查询词典 comparison operator

In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

A complete boundary integral formulation for incompressible Navier Stokes equations with time discretization by operator splitting is developed by using the fundamental solutions of the Helmhotz operator equation with different orders.

利用不同阶次的Helmhotz算子方程的基本解，建立了时间离散不可压缩Navier－Stokes方程的完全边界积分表示式。

In chapter two,we find a completely continuous operator,the original operator equation is transformed a fixed point problem.

在第一章中，我们给出本文要用到的一些预备知识和本文的主要结果。

The main tools are the iterative method of monotone operator and the cone-compression theory of completely continuous operator.

主要工具是单调算子的迭代方法和全连续算子的锥压缩理论。

Firstly,we introduce its definition,then construct two groups of operator functions by an elementary method,and extend the function f= t(t+2)log(t+2)/(t+1)~2 to linear situation,at last we discuss some results about operator monotone function under the complex order and conjugate complex order.

首先介绍了Furuta不等式的几何结构，将普通的算子序推广到更弱的算子序A~4≥(A~2B~2A~2)~2/3，讨论在此序下的函数的算子单调性，并且推广到更一般的序A~(2m)≥(A~mB~2A~m)~m/m+1，得到了一些新的研究方法与结果。

Based on the technique of transparent degree ruler, the operator of color composition is improved in the unchangeable sampling range. When the classifications of the volume data are small, this operator can obviously accelerate the rendering procedure.

对于稳定采样区间的颜色合成，提出了基于透明度标尺的颜色合成新算子，该方法对于类属较少的体数据，其绘制加速效果是十分明显的。

Secondly, a projector operator Q is defined in the Lebesgue integrable functions' space Y such that the composition of the inverse operator of L, I-Q and the nonlinear term f is compact, where I is the identity mapping in Y.

然后，在Lebesgue可积函数全体所成的空间Y上定义了投影算子Q，使得L的逆与I-Q及非线性项f的复合是紧算子，其中，I是Y上的恒同算子。

If F is a space of functions defined on a domain Ω and ψ is a function taking Ωinto itself, then the composition operator C〓 induced by ψ is defined by C〓: f〓fοψ,〓f∈F. It is obvious that C〓 is a linear operator.

设F是定义在区域Ω上的一个函数空间，φ：Ω→Ω是Ω到自身的一个映射，则可通过函数的复合定义一个线性算子C〓：f→foφ，〓f∈F，称为由φ诱导的复合算子。

Iii By using the well-known properties of the dela vallee-poussin summability kernels and the pass principle of weakly compact operator, we study the weak compactness of C〓 on vector-valued analytic function spaces H〓, B〓, N and N〓, establish some connections between the weak compactness of composition operators and the structure properties of Banach spaces. These generalize and unify the corresponding results in the scalar-valued setting and enrich the content of the study of composition operator in another way.

第三，利用著名的de la Vallee-poussin可和核及有关算子的弱紧性的传递原理给出了向量值解析函数空间H〓、B〓、N及N〓上的复合算子的弱紧性的刻画，建立了复合算子的弱紧性与Banach空间的结构性质之间的联系，统一和推广了对应的数量值解析函数空间上的复合算子的弱紧性，这从另一种途径极大地丰富了复合算子的研究内容。

We establish some connections between geometric properties, properties in analysis and analytic properties of the inducing map ψ and operatortheoretic properties of composition operator C〓: f〓fοψ on various analytic function spaces mentioned above, include the boundedness, compactness, weak compactness, collective compactness and the Schatten class operator ideal, etc. Our results extend some previous results, for instance, the Shapiro's Nevanlinna counting function condition and the MacCluer's Carleson measure condition for the compactness of C〓 on Hardy space.

本文建立了D上解析自映射φ：D→D的几何性质、分析性质和解析性质与复合算子C〓：f→foφ在上述各种解析函数空间上的限制的算子性质之间的联系，涉及到复合算子C〓的有界性、紧性、弱紧性、总体紧性及Schatten类算子理想等算子特征，推广了前人的一系列结果，如Shapiro关于C〓的紧性的Nevanlinna计数函数条件，MacCluer关于C〓的紧性的Carleson测度条件等。

There had been a moment during the breakfast meeting, though, after the backslapping and the small talk and when all of us were seated, with Vice President Cheney eating his eggs Benedict impassively and Karl Rove at the far end of the table discreetly checking his BlackBerry, that I witnessed a different side of the man.

那次早餐会期间，在表示过关心和寒暄以后，我们所有人坐了下来，我注意观察了一下，副总统切尼面无表情地吃着班尼迪克蛋（Eggs benedict，源自美国，以英式松饼、火腿、水煮蛋以及荷兰酱组合而成），卡尔。罗夫在餐桌的远端谨慎地经常查看他的黑莓手机，我目睹了他所不为人知的一面。

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