行列式方程

It has been showed that the quantum PCII can be still valid for the general case Jacobi J 1, which is different from quantum Noether theorem. The equivalence between quantum canonical equation and PCII is deflved at the quantum level. The comparisons of these results in quantum level with those in classical theories are discussed in detail. The relationship of canonical transformation with quantum PCII is obtained.

结果表明，当变换的Jacobi行列式不为1时，量子PC积分不变量仍然存在，从而把PC积分不变量推广到了最一般情形；在量子水平上，证明了量子正则方程与该积分不变量之间的等价性；比较了经典与量子PC积分不变量以及PC积分不变量与Noether定理；给出正则变换与量子PC积分不变量间的关系。

Dixon method was adopted to construct a 22×22 Dixon matrix and then the greatest common divisor of two columns was extracted.

结合矢量法和复数法建立了4个几何约束方程式，使用Dixon结式构造22 22的Dixon矩阵，对两列提取公因式后展开矩阵的行列式得到一元64次多项式方程，回代过程中去掉6组增根后得到58组解。

Considering the mechanical and electrical boundary conditions of AlN/GaN structures, determinantal equation which is used to solve the phase velocity of surface acoustic wave is given from the basic principle of matrix methods.

从矩阵方法的基本原理出发，结合AlN/GaN结构的机械和电学边界条件，推导出用于求解声表面波在AlN/GaN结构中的相速的行列式方程。

With solving the determinantal equation, SAW propagation properties in AlN/GaN structures are acquired, including the phase velocity and electromechanical coupling coefficient which is vary with frequency, film thickness and c-axis orientation.

通过求解该行列式方程，分析了声表面波在AlN/GaN结构中的传播特性，包括声表面波相速和机电耦合系数随频率、AlN的膜厚和c轴取向的变化规律。

With solving the determinantal equation, SAW propagation properties in AIN/GaN structures are acquired, including the phase velocity and electromechanical coupling coefficient which is vary with frequency, film thickness and c-axis orientation.

通过求解该行列式方程，分析了声表面波在AIN／GaN结构中的传播特性，包括声表面波相速和机电耦合系数随频率、AIN的膜厚和C轴取向的变化规律。

So the hot cavity dispersion equation can be derived on the basis of the matched boundary conditions and the wave growth rate is obtained by means of equipotential line method.

得出了通入相对论电子注时行列式形式的热腔色散方程，并求出了波增长率。

Dixon method was adopted to construct a 22×22 Dixon matrix and then the greatest common divisor of two columns was extracted. After expanding the determinant of the matrix, a 64 degree univariate polynomial equation was obtained and 6 extraneous roots were canceled in the process of solving the other 3 variables.

结合矢量法和复数法建立了4个几何约束方程式，使用Dixon结式构造22×22的Dixon矩阵，对两列提取公因式后展开矩阵的行列式得到一元64次多项式方程，回代过程中去掉6组增根后得到58组解。

Firstly, four geometric loop equations are set up by using vector method in complex number fields. Secondly, three constraint equations are used to construct the Dixon resultants, which is a 6×6 matrix and contain two variables to be eliminated. Extract the greatest common divisor of two rows and two columns of Dixon matrix and compute its determinant to obtain a new equation. This equation together with the forth constraint equation can be used to construct a Sylvester resultant.

首先使用矢量法和复数法建立4个几何约束方程式；再使用Dixon结式法对3个方程式构造一个含有2个变元的6×6 Dixon矩阵，提取其中2行列元素的公因式，将新矩阵的行列式展开后得到二元高次多项式方程，该方程与剩下一个方程使用Sylvester结式消去一变元，得到一元高次方程。

Content of the course consists of:(1)Basic Theories of Polynomials ;(2)Linear Algebra: topics on basic matrix theory, determinant, system of linear equations, vector space, linear transformation, eigenvalue problems, inner product and Euclidean space , and quadratic form etc.;(3) Analytic Geometry: topics on algebraic operations of vectors, coordinates, lines and planes, curves and curved surfaces, etc.

学习本课程后，学生应学会用线性空间与线性变换的观点处理包括线性代数方程组在内的有关理论与实际问题；学会熟练地运用矩阵工具；本课程还学习基本的多项式知识和空间解析几何的基本知识。课程内容包括几个主要部分：（1）多项式代数；（2）线性代数：矩阵，行列式，线性代数方程组，向量空间与线性变换理论，特征值问题，欧氏空间理论，二次型等；（3）解析几何：几何空间向量代数，通过建立坐标系以及借助向量方法研究空间平面与直线及点﹑线﹑面的相互关系，借助曲面方程研究空间曲面，尤其是柱面，锥面，旋转面和二次曲面以及曲面的交线等。

Based on the instantaneous motion of the moving platforms, the uncertainty configuration conditions and simplified uncertainty configuration equations are obtained for the widely studied parallel manipulators, such as planar 3-DOF parallel manipulator, spherical 3-DOF parallel manipulator, 6-SPS triangular platform parallel manipulator, three-branch 6-DOF parallel manipulator, twotriangular-platform parallel manipulator, DELTA parallel manipulator, 5-DOF parallel manipulator, two-tetragonal-platform parallel manipulator, pentagonal platform parallel manipulator and Stewart platform parallel manipulator.

采用这一方法，根据国内外常用的并联机器人机构的形式，建立了平面3自由度并联机器人、球面3自由度并联机器人、三角平台并联机器人、三支链6自由度并联机器人、双三角平台并联机器人、DELTA并联机器人、5自由度并联机器人、双四角平台并联机器人、五角平台并联机器人和Stewart平台并联机器人的奇异位形条件方程，除了Stewart平台并联机器人外，这些条件方程均为低于6阶的行列式，机器人结构类型不同，其简化程度各不相同。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。