关于矩阵病态程度的一种新度量

1.引言 许多数值计算问题都能用下列方式来描述:给出一个数学上定义的函数f:S(?)C~m→C~n,这里C~m、C~n分别表示m维和n维向量空间,S是C~m的一个子集,f的自变量x的m个分量是确定问题的数据,而f(x)的n个分量是问题的答案。     

单位圆盘上全纯映照模的精细Schwarz引理

记DC为单位圆盘,B~p={z∈C~n:n∑i=1|z_i|~p1},1p+∞.该文证明了若f∈H_m(D,B~p),则|▽||f||(z)≤m|z|~(m-1)/1-|z|~(2m)(1-||f(z)||~2),z∈D.同时,当p为偶数时,该文也讨论了相应的极值问题,所得结论推广了一些相关结果.     

球上α-Bloch函数的一类特征

对于C~n中单位球上的α-Bloch函数,利用D~βf(β>0)给出了它的一种刻画,并用Carleson测度的形式予以表示,推广了原有的单位圆盘和单位球上的几个结果.     

多复变Fekete-Szeg问题

令y为单位圆盘上正规化单叶函数族.Fekete和Szeg证明了如下的著名结果:对λ∈[0,1],成立max_(f∈y)|a_3-λa_2~2|=1+2~(-(2λ)/(1-λ)).本文研究了C~n中有界星形圆形域上的星形映照的相应问题.定理的证明有假设条件,但该条件在单复变情形下是自动满足的.     

多复变量Toeplitz算子的交换性

本文刻画了C~n中单位球和多圆盘Bergman空间上一些Toeplitz算子的换位。首先,对双圆盘Bergman空间,刻画了什么时候 Toeplitz算子T_f和T_g交换,这里 f=f1+,g=g1+,fi,gi∈H~∞(D~2)(i=1,2)。其次,如果表示由多复变量 Toeplitz算子生成的赋范闭子代数,证明了对每个正整数m,{T_z_1~m,…,T_z_n~m}′∩是所有解析Toeplitz算子的集合,这里z_i(i=1,…,n)是坐标函数。     

The degree of biholomorphic mappings between special domains in C~n preserving 0

Let G_i be a closed Lie subgroup of U(n), ?_i be a bounded Gi-invariant domain in C~n which contains 0, and O(C~n)~(Gi) = C, for i = 1, 2. If f : ?_1→ ?_2 is a biholomorphism, and f(0) = 0, then f is a polynomial mapping(see Ning et al.(2017)). In this paper, we provide an upper bound for the degree of such polynomial mappings. It is a natural generalization of the well-known Cartan's theorem.     

多复变数准凸映射的偏差定理

首先给出了C~n中单位多圆柱D~n上准凸映射f关于Jacobin矩阵J_f(z)的偏差定理.该定理是单位圆盘凸函数的偏差定理在多复变中的推广.其次得到了Banach空间单位球上准凸映射的偏差定理的上界.最后给出了关于准凸映射偏差定理的两个猜想.     

多复变整函数涉及全导数的唯一性定理

结合金路提出的多复变上整函数全导数的概念,得到了如下定理:对于n维复欧式空间C~n上两个非常数整函数f和g,以及一个正整数k,如果δ(0,f)+δ(0,g)1,D~kf=1D~kg=1,那么f≡g.这一结论是仪洪勋和杨重骏的定理的推广.     

Schwarz引理与Schwarz-Pick引理在单位球B_n上的推广

对单复变中的Schwarz引理与Schwarz-Pick引理在C~n中的超球上进行了推广.考虑C~n中单位球B_n上模小于1的全纯函数f(z),并在f(0)=0的条件下给出函数在原点的任意阶导数的估计.更进一步地,得到了B_n上模小于1的任意全纯函数在任意点的高阶导数的估计.     

关于有界对称域中全纯函数的零点集

<正> 熟知对复平面中单位圆盘U中任一趋于边界的点列{a_i},它是H~p(U)中某函数的零点集的必要且充分条件为时,全纯函数零点集的情况非常复杂.首先,Miles在1973年证明了对C~n中多圆柱U~n,当0相似文献   

废弃食品回流再造问题的产品价格分析

针对废弃食品回流再造的食品安全问题,建立相关利益主体包括食品制造商、废弃食品收购者在各自独立以及作为利益共同体的不同条件下的优化模型,分析新生产食品价格和回流再造食品价格以及相应的利润、影响因素.结果表明:作为同一利益主体,生产制造昂贵食品对食品制造商获利不利,而回流再造成本越低,对食品制造商通过回流再造获利是有利的;若食品制造商和收购者各自独立决定价格,收购者进行回流再造的行为会干扰当前食品零售市场;由于回流再造食品的价格比较优势,在信息不对称时消费者会倾向选择回流再造食品.     

