查询词典 algebraic equation

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

Divide the whole region D into finite units and corresponding link points may be obtained. Constructing the equation of variation calculation about every element leads to the finite number of equations. Further more, algebra equation group for general synthesis are gained by adding these finite number of equations, that is,{T}={P} where is the coefficient matrix of the equation group, or say the temperature rigidity matrix,{T} is the row vector of unknown temperature and {P} is the row vector of the terms on the right side of the equation.

然后将整体区域D划分成有限个单元并得到相应的有限个节点，从而可以得到关于每个单元的变分计算方程，将这有限个方程相加就得到了总体合成的代数方程组，即{T}={P}，其中为方程组的系数矩阵，也称温度刚度矩阵，{T}为未知温度值的列向量，{P}为等式右端项组成的列向量。

In Chapter 2, we study exact solutions of the separated parts of Klein-Gordon field equation on some stationary and axisymmetry black hole backgrounds. We demonstrate that the radial and angular parts of a massive scalar field equation in the Kerr-Newman and Kerr-Sen black hole space-times satisfies the generalized spheroidal wave equation which is, in fact, a confluent Heun equation.

在第二章中我们研究了稳态轴对称黑洞背景几何中Klein-Gordon场方程分离变量部分的精确解，表明了Kerr-Newman黑洞及Kerr-Sen黑洞中有质量复标量场方程的径向部分和角向部分均满足广义椭球波方程，而后者实际上就是合流的Heun方程。

The bubble-point method and tridiagonal matrix method are proposed as solution of MESH equations(Material equation, phase Equilibrium equation, Summation equation, Heat equation), through which equations could be solved quickly and steadily, and the composing mole fraction at the top of tower and Key composition profiles and temperature of every stage are given.

提出采用三对角矩阵法和泡点法(BP，Bubble Point)相结合作为模型求解的解决方案，可快速稳定地求解复杂的MESH方程组，并给出塔顶液相组分组成和各塔板的关键组分分布及温度分布。

The results showed that both of Michaelis-Menten equation and Dagneli equation primely simulated response of photosynthesis rate to light intensity, and their effect was consilient. But the parameters of maximum photosynthesis, initial quantum efficiency and dark respiration by Michaelis-Menten equation was very distinctly bigger than them by Dagneli equation.

结果表明，两种方程均能很好地描述大豆和玉米叶片光合速率对光强的响应特征，两种方程的模拟效果是一致的，但两种方程得到的参数存在极显著差异，用Michaelis-Menten方程模拟得到的表观初始量子效率、表观最大光合速率、表观暗呼吸速率极显著大于用Dagneli方程得到的参数。

Here, we point out that, within the frame of general relativity, the basic astrophysical equations are Einstein equation, Boltzmann equation of the distribution function of real matter in the presence of electromagnetical field in curved spacetime, Maxwell equation and the equation of radiative transfer of Stokes parameter of photons in curved spacetime.

这里，我们指出，在广义相对论框架下，天体物理基本方程为Einstein场方程，弯曲时空中实物质分布函数所满足的含有电磁场的Boltzmann方程，弯曲时空中Maxwell方程组和弯曲时空中光子Stokes参量所满足的辐射转移方程。

A general laser scanning altimetry equation is developed that describes an ideal system, followed by developing an error model for the laser scanner, and the INS and GPS units. The result is a modified laser equation that contains all errors introduced. The error model is evaluated by analyzing the difference between errorless equation and laser equation with errors.

本文从机载激光扫描测高对地定位的几何模型出发，详细推导了各项误差对机载激光扫描测高对地定位结果的影响关系式；详细分析了不同误差对激光脚点坐标的影响规律，并给出了相应的数值结果和量化指标。

This one-way wave equation fits eikonal equation and transport equation corresponding to full acoustic wave equation in travel-time and first order amplitude. According to the perturbation theory often used in inverse solution, we split the velocity field into intraformational constant velocity background and variable velocity disturbance. Then we calculate time-shift quantity of migration and amplitude correction coefficients for wavefield depth continuation in total uniform formation and each formation.

基于反问题求解中常用的摄动理论，把速度场分裂为层内常速背景和变速扰动，求得整个均匀层波场深度延拓的偏移时移量及振幅校正系数、各层的偏移时移量及振幅校正系数，从而得到一个基于傅里叶有限差分法的双域保幅叠前深度偏移算子方程。

Elovich equation,zero order equation ,first order equation and parabolic equation was used to describe the nonexchangeabe k releasing process.Then the best model was selected to describe nonexchangeable k release and its velocity.

利用Elovich方程、零级方程、一级方程和抛物线扩散方程对土壤的累积释放量进行模拟，研究探讨了描述土壤非交换性钾释放及其速率较为理想的动力学模型。

The relationship equation is formally comporting with Huggins equation, Batchelor equation and Simha equation, and can explain the intrinsic property of latex systems.

该关系方程式与Huggins方程式、Batchelor方程式、Simha方程式形式上一致，但更能说明乳胶粒子体系的内在属性。

The network space is the typical form of abstract space when it comes to the digital stage.

网络空间是抽象空间数字化阶段的典型形式。

The Notarial System,as the system of judicial certification in our country,is both the constructor and the defender of social credit system,It has its special value and function in the social honesty.

公证制度作为我国司法证明制度，既是社会信用体系的建设者，同时也是社会信用的捍卫者，在诚信中有其特殊的价值和功能。