一类连续体上连续映射的周期点

设X是个阶有限的遗传可分解可链连续体, f:X→X是X上的连续自映射, On(x,f)={fi(x):0≤i≤n)是f的一个返回轨道, inf(On(x,f))相似文献   

应力和位移约束下连续体结构拓扑优化

同时考滤应力和位移约束的连续体结构拓扑优化问题,很难用现有的均匀方法或变密度方法等求解。主要困难在于难以建立应力和位移约束与拓扑设计变量间显式关系式;即使建立了这种关系,也由于优化问题规模过大,利用常规的数学规划方法难以求解。隋允康、杨德庆曾提出了基于独立连续拓扑变量及映射变换（ＩＣＭ）的桁架结构拓扑优化模型。本文在此基础上,建立了以重量为目标,考虑应力和位移约束的连续体结构拓扑优化模型,并推导出     

遗传可分解可链连续体上的动力系统

证明遗传可分解可链连续体上,不含非２方幂周期轨道的连续映射限制到每个非周期回复点的ω极限集上拓扑半共轭于加法机器,得到 Ｓｕｓｌｉｎｅ可链连续体上连续映射拓扑熵为 ０的五个充要条件．     

遗传可分解可链连续体上的动力系统

证明遗传可分解可链连续体上,不含非2方幂周期轨道的连续映射限制到每个非周期回复点的ω极限集上拓扑半共轭于加法机器,得到Susline可链连续体上连续映射拓扑熵为0的五个充要条件.     

M－连续格到Hilbert方体的嵌入

本文主要讨论Ｍ－连续格到Ｈｉｌｂｅｒｔ方体的嵌入问题．我们建立了Ｍ－连续格的次直积表示理论，推广并统一了Ｒａｎｅｙ，Ｂｒｕｎｓ，Ｌａｗｓｏｎ，Ｂａｎｄｅｌｔ和Ｅｒｎｅ等人的相应工作．Ｒｅｎａｙ与Ｂｒｕｎｓ的经典方法是建立在对相应的弱辅助关系的极大完备链作深入分析之上的，富于技巧性，且有局限性．与之相比，本文所使用的方体则相当朴素而自然，但却能处理更为广泛的情形．     

M－连续格到Hilbert方体的嵌入

本文主要讨论Ｍ－连续格到Ｈｉｌｂｅｒｔ方体的嵌入问题．我们建立了Ｍ－连续格的次直积表示理论，推广并统一了Ｒａｎｅｙ，Ｂｒｕｎｓ，Ｌａｗｓｏｎ，Ｂａｎｄｅｌｔ和Ｅｒｎｅ等人的相应工作．Ｒｅｎａｙ与Ｂｒｕｎｓ的经典方法是建立在对相应的弱辅助关系的极大完备链作深入分析之上的，富于技巧性，且有局限性．与之相比，本文所使用的方体则相当朴素而自然，但却能处理更为广泛的情形．     

基于Cosserat连续体理论的粉末高温合金弹塑性损伤分析

回顾了航空发动机涡轮盘粉末高温合金材料的发展及研究方法,基于Cosserat连续体理论,建立了粉末高温合金材料的弹塑性损伤模型,可通过特征长度考虑材料的微结构特征,并在模拟软化问题时消除局部化带的网格依赖性.在软化问题中,经典弹塑性理论在计算时需要较多迭代,有时甚至不能收敛.该文基于参变量变分原理,把原非线性问题转化为互补问题来求解,可大大提高求解效率和收敛性.最后通过数值算例验证了本文提出方法的有效性.     

财务领导力三问

领导,冒号;领导力,句号;财务领导力,问号!虎年之春,《新理财》一年一度的中国CFO年度人物评选已近尾声,通过与入围CFO的对话,我们正试图解开这个问号。     

大学生领导力水平的言语产出流量检测

在互动交际过程中,人们的心理活动和言语产出是同时发生的,言语行为具有词量和词序的流量特征。大数据时代,利用自然语言分词技术和文本数据的言语流量特征,分析用户的心理特征,已成为新的言语认知科学研究趋势。领导力是一种典型的期望沟通影响最大化的心理活动,在基于4928份数据的领导力水平言语产出流量特征的模式识别实例中,证实了名词词量、词序等言语流量特征识别高领导力水平的有效性。     

代数体函数的正规定理

为克服代数函数多值的困难,我们定义了一种新的“距离”,运用它我们证明了一个正规定理,代数体函数族{fj}在区域D上是正规的,当且仅当{fj}是等度连续的。     

微极连续体力学比经典连续体力学更深入一层次

本文通过刚删架(动静态响应与屈曲)的微极梁板模型,血液的牛顿-微极分层流模型以及人骨微极特性的实验论证等阐明微极连续体理论的本质特点,从应用侧面阐述微极连续体力学比经典连续体力学更深一层次的观点,并介绍该理论及其近期应用的部分进展情况。     

Infinitesimals and the Continuum

The Mathematical Intelligencer -     

Continuum analogue of bimodal distributions

We consider the Boltzmann equation for the hard-sphere model. We construct an explicit approximate solution of this equation in the form of a continuum distribution in the case of global Maxwellians. We obtain some sufficient conditions for attaining the minimum of the uniform-integral mismatch between the sides of the equation.     

