稀疏

Eight dimensions is a rarefied space that is home to the octonions -"the crazy old uncle nobody lets out of the attic", as mathematician John Baez of the University of California, Riverside, puts it.

8维空间，是容纳八元数的稀疏空间——"没有人要这位疯狂的老叔父离开他的阁楼"，正如加州大学河滨分校的数学家约翰·贝茨所说的那样。

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

Using varied band matrix and one-dimension array to collect the large sparse matrix, the integral coefficient of all the nodes, we could save memory space.

采用变带宽、一维数组方式只存储稀疏刚度矩阵中非零元索，能够节约内存。

First, the input model is embedded into a coarse tetrahedral control mesh, and the modified barycentric coordinates are employed to establish their relationship. Then according to users editing, the control mesh is deformed by solving a quadric nonlinear energy minimization problem, and the deformation is passed to the embedded model by interpolation.

首先将输入模型嵌入到一个稀疏的四面体控制网格中，并且通过一种改进的重心坐标来建立两者的对应关系；然后通过用户的交互，对控制网格建立一个二次非线性能量函数对其进行变形，而输入模型的变形结果则可以通过插值来直接获得。

For the sparseness of oilseed rape stubble and thin stem of benne stubble, their wind-breaking effects were worse than wheat stubble and naked oats stubble.

高度相同时不同类型的留茬比较，莜麦和小麦茬下风速降低幅度较大，植株稀疏的油菜茬和秸秆较细的胡麻茬的防风效果较差。

Secondly, we discuss the boundary value problem of two dimensional biharmonic equation in a rectangular field and its variational problem,discretize it by using dual tensor product of and the direct product and lining up of matrices, we get some special matrices which are the presupposition in exploring the fast computation, then solve the system of linear equations.

其次本文讨论了矩形域上二维双调和方程边值问题及其相应的变分问题，利用二元张量积小波分析和矩阵的直积、拉直技巧将变分问题离散化，从而使求解偏微分方程问题变为求解线性方程组的问题。一维情况两组基的张量积下得到的系数矩阵分别为块状七对角阵和稀疏矩阵。这些特殊结构为以后快速算法的研究打下一个基础。

The old woman had very little hair and a bony face.

这名老妇人有著稀疏的头发及一张消瘦的脸。

From where Simon sat, the doctor's thin hair was a bristly halo above his narrow shoulders.

从Simon坐的地方能看到，大夫窄窄的肩上，稀疏的头发竖起，环绕着脖颈。

The other, Mr William de Burgh Cokane, is probably over 40, possibly 50: an ill-nourished, scanty-haired gentleman, with affected manners: fidgety, touchy , and constitutionally ridiculous in uncomp- assionate eyes

另外那位是威廉·德·布·高坎先生，年龄大约四十开外，也许五十岁了，这位先生营养不良，头发稀疏，喜欢装腔作势；老是坐立不安，易动肝火，在一个不体谅的人看来，是个天生可笑的人物。

Colonel Ackerson ran both hands through his thinning hair, and poured himself a glass of water from the carafe on the table.

埃克森上校双手在他稀疏的头发上梳过，从桌子上的瓶子里给自己倒了一杯水。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。