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．     

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.     

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.     

啁啾微波场中里德伯锂原子的相干激发与控制

运用含时多态展开方法和B-样条函数研究了微波场中里德伯锂原子高激发态的性质,得到锂原子量子态n=70-75,l=0-5的能量,并分析了里德伯锂原子高激发态n=70-75,l=0-5在微波场中的跃迁几率.结果表明:通过优化微波场参数可以实现量子系统从初始态到目标态的完全跃迁,且在跃迁过程中,每个l态都起至关重要的作用.     

A Quantum Watermark Protocol

Quantum watermarking is the technique which embeds the invisible quantum signal such as the owner’s identification into quantum multimedia data (such as audio, video and image) for copyright protection. In this paper, a watermark strategy for quantum images is proposed based on flexible representation for quantum images (FRQI). Compared with the former strategy, which can only be used to verify the identity of the true owner of a carrier image, the proposed method can be used to find out who is the real owner, and our strategy’s capacity reaches the largest. It is impossible for anyone except the copyrighter to clear off or extract the watermark images.     

反射率的数值反演

通过分析热流边界条件下的一维热传导过程,提出并实现了由后表面温度变化历史曲线反演前表面反射率变化历史曲线的数值方法。通过一维热传导的正向和反演计算过程,验证了反演程序的可靠性。对数值反演计算和实验测量两种方式得到的反射率曲线进行了对比,结果显示,两条反射率曲线在变化趋势上符合较好,初步验证了一维温度场中数值反演方法的可行性。     

Research on front-end electronics gain compensation of MCP imaging detector北大核心CSCD

基于微通道板电子倍增电荷分割型阳极的成像探测器常用于行星大气、气辉等微弱信号探测。针对探测器读出电路增益不相等导致探测器成像产生畸变的问题,利用理论分析结合MATLAB仿真揭示了不同畸变图像的形成机制,在该基础上提出了一种探测器读出电路增益补偿方法减小探测器成像畸变。通过MATLAB仿真和实验测试结果表明该文提出的方法能够有效减小由于读出电路增益不相等导致的探测器成像畸变。     

Some mathematical aspects of Anderson localization: boundary effect,multimodality, and bifurcation

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach, and further investigate some mathematical aspects of Anderson localization that are rarely discussed before. First, we observe that under the Neumann boundary condition, the low energy quantum states are localized on the boundary of the domain with high probability. We provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional case. Second, we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary conditions. Finally, we examine a bifurcation phenomenon of the localization subregion as the strength of disorder varies. The critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.