线性算子

Subsequently, we discuss the generalized derivable mappings at zero point on standard operator algebras and show that every generalized derivable mapping at zero point on standard operator algebras is a generalized inner derivation.

其次又对标准算子代数上的在零点广义可导的线性映射进行了讨论，证明了标准算子代数上的在零点广义可导的线性映射是广义内导子。

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。

Moreover, we give some dual properties of these problems, and on this basis, we present a dual algorithm for solving the nonconvex conic model trust-region subproblem.

论文分析了这些问题的对偶性质，在此基础上，通过对偶提出了求解锥模型信赖域子问题的算法，同时证明了算法的全局收敛性以及局部Q-超线性收敛性，并给出了一些数值算例以说明算法的有效性。

The ground-state energy and the average number of virtual phonons around the electron of a hydrogenic impurity confined in a parabolic quantum dot are calculated using the squeezed-state variational approach,which is based on two successive canonical transformations and uses a displaced-oscillator type unitary transformation to deal with the bilinear terms,which are usually neglected.

李伟萍 内蒙古赤峰学院物理与电子信息工程系，赤峰 024000肖景林内蒙古民族大学物理与电子信息学院，通辽 028043采用基于逐次正则变换的变分方法，利用单模压缩态变换处理包含声子产生湮灭算符的双线性项，研究了抛物量子点中束缚极化子的性质。

In the last part, we study the existence of the solutions for semilinear subelliptic equations and the estimates of the eigenvalues for subelliptic operators on H.

另外我们还研究了Heisenberg群上一类半线性次调和方程的解的存在性问题及Heisenberg上群一类次调和算子的特征值估计问题。

Due to the linear subjectional function and the linear fuzzy enhancement operator, the algorithm not only speed the process, but also voids the losses of particular information.

由于采用的隶属函数和模糊增强算子均为线性的，不仅能够提高增强的速度，而且也有效避免体数据场细节信息的丢失。

Advancing wavefields by the degenerate migrators is actually a linear interpolation between two splitstep terms in the wavenumber domain.

退化的Fourier偏移算子通过在两个分裂步项之间作波数域线性插值来实现波场延拓，每延拓一层需要比常规的SSF地震偏移方法多一次快速Fourier变换。

In Chapter 2, an existence theorem is obtained for periodic solutions of non-autonomous second order systems with even-typed potentials. We also investigate solutions of linear bounded positive self-conjugation operators equations in Hilbert Space by variation methods.

第二章主要利用临界点理论中的归药方法、极小作用原理研究具偶型位势的二阶非自治系统周期边值问题，得到了周期解的存在；利用变分方法证明了Hilbert空间中有界线性正自共轭算子方程解的存在性。

We study on the controllability of parabolic systems with a nonlinear term involving the state and the gradient ,the null controllability property of a 1-d parabolic equation involving a fractional power of the Laplace operator ,null controllability of some systems of two parabolic equations with one control force ,and exact controllability of the parabolic system with bilinear control.

我们研究了含有状态和梯度的非线性的项抛物系统的能控性，含有拉普拉斯算子的分数阶的1-d抛物方程的零能控性，带有一个强控制的两个抛物方程的一些系统的零能控性和具有双线性控制抛物系统的精确能控性。

The second part is the controllability of parabolic equation .We study on the controllability of parabolic systems with a nonlinear term involving the state and the gradient ,the null-controllability property of a 1-d parabolic equation involving a fractional power of the Laplace operator ,null controllability of some systems of two parabolic equations with one control force ,and exact controllability of the parabolic system with bilinear control .

第二部分写的是，抛物方程的能控性，我们研究了含有状态和梯度的非线性的项抛物系统的能控性，含有拉普拉斯算子的分数阶的1-d抛物方程的零能控性，带有一个强控制的两个抛物方程的一些系统的零能控性和具有双线性控制抛物系统的精确能控性。

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。