等价的

In the first part, convex duality method linearizes convex wealth equation, and the introduction of Lagrange multiplier converts original problem to an unconstrained static optimum problem. At last, we obtain another equivalent optimum problem with convex control domain.

文章前一部分运用凸对偶的方法先将财富方程线性化，Lagrange乘子的引入使最优问题等价与一个无约束的静态最优问题，最后转化为一个凸控制域的最优问题。

The discriminance methods and expression of generalized alternative optimum solutions of linear programming is given by proving that the equivalent of optimum extreme point and extreme point of optimum solution sets of linear programming and applying the theorem of convex polyhedron.

通过证明线性规划最优解集的极点与线性规划最优极点的等价性，利用凸多面体的表达定理，给出了广泛意义下线性规划无穷多最优解的判别方法及表达式。

Chapter 2 is devoted to the effects of cross correlation between additive and multiplicative noises in a single-mode laser.

从泛函的途径建立了与具有相关加法和乘法噪声的单模激光场方程随机等价同时描述光强和位相的一个普遍的二维模型。

The past earnings requirements for under 28s and 28s and over are both broadly equivalent to the top decile earnings of all full time workers in the respective age groups.

对28岁以下，28岁和28岁以上的申请人的过去收入要求，都是广义上等价于各自年龄组的全职工人的全部统计收入。

The properties of the λ-cut sets of the lower and upper approximation are discussed,and then the F-Union Decomposition theorem of the lower and upper approximation of rough fuzzy sets is given.

基于此，本文在逐一增加属性形式下的等价类F-分解的基础上，讨论了粗模糊集的F-分解形式，并给出了粗模糊上、下近似集合的F-分解定理及相关推论。

As we all know, it is equivalent to the null controllability of a cascade system governedby two linear degenerate parabolic equations. Next, we study the null controllability of acascade system governed by a semilinear degenerate parabolic equation and a semilinear heatequation.

众所周知，这等价于两个线性退化抛物方程构成的耦合系统在单个控制作用下的零能控问题；接下来我们又考虑了一类半线性退化抛物方程与半线性热方程构成的耦合系统的零能控问题。

In the fourth chapter, using algebraic method, we prove that tubular mutations are auto equivalences of the derived category of a derived tubular algebra, and apply this method to the case of tame concealed algebras, which generalizes a result of Meltzer .

第四章我们用纯代数的方法证明：tubular mutation是tubular型标准代数的导出范畴的自等价，并把该方法应用到tame concealed代数，从而推广Meltzer的结果。

The analysis in theory proves that cellular automaton is equal with a stochastic process that described by stochastic difference equations. The primary differential equation is expectation of this stochastic process. And its variance function is controllable. These results show that cellular automata are in agreement with primary differential equation in the statistical sense.

理论分析证明：该方法设计的细胞自动机等价于一个可用随机差分方程描述的随机过程，该随机过程以原微分方程为期望函数，并且，其方差函数是可控的，表明细胞自动机和原微分方程在统计意义上是一致的。

By the aid of defineding an equivalence relation on the disjoint union of a family of quantales, the direct limit structure in the category of quantale was obtained.

利用在一族Quantale的不交并上定义的等价关系，给出了范畴Quant的定向极限的结构。

On fuzzy mapping F :〓→〓, the concepts of directional derivative and integralover a line segment are defined, and the increase, convexity and continuity are investigated.

作为应用，给出了一个这类凸模糊映射在〓的某一凸子集中某一点达到最小值的等价条件，并得到了某点是一个凸模糊优化问题的最优解的一个充分条件。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。