查询词典 mapping theorem

Next in section 2.3,usingthe finite isolated regular representations in SO(3)character varity of 〓,weobtained a computation formula of SO(3)Donaldson invariants with degree 1 of4—manifold 〓(Theorem 2.3.1).Finally in section 2.4 wediscussed the Donaldson invariants of 4—manifolds with smoothly embedded 2—torus 〓 whose selfintersection is +1,with the help of the single irreducibleSU(2)representation of the principal 〓—bundle over a 2—torus with Eulernumber—1,we got a gluing formula of the Donaldson invariant on the 2—homology represented by 2—torus 〓(Theorem 2.4.1),it is a supplement of P.

最后在§2.4我们讨论了具有自交数为+1的嵌入环面〓的4—流形的Donladson不变量，运用环面上欧拉数为-1的圆丛的单个不可约SU（2）表示给出了Donaldson不变量在环面表示的同调类上的一个粘合公式（定理2.4.1），这一结果补充了P。

The computational formula of the gradient matrix in subspace is obtained by applying Taylor series expansions, decomposition theorem of space and projective theorem (The gradient matrixs in different subspace are different).

利用子空间上的泰勒展式、空间分解定理以及投影定理得到了子空间上梯度矩阵的计算公式(不同的子空间，梯度矩阵是不相同的)。

A theorem of the alternative for the generalized subconvexlike set-valued maps is established using the separation theorem of convex sets in a Banach spaces, the concept of weak Benson proper efficient elements for a vector optimization problem is introduced, and the optimality necessary and sufficient Lagrange conditions for a vector set-valued map constrained optimization problem with the weak Benson proper efficiency is developed, with which the optimality Lagrange conditions for a nonconvex vector top-base constrained optimization of set-valued maps with the Benson proper efficiency are obtained.

刘莹 ，刘三阳，盛宝怀运用凸集分离定理对广义锥次类凸集值映射建立了一种择一性定理。引入向量优化弱Benson真有效元的概念，对带约束的非凸向量集值优化问题建立了在弱Benson真有效意义下有效元应满足Lagrange乘子型的必要及充分条件，并用这一结果建立了多目标主从非凸向量集值优化在弱Benson真有效意义下最优解的Lagrange乘子型充要条件。

By using the model of this interpretation, the reliability theorem and the uniformity theorem are proved of the propositional calculus plus syllogistic system.

本文最主要的工作是建立了三段论的一种解释，并且在这种解释模型中，证明了命题演算+三段论系统的可靠性定理，一致性定理，还从语义角度，对项的周延性等问题发表了一些意见。

This paper makes studies of researched proposition on Pythagorean theorem an Projection theorem.

本文对勾股定理、射影定理的研究性论题进行了研究。

Suppose John is thinking about the Pythagorean Theorem and you ask him to say what's on his mind. His response is an event: the utterance of a sentence; and one of its causes is the event of John's thinking about the theorem.

假设张三在思考勾股律，你问她什么东西在她心里，她的回答是一个事件：说出一句话，其原因之一是'张三思考勾股律'这个事件。

In this paper,pose representation by quaternions are researched.With the basic quaternion algebra,the "quaternion based rotations combination theorem" is introduced and proved theoretically.On the basis of this theorem,a method for compute of pose nonliear state transfer function and its linearization is purposed.Then,the computing of the measurement function and the linearization is studied.With the Extended Kalman Filter,the pose is tracked and estimated.

研究用四元数表示物体的姿态，在四元数基本运算法则基础上提出并证明了"基于四元数的多个旋转运动合成规则"，然后将此规则为依据，推导出一种用来计算姿态非线性状态方程系数的方法，对非线性状态转移函数进行线性化，并且研究了测量方程函数的确定及线性化，借助扩展Kalman滤波实现了对姿态的跟踪。

We consider Theorem 1 to be highly significant and apply it to obtaining the rank of a certain augmentation quotient group by proposing Theorem 3 and giving its complete proof.

应用具有Np-序列有限p-群的特殊性质和重量函数，基本序列等概念以及已有的一些结果，分别研究了类为1的pk(k 2)阶A bel基本p-群和类为2的p4阶基本p-群之增广商群Qn的结构，得到了当n足够大时Qn作为A bel基本p-群的秩。

We first use the method similar with that in EL.karoui[1] to get the comparison theorem of K in the case of one reflecting barrier,At last,we use the idea of penalization to prove one existence result of the solution for the multi-dimensional RBSDE where the coefficient is continuous and has the linear growth,this also help us to give the comparison theorem of K~+ and K~- in the case of two reflecting barriers.

最后，用惩罚方法证明了当多维双边界反射倒向随机微分方程的生成元满足连续和线形增长条件时解的存在性，并同时得到了双边界情形下，K~+和K~-的多维比较定理。

The use of the Chinese remainder theorem transforms the operation of producing the multiplicative inverses into two corresponding operations with shorter numbers and a faster combination step so that, compared with methods not using the Chinese remainder theorem, an acceleration by factor 4 can be achieved.

采用中国余数定理，形成将倍数逆数的运算转换为两个具有较短数字和一个较快结合的运算的步骤，使得相较于没有中国余数定理的方法可获得因子4的加速。

In other research, chondroitin is being investigated for use in several other conditions.

在其它研究，软骨素被调查用於几个其它情况。

They would make fun of him for having to work.

他们拿他的工作来开玩笑。