模糊集的基数与连续统假设

本文在模糊映射的基础上给出了模糊集基数的定义，它把普通集的基数作为特款；不但得到有关基数的大部分结论，而且有其自身的特殊性质；特别，对于连续统假设这一世界难题可能有新的启示．     

连续统与Turing度

令Ｄ为所有Ｔｕｒｉｎｇ度的集合，≤为Ｄ上的图林化归关系．一函数ｆ：Ｄ→Ｄ称为前进函数如果对任何ａ∈Ｄ，ａ≤ｆ（ａ）。对于一个前进函数ｆ，我们说Ｄ中的两个度ａ，ｂ是ｆ－不可比较的，如果ａ≮ｆ（ｂ）且ｂ ≮ｆ（ａ），否则是ｆ－可比较的．本文的一个主要结果是：在ＺＦＣ中连续统假设成立当且仅当存在一个前进函数ｆ：Ｄ→Ｄ使得Ｄ中任何两个度都是ｆ－可比较的.     

Thermodynamic Inequalities in Continuum Mechanics

The constitutive relations for the transport of heat, stress,electric charge, etc., in a continuum must be chosen so thatthe second law of thermodynamics is not violated; the constraintstake the form of inequalities, typically requiring the entropygenerated within a material element to be non-negative. Thepaper is concerned with this concept—its history, thephysical principles on which it depends, how to apply it whensecond-order or non-linear effects are important and how itis widely misused in modern continuum mechanics. The history is reduced to the contributions of five leadingthermodynamicists—Clausius, Maxwell, Gibbs, Boltzmannand Duhem. The object here was to try to discover which formof the inequality one should regard as being fundamental. Oneimportant conclusion is that entropy S must be defined simultaneouslywith the identification of the inequality, and that in generalthis cannot be done until the constitutive equations are known.The empirical element enters with the notion of irreversibility,which is given a precise meaning with the aid of the motionreversed parity (x), a variable x having = +1 or = –1if, when time and motions are reversed, x x or x –x.The macroscopic parity of x, _*(x), is obtained by first replacingx by the constitutive equation for x. The entropy production rate has both irreversible (f) and reversible(r) parts. It is shown that the reciprocal relations followfrom the requirement that the macroscopic parity of (i) mustbe +1. Continuum thermodynamics is based on various principles extractedfrom theory developed for uniform systems, the example chosento illustrate the ideas being the simple monatomic gas. Second-orderconstitutive relations are introduced, and the expressions forentropy and its production rate per unit volume, , obtained.It is shown that the stability condition 0 cannot, in general,be satisfied merely by imposing constraints on the constitutiverelations. To second-order = ₁ + ₂, where ₁ is the usual bilinearform, and the terms in ₂ have an additional derivative. Thesecond-order term ₂ can have both signs, and is not dissipative.The relation between this fact and the frame-dependence of constitutiverelations is explained. The final section illustrates the errors frequently found inthe thermodynamic arguments appearing in books and papers onrational continuum mechanics. The principle of these is that 0 is interpreted as being a constraint on the constitutiverelations alone. Another is the idea that the balance equationscan be set aside as constraints by regarding them as mere definitionsof a heat source and a body force, an error based partly onthe misconception that constitutive relations should be frame-indifferent.Finally, an inequality due to Glansdorff & Prigogine isexamined and found to be in error.     

Continuum Thermodynamics and Phase-Field Models

Phase transitions between two phases are modelled as space regions where a phase-field changes smoothly. The two phases are separated by a thin transition layer, the so-called diffuse interface. All thermodynamic quantities are allowed to vary inside this layer, including the pressure and the mass density. A thermodynamic approach is developed by allowing for the nonlocal character of the continuum. It is based on an extra entropy flux which is proved to be non vanishing inside the transition layer, only. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type. Necessary and sufficient restrictions placed by thermodynamics are derived for the constitutive equations and, furthermore, a general form of the evolution equation for the phase-field is obtained within the schemes of both a non-conserved and a conserved phase-field. Based on the thermodynamic restrictions, a phase-field model for the ice-water transition is established which allows for superheating and undercooling. A model ruling the liquid-vapor phase transition is also provided which accounts for both temperature and pressure variations during the evaporation process. The explicit expression of the Gibbs free enthalpy, the Clausius-Clapeyron formula and the customary form of the vapor pressure curve are recovered.