弱解

Moreover compared with the Taylor series solution, the frequency shifts in our solutions appear in the expression of oscillations of all orders in both classical and quantum cases, so multiple-scale perturbation method is more suitable for solving the weak-coupling anharmonic oscillation than the Taylor series approach.

与Taylor级数解相比较，无论是在经典还是在量子解中频率移动都出现在各阶振动表达式中，所以多尺度微扰解是弱耦合非简谐振动的较好解法。

By extending the concepts of supremum and infimum in real space to the casein any finite-dimensional Euclidean space a weak supremum set and infimumset theory with respect to cones for the set in finite-dimensional Euclideanspace is developed,and several similar properties to the set in real space are ob-tained,with the concepts of this weak supremumset,w-D-conjugate maps and w-D-subdifferentials theory for the point-to-setmap are developed,and its several properties and its relationships with weakefficient solutions of the multiobjective programming are studied.

推广实空间中上、下确界的概念至任意有限维欧氏空间，建立了有限维欧氏空间中集合的锥弱上、下确界集理论，得到了与实空间中十分相似的性质。借助于这一理论，应用上、下确界的概念，给出了点集映象的w-D-共轭映象及w-D-次微分理论，并研究了它们的若干特性及其与弱有效解之间的关系，此外还讨论了弱鞍点问题。

This paper study the character and application of the solution of BSDE, the main results include: for the second kind of BSDE, the existence and uniqueness of the solution under non-Lipschitz condition, comparison theorem and stability are established , under weaker condition , the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given; for the first kind of BSDE, under weaker condition , the existence of minimal and maximal solution .stability, comparison theorem and application to utilityfunction are proved.

本文研究倒向随机微分方程解的性质及其应用，主要结果有：针对第二类方程，讨论了在非Lipschitz条件下倒向随机微分方程解的存在唯一性，比较定理及稳定性等，在更弱条件下，得到了倒向随机微分方程的最大解和最小解的存在性，在此基础之上，给出了在随机控制及效用函数方面的应用；针对第一类方程，同样在较弱条件下，证明了方程最大、最小解的存在性、稳定性、比较定理及其在效用函数的应用。

In this paper, first of all, we study the set-valued vector equilibrium problems and the set-valued vector Hartman- Stampacchia variational inequality in normed linear space.

本文首先在赋范线性空间中，研究了集值向量均衡问题和集值Hartman-Stampacchia变分不等式这两个问题的弱有效解的存在性，得到了弱有效解集的连通性和紧性结果。

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。

Firstly, this paper definited pseudometric d for n -foldproduct of σ-algebra A of subsets of a given set X , and definited indicator function ; secondly, gave the concept of differentiable of set function at S° and concept of partial derivative at S° with respect to the ith argument Si through indicator function, and defound the weak efficient solution of and optimality necessary condition; Finally, obtained three weak duality results and strong duality results under generalized convexity conditions.

首先，对已知集X的子集的σ-代数A的n-折积A^n，定义了伪度量d，给出了相应的特征函数〈h，Is〉；其次，通过特征函数给出了集函数在S 可微的定义及集函数在S 关于第i个变量Si的偏导数定义；给出了多目标规划问题的弱有效解概念及的最优性必要条件；最后，分别在目标函数和约束函数的3种较弱凸性条件下，研究n-集函数多目标规划问题的对偶问题，获得了3个弱对偶结果和强对偶结果。

For the Weak-All-Colors Problem, we give a rule named"adding a leaf", and prove that any tree has a solution to the Weak-All-Colors Problem.

同时还证明了圈和单圈图的弱全色问题都是有解的，并猜想任意图的弱全色问题有解。

Applying the boundness and some propertities of the mean of integration, we get the sufficient condition of weak persistence in the mean, and the curve of demarcation between weak persistence in the mean and going-to death.

本文利用比较原理证明系统解的有界性，由解的有界性及积分均值的一些性质得到了种群弱平均持续生存的充分条件，并在一定条件下得到了种群弱平均持续生存与绝灭之间的分界曲线。

Applying the boundness and some propertities of the mean of integration, we get the sufficient condition of weak persistence in the mean, and the curve of demarcation between weak persistence in the mean and going-to death. An optima!

本文利用比较原理证明系统解的有界性，由解的有界性及积分均值的一些性质得到了种群弱平均持续生存的充分条件，并在一定条件下得到了种群弱平均持续生存与绝灭之间的分界曲线。

Through the experiment results, in different phonation model, analysis the properties of glottal vocal efficiency, vocal folds vibration, and voice source.

我们在对嗓音—呼吸系统进行自动分割与分段特征表达的目标指引下，建立了具有国内一流水平的嗓音声学实验室；从概念上对嗓音—呼吸系统重新划分，以声门为中心分别建立去耦合和弱耦合条件下的嗓音—呼吸系统和肺胸系统数学模型；采用离体犬喉作为声带振动的物理模型，对数学模型进行完善与证实；采用盲解卷技术在去耦合和弱耦合条件下，提取上下声道传递函数、嗓音源和发声效率，研究上下声道去耦合和弱耦合条件下不同发声方式与状态对发声效率的影响。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。