查询词典 consistent system of equations

This paper systematically discussed the definition, nature and calculation of two kinds of generalized inverse matrix related to the compatible linear equations, and their relations with the compatible linear equations.

本论文系统地论述与相容线性方程组相关2种广义逆矩阵的定义、性质和计算，以及与相容线性方程组的关系。

The two kinds of symmetries in holonomic and non-holonom-ic mechanical systems,i.e.symmetries of differential equations of motion(ab-breviated as SDEM)and symmetries of Noether-type,and interrela-tions among all kinds of symmetries are investigated.The necessary and suffi-cient conditions of SNT to be SDEM are found out.It is pointed out thatSDEM have distinct geometric properties which are equivalent to the geodesiccharacteristic of differential equations of motion and geodesic deviation.

文中研究了完整与非完整力学系统的两类对称性，即运动微分方程的对称性和Noether型对称性，以及各种对称性之间的相互关系，确定了Noether型对称性为运动微分方程对称性的充分必要条件，并指出运动微分方程的对称性具有明确的几何性质，即它等价于运动微分方程的测地性质以及测地偏离性质。

The topics covered in these sections are the geometric interpretation of systems of linear equations, the classification of finite symmetry groups in two and three dimensions, the exponential of a matrix and its application to solving systems of first order linear differential equations with constant coefficients, and Hurwitz's theorem on the composition of quadratic forms.

这些条文所涉及的主题是线性方程组的几何解释，在两个和三个有限对称群的分类方面，一个矩阵及其应用，以解决一阶常系数线性差分方程，系统指数赫尔维茨定理在二次形式组成。

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。

In this paper, we study the existence of global solution and its property of the initial boundary value problem for Camassa—Holm equations and Ginzburg—Landau equations.

本文研究了Camassa—Holm方程和Ginzburg—Landau方程初边值问题整体解的存在性及其性质。

The second-order linear homogeneous differential equations in differential equation theory occupies an important position, but the second order differential equation has no general solution method, most of the solutions of these equations is difficult to obtain analytical expressions and even some impossible to obtain the solution of the form, and the second order differential equation solving is divided into homogeneous and inhomogeneous problems.

二阶线性齐次微分方程在微分方程理论中占有重要位置，但二阶变系数微分方程却没有一般的求解方法，大多数这类方程很难求得解的分析表达式甚至有的根本不可能求得其解的分析形式，并且二阶变系数微分方程的求解又分为齐次的和非齐次的问题。

First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

首先给出了微分方程的一些基本概念，讲述了常系数线性常微分方程的解法，针对一类二阶变系数线性常微分方程初值问题，提出了一个近似解法，本方法是先对未知函数的一个定义区间作N等分，然后在每一个小区间内用一个常系数常微分方程近似替换，所得到的解作为原问题的近似解析解，随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例，该实例说明本文提出的近似方法是有效的。

This dissertation's main work and innovations is following: 1. The 6DOF kinematic and dynamic equations of motion for multiple thrusters AUV are derived and presented in a compact form using vector notation. The hydrokinetics of the MTAUV is classified anew. The MTAUV has two kinds of work modes which are cruising and hovering. The fluid dynamical mathematics description of the MTAUV is given anew. 2. The kinetics equations of the MTAUV in the low speed hovering are analyzed and studied.

本文主要的工作和创新点主要有以下几个方面：一、采用矢量参数的形式建立了基于多推进器自主水下航行器的六自由度运动学方程和动力学方程；对基于多推进器自主水下航行器的流体动力进行了重新分类，给出了基于多推进器自主水下航行器在巡航工作模式和悬停工作模式两种不同工作状态下流体动力的数学描述。

In this paper, we consider neutral functional differential equations and study the global existence of their solutions, stable subspaces and unstable subspaces of linear autonomous dynamical systems, local stable manifolds and local unstable manifolds of near hyperbolic equilibrium point of nonlinear autonomous dynamical systems, periodic solutions and oscillation of the neutral equations.

本文主要研究中立型泛函微分方程解的整体存在性，自治线性动力系统的稳定子空间与不稳定子空间、自治非线性动力系统在双曲平衡点的局部稳定流与局部不稳定流，周期解与解的振动性。

The flow of incompressible viscous fluid is controlled by Navier-Stokes Equations.The qualititave analysis of the solutions of the equation is important to the studies of bifurcation problems and numerical solutions of the equations.

对于描述不可压缩粘性流体流动的Navier-Stokes方程，其解的定性分析结果对于该方程的数值求解及其分歧问题的研究都是十分重要的。

There are different types of personal loans available.

有许多不同类型的个人贷款优惠。

The above mentioned teaching model of spiral rising can be used to avoid rigidness in teaching.

上述螺旋式上升的教学模式，可以避免教学形成模式後的僵化现象。