查询词典 poincare matrix

This chapter clarifies the nested relationship between the matrix family of unitary, orthogonal, Givens, Householder, permutation, and row or column symmetric matrices. A precise correspondence of the singular values and singular vectors between the unitary-symmetric matrix and its mother matrix is derived and proved (hence a fast algorithm of singular value decomposition for unitary-symmetric matrix is straightforwardly obtained), and the corresponding perturbation bound is provided.

该章揭示了酉对称矩阵、正交对称矩阵、 Givens 对称矩阵、 Householder 对称矩阵、置换对称矩阵和行对称矩阵之间的逐级包含关系；推导并证明了，酉对称矩阵的奇异值和奇异向量与母矩阵的奇异值和奇异向量之间的定量关系，据此可得酉对称矩阵奇异值分解的快速算法；给出并证明了摄动矩阵的摄动界。

The Laplacian matrix of G is the difference of degree matrix of G and the adjacent matrix of G, And the Laplacian spectral radius of a graph is the maximum eigenvalue of the Laplacian matrix of G.

图G的拉普拉斯矩阵为图G的度矩阵和它的邻接矩阵之差，而图G的拉普拉斯谱半径为图G的拉普拉斯矩阵绝对值最大的特征值。

Commencing from the character analysis of overall stiffness matrix of finite element method, the author brings forward it which is important to realize full nonzero memory of overall stiffness matrix, obtains correlative interlink of nodal point from analyzing affiliated element of nodal point, conforms every submatrix's position in overall stiffness matrix, realizes full nonzero memory of overall stiffness matrix.

论文根据面向对象程序设计的特点，建立了有限元模型的相关类，给出了基本的程序设计框架。

It investigates mainly infinite matrix conver-gence、infinite matrix transformations、the automatic continuity and boundedness of infinitematrix operators、infinite matrix topological algebras、invariant theory、infinite matrix meth-ods、compact operators series and Eberlein-Smulian theorem,etc.

主要研究了无穷矩阵收敛、无穷矩阵变换、无穷矩阵算子的自连续性和自有界性、无穷矩阵拓扑代数、不变性理论、无穷矩阵方法、紧算子级数与Eberlein-Smulian定理等。

Because there are many kinds of matrixes in titanium matrix composite, we select some typical ones as investigated subject in many titanium alloys or titanium aluminide intermetallics, and then simulate the distribution of thermal residual stresses under the appropriate composites fabrication and heat treatment parameter. We not only hope to seek better titanium matrix, but also discover the relationship between the material properties and the thermal residual stresses, and then provide some theoretical guidance for the selection of the matrix in titanium matrix composites.

鉴于当前钛基复合材料中钛基体的多样性，我们将在各种类型的钛合金和钛铝金属间化合物中，挑选出较为典型的作为研究对象，利用本文得到的较为理想的复合材料加工和热处理工艺参数，逐一模拟它们的残余热应力，找到残余热应力分布较为理想的钛基体，并且，希望能够寻找到材料性能与热残余应力的相互关系，为钛基复合材料基体的选择提供一定的理论指导。

By this iterative method ,the solvability of the matrix equation can be judged automatically.When the matrix equation is consistent ,then,for any initial centrosymmetric matrix pair ,a centrosymmetric solution pair can be obtained within finite iteration steps in the absence of roundoff errors, and the least norm centrosymmetric solution pair can be obtained by choosing a special kind of initial centrosymmetric matrix pair.

当矩阵方程相容时，对任意初始的中心对称矩阵对在没有舍入误差的情况下，经过有限步迭代，得到它的一个中心对称解，并且，通过选择一种特殊的中心对称矩阵对，得到它的最小范数中心对称解。

This article adopts many methods such as AHP, EFE matrix, IFE matrix and SWOT matrix to analyze the internal and external environment in theory. Combining qualitative analysis with quantitative analysis, this paper provides spare strategy plans that might be adopted by NRHIB. With QSPM matrix this paper analyze the spare schemes and choosable four feasible plans.

在此基础上，本文应用了AHP法、EFE矩阵、IFE矩阵和SWOT矩阵等技术和定量方法，对外部环境和内部环境进行了理论分析，提出了可供企业选择实施的战略方案，利用QSPM矩阵对备选方案进行了定量分析，得出了4个较为可行的战略方案。

The transfer matrix method is used to carry out the vibration characteristic analysis of the fluid-filled piping system. The transfer matrix of the axial, transversal and torsion vibration of the fluid-filled straight pipe element is presented. And the transfer matrix of the elbow is derived according to the discrete model of the inextensible theory of the curve pipe. The effect of the flexural factor on the elbow's transfer matrix is studied.

基于充液直管的梁模型，考虑液体与管道之间的泊松耦合，详细推导了充液直管单元的轴向、横向及扭转振动传递矩阵；采用弯管不延伸理论的离散模型，将变管离散为一组首尾相连，并成一定角度的短直管单元，通过建立弯管处力平衡方程与连续性方程，建立了弯管平面内振动的传递矩阵，并研究了弯曲因子对传递矩阵的影响。

By comparing the matrix theory over number field,we mainly discussed the quaternion matrix norm theory,the quaternionic determinant,the complex number expression of the quaternion matrix and the quarternion linear matrix equation.

通过对比一般域上矩阵理论，本文主要从四元数矩阵范数理论、四元数矩阵行列式、四元数矩阵的复表示以及四元数线性方程组和线性矩阵方程四个方面阐述了四元数矩阵理论。

The matrix =( xi, xjp having the e-th power of the greatest common P-divisorp of xi and xj as its-entry is called the e-th power GCD matrix on S. The matrix = having the e-th power of the least common P-multiple p of xi and xj as its-entry is called the e-th power LCM matrix on 5. We obtained the following results:(1) is nonsingular for any set S;(2) If S is an FC set, then the determined of has formula Det =Jpe(x1)...Jpe, where the function Jpe is the generalized Jordan totient function;(3) A formula of the inverse of is given when S is an FC set;(4) If S is an FC set, then |.

以_P的e次方为第i行j列元素的矩阵称为定义在S上的e次幂GCD矩阵，记为；以_P的e次方为第i行j列元素的矩阵称为S上的e次幂LCM矩阵，记为，我们得到了如下结果：①定义在集合S上的e次幂GCD矩阵是非奇异的；②若S是R上的FC集，则S上的e次幂GCD矩阵的行列式Det=J_p~e(x_1)J_P~e(x_2)…，J_p~e，其中J_p~e为R上的Jordan函数；③当S为FC集时，得到了的逆矩阵~-1的表达式；④证明了当S是FC集时，整除，即等于与R上另一个矩阵的乘积。

More direct, directer ; most direct, directest

径直的，笔直的

Do you know how to use a chain saw?

你知道如何使用链锯吗？