条件方程

The theory of high-strain dynamic testing of pile bearing capacity. The basic calculation expression of pile high-strain dynamic testing is rederived in a simple way, especially the semi-empirical analytical expression of wave equation . Besides, theoretically it has been proved that it's not necessary to have identic section hypotaxis along pile, and the application condition and reasonable operation have been pointed out. the CASE comprehensive method is suggested to replace the traditional CASE method. author has made a lot of improvement for the mathematical model of the matching analysis measured curves in the business software CCWAPC and scientific research software JXWAPC of which the author is in charge.

关于高应变动力试桩法的理论研究以简明方式重新推导了高应变动力试桩法基本计算表达式，尤其波动方程半经验解析表达式，同时从理论上证明了CASE法并不需要桩身等截面假设，亦指出了该方法的适用条件及合理使用办法，并建议利用CASE综合分析法取代传统的CASE分析法；作者在其负责编制的商业软件CCWAPC及科研软件JXWAPC中，对波动方程拟合分析法数理模型进行了一系列重大改进，考虑了灌注桩桩周土体的变形特性和动荷截作用下的非线性效应、大直径桩的横向惯性效应。

In Chapter 4,we consider the problem of totally characteristic type equation,whose indicial exponent takes positive integers.

在第四章中，我们对全特征型微分方程也讨论了一类不满足第二、三章中定理条件的问题，即对全特征型偏微分方程也考虑了Yamane在文[11]中考虑的问题。

It has important significance to consider backward stochastic Volterra type integral equation in infinite dimensional space.By a similar calculation as in the second part,we study this kind of equations driven by cylindrical Brownian motion under non-Lipschitz condition.

3在无穷维空间中研究倒向随机Volterra型方程也是有着重要意义的，论文利用与第二部分相同的思路将前面的结果推广到无穷维中，在非Lipschitz条件下对由柱Brown运动驱动的这种方程建立了解的存在唯一性。

There exists a dual symmetry between the equations of motion and the Maurer-Cartan equations of the type IIB superstring on AdS〓 S〓. We generalize the finite dual transformation to the infinitesimal dual transformation by the twisted dual.

根据Euler-Lagrange运动方程与Maurer-Cartan方程的扭曲对偶变换，我们可得到AdS〓×S〓中IIB超弦的Lax平联络及其相应的可积的相容条件，由此可以说明体系是一个可积系统。

By means of integral inequality and Kartsatos transformation, we investigate first-order impulsive delay dynamic equations on time scales. Several sufficient conditions of oscillation are obtained.

利用积分不等式和Kartsatos转换技巧，研究了时标上一阶时滞脉冲动力方程，得到了一些判断这类方程解的振动性的充分性条件。

For the admissible time-delay as well as non-linear disturbances, an time-delay integral transformation and a matrix inequality method are developed. The design of observer and stability of error systems can be represented as a matrix inequality, matrix of observer gain and condition of global asymptotically stable of error systems are obtained. An example is included to illustrate the pratical applicability of the proposed theory.

对于允许的时滞和非线性干扰，利用一个变换和不等式技巧，将观测器的设计，误差方程的稳定性归结为一个矩阵不等式，给出了观测器增益阵的解析式和误差方程全局渐近稳定的条件，一个例子说明了所提定理的可行性。

The proposed method applies the ellipsoid invariant set to the estimated state and state estimation error. The conditions of invariance and feasibility of estimated state, as well as the stability of the closedloop system are given.

该方法采用双模控制策略，将不变椭圆集概念同时应用于观测器的状态方程和误差方程，给出估计状态不变性和控制输入可行性条件并给出了闭环系统的稳定性定理。

Three common mathematic models are always employed to predict the growth of regional or urban population,including exponential function,inverse hyperbolic function,and logistic function.

预测人口增长的数学模型通常采用3种函数，即指数函数、Logistic函数和双曲函数。3种模型的数学根源都在于二阶Bernoulli式微分方程，它们是不同的生长条件下的Logistic方程的特解。

Meanwhile, we proved the unboundedness of solutions of Lienard equations with weaker damping terms when the rotation number is irrational. We still obtained the unboundedness of solutions of Lienard equations with asymmetric nonlinearities at resonance.

另外，还通过应用Birkhoff遍历定理证明了当旋转数为无理数时，弱阻尼的Lienard方程无界解的存在性；同时，证明了共振条件下具有不对称非线性项的Lienard方程无界解的存在性。

Based on the small steepness parameter, three-layer incompressible, inviscid and irrotational fluid system of arbitrary depth is discussed by using the perturbation method, and a unified theory of nonlinear interfacial-internal wave propagation and the approximate nonlinear evolution equations for interfacial-internal elevations are given on the basis of the rigid upper boundary and the flat impermeable bottom.

基于波陡很小的假设下，利用摄动法，讨论了任意深度的二维不可压缩、无黏性、无旋的三层流体系统，在刚性上边界、平底不可渗透条件下，给出了界面内波传播的统一理论以及描述界面内波波剖面的近似非线性演化方程，最后还讨论了几种特殊情形下的近似非线性演化方程。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。