关于积流形的P－形式上的Laplace算子谱

本文讨论了积流形的Ｐ－形式上Ｌａｐｌａｃｅ算子谱的唯一性问题，在紧Ｋａｃｈｌｅｒ流形乘积和紧Ｓａｓａｋｉ流形乘积的两类积流形中，ＣＰ^ｎ×ＣＰ^ｎ和Ｓ^２ｎ＋１（１）×Ｓ^２ｎ＋１（１）是Ｐ－形式上Ｌａｐｌａｃｃｅ算子谱特征。     

Borel on the Questions Versus Borel on the Answers

We consider morphisms (also called Galois-Tukey connections) between binary relations that are used in the theory of cardinal characteristics. In [8] we have shown that there are pairs of relations with no Borel morphism connecting them. The reason was a strong impact of the first of the two functions that constitute a morphism, the so-called function on the questions. In this work we investigate whether the second half, the function on the answers' side, has a similarly strong impact. The main question is: Does the nonexistence of a Borel morphism imply the non-existence of a morphism that is only Borel on the answers' side? We give sufficient conditions for an affirmative answer. The results are applied to the unsplitting relations where it has been open whether there is a morphism that is Borel on the answers' side.     

Sets with the Pompeiu property on the plane and on the sphere

We obtain new sufficient conditions under which a set on the plane has the Pompeiu property. This result allows us to construct first examples of domains with the Pompeiu property with non-Lipschitz (and even fractal) boundary. In addition, we study the problem of determining the least radius of the ball on the sphere in which a given set is a Pompeiu set. We obtain the solution of this problem in the case of a biangle and a spherical half-disk. We also consider some applications to questions of complex analysis.     

关于二维球面上的Ricci流的一个注记

给出Hamilton和Chow关于二维球面上的Ricci流的一个定理的新证明．这个证明结合了Hamilton关于Ricci流的紧性定理和二维ancientp解的分类和Perelman的非塌缩定理．     

服务管理差距与服务质量差距之间关系模型的研究

在服务质量差距分析模型的基础上,基于服务管理差距和服务质量差距测评体系,运用结构方程建模方法,建立了企业内部服务管理差距与顾客感知服务质量差距之间的关系路径图和关系模型,定量研究了四个服务管理差距对服务质量差距的影响关系、服务管理差距测评指标对相应的四个服务管理差距的影响关系,为顾客感知服务质量差距的测量和评价提供了技术和方法.结合某外语培训学校服务管理实际进行了案例研究,为企业服务质量的诊断和改进提供了科学依据.     

基于一类分类方法的多类分类研究

在分析非线性数据处理新方法—核方法理论的基础,研究基于一类分类方法的多类分类的基本原理,提出应用于多类分类的可信度函数,使分类的结果更具有可信度.最后,以某企业对供应商关系调查数据为例,将这种方法应用于企业商业关系分析中,结果表明该方法的有效性,为非线性数据分类提供了一种新方法.     

基于元胞自动机的“右行左超车”规则作用与影响分析

研究“右行左超车”规则在高速公路不同交通负荷下对通行能力及安全性的影响。引入超车欲望值及状态改变率的概念,基于交通流元胞自动机模型,建立了“右行左超车”规则下的单向双车道和三车道换道规则及相应的超车规则。选取5个评价参数,针对两车道模型,将“右行左超车”规则与无规则下的换道超车对交通效率与安全表现的影响进行对照试验。试验结果表明：在安全表现方面,低负荷状态下“右行左超车”规则较无规则情形要差,而在高负荷状态下,该规则较无规则情形好;在通行能力方面二者差别不大;试验结果还表明：无论是有规则还是无规则,提高车道的最大与最小限速不仅可以提升道路的通行能力,而且可以提升安全性。最后分析了模型的优缺点,并指出了改进的方向。     

