矢算

The fast Fourier transform technology is adopted to calculate the dyadic Green's operator and its adjoint operator during each iteration of CSI, which ensures the high efficiency of the algorithm in stratified medium.

CSI的每一次迭代过程均采用快速Fourier变换技术计算并矢Green函数算子及其共扼算子，确保了该算法在三维层状介质情况下的高效率。

The rules include not only the complete procedures to construct the three-powered interpolation used by Shoushi Computus in calculating the solar, lunar and planetary equations of center, but also the detailed routines, namely the Geyuan Shu (the procedure of circle division), to derive the table contained in the Shoushi Computus for transferring the pseudo-ecliptic longitudes of the sun into equatorial coordinates, which turns out to be compatible with the results obtained with spherical trigonometry.

从总体角度来看，他在《授时历》立法原理方面的工作已经超过了嘉靖年间顾应祥和周述学等学者的工作，不过，在弧矢割圆术中应用的高次方程解法方面，邢云路的工作则可能直接受到了顾应祥、周述学等学者相关工作的影响，而且邢云路在高次方程解法方面也没有超出明代历算家对高次方程数值解法的认识水平。

The vactrix method is further developed, a vectrix Skew-symmetric crossproduct identity is presented and the dyadic form of the derivative of a vector with respect to another vector in terms of vectrix is also offered.

进一步发展了矢阵方法，提出了矢阵叉积算子恒等式及矢量相对于矢量的导数以矢阵表示的并矢形式，并给出了若干应用实例。

After that, by making use of dual basis, the general reconstruction formula about frame is discussed, and the computation formula for the dual frame is presented, in which no operators are contained.

然后，利用对偶基概念讨论了一般框架下信号的重构公式，并给出了对偶框架的具体计算公式，该公式不包含任何算符，可以明显看出基矢的相关性与框架类型之间的关系。

Vector partial differential operator ; Dyadic Green function ; Heteromophic waveguide ; Cutoff frequency

矢量偏微分算子；并矢格林函数；异形波导；截止频率

The Hamiltonian operator of system of heisenterg chain function the complete basis vectors produced with permutation group to form energy matrix.

将一维海森堡体系的哈密顿算符作用于完备基矢形成能量矩阵。

For the analysis properties of infinite matrix,first,it establishes the automatic conti-nuity theorems on the sequence spaces with 0-GHP or WGHP,and the automaticboundedness theorem on the sequence spaces with 0-GHP.

在无穷矩阵的分析性质方面，建立了具有0-GHP或具有WGHP的矢值序列空间上无穷矩阵算子的自连续性定理，以及具有0-GHP矢值序列空间上无穷矩阵算子的自有界性定理。

The interpolate algorithms of three-order NURBS curve and double three-orders NURBS surface are presented. The expressions of partial derivative and normal curvature of NURBS surface are derived by the theory of differential geometry. The geometric characteristics of different curvature area of the free-form surfaces are analyzed in detail. All these work lays a theoretical foundation for constructing the cutter location calculating model of free-form surfaces NC machining. 2 On the basis of analyzing the methods of cutter path generation, the standard of evaluating the various methods of cutter path generation is presented. The method of generating cutter path with constant scallop height is presented for the first time.

本文以提高复杂曲面多坐标数控加工精度和加工效率为目的，在对国内外研究现状进行深入分析的基础上，对数控编程中各环节的关键技术问题进行了深入研究，主要内容包括以下几方面： 1 分析了复杂曲面各种造型方法的优缺点，给出了根据各种边界条件所确定自由曲面的NURBS表示方法以及三次NURBS曲线曲面反算算法；用微分几何理论推导了NURBS曲面的偏导矢及法曲率计算表达式；对曲面不同曲率特性区域的几何特征进行了深入分析，为建立复杂曲面的数控加工刀位计算模型奠定了理论基础。

As for the parametric space calculation to find an optimal 3D point, the Tangent Vector Inversion is presented so as to cut down iteration.

针对求解曲面上最优点的参数域反算问题，引入了切矢逆求方法，可使迭代次数大为降低。

In this new theory system, according to non-inertial tow motion system various multi-linear vector concrete deductive calculus and analyse, it can be determined that after electron and positron collide (combined at shout-range distance reacted by strong force), they form excited state neutrino,then reacted by weak force for a relaxation time becomes un excited state neutrino and release large energy photon or phonon, its mass tends to zero.

新理论体系，按非惯性牵引运动系，各类多线矢的具体演绎矢算分析，可以判定：电子与正电子碰撞(在近程条件强力作用下结合)成激发态中微子后，再在弱力作用下，经一定的弛豫时间，形成非激发态中微子并释放大能量的光子或声子，其质量近乎为零。

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。