具P-Laplacian算子型周期边值问题解的存在性

本文利用拓扑度理论和一些分析技巧讨论了具p—Laplacian算子型周期边值问题(φp(χ’))’+d/dt gradF(χ)+gradG(χ)=e(t),χ(0)=χ(T),χ’(0)=χ’(T)解的存在性,在对阻尼项d/dtgradF(χ)没有任何限制的前提下,给出了解存在的充分条件.     

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.

     

Long lasting phosphorescent properties of Ti doped ZrO2

A novel long-lasting afterglow phosphor ZrO₂:Ti is prepared by the conventional solid-stated method and their luminescent properties are investigated. A bluish white strong and broad emissive band, which is attributed to originate from the recombination of electrons trapped by F⁺ centers and the holes created in Valence band, is observed under 254 nm UV irradiation. The identical color long afterglow, which lasts about 1 h, is found in the ZrO₂:Ti phosphor after removing the 254 nm UV light. The mechanism of the long lasting phosphorescence (LLP) has been discussed based on the thermoluminescence (TL) results. The replacement of Zr by Ti produces more anion vacancies, resulting in the enhanced photoluminescence (PL) and LLP of ZrO₂:Ti sample. These results indicate that ZrO₂:Ti phosphor has potential promising applications.     

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.     

Two-Flux Colliding Plane Waves in String Theory

We construct the two-flux colliding plane wave solutions in higher-dimensional gravity theory with dilaton,and two complementary fluxes. Two kinds of solutions have been obtained: Bell-Szekeres (BS) type and homogeneous type. After imposing the junction condition, we find that only the BS type solution is physically well-defined. Furthermore, we show that the future curvature singularity is always developed for our solutions.     

机器人通过奇点的运动学逆问题的数值解法

机器人在完成其规划动作时,常可能要通过其运动链的奇点,这时求解其运动学逆问题的通用算法遇到本质的困难,本文给出了一种算法,它可以成功地克服这个困难。文中还给出了计算实例。     

H_2—O_2爆轰时Ar浓度对产生胞格结构的影响

作者在方形爆轰管中进行了H_2—O_2—Ar系统的实验研究。在由Ar稀释的H_2—O_2混合物的爆轰实验中得到了规则的胞格结构图案。也得到了胞格形成的临界曲线,并与爆炸极限曲线进行了对照,两者的趋势是一致的。另外,测量了从点火处到胞格形成处之间的距离及胞格区的长度。最后分析了氩Ar浓度对H_2—O_2爆轰的抑制作用。     

球面激波在固壁的马赫反射

本文对金属丝电爆炸产生球面激波在固壁上的马赫反射作了研究。由高速纹影摄影系统将反射图像拍摄下来,从而测量出马赫杆在壁面的马赫数,进而得到超压以及三波点迹线,实验结果与我们的数值计算结果作了比较,二者比较吻合。     

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.