查询词典 compactness

A L(superscript ∞) bound estimate is provided on the solutions of a semi-linear parabolic system by the theory of phase transitions. The existence of solutions of corresponding hyperbolic system of conservation laws is studied by viscosity methods and compensated compactness framework.

讨论来源于物理相变理论的一类半线性抛物型方程组解的一致L估计，该结果是利用粘性法和补偿列紧框架研究相应的双曲型守恒律解的存在性的重要内容。

A L∞bound estimate is provided on the solutions of a semi-linear parabolic system by the theory of phase transitions.The existence of solutions of corresponding hyperbolic system of conservation laws is studied by viscosity methods and compensated compactness framework.

讨论来源于物理相变理论的一类半线性抛物型方程组解的一致L∞估计，该结果是利用粘性法和补偿列紧框架研究相应的双曲型守恒律解的存在性的重要内容。

However, the solutions of the Cauchy problem of the nonlinear hyperbolic system generally develop singularities in finite time even if the initial data are small and smooth.For this reason, solutions must be found in the space of discontinuous functions. Therefore, one can not directly use the classical analytic techniques that predominate in the theory of partial differential equations of other types. Instead, we construct approximate solutions via the singular perturbation methods. By using the compactness of the approximate solutions, we can obtain the existence of the solutions of original system.

然而一般而言，即使是在初值很小且光滑的情况下，非线性双曲型守恒律的Cauchy问题的解在有限时间内也会出现奇异性，为此，我们必须在不连续函数空间中寻找上述问题的解，因此对这类问题的研究，我们也不可能直接利用在其它类型的偏微分方程中占主导地位的解析方法来解决问题，而是通过奇异扰动法构造近似解，由近似解的紧性得到原问题解的存在性。

Ablish two decision theorems of relative compactness for unbounded function groups in an infinite interval.

sect；2.3我们建立了判定无穷区间上抽象无界连续函数组和抽象无界可微函数组相对紧性的充分必要条件，并对无穷区间上抽象二阶微分方程两点边值问题无界解的存在性做了研究。

Uniform continuity;Lebesgue number;property L ;compactness

一致连续；；Lebesgue数；；性质L；；紧性

uniform continuity ; Lebesgue number ; property L ; compactness

在〔11中，常庚哲等证明了R中的有界闭集具有这样的

In elliptic case,the compactness of"convex polyhedrons"is destinedto be true because of the"local Lipschitz continuity of convex functions",whilein parabolic case,we cannot expect convex-monotone functions have such goodproperties as convex functions.

在广义解存在性的证明中，参考椭圆情形由"凸多面体"逼近的思想，我们采用了由一种特殊构造的"凸单调多面体"逼近的途径，但在证明这种凸单调多面体族的紧性时，我们遇到了困难。

Their manifesto emphasizes infill development, mixed uses, compactness, and local geography as the main constituents of a balanced urban development.

他们强调，填充式发展，混合式利用，紧凑性和当地地理特性是城市平衡发展的主要要素。

In this paper, a varieties of concepts of compactness of sets and sunsets are introduced in a complex locally convex space, which are respectively the generalizations of the known sunsets and convex sets. By establishing the relationship between restricted p-centers of a set in a complex locally convex space and restricted Chebyshev centers of the corresponding set in the quotient space with respect to ker, characterizations and uniqueness of restricted p-centers of sets in a complex locally convex space are obtained. These results are better than any other known ones when we restrict them in real normed linear spaces and real locally convex space.

本文首先在复局部凸空间中引入了几种紧性及几种太阳集的概念，它们分别是已有紧性和凸集概念的推广；然后通过建立局部凸空间中集的限制p-中心和关于ker的商空间中对应集的限制Chebyshev中心的关系，来研究局部凸空间中集的限制p-中心问题，本文即使是在实赋范空间和在实局部凸空间中所得的结果都分别是有关已知结果的深化和推广。

Compactness of design, lowest possible mass, extremely low friction and maximum precision were also critical considerations.

压实度的设计，尽可能最低的质量，极低的摩擦和最大精确度是同样重要的考虑因素。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。