查询词典 functional differential equation

This paper consists of three parts:We first consider the non-autonomous predator-prey system with both Beddirigton-DeAngelis functional response and dispersion. By using comparison theorem of differential equation, we study the permanance of the system. After that, by constructing suitable Lyapunov function, we obtain some sufficient condition which guarantee the existence of globally asymptotically stable almost periodic solution of the system.

本文研究三方面的内容：第一部分考虑具有扩散和Beddington—DeAngelis功能反应的捕食-食饵系统，利用微分方程比较原理得到该系统一致持续生存的条件；通过构造适当的Lyapunov函数得到了该系统存在全局渐近稳定概周期解的充分条件。

Existence, uniqueness and continuous dependence of C〓 solutions for an iterative functional equation related to invariant curves of functional differential equations with piecewise constant arguments are given under weaker conditions than that known results of C〓 solutions.

本章首先讨论了与逐段常时滞泛函微分方程不变曲线有关的一类迭代函数方程的连续解的存在唯一性和连续依赖性，不但弱化了已有结果的C〓光滑性的条件，还讨论了连续解的对称性，并根据对称性将一些结果推进到高维。

This paper gives a mathematical definition to that two open planar curves have the same shape based on curvature representation, therefore, a new kind of shape distance is proposed. It is concluded that the problem of computing the shape distance between two open planar curves can be changed to the problem of a functional extremum, and the differential equation is given, which can be used to figure out the shape distance.

本文为基于曲率表示的两条平面开曲线的等形下了严格的数学定义，从而找到了一种新的形状距离度量，并且证明了这种形状距离的计算问题可以转化为一个泛函的极值问题，同时给出了求解形状距离的微分方程。

Using the theory on delay functional and impulsive differential equation, sufficient condition with time delay for the permanence of the system was obtained. And it was proved, that time delays, pulse vaccination and vertical transmission can bring obvious effects on the dynamics behaviors of the model.

运用脉冲时滞泛函微分方程理论，获得了含有时滞的持久性的充分条件，并且证明了时滞、脉冲免疫与垂直传染对模型的动力学行为能够产生显著的影响。

In this thesis, using the qualitative theory and stability theory of ordinary differential equation, we study the global stability of equilibrium, existence and uniqueness of limit cycle for a predator-prey model with sublinear functional response function.

本学位论文利用常微分方程定性理论和李亚普诺夫稳定性理论的基本方法，研究了具次线性功能性反应函数的食饵-捕食者模型的平衡点的全局稳定性，极限环的存在性和惟一性。

Then, it studies the supply chain management system as a complex system to confirm the state existing during operating of the system. After that, it conducts a probability analysis on the state which the system located by applying supplement variable method, and establishes the model of distributed parameter system in a form of partial differential equations. Combining C0 ? semigroup theory in the functional analysis, it conducts a dynamic analysis on the established mathematical model. Using this method, it obtains the mathematical expression of the dynamic solution and the steady state solution, and proves the uniqueness, non-negativity and the asymptotic stability of the system solution. This dissertation applies the Matlab tool and uses two-step, three-step Simpson integral equation to imitate the condition of system solution. Then, it adds possible mode of failure and the optimization adjustment state to the system, based on which it has established the distributed parameter system model which is described by partial differential system of equations. Combining the functional analysis C0 ? semigroup theory, it studies the established mathematical model, and obtains the mathematical expression of the dynamic solution system and the steady state solution. It has proven the existing of uniqueness of the system solution, the asymptotic stability of system solution and the system solution. In addition, it has lying the theory rationale for further analysis and the research on the optimization of system.

本文首先简要综述了供应链理论、可靠性研究、鲁棒性研究以及供应链鲁棒性研究的现状；然后，将供应链系统作为一个复杂系统来分析，确定了系统运行过程中所经历的状态，通过引入补充变量的方法，建立了用偏微分方程组描述的分布参数系统模型，用泛函分析中的C_0 -半群理论得到了系统动态解和稳态解的数学表达式，证明了系统解存在的唯一性、非负性和指数阶渐近稳定性；并借助Matlab工具，利用二阶、三阶辛普森积分方程模拟系统解的性态，并给出系统动态解的仿真图；本文又对上述系统增加了系统可能失效状态和优化调整状态，并在此基础上建立了用偏微分方程组描述的分布参数系统模型，同样用泛函分析中的C_0 -半群理论对所建立的数学模型进行了研究，得到系统动态解和稳态解的数学表达式，证明了系统动态解存在的唯一性、非负性及渐近稳定性，为进一步分析和研究供应链优化奠定了理论基础。

By using the comparison theorem of differential equation, we study the permanance of the system; After that, by constructing sutiable Lyapunov functional, we obtain some sufficient condition which guarantee the global attractivity of the system.

利用微分方程比较原理得到保证系统持续生存的条件；通过构造适当的Lyapunov泛函得到保证系统正解全局吸引的充分性条件。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。