微分

By averaging the nonzero weights of operator template to the image pixels which have the same distance to constant coefficient "1" as well as utilizing self-dependency of surrounding pixels, an improved fractional order differential operator template was achieved.

将算子模板的非零权值平分到与常系数"1"距离相同的像素点中，利用周围像素点的自相关性，得到一种改进的分数阶微分算子模板。

The solution of a backward stochastic differential equation is a pair of process satisfyingwhere g is the generator, and ξ is the terminal condition.

倒向随机微分方程的解是一对过程满足其中g是生成子，ζ是终端条件。

Firstly, we prove the existence and uniqueness of the adapted solution of multi-dimensional backward stochastic differential equations driven by Brownian motion and Lévy process by using predictable representation theorem and the fixed point theorem about contract mapping, and also prove the comparison theory.

第一部分运用可料表示定理和压缩映射原理证明由布朗运动和Lévy过程共同驱动的多维倒向随机微分方程适应解的存在唯一性及其相应的比较定理。

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。

Secondly, we consider stochastic LQ optimal control problem driven by Lévy processes and Brownian motion. By applying the -Lévy formula, Gronwall's inequality, Young's inequality and Cauchy-Schwarz inequality, we obtain the closeness property of the solution of multi-dimensional backward stochastic Riccati differential equations.

第二部分首先研究由布朗运动和Lévy过程共同驱动的随机LQ最优控制问题，接着利用-Lévy公式、Gronwall不等式、Young不等式及Cauchy-Schwarz不等式证明多维倒向随机Riccati微分方程适应解的闭性质，并利用此性质证明一维BSRDE解的存在唯一性。

And the general thoughts in which we can deal with the nonlinear integro-differential equations in Banach space.

全文共分为三章，在第一章中，我们对具有凹凸性的非线性算子的研究现状及我们在本文中将要做的工作进行了阐述；同时给出了我们处理本文所讨论的非线性积分-微分方程的总体思路。

By normalizing the system which is described by differential equations, we transform the system to an abstract Cauchy problem in a Banach space.

通过对描述其系统行为的偏微分方程组的规范化，将其转化为Banach空间中抽象的Cauchy问题。

The purpose of this part is to study the delay differential systems in Banach space using the method of fixed point theorem.

一方面在非时滞的情况下通过构造比较函数，利用Brouwer不动点定理得到非时滞微分方程正周期解的存在唯一性，及周期解全局吸引的充分条件。

In this paper a class integral differential equation on Banach space is studied.Existence,uniqueness and regularity of mild solutions are proved.

研究了Banach空间上的一类非线性脉冲积微分方程温和解的存在唯一性以及其正则性。

The existence of periodic solutions to the second order ordinary differential equation in Banach space is discussed.

本文利用半序理论，非紧性测度，凝聚映射的拓扑度，不动点定理及锥上不动点指数理论，讨论了Banach空间E中二阶常微分方程周期边值问题解的存在性，主要结果有一。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。