奇异函数

Based on a localization principle and subband decomposition, monoscale ridgelet and curvelet were proposed, both of which were derived from ridgelet transform and can efficiently deal with smooth images with smooth edges including straight and curve singularity. They, hence, are of better application potention. sparse representation;optimal basis;ridgelet;curvelet;image denoising;non-parametric estimation

单尺度脊波和Curvelet变换由脊波变换发展而来，分别利用了函数局部化和频带剖分的思想，将脊波理论发展到了一个更高的阶段，这两种变换都能"近似最优"的表示直线和曲线奇异，因而具有更好的应用前景。

Let〓be a meromorphic function of finite order and〓z,where qis rational and pis a polynomial.Then every cycle of Bakerdomains of f contains a singularity of〓.

推论3.4设q是一个有理函数，p是一个多项式，m，n是满足〓的两个正整数，又设f是一个满足如下微分方程的亚纯函数〓（3.2）则f的每一个Baker域循环一定含有〓的奇异点。

Selecting proper single valued variable separation functions in the 2+1 variable separation solutions,we construct many types of single valued coherent soliton structures such as dromion,dromion lattice,solitoff,2-solitoff,static and kinetic breather,instanton,compacton, peakon,and so on.The interactions among these coherent localized excitations including the collisions of compaction and compacton,peakon and peakon,line soliton and y-periodic soliton,dromion and dromion,dromion and solitoff,et al,are investigated analytically and graphically,and found that can be elastic and nonelastic respectively,which reveal various exotic and important nonlinear characters and interaction properties.

在2+1维分离变量解中选择适当的的单值分离变量函数，构造了2+1维非线性波动模型多种单值相干孤子结构如Dromion，Dromion格子，Solitoff，2-Solitoff，静止和运动呼吸子、瞬子、Compacton、Peakon等；考察了一些典型的非线性激发模式间如Compacton和Compacton，Peakon和Peakon，线孤子和y-周期孤子，Dromion和Dromion，Dromion和Solitoff之间等相互作用行为，发现其相互作用可以弹性的也可以是非弹性的，揭示了多样奇异而重要的非线性特性。

In order to locate direct singular positions, we begin by expressing the determinant of the Jacobian matrix Jx in terms of position of the center P of the moving platform. The Z and the Y coordinates of P may be chosen from the workspace, then the determinant of Jx is now a six order polynomial of X, the x coordinate of P. The direct singular positions corresponding to are obtained by solving the polynomial equation, and retaining all real roots in the workspace.

由速度分析的Jacobian矩阵Jx，将其行列式值表示成活动平台中心点P位置的函数，寻找奇异位置的方法是先假设平台高度，再假设工作空间内P点的Y座标，使Jx行列式成为P点X座标的六次方程式，求解方程式并保留在工作空间内之实根。

The detailed algorithm on analyzing cracks exploration inside blocks is: enriched approximations which describe singular crack tips fields and discontinuous crack faces are employed under the Partition of Unity theory; the enriched nodes surrounding crack tips or faces are respectively mapped with corresponding enriched degrees of freedom, and the solution of all these degrees of freedom is uniformly proceeded by the implicit iteration algorithm of DDA, then fracture and breakage of DDA blocks can be analyzed. The numeric examples show this algorithm is rational and efficient.

为此建立的无网格法裂纹扩展分析算法，采用满足单位分解条件的特殊增强型函数表达裂纹周围应力场的非连续、奇异特性，将对应的扩展自由度动态映射到裂纹周围的节点上，统一按DDA法隐式迭代方式求解，实现块体裂纹扩展和强度分析，相关算例结果显示该算法是合理有效的。

Based on the fundamental solution of two perfectly bonded elastic halfspaces, the boundary integral equation method is used to reduce the problem to a hypersingular integral equation in which the unknown function is the crack opening displacem...

首先根据双材料空间的弹性力学基本解，使用边界积分方程方法，在有限部积分的意义下导出了以裂纹面位移间断为未知函数的超奇异积分方程，并为其建立了数值法。

Correlation dimension is the concept corresponding to correlation function in random process.

关联维数是与随机过程中相关函数相对应的概念，对于混沌过程的奇异吸引子，其关联维D2一般为分数。

Our results show that fitting the spectrum of residual function in FT method gives more accurate rCBF than that of the two SVD methods. But FT method takes more computational time to remove recirculation.

实验结果显示争Q用傅立叶转换法，并对残余函数的频谱加以拟合，所得到的rCBF ，较不易产生rCBF低估的现象，但为了去除再循环的部分，则必须花费较多的时间；而奇异值分解法则容易产生rCBF低估的现象。

In this paper,the author give the spectra characterizations of nonsigular feedback polynomials and local permutation polynomial s over finite fields and residue class rings,and simplify existing results over prime fields,and provide a new proof method for the spectra characterization of correlation immune functions over finite fields and residue class rings.

本文给出了有限域和剩余类环上非线性反馈移存器的非奇异反馈多项式及局部置换多项式的谱刻划，简化了素域上的现有结果，并对有限域上和剩余类环上相关免疫函数的谱特征给出了一个新的证明方法。

Besides, the concepts, such as SIB and multiple energy function sheets, are explained by picture.

此外，还以图形形象地解释了多能量函数面和奇异诱导分岔等概念。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。