Rh13团簇的几何结构和电子与磁性性质的计算

利用密度泛函理论，对Rh13团簇的几何结构、电子和磁性性质进行了研究，在优化过程中，其几何结构由正二十面体演化为变形的非对称结构，相邻原子间由等键长变为不等键长。优化后Rh13团簇的结合能比前面的其他研究者所得的结果大得多，这表明变形后的非对称结构比对称的正二十面体结构更为稳定。虽然我们得到的原子平均磁矩较之前面的研究者的结果小了一些，但是仍然比实验结果大，这一情况说明我们所得到的变形的非对称几何结构与真实的未知基态结构仍还有差异。同时我们还发现优化后的Rh13团簇的价带宽度和交换劈裂都一定程度的展宽和变大，态密度的峰值有远离费米能级向两侧移动的趋势。     

Mg掺杂CuAlO2电子结构的第一性原理研究

利用基于密度泛函理论的第一性原理方法，研究了CuAlO2晶体电子结构以及替位Mg杂质的特性。结果表明，Mg替代Al原子时形成受主杂质能级，而替代Cu原子时形成施主杂质能级；同时也计算了它们的形成能，发现前者是吸热反应，而后者是放热反应。另外，比较Mg替代Al与Mg替代Cu掺杂前后计算结果，发现前者费米能级变化不是很明显；而后者掺杂后费米能级明显向导带底移动。研究表明掺杂可改变CuAlO2的导电类型和电导强弱，此结果对实验具有很好的参考价值。     

Incomplete quenching of heat equations with coupled singular logarithms boundary fluxes

This paper deals with quenching phenomena for a heat equations with coupled singular logarithms boundary fluxes. Under appropriate hypotheses, the non-simultaneous quenching of the solution for the system is proved, and the estimates of quenching rates are given. Then we give a natural continuation of the solution (u,v) after the quenching time when the equations occurs non-simultaneous quenching. Moreover, we identify the heat equations verified by the continuation beyond quenching time, i.e., the equations occurs incomplete quenching.     

Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind

Recently, the authors introduced some generalizations of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials (see [Q.-M. Luo, H.M. Srivastava, J. Math. Anal. Appl. 308 (2005) 290-302] and [Q.-M. Luo, Taiwanese J. Math. 10 (2006) 917-925]). The main object of this paper is to investigate an analogous generalization of the Genocchi polynomials of higher order, that is, the so-called Apostol-Genocchi polynomials of higher order. For these generalized Apostol-Genocchi polynomials, we establish several elementary properties, provide some explicit relationships with the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, and derive various explicit series representations in terms of the Gaussian hypergeometric function and the Hurwitz (or generalized) zeta function. We also deduce their special cases and applications which are shown here to lead to the corresponding results for the Genocchi and Euler polynomials of higher order. By introducing an analogue of the Stirling numbers of the second kind, that is, the so-called λ-Stirling numbers of the second kind, we derive some basic properties and formulas and consider some interesting applications to the family of the Apostol type polynomials. Furthermore, we also correct an error in a previous paper [Q.-M. Luo, H.M. Srivastava, Comput. Math. Appl. 51 (2006) 631-642] and pose two open problems on the subject of our investigation.     

Mixed-type reverse-order laws of (AB) and (AB)

In this paper, by using the extremal ranks of generalized Schur complements, we study the mixed-type reverse-order laws for (AB)^(1,2,3) and (AB)^(1,2,4), and the sufficient and necessary conditions are established for these two reverse-order laws. Finally, two numerical examples are given to illustrate our results.     

Zero-based subspaces and quasi-invariant subspaces of the Bargmann-Fock space

We use the Weierstrass σ-function associated with a lattice in the complex plane to construct finite dimensional zero-based subspaces and quasi-invariant subspaces of given index in the Bargmann-Fock space.     

Penalty methods for a system of constrained variational inequalities

In this paper, using the penalty method in conjunction with graph-convergence, we study the existence of solutions for a class of generalized variational inequalities with variational problem constraints. Our results extend, improve and develop some known results in this field. Our method of proofs is very simple and does not use the hemicontinuity nor the pseudo-continuity properties of monotone operators.     

小信号脉冲抽运时掺铒光纤自发辐射的研究

自发辐射(ASE)是掺铒光纤放大器(EDFA)的重要噪声源,对于由EDFA构成的光纤激光器有重要影响。理论与实践证明,它与抽运方式紧密相关,所以研究脉冲抽运时掺铒光纤(EDF)的自发辐射有重要的学术价值。同时,脉冲抽运对于EDFA锁模激光器的研究也有一定意义。从理论和实验两方面研究了小信号脉冲抽运时,抽运脉冲宽度和幅度对于EDF的自发辐射特性的影响,得到了小信号抽运时输出ASE噪声平均值的近似解析解。研究发现,小信号脉冲抽运时输出信号的幅度与抽运脉冲的宽度成正比。这个新现象可用于脉冲宽度的全光检测。     

LiF插层对有机发光二极管磁场效应的调控

制备了有LiF插层的有机发光二极管，以八羟基喹啉铝（Alq₃）作为电子传输层，N, N′-二苯基-N, N′-二(1-萘基)-1,1′-联苯-4,4′-二胺（NPB）作为空穴传输层.通过改变Alq₃与NPB间LiF插层的厚度，研究了不同温度下器件的光电特性及电致发光的磁场效应.测量结果表明:LiF插层可以影响器件内部载流子的输运和激发态的形成.较厚的插层阻碍了空穴的传输，使器件的电流效率变低.但实验中发现， 关键词： LiF插层结构 磁场效应 三重态激子     

温度对光学微腔光子激子系统玻色凝聚的影响

建立了光学微腔中光子激子系统的物理模型,确定了光学微腔宽度为常数和可变这两种情况下玻色凝聚时化学势的变化范围和粒子数密度随温度和位置的变化规律.以半导体GaAs光学微腔为例,探讨了温度对玻色凝聚的影响.研究表明:系统出现玻色凝聚时激子化学势的变化范围与材料介电函数、微腔宽度有关,而光子和激子的粒子数密度及总粒子数还与温度有关.玻色凝聚温度理论值与实验值接近.刚出现玻色凝聚时,光子和激子的粒子数密度几乎相等,且局限在r=0的附近;随着温度的降低,光子和激子的粒子数密度都增加,且存在的范围也不断扩大;不论光学微腔宽度是否可变,光子和激子的粒子数密度以及总粒子数都随温度的降低而增大,光子数总是多于激子数. 关键词： 光学微腔 光子激子系统 玻色凝聚 温度