查询词典 solution set of equation

In this paper, by discussing the basic hypotheses about the continuous orbit and discrete orbit in two research directions of the background medium theory for celestial body motion, the concrete equation forms and their summary of the theoretic frame of celestial body motion are introduced. Future more, by discussing the general form of Binet's equation of celestial body motion orbit and it's solution of the advance of the perihelion of planets, the relations and differences between the continuous orbit theory and Newton's gravitation theory and Einstein's general relativity are given. And by discussing the fractional-dimension expanded equation for the celestial body motion orbits, the concrete equations and the prophesy data of discrete orbit or stable orbits of celestial bodies which included the planets in the Solar system, satellites in the Uranian system, satellites in the Earth system and satellites obtaining the Moon obtaining from discrete orbit theory are given too.

摘 要：通过讨论天体运行背景介质理论的连续轨道及离散轨道这二个研究方向的基础假设，介绍了天体运行轨道的具体方程形式及理论框架概要；进一步地通过讨论天体运行轨道 Binet 方程的一般形式及其行星近日点进动角的解，给出了连续轨道理论与 Newton 理论及 Einstein 广义相对论的联系与区别；通过讨论天体运行轨道的分维扩展方程，给出了包括太阳系行星、天王星卫星、地球卫星、绕月航天器等在内的离散轨道方程及其预言数据。

By discussing the basic hypotheses about the continuous orbit and discrete orbit in two research directions of the background medium theory for celestial body motion, the concrete equation forms and their summary of the theoretic frame of celestial body motion are introduced. Future more, by discussing the general form of Binet's equation of celestial body motion orbit and it's solution of the advance of the perihelion of planets, the relations and differences between the continuous orbit theory and Newton's gravitation theory and Einstein's general relativity are given. And by discussing the fractional-dimension expanded equation for the celestial body motion orbits, the concrete equations and the prophesy data of discrete orbit or stable orbits of celestial bodies which included the planets in the Solar system, satellites in the Uranian system, satellites in the Earth system and satellites obtaining the Moon obtaining from discrete orbit theory are given too.

在深入研究引力理論及廣義相對論的基礎上，通過討論天體運行背景介質理論的連續軌道及離散軌道這二個研究方向的基礎假設，介紹了天體運行軌道的具體方程形式及理論框架概要；進一步地通過討論天體運行軌道Binet方程的一般形式及其行星近日點進動角的解，給出了連續軌道理論與Newton理論及Einstein廣義相對論的聯繫與區別；通過討論天體運行軌道的分維擴展方程，給出了包括太陽系行星、天王星衛星、地球衛星、繞月航天器等在內的離散軌道方程及其預言資料。

This paper presents the boundary value problem solved as the biharmonic equation of upper plane and strip domain with Green functional method and it deals with the numerical solution of bihormonic equation, using the Matlab program calculation to realize the visualization of numeric solution.

用Green函数法求解了区域为上半平面和带形区域的双调和泊松方程的边值问题；以及探讨了双调和方程的数值解，并用Matlab编程计算实现了双调和方程数值解的可视化。

When scaled factor circulant matrices are nonsingular, we can find the single solution of the scaled factor circulant matrix equation; When scaled factor circulant matrices are singular, we can find the special as well as the general solution of the scaled factor circulant matrix equation; There is only an error of approximation when the fast algorithm is implemented on computers, and only the elements in the first row of the scaled factor circulant matrix and the constants in the diagonal matrix are needed by the fast algorithm.

当鳞状因子循环矩阵非奇异时，该快速算法求出线性方程组的唯一解；当鳞状因子循环矩阵奇异时，该快速算法求出线性方程组的特解与通解。该快速算法仅用到鳞状因子循环矩阵的第一行元素及对角矩阵中的对角上的常数进行计算。在计算机上实现时只有舍入误差。

In addition, the voltage-current characteristic of linear resistive components is the general solution of Clairaut equation, and the voltage-current characteristic of non- linear components is the singular solution of Clairaut equation.

论文摘要：本文讨论了任意伏安特性电阻元件满足的基本微分方程以及非线性电路的功率匹配问题的几个定理，指出任意伏安特性电阻元件均满足非线性一阶的clairaut方程，并且，线性电阻元件的伏安特性是clairaut 方程通解，而非线性电阻元件的伏安特性是clairaut 方程的奇解。

In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

In this paper, we will discuss the existing condition of the periodic solution of Duffing type equation with damping term. We use homeomorphism and fixed point method to prove the periodic solutions existence. We try to loose its condition, analysis and then get the existing condition of periodic solution according to defining atmospheric dynamics equation.

本文中，我们探讨带阻尼项的Duffing型方程周期解的存在性条件，运用不动点方法和Leray-Schauder度理论来证明其存在周期解，尽可能放宽其约束条件，并针对具体的大气动力学方程，分析并求取其周期解的存在性条件。

Apparently, the approximate controllability doesn"t hold for generally linear parabolic equations with bounded control. It doesn"t hold for the semilinear heat equations presented there,either. Then, it is proved by analyzing its" solutions that no matter how long the time T is , there are targets that can"t be approximated by the solution of heat equation with Dirichlet boundary conditions;If a given target satisying certain conditions can be reached by the solution of heat equation .

本文先针对两个具体的半线性热方程系统证明了控制加约束后系统是不能控的；然后通过分析方程的解，对带位势及Dirichlet边界条件的热方程系统，无论时间多大，都存在不能控的目标；文中还证明了满足一定条件的目标可达。

If the solution of the equation is existent and unique, the exact solution of the equation is given.

如果该方程的解存在且唯一，文章给出了该方程的精确解的形式表示。

The main contents of this course include: introduction, extraction of root from an equation, numerical solution of a system of linear equations, interpolation method, the method of fitting of a curve, numerical integration and differentiation, numerical solution of a differential equation, one-dimensional search method of extreme value problem, etc.

本课程包括以下内容：绪论、方程求根、线性方程组数值解法、插值法、曲线拟合法、数值积分与数值微分、微分方程数值解法、极值问题的一维搜索法。

The second is to cut a mere 100 calories from your diet , which is the equivalent of a tablespoon of butter.

第二个就是从你的饮食中减少一百卡路里，只是相当于一大汤匙的黄油。

This is where the Rorschach test comes in.

现在，罗氏测试就出现了。