必要条件

In the second chapter, firstly, the definition of triangular matrix rings Γ, which is of order 3, is introduced.

在第二章中，我们首先引入了三级三角矩阵环Γ的定义，给出了三级三角矩阵环是左阿丁环、右阿丁环、阿丁R-代数的充分必要条件。

Trivial Solution conception is put forwarded based on the theorem of K〓nig and forbidden node----for the n×n 0-1 degeneracy matrix, the solution under the condition that all element 1 can not be covered completely by n lines that must have intersects or can be covered completely by n lines that must have cross, without forbidden node, are called TS matrix.

本文在K〓nig定理和禁点定理的基础上，提出了平凡解的概念，即对于n×n阶的退化矩阵，全部1元素不可能被n条有交叉的直线全部覆盖或能用n条直线覆盖全部1元素，但无禁点的情况称为平凡解。并证明了如下的平凡解产生的充分必要条件：对退化矩阵A〓，若

The authors believe that the diversification of rock zonation and lithology of these high pressure rocks can be attributed to the metasomatism that took place between deep melt and ultrabasic rocks in the subduction zone, and thus propose a hypothesis of subduction melt metasomatism to explain jadeite formation.

笔者认为俯冲带中形成的深部熔体与超基性岩之间的交代变质是导致岩石分带和岩性多样化的根本原因，提出了俯冲带熔体交代成因说，认为俯冲带、深部流体和超基性岩体是形成翡翠及其过渡品种的3个必要条件，并因此指出在人工合成过程中引入流体相很可能是降低实验条件的苛刻程度、从而合成出真正具有商业意义的翡翠的途径。

A necessary and sufficient condition for the unbiasedness of Balanced LS Estimation is gained, and for the given L, t can be chosen to make the MSEM of the Balanced LS Estimation less than that of OLS Estimation.

给出了平衡LS估计为无偏估计的充分必要条件，对于给定的L，适当地选择参数t可使平衡LS估计的均方误差矩阵小于OLS估计的均方误差矩阵。

A method is proposed to solve the identical self-synchronization of undecomposable chaotic system based on He and Vaidya's necessary and sufficient condition for synchronization.

基於He和Vaidya的同步充分必要条件，提出了一个解决未拆分混沌系统恒等自同步的方法。

Explosive welding process is characterized in large plastic deformation and undulate interface in bonding zone.

爆炸焊接结合区产生大的塑性变形及波状结合，是爆炸焊接工艺的主要特征，也是实现良好冶金结合的必要条件。

The paper introduces the working principle and structure of velocity type geophones,expounds the prerequisite for producing uniform magnetic field and the influence of the uniform magnetic field on geophone′s distortion.

文章在介绍了速度型检波器的结构和工作原理后，阐述了检波器中产生均匀磁场的必要条件及均匀磁场对检波器失真度的影响。

We define Condition A,and show that Condition A is thenecessary condition of discrete groups,and uniformly bounded torsion isspecial case of Condition A.

我们引入条件A，并且指出条件A是离散的必要条件，一致有界挠是它的特殊情况，同时在条件A之下，建立了PinchedHadamard流形的等距群的离散准则。

Parabolic equation ; European option ; volatility ; existence ; uniqueness ; necessary condition

抛物型方程；欧式期权；波动率；存在性；唯一性；必要条件

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。