算子域

It obtains that the transport operator A has no complex eigenvalue s, and the spectrum of the transport operator A consists of finite real isolated eigenvalues which have a finite algebraic multiplicity in trip Pas.

本文研究了板几何中一类具各向异性、单能、均匀介质迁移算子A的谱，得出了该算子A在带域Pas中无复本征值和由有限个具有限代数重数的实离散本征值组成等结果。

Let A" denote the commutant of a bounded linear operator S on H and R denote the collection of all operators in A" which are compact and upper triangular operators with diagonal sequence being zeros. In this paper, we show that if A"= CI + R, the K_0-group of A" is isomorphic to the integer group.

本文指出若H上的有界线性算子S的换位代数A′=CI+R，其中C是复数域，I是H上的单位算子，R是所有与S可交换的对角线为0的紧上三角有界线性算子的集合，则K_0A′

In view of crosswell and 3D VSP layout, we use high resolution Radon transform based on Cauchy distribution to perform Radon transform for hole data. In this process, we study discrete dip overlay operator, improve damping factor that affects Radon energy convergence in order to let Radon energy converge, 6 resolve leggy in Radon data, and decouple smoothing effect among each energy group, we use Cauchy distribution to regularize data, let energy focus on one point, and improve Radon resolution. All these work well in wavefield separation. Finally, by inversion results and model trial, we verify the feasibility and stability of this method.

在Radon变换原理分析基础上，采用基于柯西分布的高分辨率线性Radon变换对井孔数据进行Radon变换，其间通过对离散倾角叠加算子求取的研究，及对影响Radon能量收敛的重要参数阻尼因子算法的改进，使数据在Radon域以能量团的形式呈现，得到很好的收敛效果，基本解决了Radon域数据的一定程度的拖尾现象，消除了各能量团之间的平滑效应，采用柯西分布来规则化数据，提高了Radon域的分辨率，Radon域能量也收敛到一个点上，有利于上下行波或纵横波波场分离。

In view of crosswell and 3D VSP layout, we use high resolution Radon transform based on Cauchy distribution to perform Radon transform for hole data. In this process, we study discrete dip overlay operator, improve damping factor that affects Radon energy convergence in order to let Radon energy converge, 6 resolve leggy in Radon data, and decouple smoothing effect among each energy group, we use Cauchy distribution to regularize data, let energy focus on one point, and improve Radon resolution. All these work well in wavefield separation.

在Radon变换原理分析基础上，采用基于柯西分布的高分辨率线性Radon变换对井孔数据进行Radon变换，其间通过对离散倾角叠加算子求取的研究，及对影响Radon能量收敛的重要参数阻尼因子算法的改进，使数据在Radon域以能量团的形式呈现，得到很好的收敛效果，基本解决了Radon域数据的一定程度的拖尾现象，消除了各能量团之间的平滑效应，采用柯西分布来规则化数据，提高了Radon域的分辨率，Radon域能量也收敛到一个点上，有利于上下行波或纵横波波场分离。

In theory Canny operator is optimal in continuous domain for edge detection, but not optimal in discrete case, which may lead to inaccurate result.

从理论上来说，Canny算子是连续域最优的边缘检测算子，但在离散域中却并非最优，对于数字图像可能存在误差。

Firstly, in the frequency domain, differentiatial operator is decomposed into magnitude and phase operator, and the fractional order expressions of periodical signals, such as sine wave, cosine wave and complex exponent signal, are deduced.

首先，在频域中将微分算子分解为幅度算子和相们算子，导出正弦、余弦和复指数信号的分数阶微分表达式；然后考察矩形、三角形、梯形等常用周期信号的分数阶微分。

It carries out the amplitude-preserved migration with the phase shift amplitude-preserved correction operator in frequency-wave number domain and time shift amplitude-preserved correction operator in frequency-space domain.

文中引入了裂步傅里叶保幅偏移算法，分别通过频率－波数域的相移保幅校正算子和频率－空间域的保幅时移校正算子实现了保幅偏移。

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。

First it selects a 3×3 neighborhood.According to whether gray value of arbitrary pixel is its neighborhood's extremum,all pixels are divided into doubtful noises pixels and signal pixels.Then it constructs 8 templets of orientation gradient for each doubtful noise,makes the sure of the noises sets according to the magnitude of 8 values of orientation gradient.

该算法首先对含有噪声的图像取3×3邻域，判断某点是否为邻域极值将全部像素点分为可疑噪声与信号点集合；其次对每一个可疑噪声点在其3×3邻域内构造八个方向的梯度算子模板，通过比较8个方向梯度的大小，进一步确定其是否为噪声点；最后对噪声点进行邻域的中值滤波。

Scientists' attention is paid to the discription of the self-adjoint boundary condi-tions of singular differential operators during 50 years recently.

对称微分算子理论中自共轭域的描述，是微分算子理论中的基础问题之一，常型的问题在五十年代已得到解决，五十余年来人们更多的注意力放在奇型微分算子自共轭边界条件的描述上。

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。