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Two above methods are generalized to tensor product Bézier surfaces and triangular Bézier surfaces, we give two approaches of degree reduction for tensor product Bézier surfaces, each of which reduces a given degree n×m tensor product Bézier surface to a n〓×m〓 one, and two methods of degree reduction for triangular Bézier surfaces, which reduce a given degree n triangular Bézier surface to a degree m one. The explicit formulas of control points for reduced tensor product and triangular Bézier surfaces are obtained respectively.

张量积Bézier曲面的两种降阶方法均可把n×m阶张量积Bézier曲面一次降阶为n〓×m〓阶张量积Bézier曲面；三角Bézier曲面的两种降阶方法均可把n阶三角Bézier曲面一次降阶为m阶三角Bézier曲面，并给出降阶张量积Bézier曲面和降阶三角Bézier曲面控制顶点的显示表示式。

Antiplane responses of a scalene triangular hill or structure, an isosceles triangular hill or structure, an isosceles triangular hill with a subsurface cavity to incident SH waves are studied in this paper based on methods of wave function expanding, complex function, moving coordinates and by employing idea of assistant function.

本文在"分区"和辅助函数思想的指导下，综合利用了波函数展开、复变函数、移动坐标三种方法，研究了等腰三角形凸起地形和坝体结构、非等腰三角形凸起地形和坝体结构、浅埋圆孔附近等腰三角形凸起地形等三类问题对SH波的散射。

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。

This is the so-called Duerlite algorithms: from the bottom row of the matrix A do elementary transformation, the diagonal elements into the bottom left of zero, and then show the effect of these lines is equivalent to transform the left by a unit lower triangular matrix, this series of unit lower triangular matrix inverse is the product of L matrices, it is also a unit lower triangular matrix.

这正是所谓的杜尔里特算法：从下至上地对矩阵A做初等行变换，将对角线左下方的元素变成零，然后再证明这些行变换的效果等同于左乘一系列单位下三角矩阵，这一系列单位下三角矩阵的乘积的逆就是L矩阵，它也是一个单位下三角矩阵。

In Chapter 4, a symmetric triangular partitioned secant method for solving large scale sparse unconstrained optimization problems is constructed, which is a combination of a secant method and a finite difference method, and depends on a consistent partition of the columns of the lower triangular part of the Hessian matrix; it reduces the number of gradient evaluations required by Powell and Toints algorithm (the indirect lower triangular substitution algorithm) by one at every iterative step.

此算法是基于稀疏Hesse阵的下三角部分的列的相容分划的基础上建立起来的，把割线法和有限差分法有机的结合在了一起，在每次迭代中，把由Powell和Toint的算法所需要的梯度赋值次数减少了一。

And three special kind of triangular decomposition is introduced. In addition, the calculation of matrix's triangular decomposition and the application on matrix's triangular decomposition are detailedly discussed.

并介绍了三类特殊矩阵的三角分解，且对矩阵三角分解的计算及应用作了较详细的论述。

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。

A backer of an Afghan law that critics say legalizes marital rape has rejected the international outcry as foreign meddling.

饱受批评的一项法律的拥护者说合法化的婚内暴力不会受国际舆论的干涉。

Years ago, a ancient Egyptian fleet went to the Land of punt for seeking a kind of flavor named "myrrh", and aromatic plants which has dense exotic style for the queen Hatshepsut.

3500年前的一个古埃及的舰队到&彭特之地&寻找一种叫没药的香料。