查询词典 mixed differential parameter

Chapter 4 discusses the stability of a class of nonlinear impulsive partial differential equations. The main idea is translating the stability of the considered nonlinear impulsive partial differential equation into that of the corresponding linear impulsive ordinary differential equation via Gronwall-Bellman inequality with impulse on the basis of comparison theorem.

第四章基于比较定理，主要利用含脉冲的Gronwall-Bellman不等式初步讨论了脉冲偏微分系统的稳定性，将一类非线性脉冲偏微分方程的稳定性化归为线性脉冲常微分方程的稳定性，为将脉冲常微分方程稳定性的有关结论推广到脉冲偏微分方程提供了理论依据并奠定了基础。

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

By means of the qualitative theory and method of delay differential equations, the weak conditions for the bound-edness of the system are obtained. By use of differential mean value theorem and computational techniques on delay differential equations, we show that the system is globally asymptotically stable under condition for the boundedness.

用时滞泛函微分方程的定性理论得到了系统有界的较弱的条件，并运用微分中值定理及有关时滞微分方程的计算技巧，我们获得了在系统有界这样弱的条件下就能保证系统全局渐近稳定的结论。

Our analysis framework relies on the reflected Backward Stochastic Differential equation approach.We characterize the value functions of the noncallable bonds in terms of the reflected Backward Stochastic Differential equation,Then the relationship between the value function of convertible bonds and reflected backward stochastic differential equations with single reflect is built at the same time,and provide the optimal conversion strategy for bondholders.2:We get the value of non-callable convertible bonds by numerical methods.

探讨了可转换债券的最优停时价值与带反射边界倒向随机微分方程解的关系，在市场完备，公司价值只包括股权和可转债这两种权益等各种假定下，给出不可赎回可转换债券的价值函数，证明了不可赎回可转换债券的最优停时问题的解是存在的，同时给出了其最优的转换策略。2：通过数值方法求解不可赎回可转换债券的价值。

The question of searching characteristic points or straight lines on moving rigid body is decomposed into two relatively independent sub-questions. The first one is to evaluate the characteristic of points and straight lines on moving rigid body, whose mathematics model is a kind of special non-differential max-mini optimal problem with inequality constraints. By the method of Saddle-point Programming and maximum entropy, the problem can be transformed as a differential optimal problem with single objective. The second oner is to search approximative character points or straight lines on moving rigid body within design space, whose mathematic model is nonlinear and non-differential problem with multiple constraints.

本文将在运动刚体上寻找特征点或直线的优化问题分解为两个相对独立的子问题，一是对运动刚体上点或直线的特征性评定，其实质是平面曲线的圆度或直线度的评定问题，优化模型是以最大误差为最小作为优化目标的约束不可微的优化问题，本文采用鞍点规划和极大熵方法，将其转化为单目标可微优化模型；二是在设计空间内，寻找运动刚体上特征性评定指标最小的近似特征点或直线，其优化模型是非线性、多约束的不可微优化问题，本文提出用遗传算法和BFGS局部搜索法相结合来求解。

Using PH linearization ,the nonlinear partial differential equation was transformed into linear partial differential equation,and then,by introducing a complex function,it was further transformed into a set of two linear differential equations.

应用 PH线性化方法，将非线性偏微分方程转化为线性偏微分方程，引入复函数将复常数偏微分方程变为两个线性实常数微分方程组，并采用小参数迭代法进行求解，近似求得了螺旋槽内气体动压分布的解析解。

In studing methods,partial func-tional differential equations sum up the theories and methods of ordinary differentialequations,partial differential equations,the semigroup theory and the fixed-pointtheory in functional analysis and the basic concepts,theories and methods suit-able for the partial differential equations with delay are formed.

偏泛函微分方程在研究方法上综合了常微分方程的理论方法和泛函分析中算子半群、不动点理论以及偏微分方程的理论方法，并形成了以时滞为基本特征的泛函微分方程的基本概念、理论和方法。

Linear differential equations of the principle of superposition theory of linear differential equations play an important role, especially in solving linear differential equations of the nature and structure of play to solve the problem of reducing the complexity and difficulty of the role.

请帮忙翻译一下摘要，跪谢线性微分方程解的叠加原理在线性微分方程理论中占有重要地位，尤其是在解决线性微分方程解的性质和结构问题中起到了降低解决问题的复杂度以及难度的作用。

Image for the differential procedures, including the differential horizontal and vertical differential once, such as second derivative.

求图像的微分程序，包括横向微分，纵向微分，一次，二次微分等。

Therefore, basic methodologies for stochastic seismic and filtering responses of nonlinear structure are studied, the approximate solution methodologies and their practical applications are investigated in the dissertation employing equivalent linearization and moment equations method based on FPK equations and Ito stochastic differential equations. The research works are mainly concerned with the following aspects:Firstly, the differential expression of bilinear hysteretic is studied and a new differential expression is developed, then they are demonstrated.

因此，本文基于FPK方程和伊藤随机微分方程，研究了滞后结构物的随机地震反应和随机滤波问题的基本方法，并利用等效线性化法和矩方程法，研究了非线性结构随机地震反应分析和随机滤波分析的近似解法及它们的工程应用。

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48