可解方程

By means of integralequation methods creatively along with other modern mathematical theories,this paperfocuses on finding solvability conditions and conditional well-posedness(especiallyconditional stability),constructing stabilized algorithms,and carrying throughnumerical simulation.

本文创造性地应用积分方程方法，借助现代数学手段，着重研究这些问题的可解性条件、条件适定性，构造稳定化算法，并进行数值模拟。

These two problems are converted to mathematical problems of solving some matrix inequalities and Riccati equations which are dependent on the time delays.

它们的可解充分条件可以化为与时滞相关的矩阵不等式和 Riccati方程的形式。

We prove the solvability of the first eigenvalue problem for a class of quasilinear elliptic equations including distance potential with homogeneous Dirichlet boundary condition.

变分原理证明了一类含距离位势的拟线性椭圆方程齐次Dirichlet边界条件下第一特征值问题的可解性。

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。

The orthogonality of the modal functions is employed to decouple the governing equation into a set of infinite ordinary differential equations that are independent of each other.

将梁的控制方程写作状态变量的形式，然后利用复模态的正交性可解耦为无穷多个彼此独立的常微分方程组。

In fact, for interior problem, solution of the direct boundary integral equation always exists.

事实上，对内边值问题，第一类Fredholm 直接边界积分方程的可解性条件是自然得到满足的，本文对此做了验证。

Criterions of partial stable matrix and normal form of partial positive definete matrix are given, some conditions of solvability and uniqueness of Lyapunov matrix equation are discussed.

给出了部分稳定矩阵的几种判据与部分位正定矩阵的标准型，研究了矩阵方程可解性、唯一性的几种条件，提出一些可供进一步研究的问题。

If the neighborhood of equation solution is solvable and meets the point- by-point Lipschitz condition, stable boundary could be obtained as the convergence of the difference method is realized, and thus the stability is ensured.

方程解的邻近如果可解并具备逐点Lipschitz条件，则差分法收敛必有稳定界存在，从而差分格式收敛性保证其稳定性，因此可以放弃线性这一重要条件。

Because the coefficient matrix of system equation with mixed method is indefinitive, an iterative solution method of the system equation is given out.

由于后者系数矩阵非正定，为使方程唯一可解，要求压力插值函数的阶必须低于固体相位移插值函数的阶，对此提出了一种系统方程的迭代求解方法。

The theory is based on the complex hydromagnetic equations of nebula ,which are simplified approximately to the equations of velocity.

把星云的复杂的磁流体动力学方程，近似简化为只与速度相关的方程，则得到一个可解的简单模型。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。