Time-linearized,compact methods for the inviscid GRLW equation subject to initial Gaussian conditions

The objective of this paper is three-fold. First, four time-linearization methods that are second- and fourth-order accurate in time and space, respectively, are presented and used to study the dynamics of the modified and generalized regularized-long wave equations (mRLW and GRLW equations, respectively). Two of the methods use the conservation-law form of the equations and treat the wave amplitude and its second-order spatial derivative and the linear and nonlinear advection fluxes as unknowns, whereas the other two employ the non-conservation-law form of the equations and consider the wave amplitude and its first- and second-order spatial derivatives as unknowns. The methods employ three-point fourth-order accurate Padé discretizations for the first- and second-order derivatives, are second-order accurate in time, and yield linear systems of blocktridiagonal matrices. Second, the accuracy of these methods is assessed by comparing their results with those of the exact solution of the mRLW equation. It is reported that the four methods predict nearly the same values of the three invariants and have the same accuracy, and that an accurate prediction of the invariants may not correspond to small errors in space and time. Third, the dynamics of the inviscid GRLW equation is studied first qualitatively in terms of length and time scales and then numerically as a function of the linear advection speed, the exponent of the nonlinear advection flux, the dispersion coefficient and the amplitude and width of the initial bell-shaped or Gaussian conditions. It is shown that wide initial conditions result in wave steepening and breakup and the formation of solitary waves whose amplitude and speed decrease as the time for their formation increases. For narrow initial conditions, it is shown that only a single solitary wave may form. Behind this wave and depending on the parameters that characterized the inviscid GRLW equation, rarefaction or negative amplitude waves that propagate towards the upstream boundary or a train of localized oscillatory waves that do not emerge from the trailing edge of the leading solitary wave may be formed. These oscillatory waves exhibit the characteristics of, but are not dispersive shock waves and their amplitude and frequency increases as the width of the initial conditions is decreased. The results presented here do not only complement previous work by the authors, they also show that the dynamics of the inviscid GRLW equation undergoes new and interesting phenomena as the width of the initial conditions is decreased.     

带有能源的随机动态柯布—道格拉斯生产函数

在考虑能源作为投入要素和经济环境随机动态变化的情况下,将经典的柯布-道格拉斯生产函数推广到随机动态的形式.首先给出了随机动态C-D生产函数的随机微分方程形式,证明了该生产函数解的存在性和唯一性;其次,进一步分析了解的Markov性质和扩散性质,并分别利用漂移系数和扩散系数给出了产出弹性的计算公式.最后,还给出了经济增长...     

Place and use of new technology in the teaching of mathematics: ICMI activities in the past 25 years

Looking back at the place of technology in the past ICMEs during the last decades and on the two ICMI studies devoted to technology, it is obvious that the role and use of technology has given rise to a diversity of points of view and attitudes across the world. The ICMEs and the two studies are places where researchers, teacher educators and practitioners meet. To what extent do they reflect the evolution of the trends of research and/or of integration of technology into real practice? The study will develop a general analysis of the theoretical frameworks, issues and wishes related to the use of technology in mathematics teaching from the proceedings of past ICMEs and of the two ICMI studies. Both a quantitative and a qualitative point of view will be adopted. From the great diversity of questions and approaches, the study attempts to formulate the main trends and their evolution over time within the ICMI community, as well as some pertinent issues for the coming years.     

