方程的解集

In this paper,four aspects of the above problems were studied:Firstly, the problem of solving continuous linear operator equation inseparable Hilbert space is studied .

通过把第一类连续不适定算子方程转换为等价的无穷维方程组，然后利用投影法，给出了解存在唯一的充要条件；给出了连续线性不适定算子方程解析解，解决了不适定情况下解的表示问题，由此给出了算子方程的数值求解公式；进一步证明了，在解不唯一情况下，此表达式给出的解为算子方程的最小范数解，同时表示出了连续线性不适定算子方程的解集。

This main approach is also coincidence degree theory. Moreover, when the time scale T is chosen as the sets of real or integer numbers, the existence of periodic solutions for its differential or difference equation are obtained respectively.

若分别选取时标T为实数集或整数集时，则分别得到它的微分方程或差分方程周期解的存在性，这就避免了对这些生态系统的微分和差分方程周期解的存在性分别进行讨论。

Due to equivalent transformation during the simplification procedure of equations, the solution set of equations can neither expand and nor contract, and also the transformed equations for four displacement functions are compact in the form and easy to find their solutions.

由于方程化简过程是等价变形，从而可以保证方程的解集既不会扩大也不会缩小，而位移势函数便给出了一维六方准晶中弹性解的一个通解公式。

Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability.

然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系，这个引理将在能控性的判定中起关键作用。

Chapter 3, we study the stability of approximate solutions of nonlinear equation problems(the continuous function is defined in the linear normed space).We prove that most of approximate solutions of nonlinear equation problems are stable; all accurate solutions are the essential points of the set of approximate solution; the connected component which contains the accurate solution is the essential component of the set of approximate solution; especially the number of essential components is finite.

第三章，研究定义在线性赋范空间上的非线性方程问题近似解及其解集的稳定性，得到线性赋范空间上在Baire分类下大多数非线性方程问题的近似解都是稳定的；精确解是近似解集的本质解；包含精确解的近似解集的连通区是本质连通区；包含精确解的近似解集的连通区为有限个。

Within algebraic geometry is the description of geometric objects as solution sets of polynomial equations, combining the concepts of quantity and space, and also the study of topological groups , which combine structure and space.

在代数几何里，把几何对象描述成多项式方程的解集，结合数量和空间的概念；也研究拓扑群，结合了结构和空间。

Further, when the solution setis nonempty, the structure of the solution set of the equation is given.

进一步，当方程解集非空时，给出了方程解集的结构。

In order to determine the solution set of the equation , by the means of meet-irreducible element and irredundant finite meet-decomposition, we first obtain the maximal solutions to the simple equation in the case that b has an irredundant finite meet-decomposition, and then consider the relation between the equation and the equation , based on this, we obtain the maximal solutions to the equation in the case that each element of the matrix B has an irredundant finite meet-decomposition and so determine its solution set completely.

为了确定方程的解集，本文利用交既约元与不可缩短的有限交分解等工具，同样地先求出简单形式的型矩阵方程的所有极大解，然后讨论方程与方程之间的关系，在此基础上，在B的每个元素均有不可缩短的有限交分解的情况下，求出了方程的所有极大解，从而完全确定了方程的解集。

Neutral differential equations with variable sign coefficients are separated into neutral differential equations with positive and negative coefficients by transformation. According to the characteristic of these equations, a real number set with supremum is constructed, and sufficient conditions for oscillation of all solutions to neutral equations with variable sign coefficients are obtained.

通过变换将具有变号系数的中立型微分方程分解为具有正负系数的中立型微分方程；分析具有正负系数中立型微分方程的特征，构造存在上确界的实数集；并对中立型微分方程的解作细致分析，得到了具有变号系数中立型微分方程所有解振动的充分条件。

Neutral differential equations with variable sign coefficients are separatedinto neutral differential equations with positive and negative coefficients bytransformation.According to the characteristic of these equations,a real number setwith supremum is constructed,and sufficient conditions for oscillation of all solutionsto neutral equations with variable sign coefficients are obtained.

通过变换将具有变号系数的中立型微分方程分解为具有正负系数的中立型微分方程；分析具有正负系数中立型微分方程的特征，构造存在上确界的实数集；并对中立型微分方程的解作细致分析，得到了具有变号系数中立型微分方程所有解振动的充分条件。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失