查询词典 singular boundary point

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

With the help of the fundamental theory to singular measure differential system, Green's function matrix expression of solution and well-posed boundary condition are given, together with discussing the properties of the Green's function matrix under the influence of impulsive effect In section 5, based on Lyapunov function method, we investigate that the existence of the first boundary value problem to second-order singular system by macthing the solutions to the second boundary value problem; and the existence and uniqueness of three-point boundary value problem to third order singular system by macthing the solutions to two-piont boundary value problem.

第五部分借助Lyapunov函数法，通过将第二类边值问题的解对结成第一类边值问题的解，得到了二阶广义系统的第一类边值问题解的存在性；通过将两点边值问题的解对结成三点边值问题的解，得到了三阶广义系统的三点边值问题解的存在性和唯一性。

Compared with the initial value problems of scalar conservation laws with smooth flux function, the global weak entropy solutions for the initial-boundary value problems of scalar conservation laws with weak discontinuous flux function include the following new interaction types: a rarefaction wave collides with the boundary and is absorbed compltetely or partially by the boundary; a rarefaction wave collides with the boundary and the boundary will reflect a contact or non-contact shock wave; a contact or non-contact shock wave collides with the boundary and is absorbed by the boundary; a contact or non-contact shock wave collides with the boundary and a new non-contact shock will rebound from the boundary simultaneously or later.

与具有光滑流函数的单个守恒律的初始值问题相比，具有弱间断流函数的单个守恒律初边值问题的整体弱熵解中包括下列新的相互作用类型：稀疏波碰到边界并被边界部分或全部吸收；稀疏波与边界相撞，边界反射出一个接触或非接触激波；接触或非接触激波碰到边界并被边界吸收；接触或非接触激波与边界相撞，边界同时或稍后反射出一个新的非接触激波。

Then the boundary element integral equation of interior and exterior form is deduced in detail, also the form with corner coefficient. The significance for numerical calculation and principle of the singular integral is analyzed, and a non-isoparametric transformation method is presented to calculate weak singular integral and Cauchy integral, the method presented provides us a very simple way to computer the two kinds of singular integral of Helmholtz boundary integral equation, and it is easy to program in computer. After the difficulty of the calculation for multi-frequency of Helmholtz boundary element is explained, a method named SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation), which is focused on the computational efficiency, is presented.

对结构声辐射的边界积分方程的内部形式与外部形式进行了详细的推导，给出了角点系数的计算方法与边界积分方程的形式，在此基础上，分析了奇异积分产生的原理及其对数值计算的重要性，提出了一种计算奇异积分的非等参(来源：Ae8a8BC论文网www.abclunwen.com)单元的变换方法，该方法给Helmholtz 声学边界积分方程中的弱奇异积分与Cauchy 奇异积分的计算以及编程提供了极大便利。

The result shows that the mixed boundary condition can greatly reduce the calculation area without affecting accuracy of the solution.It is followed by the higher accuracy of Dirichlet boundary condition which makes the boundary error greater when measured points is near the boundary, so we must take a sufficiently large border region.The homogeneous boundary condition has relatively large error, but the use of non-triangle poles devices makes apparent resistivity calculation error become small, because of elimination of the effect on potential difference for the infinite boundary. In inversion, in order to save computing time, homogeneous boundary conditions are often used to perform finite element forward calculation.

结果表明，混合边界条件精度最高，可大大缩小求解区域而不影响计算精度，其次是Dirichlet边界条件精度较高，但测点越靠边界误差会越大，必须取足够大的边界区域，齐次边界条件的误差比较大，但如果采用非二极装置，通过电位差计算得到的视电阻率，由于无穷远边界对电位差的影响基本消除，视电阻率计算误差与混合边界条件下的接近，在反演中，为了节省计算时间，经常使用齐次边界条件进行有限元正演。

The boundary contour formulations of evaluatingstresses from the Somigliana stress identity are derived for 2-D problemswith quadratic boundary elements.The boundary contour method basedon the traction boundary integral equation is further discussed.Elasticproblems are first solved using the traction boundary contour method.Amixed collocation of the displacement boundary contour formulation andtraction boundary contour formulation is given.(4)The dual boundarycontour method is developed for the analysis of crack problems.