行业结构环境的序参量分析方法研究

行业结构环境分析是发现和掌握行业运行规律与发展状况的必经之路,也是在企业战略管理中的重要组成部分,其结果直接影响着企业战略决策与实施。针对企业战略管理的新价值理念,本文在协同学与竞优理论的基础上,通过对行业内群体结构特性与企业行为的重新考察,建立了行业结构环境分析的一种新方法即序参量分析方法与其应用范例。本文的研究结果,如行业内多层结构、企业群组定位及分布特性、行业基本发展模式、标杆与协同伙伴、企业群组或群组内企业构成与绩效之间的关系等都可为实现符合现代产业发展环境的企业战略管理提供方向性辅助与技术支持。     

基于关系契约视角的农户与农产品电子商务企业合作机制演化博弈分析

本文基于关系契约的视角,运用演化博弈理论,构建有限理性特性下的农户与农产品电子商务企业合作演化博弈模型,分析双方合作策略的演进过程、稳定策略及其影响因素,并通过Matlab仿真模拟分析影响双方合作策略选择的因素,验证博弈结果正确性。研究结果表明:农户和农产品电子商务企业选择合作策略与合作投入成本、实现的超额收益密切相关,博弈初始状态、再交易成本、单方不合作获得的收益及违约罚金等因素影响系统的演化稳定结果。因此完善农户与农产品电子商务企业的合作机制,需要构建合理的利益分配机制、良好的关系治理机制、有效的监督和惩罚机制和信息共享、沟通与协调机制。     

基于“动态生成”的大学数学课堂教学

"动态生成"教学观的建立旨在摆脱课堂教学中以教师为中心、强调知识传授的传统教学模式的缺陷,从根本上正确理解课堂教学的复杂性和动态性,构建充满生命活力的大学数学课堂教学生态环境.在用动态生成的视角审视当前大学数学课堂教学中存在的问题的基础上,文章对在课堂教学中如何有效地进行动态生成提出了一些具体的策略:更新教学观念,精心预设弹性化的数学课堂教学方案;根据学生课堂反馈情况及时调整预设,并及时捕捉可利用的动态资源,为学生的生成创造可能的机会;加强教学研究,不断提高课堂教学智慧.     

Boundary-Value Problems of the Theory of Thin and Nonthin Orthotropic Shells with Account of Nonlinearly Elastic Properties and Low Shear Rigidity of Composite Materials

The basic geometric and physical relations and resolving equations of the theory of thin and nonthin orthotropic composite shells with account of nonlinear properties and low shear rigidity of their materials are presented. They are derived based on two theories, namely the theory of anisotropic shells employing the Timoshenko or Kirchhoff-Love hypothesis and the nonlinear theory of elasticity and plasticity of anisotropic media in combination with the Lagrange variational principle. The procedure and algorithm for the numerical solution of nonlinear (linear) problems are based on the method of successive approximations, the difference-variational method, and the Lagrange multiplier method. Calculations of the stress-strain state for a spherical shell with a circular opening loaded with internal pressure are presented. The effect of transverse shear strains and physical nonlinearity of the material on the distribution of maximum deflections and circumferential stresses in the shell, obtained according to two variants of the shell theories, is studied. A comparison of the results of the problem solution in linear and nonlinear statements with and without account of the shell shear strains is given. The numerical data obtained for thin and nonthin (medium thick) composite shells are analyzed.     

The oscillations of a body with an orbital tethered system

The motion about a centre of mass of a rigid body with a tethered system, designed to launch a re-entry capsule from a circular orbit is considered. In the deployment of the tethered system the direction and value of the tensile strength of the tether vary and, if the point of application of the tensile strength does not coincide with the centre of mass of the body, a moment occurs which leads to oscillations of the body with variable amplitude and frequency. A non-linear equation of the perturbed motion of the body about the centre of mass under the action of the tensile force of the tether and the gravitational moment is derived. Assuming that the change in the value and direction of the tensile force is slow and also that the gravitational moment is small, approximate and exact solutions of the non-linear differential equation of the unperturbed motion are obtained in terms of elementary functions and elliptic Jacobi functions. For perturbed motion, the action integral is expressed in terms of complete elliptic integrals of the first and second kind.     

Theory and classification of the reversible structures of discontinuities in hydrodynamic-type models

The results of an analysis of the numerical and analytical solutions of the partial differential equations for different models of continuum mechanics and also the solutions of the ordinary differential equations of the travelling waves for these models are presented. Typical models, the basic theses of the theory of discontinuities in models of the reversible and weakly dissipative type, the classification of time-invariant structures and time-varying ordered structures are considered. The theory includes elements such as the use of averaged equations, evolutionary conditions, conditions for the complete and partial reversibility of a discontinuity, conditions for the existence of a solution in the typical case obtained using dimensional analysis of the invariant manifolds and the number of additional parameters varied and the classification of the periodic waves, solitary waves and kinks with respect to the number of free parameters.