算子方程

According to the studies for this zero-order differential operator to make an expansion of a function, it can restrain border effect and control Gibbs effect.

并进一步构造了1阶和2阶导算子，对它们的导数矩阵的特性进行了研究，实现了用这样的导算子对微分方程的求解。

In this paper we will generally discuss the WEMVA method by Double Square Root for the convenience of mathematic expression, and demonstrate how it works in numerical model.

在叠前偏移算子中，因为双平方根算子的数学表达式更为简洁，所以本文基于对波动方程偏移速度分析初步讨论，并通过模型验证其原理。

First of all, the report introduced evolution, achievments and problems in the study of anisotropy in the inner of earth. The first-order hyperbolic system of equations is work out, which is used to describe the wave motion in 2D transversely isotropic media. Utilizing the characteristics of free-divergence, We have imposed MacCormack theme that is used to simulate multicomponent records in anisotropic media and have developed a fast high order vectorized finite-difference algorithm adapted for the vector supercomputer.

本文首先阐述了地球内部介质各向异性研究的沿革、成就和问题，接着给出了描述二维横向各向同性介质中波动的一阶双曲型方程，利用其自由发散特性，构制了各向异性介质中多波多分量地震记录数值模拟的MacCormack算式，导出了适用于并行计算的二维横向各向同性介质中波动的有限差分模拟算子，该算子具有可并行化计算、相位差小等优点。

In chapter 1, as a preparative knowledge, the main results about symmetry theoryand Wus method are introduced, in addition some fundamental definitions, such as trans-formation group, infinitesimal operator, prolongation, first integral, infinitesimal criterionfbr invariance of an ODE, characteristic set are recalled.

第一章中作为预备知识简单介绍了对称理论和吴方法，并给出了一些基本概念和理论，如变换群、无穷小算子、算子延拓、首次积分、微分方程在对称下不变的判别准则和微分特征列集算法。

And the tangent linear operator of the forward model also exists, which is the same as the resolvent of the tangent linear model derived by the conventional method.

对连续"开关"，代价函数的梯度处处存在的，非线性方程的切线性算子也是存在的，并且与传统方法得到的切线性模型的解算子是一致的。

This paper studied a filtering high order numerical method for one dimension constant coefficient hy2 perbolic function. The stability and error analysis show the efficiency of this method. Numerical examples are also given to verify the analysis results.

摘 要 考虑一维常系数双曲型方程的高阶数值解法，引进了一种稳定性过滤算子FN ，最后从理论和数值实验上分析了该过滤算子对数值解稳定性和精度的影响。

Using the wave equation prestack depth migration on SEGEAGE 2_D salt dome model as an example, the twoorder generalized screen propagator increases 30% calculation work relative to the conventional generalized screen propagator.

以SEGEAGE二维盐丘模型数据的波动方程叠前深度偏移为例，二阶广义屏传播算子相对于常规广义屏传播算子增加了30%的计算量。

In chapter 2, we introduce the solitary wave, its definition and generation mechanism and classify these solitons that are known up to now.

本文在TTE的框架下，运用算子理论和方法，证明了组合KdV方程的解算子是可计算的，从而可以。。。

The self-adjoint boundary-value problems and spectral theory of differential operators are important and fundamental problems in the operator theory.

微分算子自伴边值问题及谱理论是算子理论的重要而基本问题，它是同微分方程、数学物理和量子力学的某些重要问题相联系而发展起来的。

Using 〓-theory in partial differential equation,I find out a sufficient condition on A,B,under which ican be extended to andreplaced by a self-adjoint operator.

利用偏微分方程中的〓理论，我对算子A和B找到了一个充分条件，在该条件下，i可以扩张成一个自共轭算子。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。