等价方程

And to solve the linear problem is turned to obtain the solution of an operator equation equivalent to it.

相应线性方程的带积分边值条件的混合问题，则是通过求解与线性方程等价的算子方程解决的。

Study of dynamical characteristics: The dynamics of DRNN network is studied through a matrix inequality, which is shown to be equivalent to the state transition equation of the network.

利用DRNN网络的状态转移方程与矩阵不等式的等价性，研究网络的动力学性质。

The fact that solution of wave equation is equivalent to the extreme value of quadratic function solution was verified, and the existence and uniqueness of the quadratic function solution was also proved.

证明了波动方程的解和二次泛函极值解的等价性，以及二次泛函极值解的存在唯一性，为其在液压传动中流体瞬变分析的进一步应用提供了理论依据。

Results The equivalent matrix equation is derived by the matrix transformation method.The parameter iterative algorithm and the sufficient and necessary conditions for the convergence are given.

结果基于矩阵变换方法导出了矩阵方程的等价形式，并构造出参数迭代格式，得到了格式收敛的充要条件。

We analyse the Lewy theorem and the provement idea of the theorem, and find the equation (7)and (8)are not equivalent under the reversible transformation, this lead to the absurdity in the provement does not come into existence .

分析Lewy定理及定理的证明思想，发现在证明中所述的可逆变换下，方程（7）与（8）并不等价，导致Lewy定理证明中归谬不成立。

The solution of interval finite control equation is often equated to solving the interval linear equation group.

对于区间有限元控制方程的求解，人们往往将其等价为区间线性方程组的求解。

Firstly, it's proved that the base of free monoid is unique, and that the equation of a base, a generating set and a irreducible generating set in the semigroup with length; Secondly, it's given the relation of a primitive word and a word of indecomposable--Let and is indecomposable, then is primitive ;And by using the length's method and chart,some properties of primitive word have been proved and the solutions of the equation , are discussed; Lastly, on the base of some proposition in Free monoids and Languages ,the proofs of some properties are improved by instruction. For example: Let be a primitive word over X, where .Then is a code. And let then if and only if {} is a code.

首先，讨论了含幺半群中基的基本性质及基与最小生成元集的联系，并给出了含幺半群中基、生成元集、不可约生成元集三者之间的关系；证明了在有唯一长度的半群S中，不可约生成元集、基、最小生成元集三者之间的等价关系；其次，讨论了字的组合与分解性，得出了字的本原性与不可分解性之间的关系---若为不可分解的，则一定是本原的，反之，不一定真；并运用图示法证明了字的可补性理论，讨论了方程，的可解性；在此基础上，用归纳法进一步证明了本原字与码的有关命题--若是X上的一个本原字，其中，则是一个码；若则当且仅当{}是一个码。

Moreover, this dissertation reveals an essential conclusion: The existence of the state feedback solution of H〓 problem is equivalent to that of the maximinimizing the LQ problem, by the existence of real symmetric stable solution of GARE.

文中从微分Riccati方程解的存在性及其性质的论证出发，最终得到了GARE实对称解存在条件的结论。在§2-4中，揭示了本文研究的maxmin鲁棒最优控制问题与H∞状态反馈解及GARE实对称解的存在性等价这一实质性结论。

Through the C language to achieve Gaussian elimination method, the basic idea is to eliminate every time an unknown, the original equation into the equivalent of the triangle equations.

详细说明：通过C语言实现高斯消去法，基本思想是每次消去一个未知数，把原来的方程化为等价的三角形方程组。

In mathematics, it can be boiled down to two equivalent forms of a kind of classical solutions to the general Navier-Stokes Equation of velocity fluctuations.

从数学而言，这一框架的理论基础可归结为描述不可压缩脉动场的Navier-Stokes方程的两个等价形式。

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