查询词典 maximum ergodic theorem

Part Ⅰ deals with the foundmental theory of variational technique in the lossy electromagnetic fields. In chapter two and three the Green theorem is introduced so the unified method to derive functional is given. Chapter four is devoted to discuss two type of inner product. In chapter five the generialized least function theorem is given and applied in the derivation of variational expressions.

第一篇主要是关于有耗电磁变分的基础理论，由四章组成，前二章引入了以Green定理为核心的边值问题理论，建立了电磁变分的普遍理论，第四章从对称的观点出发讨论了建立泛函的两种内积形式，第五章给出了一般电磁场的广义最小作用量原理，并用之解决变分问题。

In this chapter, firstly, the definition of rough semigroups is given afresh. Then based on rough groups, rough subgroups, rough cosets, rough invariant subgroups, some properties of rough subgroups and rough invariant subgroups and the concept of rough quotient groups are introduced. Finally, based on some concepts of homomorphism and isomorphism of rough groups, basic homomorphism theorem and isomorphism theorem of rough groups are put forward and proved.

在这一章中，首先重新给出了粗糙半群的定义，其次在粗糙群、粗糙子群、粗糙陪集、粗糙不变子群的基础上，给出了粗糙子群的若干性质、粗糙不变子群的三个重要性质和粗糙商群的定义，最后在粗糙群同态与同构的基础上，给出了粗糙群同态基本定理与同构定理。

In this paper, by computing the Laplace of the square of the length of the second fundamental form and introducing a self-adjoint operator and using Stokes Theorem and Hopf Theorem, we obtained some pinching theorems and rigidity theorems for hypersurfaces and submanifolds in hyperbolic space.

本论文通过计算双曲空间中子流形的第二基本形式模长平方的拉普拉斯和引进一个新的自共轭二阶算子，利用Stokes定理和Hopf定理得到了子流形的一些拼挤定理和刚性定理。

A pointwise characterization of fuzzy complete regularity is yielded by means of the Q- neighborhood structures and some algebraic properties of certain class of maps in lattices. The Weil theorem on fuzzy uniformity and the general imbedding theorem in the fuzzy basic cube are established.

其次给出不分明完全正则的点式刻划与关于一致结构的著名Weil定理的不分明推广并从而建立了在不分明单位方体中一般性的嵌入定理。

Applying the theory in classical partial differential equation and viscosity solutions, and Schauder fixed point theorem and Sobolev imbedding theorem, the existence and uniqueness of viscosity solution of the coupled PDE model are proved.

研究耦合PDE模型粘性解的存在性和唯一性问题。

Theorem, Implicit Function Theorem and its Applications.

分函数，可积分函数，反函数，隐函数定理及其应用，向量微积分基本定理

By using implicit function theorem, Taylor's formula and mean theorem, the form of the non-affine nonlinear systems is transformed into the form of affine nonlinear systems.

利用隐函数定理和泰勒公式及中值定理，将非仿射非线性系统转变为仿射型非线性系统。

The unique existence theorem for minimal determining set of completerational choice function is obtained,and the sufficient condition is used to show avery simple proof of Arrow Impossibility Theorem.

构造并证明了完全理性选择函数的最小决定集的存在惟一性定理，同时应用该定理的充分性条件给出了Arrow不可能性定理的一个简单证明。

This article discusses the use of the theorem of the residues to calculate Cauchy's Principal values of the improper integral, where auxiliary function has poles of higher order on the real axis and proposes a new theorem of culcuation.

在复函中应用留数定理计算广义积分的科希主值时，许多著作仅讨论了辅助函数在实轴上有一阶极点的情形[1-3]，有的则认为：辅助函数"在实轴上的奇点不能是二阶或二阶以上的极点["4，5]。

Applying this new theorem, one can easily find the auxiliary function and solve many problems of Cauchy's principal values of improper integral as well, the original theorem being unable to do so.

由于这个条件的限制，在寻找辅助函数时往往碰到困难，甚至找不到在实轴上只有一阶极点的辅助函数。

I had a lovely dog named PiPi, he was one of my best friends.

我曾经有过一只小狗，它的名字叫皮皮，它很善良，它是我最忠实的朋友。

Newly ovulated mouse oocytes were cultured in the CZB medium supplemented with different concentrations of pyruvate before treated for activation or assayed for MPF activity.

我们猜测卵母细胞在不含丙酮酸的条件下老化的更快，并且卵丘细胞可能通过消耗不含葡萄糖的CZB中的丙酮酸从而促进卵母细胞老化。