人力资本对区域可持续发展影响的实证研究

本文以我国31个省、直辖市、自治区为单位,应用聚类分析方法对各地区的人力资本、经济发展、环境状况进行分析,试图探讨人力资本对我国区域可持续发展的影响和途径。结果表明,目前我国区域环境压力随着经济的发展而不断增大,并逐步进入减速发展阶段,各地区应加大对人力资本的投资力度,实现经济的腾飞和环境保护力度的增强,最终实现我国区域可持续发展。     

A Sharp Inequality on the Exponentiation of Functions on the Sphere

In this paper we show a new inequality that generalizes to the unit sphere the Lebedev-Milin inequality of the exponentiation of functions on the unit circle. It may also be regarded as the counterpart on the sphere of the second inequality in the Szegö limit theorem on the Toeplitz determinants on the circle. On the other hand, this inequality is also a variant of several classical inequalities of Moser-Trudinger type on the sphere. The inequality incorporates the deviation of the center of mass from the origin into the optimal inequality of Aubin for functions with mass centered at the origin, and improves Onofri's inequality with the contribution of the shifting of the mass center explicitly expressed. © 2021 Wiley Periodicals LLC.     

Polynomial Interpolation on the Unit Sphere and on the Unit Ball

The problem of interpolation on the unit sphere S ^d by spherical polynomials of degree at most n is shown to be related to the interpolation on the unit ball B ^d by polynomials of degree n. As a consequence several explicit sets of points on S ^d are given for which the interpolation by spherical polynomials has a unique solution. We also discuss interpolation on the unit disc of R ² for which points are located on the circles and each circle has an even number of points. The problem is shown to be related to interpolation on the triangle in a natural way.     

Report on the activities of the working group on discrete mathematics

In the past decade there have been significant developments in computer technology and solution techniques for analysing business and industrial decision problems. In recent years good modelling systems have become available to ease the burden of model communication. Currently the single most important barrier to increased use of structured approaches to decision modelling is the acquisition of the necessary skills to initially develop models of complex decision systems. This paper examines the modelling process with reference to linear programming. Two related production planning problems are presented and their associated models developed. The relationship between the two problems is such that student modellers are forced to become involved in the important details of the problems and, by examining the nature of solution spaces in constrained optimisation, students are able to rapidly gain confidence and skills in modelling.     

基于离散选择模型DCM的产品差异市场分析

本文从计量经济学的角度,利用离散选择模型对产品差异市场进行了研究,在消费者异质性需求和厂商异质性能力假设下,利用消费者产品性能边际效用递减规律推导出产品性能消费者收益函数,利用产品性能边际成本递增规律推导出产品性能厂商成本关系函数,最后得到消费者需求弹性和厂商在最大创造价值的产品性能决策点.     

An Analog of the Appollonian Circle on the Lobachevski Plane and on the Sphere

An analog of the Apollonian circle on the Lobachevski plane is a convex analytic curve. A similar curve on the sphere may be nonconvex and may contain one singular (nonanalytic) point. It follows that there may exist more than one spherical belt separating two given compacta on the sphere and having the maximum possible ratio of the exterior and interior radii. Bibliography: 3 titles.     

Convergence of the wave equation damped on the interior to the one damped on the boundary

In this paper, we study the convergence of the wave equation with variable internal damping term γn(x)ut to the wave equation with boundary damping γ(x)⊗δx∈∂Ωut when (γn(x)) converges to γ(x)⊗δx∈∂Ω in the sense of distributions. When the domain Ω in which these equations are defined is an interval in R, we show that, under natural hypotheses, the compact global attractor of the wave equation damped on the interior converges in X=H¹(Ω)×L²(Ω) to the one of the wave equation damped on the boundary, and that the dynamics on these attractors are equivalent. We also prove, in the higher-dimensional case, that the attractors are lower-semicontinuous in X and upper-semicontinuous in H1−ε(Ω)×H−ε(Ω).     

Remark on the weierstrass points on curves

We give a treatment of the Weiertrass points of curves which is a little different from the treatment by Laksov. We introduce the notion of theith weight which makes the treatment easier and gives an algorithm for computing the gap sequence of an effective divisor and the weight at a point. Supported in part by NNSF of China.