钾原子中多种受激辐射参与的混频过程

当双原子共振激发钾原子于６Ｓ能级时,由光泵受激辐射和电离复合受激辐射参与的六波或四波混频,产生了位于紫外和紫区的诸多相干辐射、文中对多种混频机制进行了分析和讨论,并对所测得的相干辐射线进行了标识．     

有消费或投资的华氏宏观经济模型

本文对华罗庚教授的宏观经济模型进行了推广 ,在原来模型的基础上 ,分别增加了消费、投资 ,得到两种不同的模型 ,并对模型具有经济意义的解进行了研究     

变系数波动方程所决定的控制系统的最小能量控制和快速控制问题

本文研究变系数波动方程所决定的控制系统的最小能量控制和快速控制问题 .在所讨论的系统精确可控的前提下 ,得到了系统的最小能量控制和快速控制的解析表达式     

一类齐次对称多项式上的切比雪夫不等式

本文借助于控制不等式及数学归纳法，将著名的切比雪夫不等式推广到m次一般齐次对称多项式上(如文中定理及引理7)，并将此结果用于对称平均等．旨在展示证明解析不等式的一些有效的方法和技巧，同时为数学研究特别是高维几何研究提供一些新的有趣而有用的解析不等式．     

关于非线性规划问题的组合同伦内点法

文[1]在条件(C1)、(C2)和(C3)之下，利用组合同伦内点法讨论了非凸非线性规划问题K—K—T点的存在性，本文对条件(C2)和(C3)进行了改进和处理。     

Convergence rates of cascade algorithms

We consider solutions of a refinement equation of the form

where is a finitely supported sequence called the refinement mask. Associated with the mask is a linear operator defined on by . This paper is concerned with the convergence of the cascade algorithm associated with , i.e., the convergence of the sequence in the -norm.

Our main result gives estimates for the convergence rate of the cascade algorithm. Let be the normalized solution of the above refinement equation with the dilation matrix being isotropic. Suppose lies in the Lipschitz space , where 0$"> and . Under appropriate conditions on , the following estimate will be established:

where and is a constant. In particular, we confirm a conjecture of A. Ron on convergence of cascade algorithms.

     

Trapping neutral fermions with a PT-symmetric trigonometric potential in the presence of position-dependent mass

The relativistic problem of neutral fermions subject to PT-symmetric trigonometric potential (∼iαtanαx)$(\sim \mathrm{i}\alpha \tan \alpha x)$ in 1+1$1+1$ dimensions is investigated. By using the basic concepts of the supersymmetric quantum mechanics formalism and the functional analysis method, we solve exactly the position-dependent effective mass Dirac equation with the vector coupling scheme and obtain the bound state solutions in closed form. The behavior of the energy spectra is discussed in detail.     

Local hydrated structure of an Fe2+/Fe3+ aqueous solution: an investigation using a combination of molecular dynamics and X-ray absorption fine structure methods

The hydrated shell of both Fe2+ and Fe3+ aqueous solutions are investigated by using the molecular dynamics (MD) and X-ray absorption structure (XAS) methods. The MD simulations show that the first hydrated shells of both Fe2+ and Fe3+ are characterized by a regular octahedron with an Fe-O distance of 2.08 for Fe2+ and 1.96 for Fe3+, and rule out the occurrence of a Jahn-Teller distortion in the hydrated shell of an Fe2+ aqueous solution. The corresponding X-ray absorption near edge fine structure (XANES) calculation successfully reproduces all features in the XANES spectra in Fe2+ and Fe3+ aqueous solution. A feature that is located at energy 1 eV higher than the white line (WL) in an Fe3+ aqueous solution may be assigned to the contribution of the charge transfer.     

Population coherent control of Rydberg potassium atom via adiabatic passage

The time-dependent multilevel approach(TDMA) and B-spline expansion technique are used to study the coherent population transfer between the quantum states of a potassium atom by a single frequency-chirped microwave pulse.The Rydberg potassium atom energy levels of n=6-15,l=0-5 states in zero field are calculated and the results are in good agreement with other theoretical values.The time evolutions of the population transfer of the six states from n=70 to n=75 in different microwave fields are obtained.The results show that the coherent control of the population transfer from the lower states to the higher ones can be accomplished by optimizing the microwave pulse parameters.     

Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional(2D) systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded(polytope type) uncertain domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.