查询词典 triangular matrix

A third order ENO finite volume method for hyperbolic conservation laws on unstructured triangular mesh is introduced.In order to obtain the third order accuracy on spatial discretization,a weighted quadratic interpolation is constructed on every triangular mesh.Two point Gauss quadrature formula is also used on each edge of every triangular mesh and the third order TVD Runge-Kutta method is used for time discretization.The numerical order of convergence and the numerical result of a mesh 3 wind tunnel with one step are given.

摘 要 基于双曲型守恒律方程，对非结构三角形网格给出了一种ENO(Essentially Nonoscillatory Scheme)型有限体积格式，方法的主要思想是先对每一个三角形单元构造一个加权的二次插值多项式，而在计算交界面的流通量时采用了两点高斯积分公式以保证格式的整体精度，时间离散采用三阶TVD Runge-Kutta方法。

Petioles acute-triangular in cross section, 5–20 cm, sheaths triangular-ovate; leaf blade triangular-ovate, 20–45 × 17–40 cm, 2–3-ternate-pinnate; leaflets subsessile or short-petiolulate, long-ovate to elliptic, 2.5–12 × 1–6 cm, base obliquely cordate to cuneate, margin coarse-toothed or serrate, apex acuminate, glabrous or hispidulous along nerves.

叶柄锐尖三角形的在横断面上，5-20厘米，鞘三角状卵形；叶片三角状卵形， 20-45 * 17-40 厘米，羽状2-3回三出；小叶近无柄或短的小叶柄，长卵形到椭圆形， 2.5-12 * 1-6 厘米，基部斜心形对楔形，边缘粗糙的齿或有锯齿，先端渐尖，无毛的或沿着叶脉具短硬毛。

Chapter 2: The principles of triangular Bezier surface modeling were introduced, including degree elevation, differentiation, split and reginal change, etc. The explicit triangular Bezier C〓 modeling and parametric triangular Bezier GC〓 modeling were also introduced.

第二章 系统研究了Bezier三角曲面的基本理论，包括Bezier三角曲面的升阶、求导、分割和区域变换理论；给出了显式Bezier三角曲面的C〓构造和参数Bezier三角曲面的GC〓构造方法。

Cauline leaves ovate to triangular, oblong-triangular, triangular-cordate, or ovate-cordate

茎生叶卵形的到三角形，长圆状三角形，三角形心形，心形或卵形 5

Sepals broadly triangular, ovate-triangular, or triangular-ovate.

萼片宽三角形，卵状三角形，或三角状卵形。

Culm sheaths deciduous, narrowly triangular-rounded, 1/2–3/5 as long as internodes, thinly leathery, radially white-gray setose, longitudinal ribs conspicuous, margins densely ciliate; auricles and oral setae absent; ligule arcuate or nearly truncate, 0.5–1 mm; blade erect, triangular to linear-triangular, width nearly equal to apex of culm sheath.

脱落，狭三角形绕行的竿箨，节间，薄革质的1/2-3/5倍于，显眼的白色灰色具刚毛，长度肋骨，纤毛的边缘密的光线；叶耳和口头的刚毛无；叶舌弧曲的或近截形，0.5-1毫米；叶片直立，三角形到线形三角形，宽度差不多等于竿箨的先端。

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。

In Chapter 5, the least-squares solutions bisymmetric matrix set of the matrix equation ATXA = B on two linear manifolds Si ={X BSRnxn\\\XY - Z\\ = min} and S2 ={X BSRnXn\XY = Z, YtTZi = ZjYu ZtffYi = Zi,i = 1,2, Y, Z e Rnxm}, by applying the singular value decomposition of matrix and the canonical correlation decomposition of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equation ATXA = B on two linear manifolds.

在第五章，我们研究了两类线性流形S_1={X∈BSR~|‖XY-Z‖=min}和S_2={X∈BSR~|XY=Z，Y_i~TZ_i=Z_i~TY_i，Z_iY_i+Y_i=Z_i，i=1，2，Y，Z∈R~}上矩阵方程A~TXA=B的双对称最小二乘解。

From the history of Matrix and Transformation and the development of curriculum at home and abroad, putting matrix combined with the transformation, and orienting the study in 2×2 rank matrix, boosting matrix up the geometrical visualization as a algebra objects are a new perspective on knowing matrix.

从矩阵和变换的历史发展过程和国内外矩阵和变换的课程设置来看，把矩阵与变换相结合，并定位在2×2阶上研究矩阵，增强作为代数对象的矩阵的几何直观性，是认识矩阵的一个新视角。

We make the following assumption for When 2 is positive definite matrix, different estimators about matrix of regression coefficients and inefficiency of Least squares estimate have been discussed in many documents. Considered 2 is nonnegative definite matrix, this thesis derives Best linear unbiased Estimate of parameter matrix B and estimable parameter function KBL under the meaning of matrix nonnegative definite and the property of maximum probability of BLUE is investigated.

当∑＞0时，众多文献讨论了回归系数阵的各种估计及LSE的有效性，本文考虑了当∑≥0的情形，给出了回归系数阵B及其可估参数函数KBL的在矩阵非负定意义下的最优估计，研究了它的一个最大概率性质，并且讨论了最小二乘估计成为最佳线性无偏估计的充分必要条件，在此基础上给出了均值矩阵的最小二乘估计与BLUE的偏差估计，定义了LSE相对于BLUE的一个相对效率，并给出了它的界。

Fostering the concept of multi-culture firmly and mastering the development of advanced culture correctly are conductive to resisting terrorism, separatism of nationalities and ultraism of religion, which is of great academic theoretical, immediate and profound historical si...

牢固树立多元文化的理念和正确把握先进文化的发展方向，有助于在世界范围内自觉地抵制恐怖主义，民族分裂主义和宗教极端主义。不仅具有重大的学术理论意义，而且也具有重大的现实意义和深远的历史意义。

But if anyone walks in the night, he stumbles, because the light is not in him.

11：10 若在黑夜行走，就必碰跌，因为那光不在他里面。