线性算子

The new methodof defining spline function will generalize the concept to the more universal Hilbert space. Hence, we take into consideration the interpolation spline function, general linear differential operater in semi- open interval and the Green function defined accordingly, and the reproducing kernel to produce the Green function and prove the existence of the reproducing kernel.

采用了一种新的样条函数的定义方法，把样条函数的概念推广到更一般的Hilbert空间上，再考虑半开闭区间a，+∞上的插值样条函数，一般线性微分算子及其定义的Green函数和再生核，构造出Green函数并且证明了再生核的存在性。

Based on up_ and down_going wave decomposition and elastic wave power reciprocity theorem, this paper derives, in the lateral velocity varying case, linear prediction operators expression and the generalized spectral factorization equation for reflection dataset.

本文基于上下行波分解及弹性波互易定理，导出横向变速介质条件下线性预测算子的表达式和反射数据的广义谱分解方程。

In this thesis,we discuss the problems of applying regularization methods to solvelinear and nonlinnear operator ...

本文讨论了利用正则化方法求解线性及非线性第一类算子方程的问题。

Gatti studied the inverse problem of source term for semilinear parabolicequation,which arises from the industrial combustion process.

Gatti对半线性抛物算子的非线性源项进行了研究，仅仅得出了源项反问题解的存在性结果。

The first part is to discuss the solvability of Volterra-Stieltjes integral equations.

积分算子理论和积分方程是非线性泛函分析中的一个重要分支。

The eigenvalue and the spectral radius of linear completely continuous operators are very important and significant indexes.

线性全连续算子的特征值和谱半径是非常重要的、具有实际意义的指标。

Our methods are based on the the surjection of maximal monotone operators and the critical point theorem of convex functionals.

本文主要利用极大单调算子满射原理和凸泛函临界点理论对半线性抛物型方程在各种控制下的能控性进行了研究。

Based on the surjection of maximal monotone operators, we prove that some semilinear heat equations with weak Lipschitz nonlinear terms are exactly controllable by L〓 0, T: H〓(Ω control; Based on the critical point theorem of coercive convex functionals, we prove that some parabolic equations with Lipschitz nonlinear terms are globally approximately controllable and finite-dimensional exactly controllable by controls acting on mobile supports, and finally, we extend the results to parabolic equations in R〓.

首先利用极大单调算子的满射原理证明了半线性热方程在较弱Lipschitz条件下可通过L〓0.T；H〓(Ω控制实现精确能控。然后通过构造强制凸泛函并利用其临界点理论证明了带Lipschitz非线性项的抛物型方程可通过作用在在移动支集上的控制来实现整体近似能控与有限维精确能控，最后将整体近似能控与有限维精确能控结论推广到无界区域R〓上。

We prove the existence of integral solutions for semilinear integrodifferential equations with nonlocal conditions in Banach spaces.

运用预解算子理论和Schauder不动点定理，在Banach空间证明了一类非局部半线性积微分方程积分解的存在性。

Pointwise approximation theorems for combinations of the new operators are given.

给出了这个新算子的线性组合的点态逼近定理。

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。