查询词典 compatible system of algebraic equations

This dissertation studies perturbation bounds of infinite dimensional operatorsand operator equations.We obtained the following main results.

本文讨论了Hilbert空间和Banach空间上线形有界算子和算子方程的扰动理论，得到了一系列结果。

It has important significance to consider backward stochastic Volterra type integral equation in infinite dimensional space.By a similar calculation as in the second part,we study this kind of equations driven by cylindrical Brownian motion under non-Lipschitz condition.

3在无穷维空间中研究倒向随机Volterra型方程也是有着重要意义的，论文利用与第二部分相同的思路将前面的结果推广到无穷维中，在非Lipschitz条件下对由柱Brown运动驱动的这种方程建立了解的存在唯一性。

The computing plots of the solutions from the two methods were inconsistent under the specified boundary-initial conditions, which stirred up the debate of the effectiveness of Maxwell's equations in lossy medium. It is found that the differences between the two numerical curves can be viewed as the Gibbs phenomenon caused by cutting off the high frequency components in computing the infinite integral of the numerical curve of Harmuth's solution.

通过比较两种解析解的数值曲线得出：两者的差异在于求解Harmuth解的数值曲线时，采取无穷积分的高频截断近似产生了吉布斯现象；在计算Harmuth解的数值曲线时不断增大积分上限，其数值曲线的振荡不断向不连续点处收缩，而且衰减加快，因此在求解Harmuth解的数值曲线时，若积分区间取为理想无限大，则可以预见相同计算精度下两种方法的电场解的数值曲线是一致的。

Therefore, the expressions for the displacement and stress components in terms of four displacement potential functions give a general solution for the governing equations in 1D hexagonal QCs. As an application of the above theory, the problem of a circular crack embedded in an infinite 1D hexagonal QC of point group 6mm is considered.

作为应用进而考虑一个无限的，包含一个圆盘状裂纹的一维六方准晶，在裂纹的上下表面受到一均布力作用下，得到了整个准晶体的弹性场和应力强度因子的精确解。

We derived evolution equations of the corresponding Eu-clidean support functions.Finally we obtained that the solutions of the heat equation convergeto a point in infinite time,the solutions of the other equation converge to a point in a finite time

我们又得出相应的欧氏支撑函数的发展方程，最终得到热方程的解在无限时间时收敛于一点；另一发展方程的解在一个最大时间区间内存在，并且在有限时间内收敛于一点。

Functional differential equation; evolutional equations about population;neutral integral equation; cone; fixed point index; infinite delay; m -accretive operator; random fixed point; condensing map

论文导师孙涛，论文学位硕士，论文专业基础数学论文单位东北大学，点击次数 14，论文页数 70页File Size1670K

An infinite series of exact equations, relating different orders of , can be derived from the master equation.

由主方程出发可以推导出无穷组的精确方程，这些方程把各阶联系起来。

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。

On to an infinite set of quantum field-theoretical equations.

近于无穷无尽的一整套量子场论方程式。

It points out that for all the complex flows under some great non-equilibrium forces, the preconditions to make an infinitesimal analysis over all the fluid field according to a set of differential equations will not exist.

指出对于存在极大力学不平衡的复杂流动，在整个流场依靠一个同一化的微分方程组，进行解析分析的连续可微逻辑前提是不存在的。

The use of the web to spread fears that flicking the switch on the LHC could create a Black Hole that could swallow up the Earth particularly concerned him, he said.

他说，使用互联网散布恐慌说启动LHC会生成一个可能吞噬地球的黑洞的做法让他感到忧虑。

Not a single word have I written down.

我一个字也没有写下来。