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Then the relationship which unknown coefficient satisfies from additional condition is derived. We deduce the existence and uniqueness of solution of the pseudoparabolic equation at last.

首先在假定系数已知的条件下,求出方程的形式解,然后再利用附加条件得到未知系数满足的关系式,最终给出了此类反问题解的存在唯一性。

Huang and Lin proposed the weak solution concept for Backward Stochastic Differential Equation This paper based on the predecessor's work , gives the weak solution concept for Backward Stochastic Differential Equation with continuous martingale,uses the Girsanov transformation, obtains its weak solution of the existence of a necessary and sufficient conditions, and on this basis obtains its weak solution of the existence of sufficient conditions,these sufficient conditions weakened the drifting coefficient which requested in the existence uniqueness of strong solution to satisfy the Lipschitz condition the request.

本文在前人研究的基础上,给出由连续鞅驱动的倒向随机微分方程弱解的概念,利用Girsanov变换,得到其弱解存在的存在的一个充分必要条件,并在此基础上得到了其弱解存在的一些充分条件,这些充分条件减弱了在强解的存在唯一性中要求的漂移系数满足Lipschitz条件的要求。

Furthermore, under the assumption that the covariant derivative of the sectionssatisfies the Lipschitz condition with L-average along the geodesic, the estimates of the radiiof convergence balls of Newton\'s method and uniqueness balls of singular points around thesingular points of sections on Riemannian manifolds are given.

当截面的协变导数满足沿着测地线的关于取正值非减可积函数L-平均的Lipschitz条件条件时,本文给出关于截面的Newton法的收敛球半径的估计,及在奇异点附近的关于截面的奇异点的唯一性球的半径的估计。

Under the assumptionthat the covariant derivative of the sections satisfies the Lipschitz condition with L-averagealong the piecewise geodesic, a unified convergence criterion for Newton\'s method and theradii of the uniqueness balls of singular points around the initial points of sections are es-tablished.

本章的主要内容包括以下两个方面:当截面的协变导数满足沿着分段测地线的关于取正值非减可积函数L-平均的Lipschitz条件条件时,本文给出了关于截面的Newton法收敛的统一判据,同时给出了在初始点附近的关于截面的奇异点的唯一性球的半径的估计。

For the infective subsystem, we obtain the existent condition of the subsystem equilibrium point and the uniqueness of the positive equilibrium point by the no infectious subsystem's conclusion and the image analysis. The partial stability of the subsystem equilibrium points is discussed by analyzing eigenvalue. The condition that the system has no limit cycle is obtained by the Dulac function.

对染病子系统,利用无病子系统所得结论及图像分析法,得到了系统平衡点的存在条件,正平衡点的存在唯一性;利用特征根方法判断了系统平衡点的局部稳定性;利用Dulac函数得到了系统不存在极限环的条件;利用极限方程理论得到了系统疾病消除平衡点和地方病平衡点的全局稳定性。

The existence and uniqueness of the solution with the help of the Banach fixed point theorem and the theory of operator semigroups are verified .The global exponential stability of KS equation and the global exponential stability and asymptotical stability of macro KS equation with the given boundary feedbacks are proved .

通过Banach不动点原理和算子半群理论证明了方程解的存在性和唯一性,并证明了KS方程在给定的边界反馈条件下是全局指数稳定的及广义的KS方程在给定的边界反馈条件下是全局指数稳定和渐近稳定的。

The linear growth condition is the most simple condition to ensure the existence of the global solutions.

一般而言,在缺少线性增长条件下,由局部Lipschitz条件仅能得出局部解的存在唯一性,而这就无法支撑任何涉及渐近性质的讨论。

In the second chapter, we consider a kind of Kolmogorov system. The sufficient condition for nonexistence of the closed orbit and existence of the unique and stable limit cycle are obtained by using divergence integral, Poincare-Bendixson theorem and Zhang Zhifenunique theorem.

第二章讨论了一类Kolmogorov系统,利用发散量积分、环域定理和张芷芬唯一性定理,得到了该系统无闭轨的充分条件和存在唯一极限环的条件。

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。

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