查询词典 operator equation

Secondly, we combine the theories of monotone operator and maximal monotone operator's Yosida approaching with domain method to prove the solution's existence of set-valued input-output equation in R n in the similar economical backgrounds in present articles too and then gain the solution's continuity by interior approaching method,at last we give the responding economical meaning about the solution's existence and continuity.

对于R n空间中消耗为单调集值型的投入产出方程，也在现有文献类似的经济背景之下，利用单调算子的理论以及极大单调算子的Yosida逼近结合邻域逼近法给出了投入产出方程的解的存在性的证明，接着利用内部逼近法结合方程截断技巧对投入产出方程的解的连续性给予了证明，然后顺便简单的介绍了运用外部逼近法来得到方程的解的连续性的思路，最后也给出了相对应于存在性和连续性的经济意义。

A integral equation formulation is derived based on modified Green's operator with norm less or equal to one. The integral equation is convergent for any conductivity distribution and frequency if iterative solvers are used.

利用范数小于或等于1的修正Green算子得到各向异性地层中的新积分方程，由于满足压缩映射条件，该积分方程在任意参数条件下总是迭代收敛的。

Aimed to the differential equation in form of convolution and the functional presented by M. E. Gurtin, the matrix operator which includes the differential equation and the boundary condition is proved self-adjoint, furthermore a general variational principles in form of convolution and the preparation theorem are given and proved.

针对M.E.Gurtin提出的含卷积运算的抛物型偏微分方程及其对应的泛函，运用泛函势算子理论，从理论上证明了含卷积运算的抛物型偏微分方程及其边界条件所对应的矩阵算子有势，进而给出并证明了具有普适意义的含卷积运算的变分定理及预备定理。

Then, common imaging point gathers in offset domain were respectively extracted based on a single square root operator and double square root operator wave equation migration.

模型试算结果表明：与常规波动方程偏移方法相比，角度域叠加成像能够改善局部成像质量。

The existence and uniqueness of the solution with the help of the Banach fixed point theorem and the theory of operator semigroups are verified .The global exponential stability of KS equation and the global exponential stability and asymptotical stability of macro KS equation with the given boundary feedbacks are proved .

通过Banach不动点原理和算子半群理论证明了方程解的存在性和唯一性，并证明了KS方程在给定的边界反馈条件下是全局指数稳定的及广义的KS方程在给定的边界反馈条件下是全局指数稳定和渐近稳定的。

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

In order to determine the Poincare normal form of linear operator in the operator differetial equation, we need to reduce the vector-value function to the two dimensional case on center manifold.

要证明以上的结论，我们所采用的方法是[24]中的Hopf分支定理所给出的判断Hopf分支存在性及分支周期解稳定性方法。

The implementation steps are that the seismic data is collected; the Fourier transform is made for the seismic data at a certain time window; a low pass filter operator of the time domain with an interception frequency of FE and a sampling rate of DT is calculated, which is taken as the equivalent N point smooth operator; FE and DT satisfy the equation that FE*DT is equal to X*DF*1.024; the estimate value of the amplitude spectrum of the seismic wavelet and the reverse wavelet are obtained, which are convoluted with the original seismic data; and the deconvolution seismic data of the time window is obtained.

实施步骤是采集地震数据，对某一时窗的地震数据做傅立叶变换，计算截止频率为FE和采样率为DT的时间域低通滤波算子作为等效N点平滑算子，FE与DT满足FE*DT＝X*DF*1.024，进而得到地震子波振幅谱估计值和反子波，再与原始地震数据褶积，得到该时窗的反褶积后地震数据。

In Chapter 7, we prove the resolvent operator of compound KDV equation is computable via the operator method, contraction mapping principle and TTE theory.

第五章应用Backlund变换得到了变系数组合KdV-Burgers方程的N-类孤子解；第六章应用F展开法及其扩展形式得到了变系数组合KdV方程和(n+1)维Sine-Gordon方程的孤立波解；第七章运用算子方法、压缩映象原理和TTE理论，证明了组合KdV方程的解算子是可计算的；最后对全文进行了总结，并对未来的研究方向作了展望。

In constructing new solutions of Feigenbaum renor- malization group equation, it is important to know which operator commute s with the iterative operator,This paper presents a theorem about the structure of the ab.

本文揭示了与迭代算子对易的算子集合在构造Feigenbaum重整化群方程新解中的重要性。

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。