解析微分

The differential equation of the network is solved by solving a simple one dimensional differential equation.

通过求解简单的一维微分方程求出了网络的解的解析表达式。

This term studies mainly the applications of Theory of covering surface in differential equations, potential theory, complex dynamics and several complex variables, and researches the analysis and geometry properties of random Taylor series and random Dirichlet series.

本项目主要研究覆盖曲面理论及其在微分方程、位势理论、复解析动力系统以及多复变函数中的应用；研究随机泰勒级数、随机狄里克莱级数的分析性质和几何性质。

Based on the theory of thermal analysis,heat conduction equation of Nd:GdVO4 crystal slab double-side pumped by laser diode arrays was built.

以解析热分析理论为基础，建立了平板Nd：GdVO4晶体在激光二极管阵列双侧抽运时的导热微分方程。

The nonlinear equation of heat conduction is transformed into a Laplace′s equation by applying the Kirchhoff transformation ,and an analytic approximate solution of the equation is derived.

当介质的导热系数是温度的函数时，热传导方程是非线性偏微分方程，作者采用基尔霍夫变换把它变成拉普拉斯方程，于是可以找到原问题的近似解析解。

Aiming at the physical model inapplicability of flash method to measure thermal diffusivity of semi-transparentmaterials, a new physical model was proposed. In the model, according to the permeance of materials, the pulse laserabsorption of materials is of exponential type, and the authors establish a relevant differential equation and get a analyticalform.

针对传统的闪光法在物理模型上不适于用来测试半透光物质热扩散率的问题，提出了一个新的物理模型，该模型根据物质的透光性，确定样品对脉冲激光的吸收为指数型，建立了相应的微分方程并求得其解析解。

This is another novelty of this method. For a family of parameters, the analytical solutions of parabolic PDEs are given using the new method in this paper, the result schemes are posed.

给出了一类抛物型偏微分方程的解析解，并给出了其与差分数值解法所得到的解的比较，比较曲线表明了这种新解法的正确性。

The second kind of parabolic differential equation,multi-dimensional fractional equation,is generalized from the seepage flow.

遗憾的是，大多数分数阶微分方程的解析解都含有复杂的级数或者特殊函数，不利于进行近似计算。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

In Chapter 1, concepts of iteration, dynamical system, iterative functional equation and iterative functional differential equation are introduced.

本文将研究几种类型的迭代函数方程和迭代泛函微分方程的光滑解和解析解的存在性、唯一性和稳定性。

The stability analysis of the analytic and numerical solutions of the general nonlinear impulsive differential equation is considered.

考虑了一般的非线性脉冲微分方程，对该方程进行了解析解和数值解的稳定性分析。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。