定义方程

In Chapter 3, considering fractional relaxation equation, we make use of directlythe Grunwald-Letnikov definition to discrete fractional derivative, obtain a numericalmethod of fractional relaxation equation,and give the proof of consistency ,conver-gency and stability.

第三章对于一个推广到分数阶的松驰方程，直接利用Gru¨nwald-Letnikov分数阶导数定义进行离散，得到分数阶松驰方程一个数值方法，并给出了相容性，收敛性和稳定性的证明。

As is known to all,μ-invariant measure plays an important role in stochastic pro-cess,and the research of that is significant both in theory and practice.

全文分为三章；第一章对一些基本的概念作了一个简单的介绍，包括跳过程的转移函数，q-对，q-过程，向前方程，向后方程以及q-预解式的定义和性质等。

If 〓 is an absolutely continuousmeasure and is represented by a measurable function f on Q,then u is said tobe the generalized solution of(1),and 〓 to be the parabolic Monge-Amperemeasure.

定义1由legendre变换定义了一个Q上的测度〓（4）其中〓为〓空间中的Lebesgue测度，若〓是一个绝对连续测度且在Q上由可测函数〓表示，则称u为方程（1）的广义解、称测度〓为抛物型Monge-Ampère测度。

Chapter 3, we study the stability of approximate solutions of nonlinear equation problems(the continuous function is defined in the linear normed space).We prove that most of approximate solutions of nonlinear equation problems are stable; all accurate solutions are the essential points of the set of approximate solution; the connected component which contains the accurate solution is the essential component of the set of approximate solution; especially the number of essential components is finite.

第三章，研究定义在线性赋范空间上的非线性方程问题近似解及其解集的稳定性，得到线性赋范空间上在Baire分类下大多数非线性方程问题的近似解都是稳定的；精确解是近似解集的本质解；包含精确解的近似解集的连通区是本质连通区；包含精确解的近似解集的连通区为有限个。

Fractal dimension structure of the Cosmos are explored, and the mathematical foundation, which include the expressions of fractal dimension differential and calculus, regular space integral solutions of fractal dimension differential equations, the fractal calculus definitions of fractal measure as well as the measure computational equation of self-similar fractal, of fractal dimension calculus and fractal measure are given.

摘 要：探讨了宇宙分维构造的形式，给出了分维微积分及分形测度的数学基础，包括分维导数及分维微积分的表述形式、分维微分方程的规整空间积分解、分形测度的分维微积分定义及自相似分形的测度计算方程。

These transfer equations were used to reestablish the entropy transfer equation for the electromagnetic fluid,and further to reconstitute the differential component equations for different forms of exergy and the differential equation for total exergy in the fluid by the definitions of thermal,pressure,chemical,kinetic,potential and electromagnetic forms of exergy.

通过定义热火用、压火用、化学火用、动能火用、势能火用、电磁火用，重新构建了不同形式火用传递的分量方程及其总火用传递方程。

This paper gives the definition of the trivial solution to the high degree congruence x^ n = a, presents one sufficient and necessary condition for the congruence to have solutions, derives and proves one new judgment condition complementarily.

这篇文章给出了高阶同余方程 x^ n = a平凡解的定义，介绍了高阶同余方程有解的一个充要条件，补充推导和证明了另一个充要条件。

So in this paper a new damage variable was defined, then, Based on damage theory and Weibull distribution damage evolution rule, a simplified ameristic damage constitutive equation was established for concrete under uniaxial compression.

为了用简单的方程将上升段和下降段连接起来，本文以峰值割线模量为基准，定义了一种新的损伤变量；并以经典损伤理论模型为基础，根据混凝土损伤演化规律的概率密度服从Weibull分布，提出了一个统一的方程来描述混凝土单轴压缩时应力应变关系的全过程。

Some of definitions on weak attractiveness and relevant decidable theorems are obtained in the paper by extending the definition of attractiveness of equation solutions and concrete example is also given.

通过放宽方程解的吸引性定义，得出了几个关于弱吸引性的定义和相关的判定定理，并给出具体实例。

The structural form of the model consists of 66 simultaneous equations, including 28 stochastic equations and 38 definitional equations and identities.

模型的结构型由66个方程联立组成，其中随机方程28个，恒等式和定义式38个。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。