查询词典 manifold without boundary

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。

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。

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。

In this paper, the existence of isometric mapping between the manifold in the high-dimensional data space and the parameter space is proved. By distinguishing the intrinsic dimensionality of high-dimensional data space from the manifold dimensionality, and it is proved that the intrinsic dimensionality is the upper bound of the manifold dimensionality in the high-dimensional space in which there is a toroidal manifold.

首先给出了高维数据的连续流形和低维参数空间之间的等距映射存在性证明，然后区分了嵌入空间维数、高维数据空间的固有维数和流形维数，并证明存在环状流形高维数据空间的参数空间维数小于嵌入空间维数。

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。

For reducing boundary distortion area, the elevations of grid DEM are viewed as a discrete sequence under a generalized coordinate, so that the boundary problem of two-dimensional discrete wavelet transform is turned into the boundary problem of one-dimensional discrete wavelet transform, which not only greatly reduces the boundary distortion area, improves the precision of reconstructed DEM data near the boundary, but also decreases the number of zeros adding on the boundary for wavelet transform, and boosts the compression ratio. On the basis of analyzing the distribution characteristics of coefficients in low and high frequency bands, a mixed entropy coding plan is applied, and a high efficient quantizator called"self-adaptive hard threshold"is established, which is helpful for improving the precision of the reconstructed DEM data and for enhancing compression ratio.

为了减小小波变换山区格网DEM数据压缩中边界失真区域，将山区格网DEM高程值视为广义坐标下的离散随机序列，把二维离散小波变换中的边界问题转换为一维离散小波变换中的边界问题，不仅大大减少了小波变换边界失真区域，提高了重构DEM数据边界点的精度，而且减少了边界补零个数，提高了压缩比；通过对山区格网DEM数据小波变换低频区和高频区变换系数分布特点的分析，采取了霍夫曼—游程混合熵编码方案，设计了高效、低失真的"自适应硬阈值"量化器，即对低频区变换系数不进行量化，直接进行霍夫曼编码；对高频区变换系数则先用"自适应硬阈值"方法量化处理，再进行游程编码。

The linear manifold-learning algorithms represented by PCA, with their substantial mathematical foundation and simple implementation, but they are not able to show complex nonlinear manifold structure with their linear essence, which gives rise to nonlinear manifold-learning algorithms such as Isomap, SIE etc.

以PCA为代表的线性流形学习算法有较强的数学基础，实现简单，但是其线性本质并不能揭示复杂的非线性流形结构；于是又出现了以Isomap、SIE等为代表的非线性流形学习算法。

As the special characteristic of nonlinearity, several notions are introduced and used in this paper, such as differential manifold, vector field, diffeomorphism, tangent space, topological equivalence. Stable manifold and unstable manifold are also introduced.

针对非线性的特殊性，本文专门介绍了非线性中几个比较特殊的概念，如微分流形、向量场、微分同胚、切空间以及等价关系等，对稳定和不稳定流形也作了介绍。

As a new technique, the manifold method, proposed by Genhua, Shi in 1990s is based on the concept of topology manifold and differential manifold in mathematics.

其中尤以数值流形方法最为突出，以其新颖的数值思想、先进的数值技术得到了学术界的广泛关注。

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。