper we analyze a stochastic model for interactions of hot gases with cloud droplets and raindrops. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic hot gases modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any hot gas dynamics model. We also carry out analysis on the stochastically ultimate boundedness, extinction and stability of the hot gases model.     

On inverses and algebraic loops of co-H-spaces

In this paper we study the properties of homotopy inverses of comultiplications and algebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primarily interested in the algebraic loops which have inversive, power-associative and Moufang properties for some comultiplications.     

Hochschild cohomology of abelian categories and ringed spaces

This paper continues the development of the deformation theory of abelian categories introduced in a previous paper by the authors. We show first that the deformation theory of abelian categories is controlled by an obstruction theory in terms of a suitable notion of Hochschild cohomology for abelian categories. We then show that this Hochschild cohomology coincides with the one defined by Gerstenhaber, Schack and Swan in the case of module categories over diagrams and schemes and also with the Hochschild cohomology for exact categories introduced recently by Keller. In addition we show in complete generality that Hochschild cohomology satisfies a Mayer-Vietoris property and that for constantly ringed spaces it coincides with the cohomology of the structure sheaf.     

General constructions of biquandles and their symmetries

Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set theoretic solutions of the well-known Yang-Baxter equation. The first half of this paper proposes some natural constructions of biquandles from groups and from their simpler counterparts, namely, quandles. We completely determine all words in the free group on two generators that give rise to (bi)quandle structures on all groups. We give some novel constructions of biquandles on unions and products of quandles, including what we refer as the holomorph biquandle of a quandle. These constructions give a wealth of solutions of the Yang-Baxter equation. We also show that for nice quandle coverings a biquandle structure on the base can be lifted to a biquandle structure on the covering. In the second half of the paper, we determine automorphism groups of these biquandles in terms of associated quandles showing elegant relationships between the symmetries of the underlying structures.     

Optimal Open-Loop Control of Vacations,Polling and Service Assignment

We consider in this paper the optimal open-loop control of vacations in queueing systems. The controller has to take actions without state information. We first consider the case of a single queue, in which the question is when should vacations be taken so as to minimize, in some general sense, workloads and waiting times. We then consider the case of several queues, in which service of one queue constitutes a vacation for others. This is the optimal polling problem. We solve both problems using new techniques from [2,4] based on multimodularity.     

Measures of serial extremal dependence and their estimation

The goal of this paper is two-fold: (1) We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. (2) We discuss recent concepts of heavy-tailed time series, including regular variation and max-stable processes.     

Focal points and principal solutions of linear Hamiltonian systems revisited

In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.     

Geometry and asymptotics of wavefronts

Methods of convex analysis and differential geometry are applied to the study of properties of nonconvex sets in the plane. Constructions of the theory of α-sets are used as a tool for investigation of problems of the control theory and the theory of differential games. The notions of the bisector and of a pseudovertex of a set introduced in the paper, which allow ones to study the geometry of sets and compute their measure of nonconvexity, are of independent interest. These notions are also useful in studies of evolution of sets of attainability of controllable systems and in constructing of wavefronts. In this paper, we develop a numerically-analytical approach to finding pseudovertices of a curve, computation of the measure of nonconvexity of a plane set, and constructing front sets on the basis these data.In the paper, we give the results of numerical constructing of bisectors and wavefronts for plane sets. We demonstrate the relation between nonsmoothness of wavefronts and singularity of the geometry of the initial set. We also single out a class of sets whose bisectors have an asymptote.