3建出了Somigliana应力积分式的二维和三维问题的边界轮廓法理论；给立了二维问题由Somigliana应力积分式计算应力的二次形函数的边界轮廓法方程，进而给出了基于面力边界积分方程的边界轮廓法；提出了一种以位移边界轮廓法方程与面力边界轮廓法方程混合配置的方案，首次实现了用两种积分方程相结合来求解弹性力学问题。

Using algebraic methods which include extended Tanh-method,some new solitary solutions to the DBM and Log-DBM equation,such as singular solitary solutions,double singular peakon solitary wave solutions,double solitary wave solution with peakon and singular periodic solitary wave solutions are obtained..With the aid of an auxilitary function combined with the elliptic integral of the first kind,periodic solitary solution,singular and periodic singular solitary solutions can be obtained.

第三章利用扩展的Jacobi椭圆函数展开法研究了方程，并给出ZK-MEW方程的Jacobi椭圆函数解，特别的，当模数m→0和m→1时，其中一部分解退化为三角函数解和孤立波解；其次使用sn-cn拟设法，研究了K(k，s，1)方程，得到了k=s=3时的新的精确解，并在模数m→0和m→1时得到了丰富的三角函数和孤立波解。

Firstly, we analysize the boundary value problem for linear singular system, several properties for linear singular system are given, and then the existence for boundary value problem to nonlinear singular system is proved by using the previous properties discussed and Schauder's fixed point theorem.

接着，利用Banach不动点定理，研究了Volterra型广义积分微分系统边值问题解的存在唯一性，最后给出了几个推论。

By the analysis for the characteristic of singular value of ideal signal and noise, it's pointed out that there is a big turning point in the singular value curve of ideal signal, but not in the one of noise, so the concept of curvature spectrum of singular value is proposed, which can effectively describe the turning point state of singular values of noisy signal.

分析了在Hankel矩阵方式下理想信号和噪声的奇异值特点，指出理想信号的奇异值曲线存在一个很大的转折点，而噪声的奇异值曲线则很平坦。

It is the first important step in video analysis and will directly affects the effectiveness of indexing Shot boundary detection is one of our major research interests and we will tackle the following existing problems the ambiguity between gradual change and camera motion, the discontinuity during gradual change, false detection caused by illumination variation and flashlight, automatic threshold selection Firstly, we discuss shot boundary detection in non-compressed domain In chapter 2, we compare some of the commonly used detection methods which are based on frame difference and point out that single feature will not generate good results As a conclusion, we use fuzzy logic to combine multiple features Presently, most frame difference based shot boundary detection algorithms rely on threshold and hence the selection of such thresholds will greatly affect the performance of boundary detection We propose a membership function to define frame difference and calculate the membership with self adaptation according to the statistic distribution of frame differences to satisfy different type of video clips Experiments show that the proposed fuzzy shot boundary detection algorithm can be used with different video types and has a high detection precision and recall In chapter 3, we discuss model-based shot boundary detection algorithms regarding chromatic and spatial editing effects such as fade-in, fade-out, dissolve and wipe Various parameters are proposed to better describe the characteristics of each editing type.

镜头边界的检测是把视频自动地分割为一个个镜头，作为基本的索引单元，因此它是视频分析重要的第一步，直接影响到视频检索的成败。镜头边界的检测是本文研究的重点之一。目前镜头边界检测算法主要存在以下问题：渐变与镜头运动难以区别；渐变过程中的不连续与停顿、光照条件的变化及闪光灯等特殊情况会引起误检测；自动选择阈值比较困难等。本文首先针对非压缩域视频进行了镜头边界检测的研究。在第二章中我们采用了比较流行的基于帧间差的方法。在比较各种帧间差计算方法的基础上，指出使用单一的特征难以取得很好的检测效果，提出用模糊逻辑综合使用各种特征。目前大多数基于帧间差的镜头边界检测算法都采用阈值法进行镜头转换的判别。阈值选择的误差对检测性能有较大的影响，本文提出用隶属度函数定义帧间差较大、中等较大和较小等概念，并根据帧间差的统计分布自适应地确定隶属度，以适应不同类型的视频片断。实验结果表明这种基于糊逻辑的镜头边界检测算法可以适应不同的视频，并具有较高的检测精度和检出率。在第三章中采用基于模型的方法进行镜头渐变的检测，研究了淡入／淡出、慢转换和扫换的模型。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。