三角方程

By solving the SturmLiouville eigen-equation in the barycentric coordinate, the generalized sine and cosine functions in the triangular domain are constructed. Properties of these functions are systematically investigated by visualization and theoretical derivation.

本文通过求解重心坐标下的Sturm-Liouville特征方程，构造出了三角区域的广义正弦函数和广义余弦函数，并通过可视化与理论推导相结合的方法系统的研究了这两组函数的性质。

By solving the Sturm-Liouville eigen-equation in the barycentric coordinate, the generalized sine and cosine functions in the triangular domain are constructed. Properties of these functions are systematically investigated by visualization and theoretical derivation.

本文通过求解重心坐标下的Sturm-Liouville特征方程，构造出了三角区域的广义正弦函数和广义余弦函数，并通过可视化与理论推导相结合的方法系统的研究了这两组函数的性质。

Because the derivation of the extended system has a block lower triangular form, the method of splitting iteration is applied to compute simple bifurcation point, not only computational work is reduced, but also local quadratic convergence is achieved.

由于所构造的扩充系统的导数具有分块下三角形式，采用分块迭代的方法进行数值求解，不仅减少了计算量，而且是二次收敛的，从而为Navier-Stokes方程非退化简单分歧点的数值逼近提供了有效的算法。

Trigonometrical function most value solution mainly fromthe trigonometrical function domain of definition, the valueterritory, monotonous, the image and the triangle 恒等 distortionembarks, and the comprehensive utilization function, the inequality,the equation, several what kind multitudinous knowledge sides canobtain.

三角函数最值的求解主要从三角函数的定义域、值域、单调性、图象和三角恒等变形出发，并且综合利用函数、不等式、方程、几何等众多知识方能求得。

Because of using double Fourier Series, the development of equations isvery simple, and the answer has the advantages of uniform mathematic expression and easily drawing-up calculating program.

由于重三角级数的利用，使方程的推导变得简洁，所得的结果数学形式统一，便于计算机编程计算。

We can choose the type of elliptic PDE that satisfied all these conditions, the solution of elliptic PDE is what we need.

最后，根据确定的这些边界条件构造满足这些边界条件的偏微分方程，其解便是满足边界条件并插值于三角形三个顶点的三角曲面片。

To simplifying calculation, the membranee element was used, and the finite element equation for big strain was induced.

为了简化计算采用三角薄膜单元，并推导出相应的大变形有限元矩阵方程。

This paper is composed of the algorithm design of dual-tree binary coefficients complex wavelets,MGM algorithm for linear systems that can be diagonalized by generalized discrete Fourier transform and type-II discrete sine transform matrices, wavelet and MGM algorithms for Toeplitz systems and their applications in signal and image processing.

本文以多进制小波与对偶树二进制系数复数小波算法设计、三角变换对角化系统MGM算法、Topelitz系统的小波与MGM结合算法作为理论主线，以对偶树复数小波与扩散方程方法结合的图像去噪，信号与恢复作为应用背景展开讨论。

The triangle mesh model of surface was extracted by constructin g an implicit surface function.

首先建立插值散乱数据点的隐式曲面方程，然后使用步进立方体算法提取出曲面的三角网格模型。

The Neumann boundary value prob-lem is firstly reduced into the equivalent natural boundary integral equation withthe kernel possessing 2nd-order singularity,and then the corresponding variationalproblem on the boundary is obtained.By applying Quak trigonometric wavelet basisBjsee(1.2.3as boundary elements and the method of expanding kernel functionto its Galerkin discretization,we obtain simple computational formulae of the en-tries in the stiffness matrix.

首先，我们将Neumann边值问题归化为等价的带有2阶强奇性核的自然边界积分方程，然后化为边界上相应的变分形式，以Hermite插值Quak三角小波基Bj见(1.2.3作为边界元并利用积分核函数展开法将其离散，得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵具有十分简单的形式，它是分块循环对角阵。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。