线性算子

In chapter 4, a family of two-parameter operators on Abelian group is introduced and its interpolation theorem for approximation is established.

所得的结果包含了R.DeVore定理作为特款，还包含了算子逼近的插补定理，是非线性逼近方面的一项基础性工作。

In the second, we discuss the geometry of Banach space, and the bounded linear operators and bounded linear functionals on the Banach space.

第二部分，Banach空间的刻画和其上的有界限性算子和有界线性泛函的性质。

A novel neural network model, named delayed standard neural network model, is proposed, which is the interconnection of a linear dynamic system and a bounded static delayed nonlinear operator.

摘要提出一种新的神经网络模型---时滞标准神经网络模型，它由线性动力学系统和有界静态时滞非线性算子连接而成。

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。

This paper is devoted to the Cauchy problem of the degenerate quasilinear parabolic systems with p-Laplace operator in the principal part.

本文研究一类主部是m-Laplace算子的拟线性退化抛物方程组的Cauchy问题。

According to normalforms that we obtained,we study universal unfolding for some degenerate bifurcationcases of codimension three and some simple global characterizations.

利用共轭算子法研究了具有幂零线性部分和不具有Z2—对称性的非线性动力系统的2阶规范形、3阶规范和4阶规范形，讨论了几种余维3退化分岔情况下的普适开折问题及其一些全局特性。

Beginning with some cases, the article gives basic definitions of inverse problems and ill-posed problems. Then it discusses the Moore-Penrose generalized solution and the Moore-Penrose generalized inverse, and makes a conclusion that linear compact operator equations are ill-posed, that is, the Moore-Penrose generalized solution is unstable.

本文从一些实例出发，介绍了反问题和不适定问题的基本概念，并讨论了方程的Moore-Penrose广义解和Moore-Penrose广义逆，得出了线性紧算子方程的不适定性，即Moore-Penrose广义解的不稳定性的结论。

Discussions of the sparsity and condition number of the expansion matrix are presented.

本文还对一般线性积分算子在正交小波基下的展开进行了讨论。

In order to reduce the design conservativeness, a condition for the existence of a parameter-dependent separator is proposed, and further the filter design can be converted into the optimization problem involving linear matrix inequalities.

为进一步降低设计的保守性，文中还给出了一种依参数分离算子的滤波器存在条件，并将滤波器设计转化为线性矩阵不等式表述的凸优化问题。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。