解析微分

The Hankel transformation method has been used to turn the basicdisplacement equations and displacement-stress constitutive equations intoa system of first order non-homogenous ordinary differential equations inwavenumber domain,and by us of the matrix method,the transfer matrix ofthe medium layered is established.

利用Hankel变换，将轴对称静力问题的位移基本方程和位移应力本构方程转化为波数域内非齐次一阶常微分方程组，利用矩阵法，建立了介质层的传递矩阵，导出了层状弹性半空间轴对称静力问题奇异解的一般解析表达式。

However, the solutions of the Cauchy problem of the nonlinear hyperbolic system generally develop singularities in finite time even if the initial data are small and smooth.For this reason, solutions must be found in the space of discontinuous functions. Therefore, one can not directly use the classical analytic techniques that predominate in the theory of partial differential equations of other types. Instead, we construct approximate solutions via the singular perturbation methods. By using the compactness of the approximate solutions, we can obtain the existence of the solutions of original system.

然而一般而言，即使是在初值很小且光滑的情况下，非线性双曲型守恒律的Cauchy问题的解在有限时间内也会出现奇异性，为此，我们必须在不连续函数空间中寻找上述问题的解，因此对这类问题的研究，我们也不可能直接利用在其它类型的偏微分方程中占主导地位的解析方法来解决问题，而是通过奇异扰动法构造近似解，由近似解的紧性得到原问题解的存在性。

Specially, in Hilbert spaces, some necessaryand sufficient conditions are given in terms of the uniformly square integrability anduniform boundness of the resolvent on the imaginary axis respectively. Furthermore,we consider this robustness fordifferential equations with unbounded operatorin the delay term.

我们进一步研究了时滞项含无界算子的抽象微分方程的小时滞鲁棒稳定性，获得了一些充分必要条件，并应用所得结论讨论了具解析半群生成元的时滞系统。

An integral operator I(subscript n+p) defined by Hadamard product is introduced. Making use of this operator, the subclass S(superscript * subscript n+p) of p(superscript -) valent analytic function is defined in the open unit disk, the inclusion relation of S(superscript * subscript n+p+1)S(superscript * subscript n+p) and the best dominant function of differential subordination q1 are obtained. Furthermore, some conclusions are made according to the special parameters A and B.

用Hadamard卷积定义线性算子I，并利用算子I定义在单位圆内的解析的p叶函数类S(上标*下标 n+p)，给出了此函数类的包含关系S(上标*下标 n+p+1)S和微分从属的最佳控制函数q1，并根据参数A，B取不同的特殊值得出了相应的推论。

It points out that for all the complex flows under some great non-equilibrium forces, the preconditions to make an infinitesimal analysis over all the fluid field according to a set of differential equations will not exist.

指出对于存在极大力学不平衡的复杂流动，在整个流场依靠一个同一化的微分方程组，进行解析分析的连续可微逻辑前提是不存在的。

Because the workpiece is in dynamic balance, the resultant moment acting on it should be zero. Introducing the moment from lapping tool and press head a moving differential equation is built. In this equation only workpiece rotating speed is unknown. It means that workpiece rotating speed can be got by this equation. Since there is a transcendental function in integral function of the equation an analytic result can not be got, only digital result can be got by a computer. Thus a change rule of workpiece rotating speed with lapping parameters is known, e.g. the radius of press disc ball socket, radius of press head ball, the distance between the workpiece rotating axis and lapping tool rotating axis, workpiece radius, modulus of elasticity of the press head and press disc, friction coefficients between the lapping tool and workpiece, and between the head and disc, pressure between the lapping tool and workpiece and pressure between the press head and press disc.

因工件处于动态平衡状态，其上所受到的来自于磨具和压头的力矩应相等，将二力矩表达式联立，建立工件运动微分方程，该方程中只有工件的旋转角速度是未知量，因此可以求出工件旋转角速度，但该方程积分式中含有超越函数，得不出解析解，只能通过计算机求出数值解，得出工件旋转角速度随各研磨参数的变化规律，如压盖球座半径、压头的球头半径、工件回转中心相对磨具回转中心的偏心距、工件半径、压头和压盖材料的弹性模量、磨具与工件间的摩擦系数、压头压盖间的摩擦系数、磨具与工件间的压强、压头压盖间的压力等。

The stability of numerical methods for the linear Volterra delay integro differential equation was studied. A sufficient condition such that the implicit block θ-methods preserved the delay-independent stability of its exact solutions was obtained.

研究了线性中立型Volterra延迟积分微分方程数值方法的稳定性，给出了块隐式θ-方法保持系统解析解不依赖于延迟的稳定性质的一个充分条件。

Firstly, by adopting the thought of Adomian's decomposition method, the generic dynamic model in mechanical systems are transformed into a standard first-orderdifferential-equations, and then the inverse operator method for the approximate analytic solution of nonlinear mechanical system is developed based on the exact solution in form.

主要研 究工作如下：利用Adomian的分解方法的思想，把机械系统中最一般的动力学模型转化为一阶标准型微分方程组，以形式上的精确解的表达式为基础构造了求解机械系统非线性模型近似解析解的逆算符方法；针对机械系统非线性模型的特点，提出了直接处理高阶方程的不降阶逆算符方法；证明了该方法的收敛性。

Integrate the load transfer principle and shearing displacement method to set up the load transfer equation between the pile of soil, using the discrete and fitting methods to solve the equation so as to educe the pile displacement of arbitrary section as well as the analytical solution. Comparing the results with the soil settlement solved by the Mair equation, the relative displacement can be gained.

1结合荷载传递原理和剪切位移法的思想建立隧道开挖作用下的桩土荷载传递方程，采用离散和拟合两种方法来对该一元二次非齐次微分方程进行求解，可分别得到桩身任意截面处的桩体位移以及桩身位移的解析解，并与基于Mair公式求得的地面下任意深度处的土体沉降进行比较，即可求出桩与桩侧土之间的相对位移。

Using the method of dividing variables , the solution of elastic dynamics can be changed into the eigen value problem of Hamilton's space differential operator matrix , and the total solution of dual variables (modal strain and modal strain rate ) can be obtained by expanding the eigen solutions .

尽管方程的个数增加了1倍(未知量个数增加了1倍)，但方程对时间微分的次数下降到1阶。通过分离变量后，可以将其转变为Hamilton空间算子矩阵的本征值问题，从而使复杂力学问题的解析解成为可能。

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。