查询词典 uniqueness condition

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 utility function 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。

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。

Amber uniqueness , appositeness present to her, she is your uniqueness on behalf of.

琥珀的唯一性，适合送给她，代表她就是你的唯一。

We then can verify the associative law and the commutative law for multiplication, and the uniqueness of the result of addition indicates the uniqueness and the cancellation law for multiplication.

我们容易验证乘法满足结合律和交换律，并且由加法结果的唯一性得出乘法结果的唯一性和乘法消去律。

We give several sufficient conditions for existence and uniqueness of least deviation point and its application in uniqueness of best approximation.

本文在一般线性赋范空间内提出点集的最小偏离问题，给出了最小偏离点的存在性与唯一性的各种充分性判据及其对于最佳逼近元唯一性问题的应用。

By employing the theorem on existence and uniqueness of solutions, the existence and uniqueness of path is proved. A method of solving ordinary differential equation systems is proposed to get the trajectory of SVM solutions.

利用微分方程组的存在唯一性定理，我们得到了路径的存在唯一性，并给出了一种常微分方程组的近似解法求解SVM解的路径。

For the first time, in [3] the authors discussed the inequalities of B-B and by using them the authors give a proof of the existence and uniqueness of the generalized solution for magnetostatic field problem with zero boundary value. By using the inequalities of B--H in, in[-5,6] the authors give a proof of the existence and uniqueness of the generalized solutions for 3-D magnetostatic field Neumann problem and 2-D magnetic field first boundary value initial problem.

前人已讨论了B—H间的几个基本不式，并由之证明了三维静磁场带零边值问题广义解的存在与唯一性，作者也曾利用给出的B—H间的不式证明了三维静磁场Neumann问题和二维时变场第一边值初值问题广义解的存在与唯一性。

Firstly, we prove the existence and the uniqueness of the hyperfocal subalgebra when the coefficient field is split for a defect pointed group; then, considering the structural pattern of source algebras over arbitrary fields, by means of G-acted groups, we reduce the existence and the uniqueness of the hyperfocal subalgebra over an arbitrary field to the case that the coefficient field is split for a defect pointed group and the inertia group stablizes a hyperfocal subalgebra.

首先我们证明了如果系数域对亏点群是分裂的，则源代数的超聚焦子代数存在且共轭唯一；然后通过考虑任意域上源代数的结构模式，以G-作用群为手段，将超聚焦子代数的存在性和唯一性归结为系数域对亏点群是分裂的情况下惯性群稳定的超聚焦子代数的存在性和唯一性。

In the present work,the existence and uniqueness results aboutperiodic boundary value problems for different kinds of the nonlin-ear periodically perturbed nonconservative systems are establishedthrough the discretization technique,under suitable assumptions,by using global inverse function theorem and result about the ex-istence and uniqueness of periodic solution for nonhomogeneouslyfirst order linear periodic boundary value problem.

本文的第一章概述了在讨论原问题解的存在唯一性过程中以及构造和分析相关的数值求解方法时将要用到的全局反函数定理、有关矩阵特征值的若干重要引理、线性常微分方程非齐次周期问题解的存在唯一性定理和单参数影射方法及有关结论，并简单回顾了已有的证明非线性微分方程周期边值问题解的存在唯一性的方法，其中包括谱理论、最大最小化形式方法、摄动技术和全局反函数理论方法，最后，介绍了两类数值求解非线性微分方程问题的方法。

However, methods and references for difference equation are relatively less. The new method proposed in this paper transfer the complex boundary value problem into the existence and uniqueness of the solution of the linear equations. For linear case , we obtained the necessary and sufficient conditions for the existence and uniqueness of the solution for the BVP; For the nonlinear case ,we got a series of new sufficient conditions by using contraction mapping theory and cone theory .

而差分方程边值问题的研究方法和文献还很少，文中新的研究差分方程边值问题的方法是将复杂的边值问题求解转化为代数理论中的线性方程组解的存在和存在唯一问题；对线性情形，较容易地获得了边值问题的解存在以及唯一的充分必要条件，而对非线性情形，则通过压缩原理和锥理论等各种不动点定理，获得了一系列新的充分条件。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。