积分的

Baernstein[2] gave the conclusion by using Koebe function as the extremal function , Glenn Schober[6] studied the classes such as S, P, K, S* of H and represented these functions with integral formulations. Wang Jian[3] and others investigated the integral mean values. Our work is continuation of their work.

Baernstein首先在单位圆上讨论给出了以Koebe函数作为极值函数的结论，Glenn Schober对H中一些函数子类如S、P、K、S~*等作了研究，将这些子类上的函数用积分表达出来，王键结合Baernstein~*函数的定义及Glenn Schober的结论，定义了对称集的概念并得出了一些函数类在其上的积分平均。

Based on the Biot s two-phase theory for fluid-saturated porous media, considering the inertia force of the solid and the liquid, and the coupling function between the solid and the liquid, and the compressibility of the liquid in allusion to the character of the nearly saturated soils. The dynamic governing differential equations are solved by Hankel transform. Then, considering the boundary condition, the dual integral equations of vertical vibration are established which are reduced to Fredholm integral equation of the second kind.

本文基于Biot两相介质动力固结理论，针对准饱和土地基的特点，考虑了流体的可压缩性，土体和流体的惯性及水土之间的耦合作用，运用Hankel变换技术求解动力控制方程，然后按混合边值条件建立起对偶积分方程，并将其化为易于数值计算的第二类Fredholm积分方程，分别研究了准饱和土半空间地基、上覆单相弹性层的准饱和土地基和准饱和粘弹性地基上刚性基础的竖向振动特性。

In this paper, we just consider the initial-boundary value problems of aclass of two-dimensional nonlinear integro-differential equation, simultaneouslyconsidering the damped term and memory termThe details will go as follows. Firstly, the c...

本文同时考虑耗散项和记忆项等因素，讨论了一类具有记忆项的二维非线性积分微分方程的如下初边值问题具体研究内容如下：首先，文章简单介绍了国内外当前对非线性积分微分方程的研究现状；其次，文章给出了一些重要概念和引理，并对部分符号做了说明；第三，利用Galerkin方法证明了问题(1)-(3)的变形问题弱解的存在唯一性；第四，证明了问题(1)-(3)强解的存在性和能量的指数衰减性；第五，进一步证明了问题(1)-(3)经典解的存在性。

In this paper, we just consider the initial-boundary value problems of aclass of two-dimensional nonlinear integro-differential equation, simultaneouslyconsidering the damped term and memory termThe details will go as follows. Firstly, the current st...

本文同时考虑耗散项和记忆项等因素，讨论了一类具有记忆项的二维非线性积分微分方程的如下初边值问题具体研究内容如下：首先，文章简单介绍了国内外当前对非线性积分微分方程的研究现状；其次，文章给出了一些重要概念和引理，并对部分符号做了说明；第三，利用Galerkin方法证明了问题(1)-(3)的变形问题弱解的存在唯一性；第四，证明了问题(1)-(3)强解的存在性和能量的指数衰减性；第五，进一步证明了问题(1)-(3)经典解的存在性。

Based on the Guldin's first theorem, it was deduced that the general formula to calculate the rotating surface area which is shaped by rotating the curve Г in a plane around the L-axis in the space by using curve integral.

依据古鲁金第一定理推证，得到利用曲线积分计算空间某一平面上的曲线Г绕直线L旋转而成的旋转曲面面积的通用公式；利用曲线积分计算xoy面上的曲线c绕直线L旋转而成的旋转曲面面积的通用公式。

The maincontents of this thesis include:Firstly,by using inherent relationship between region integral and curve integral,designing the image transform operator,a novel snake model using both boundary andregion information was proposed,which more directly integrated the prior knowledgeincluding region information with the traditional deformable model,so that the abilityabout evolving contour curve was improved.

本论文将以严密的数学理论、可靠的物理原理和实际的应用背景为出发点，研究这一图像处理和分析的基本问题，并相应开展了以下几个方面的工作：首先，本论文利用区域积分与曲线积分之间转化的内在联系，通过设计相应的图像变换算子，提出了一种基于边缘与区域信息的图像可变形轮廓提取模型。

In this paper, we generalized the reverse Shebyshev inequality and obtained the integral inequality of two vector function s, whose monotone of correspondence elements is reverse.

推广了反向Chebyshev不等式，得到了对应分量的单调性相反的连续向量函数的积分不等式和模的单调性相反的连续向量函数的积分不等式。

In Chapter Five, we compare numerical integration of the reproducing kernel with the integral equation of complexified trapezoid through a detailed solution to the initial-value problem of ordinary differential equation to exemplify that the method of interpolation spline integrating and the reproducing kernel is not only feasible in theory but also significant in pratice.

在第五章，我们通过具体的求解一个常微分方程的初值问题，把再生核方法的数值积分和复化梯形积分公式相比较，说明样条插值和再生核相结合的方法不仅是理论上可行的，而且还具有重要的实际意义。

Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcame. Finally, natural frequency is obtained by the existence condition of nontrivial solution of the discrete algebraic equations derived from the integral equations.

边界方程有多种选择，在选定一种边界方程的基础上，可以通过建立一个新的边界方程来表示问题的边界，以克服积分核的奇异性；最后由积分方程的离散化方程组有非平凡解的条件，求得固有频率。

When computing the diagonal elements of the Galerkin matrix, one will encounter the integral of Hankel function, the Green's function of 2-dimensional Helmholtz equation and the cosine weighting function, whose integrand is singular in the integration range. A new approach is proposed to deal with this kind of singular integrals, which is pivotal but have not been reported so far.

首先建立了透镜边缘上任一点的电场满足的边界积分方程，然后选择适当的正交模式函数展开端口上的电场分布，采用边界元法的思路及Galerkin法将该积分方程离散化为—矩阵方程求解即可得到透镜的多模式散射参数。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。