查询词典 completely continuous linear operator

In order todiscuss the structure of operator algebra, in recent years, many scholars have focusedon linear maps and various multiplieative maps on opcrator algebras, and studied thealgebraic and geomrtrial properties and the problem of classification of these mapsMany deep and intercepting results have been achieved, and many new ideals and meanswas introduced.

为了进一步探讨算子代数的结构，近年来国内外许多学者对算子代数上的线性映射和各种可乘映射进行了系统研究，探讨这些映射的代数和几何性质以及刻画分类问题，取得丰富成果并不断提出新的思路和方法。

The study of operator algebra bagan in 30times of 20th century. Though compary with some other theory it is relatively new, but it has unexpected application in some mathematic theory and other subject, such as quantum mechanics, noncommutative geometry, linear system, contral theory, number theory and some other important branches of mathematics.

算子代数理论产生于20世纪30年代，它在数学和其他学科中都有着出人意料的应用，它与量子力学，非交换几何，线性系统，控制理论，数论以及其他一些重要数学分支都有着广泛的联系和相互渗透。

The study of operator algebra theory began in 30s of the 20th century: With thefast development of the theory, now it has become a hot branch playing the role ofan initiator in modern mathematics. It has unexpected relations and inter infiltrationswith quantum mechanics, noncommutative geometry, linear system and control theory,number theory as well as some other important branches of mathematics.

算子代数理论产生于20世纪30年代，随着这一理论的迅速发展，它已成为现代数学的一个热门分支，它与量子力学，非交换几何，线性系统和控制理论，数论以及其它一些数学分支有着出人意料的联系和相互渗透。

The research of these subjects has related to pure and applied mathematics such as algebra, geometry, operator perturbation theory, matrix anal-ysis, approximation theory, multivariate linear modeling, optimality principle and quantum physics etc.

对它们的研究涉及到基础数学与应用数学的许多分支，诸如代数学、几何理论、算子扰动理论、矩阵理论、逼近论、优化理论与量子物理等。

Two basic theorems are given by researching Hamilton's two steps linear differential equations of bender equations which provide widespread application methods of normal differential operator correspond to ladder operators,then the solutions of general equations are obtained by taking advantage of the two above theorems: The energy eigenvalue equation of one-dimensional oscillator; the common state of ; the radial equation of a bondage state of hydrogen atom; the radial equation isotropic three-dimensional harmonic oscillator; the infinity deep potential well of ball

本文通过研究束缚态本征方程里的哈密顿算符的二阶线性常微分形式，给出两个基本定理并证明，提供构造二阶线性常微分算符相应的阶梯算符的普遍实用的方法，然后利用这两个定理构造量子力学中常见力学量的阶梯算符，并用以计算其能量本征值和对应本征函数：一维谐振子的能量本征方程；共同本征态；氢原子束缚态径向方程；三维各向同性谐振子的径向方程；无限深球势阱。

Using Extended Virial theorem , three recurrence relation of the average value of coordinate operator for linear harmonic oscillator, spherical harmonic oscillator and like-hydrogen ion were obtained respectively.

针对一维谐振子、类氢离子和三维各向同性谐振子三个量子体系，应用超维里定理，推导了幂坐标算符平均值的递推关系，方法较通常简洁明了。

The purpose of studing LPP is to discuss and so as to solve topological algebra's problems by linear methods, and to get information of classifying operator algebras from a new direction.

线性保持问题研究的目的是利用线性手段探讨和解决拓扑代数的问题，从新的角度提供算子代数的整体结构和对算子代数分类的信息。

Using the linear-combination operator and unitary transformation methods, the vibrational frequency and the ground-state energy of weak-coupling polarons are obtained.

采用线性组合算符和幺正变换的方法得到了弱耦合极化子的振动频率和基态能量。

The properties of strong coupling magnetoploron in the semiconductor quantum dot are investigated by the linear combination operator and unitary transformation methods.

采用线形组合算符和么正变换研究了磁场对半导体量子点中强耦合磁极化子基态的影响。

With the use of linear-combination operator and unitary transformation method,the influence of the dispersion of phonons on the properties of weak-coupling magnetopolaron in a parabolic quantum dot is studied.

利用线性组合算符和幺正变换的方法，研究声子色散对磁场中抛物量子点弱耦合磁极化子性质的影响。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。