算子方程

In this paper,we study the oscillation properties of solutions to the following problems of three classes of delay parabolic equations of neutral type.where Ω is a bounded domain in R~n with a piecewise smooth boundary ?

本文研究了三类中立型时滞抛物方程：解的振动性。其中G=Ω×(0，+∞)，Γ=Ω×0，+∞，ΩR~n是有界域，边界Ω逐片光滑，Δ是拉普拉斯算子，？

Furthermore the existence condition and the variation principle of the differential equation are discussed, and the theory gist of the step-time technologies is presented.

应用相关的势算子理论对抛物型偏微分方程的泛函存在条件及变分定理进行了较系统的讨论，进而指出了"时间步进有限元法"各种处理方法的理论依据。

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。

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。

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。

In this algorithm, the strongest corner points is adaptively detected with Harris operator and (2n+1)×(2n+1) feature windows is selected for originally mutual gray correlative matching. Continental distance ratio invariant criterion is proposed, and consistency of motion vector is improved by eliminating error matching points with median filter. 9 pairs right points is preserved, 4 pairs composing 1 group, and 5 groups is random distributed to uncoil the motion vector equations. Last, stabilization precision is improved by averaging the 5 groups' solutions.

该方法用Harris算子自适应检测出最强壮的角点，开辟(2n+1)×(2n+1)特征窗进行灰度互相关初匹配；提出欧式距离之比不变准则，通过中值滤波剔除误匹配点，确保运动矢量较高的一致性；最后保留若干正确的匹配点对，分成多组解运动矢量方程，将多组解的平均值作为全局运动矢量以提高稳像精度。

Continental distance ratio invariant criterion is proposed,and consistency of motion vector is improved by eliminating error matching points with median filter.9 pairs right points is preserved,4 pairs composing 1 group,and 5 groups is random distributed to uncoil the motion vector equations.Last,stabilization precision is improved by averaging the 5 groups′ solutions.

该方法用Harris算子自适应检测出最强壮的角点，开辟(2n+1)×(2n+1)特征窗进行灰度互相关初匹配；提出欧式距离之比不变准则，通过中值滤波剔除误匹配点，确保运动矢量较高的一致性；最后保留若干正确的匹配点对，分成多组解运动矢量方程，将多组解的平均值作为全局运动矢量以提高稳像精度。

The first conclusion infers the sufficient condition with the aid of thealgebra Riccati equation solution and the semi-group theory nature which the systemmay optimize;Next discussed when the system operator characteristic vector forms theRiesz base,causes control function concrete mathematical expression which its systemmay optimize;Finally summarized the system to be possible to optimize the researchnewest conclusion and the research forecast.

第一个结论借助代数Riccati方程的解及半群理论性质推导出系统可最优化；其次讨论了系统算子的特征向量形成Riesz基时，使其系统可最优化的控制函数的具体数学表达式；最后总结了系统可最优化研究的最新结论和研究展望。

On the convergence of Newton's method in Banach space〓 Let F be an operator mapping from a real or complex Banach space X to another one Y, the Newton iteration 〓(2) is used to find the approximative solution of the equation (1), where the derivative is meant in the Frechet sense.

一、Banach空间中Newton法的收敛性〓设F是由实的或复的Banach空间X到同型空间Y的算子，求解方程(1)的Newton迭代为〓，0，1…，(2)其中的导数指的是在Frechet意义下的。

In Chapter 3, by establishing a L-operator inequality and using the properties of M-matrix and stochastic analysis techniques, some sufficient conditions ensuring the exponential dissipativity in mean square of impulsive stochastic functional differential equations of Ito-type are obtained.

第三章，通过建立L-算子不等式，运用M-矩阵的理论和随机分析技巧，获得了一类脉冲随机泛函微分方程均方指数耗散的充分条件。

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。