查询词典 extremal function

We generalize the concept of the set of variability defined in the unit diskby K.Strebel to general Riemann surfaces and prove that the set of variablity withrespect to the modulo homotopic class of a quasiconformal mapping between twoRiemann surfaces is a compact and connected subset.Consequently the num-ber of the extremal mappings in the modulo homotopic class of a quasiconformalmapping between two general Riemann surfaces is either one or infinity.

Strebel的定义在单位圆上的可变性集合的概念推广到一般Riemann曲面上去，并且证明了Riemann曲面之间的拟共形映射的模边同伦类所确定的可变性集合是一个连通的紧子集，从而得出一般Riemann曲面之间拟共形映射的模边同伦类中的极值映射要么唯一，要么有无穷多个。

In this thesis, the results of extremal work path theory are adopted, and the FEM based on deformation theory is formulated. The Inverse Finite Element Approach in sheet metal forming is studied in detail, and an Object-Oriented Finite Element Analysis program is developed, which provides rapid and effective means for stamping process planning and die design.

本文运用极值路径理论推导出基于形变理论的有限元公式，研究了钣料成形有限元逆算法，开发了面向对象的有限元分析程序，为冲压工艺和模具设计提供了快速有效的分析手段。

By using the Lie group theory of differential geometry and Pontryagin's maximum principle, it is pointed out that the mobile CRS robot on surface is controllable, and the necessary conditions and the structure equations of extremal trajectories are proposed.

为了解决曲面上移动CRS机器人的路径规划问题，在曲面上建立了机器人的动态模型，利用微分几何的李群理论和庞特里亚金最大值原理，证明了曲面上CRS机器人是可控的，并给出了机器人的最小时间控制的必要条件和结构方程。

By using the Li e group theory of differential geometry and Pontryagin's maximum principle, it is pointed out that the mobile CRS robot on surface is controllable, and the nec essary conditions and the structure equations of extremal trajectories are propo sed.

为了解决曲面上移动CRS机器人的路径规划问题，在曲面上建立了机器人的动态模型，利用微分几何的李群理论和庞特里亚金最大值原理，证明了曲面上CRS机器人是可控的，并给出了机器人的最小时间控制的必要条件和结构方程。

A key problem is: is it true that the supremum of the ratios of the moduli of quadrilaterals equals to the extremal maximal dilatation?In this chapter, firstly, for a class of quasisymmetric homeomorphisms with substantial boundary points, we apply a result of Chen Jixiu etc.

在第二章中，我们首先利用了文[16]的结果，研究了单位圆周上一类具有本质边界点的拟对称同胚，证明了它的极值拟共形延拓的最大伸缩商等于四边形模之比的上确界，改进了文[128]的有关结果。

Response intensity ; statistic characteristics ; engineering seismology ; extremal theory ; seismic risk analysis ; antiseismic parameter

影响烈度；统计特性；工程地震；极值理论；地震危险性分析；抗震设防参数

The existence and uniqueness of homogeneous elliptic polyharmonic cardinal spline interpolation are proved, the remainder formula and order of approximation in LP (1≤p≤∞)spaces are given, and the extremal problem of sobolev dass in L2 is considered.

获得Rd上齐次椭圆型Cardinal样条插值的存在唯一性，并获得Sobolev类上的函数在Lp（1≤p≤∞）尺度下的插值误差估计，以及Sobolev类在L2尺度下的一些极值问题的解；拓广了Laplace型的结果。

In this paper, we give some qualities of the set exponent of symmetric primitive digraphs, and characterize completely the extremal graphs of the κth upper generalized exponent for primitive simple graphs.

本文给出了对称本原图的集指数的一些性质，并对本原简单图的广义上指数的极图进行了完全刻划。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

We prove the equivalent conditions of completely monotone function, we also discuss the relationship of positive definite function, semi-positive definite function and completely monotone function when the function take values in a commutitive von Neumann algebras.

我们证明了完全单调函数的几个等价条件，并且讨论了取值于交换von Neumann代数的正定函数，半正定函数及完全单调函数之间的关系。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。