EXISTENCE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS AND HARDY TERMS

This paper deals with the existence of solutions to the elliptic equation -△uμu/|x|2=λu |u|2*-2u f(x, u) in Ω, u = 0 on ( a)Ω, where Ω is a bounded domain in RN(N≥3),0∈Ω,2*=2N/N-2,λ＞0,λ(a)σμ, σμ is the spectrum of the operator -△- μI/|x|2with zero Dirichlet boundary condition, 0 ＜μ＜-μ,-μ=(N-2)2/4,f(x,u) is an asymmetric lower order perturbation of |u|2*-1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.     

Frequency splitting phenomenon of dual transverse modes in a Nd:YAG laser

We observed frequency splitting phenomenon of dual transverse modes (TEM_00q and TEM_01q) in a Nd:YAG microchip standing wave laser utilizing intracavity stress birefringence effects. Four resonance frequencies (ν_00qe, ν_00qo, ν_01qe, and ν_01qo, respectively) were produced and tuned by changing the diametral compression force applied on the laser crystal. The transverse mode frequency spacing for the same longitudinal mode number (Δν_trans) was 1.16 GHz, and the magnitude of frequency splitting (Δν) ranged from 0 MHz to 1.16 GHz. Based on this phenomenon, a four-mode differential standing wave laser, whose signal characteristics were a little like those of a four-mode differential travelling wave laser gyro however with a much larger frequency splitting range, was produced. The theoretical analysis is in good agreement with the experimental results. This phenomenon not only can be used to make lasers with two or more frequency differences, but also can be used to make high-resolution self-sensing laser sensors (e.g. laser force sensors and laser accelerometers).     

均匀分布参数的无偏估计及其分布

讨论了均匀分布未知参数无偏估计量的分布密度,利用无偏估计量构造出一些新的样本函数,并且利用给出的样本函数推导出了未知参数的置信区间.所得到结果改善了现有的估计,易于计算.     

Existence of optimal solutions for general stochastic linear complementarity problems

In this paper we show the solvability of the expected residual minimization (ERM) formulation for the general stochastic linear complementarity problem (SLCP) under mild assumptions. The properties of the ERM formulation are dependent on the choice of NCP functions. We focus on the ERM formulations defined by the “min” NCP function and the penalized FB function, both of which are nonconvex programs on the nonnegative orthant.     

双层有机EL器件ITO/PPV/Alq3/Al发光稳定性的研究

制备了一组由PPV和Alq3组成的双层有机EL器件ITO/PPV/Alq3/Al;比较了两个发光层厚度不同时器件发光性能的差异.测试和分析了温度、真空度、工作电压和存放时间对器件衰减规律的影响.     

Regular maps of graphs of order 4<Emphasis Type="Italic">p</Emphasis>

A 2-cell embedding f : X → S of a graph X into a closed orientable surface S can be described combinatorially by a pair M = (X;ρ ) called a map, where ρ is a product of disjoint cycle permutations each of which is the permutation of the arc set of X initiated at the same vertex following the orientation of S . It is well known that the automorphism group of M acts semi-regularly on the arc set of X and if the action is regular, then the map M and the embedding f are called regular. Let p and q be primes. Du et al. [J. Algebraic Combin., 19, 123-141 (2004)] classified the regular maps of graphs of order pq . In this paper all pairwise non-isomorphic regular maps of graphs of order 4 p are constructed explicitly and the genera of such regular maps are computed. As a result, there are twelve sporadic and six infinite families of regular maps of graphs of order 4 p ; two of the infinite families are regular maps with the complete bipartite graphs K2p,2p as underlying graphs and the other four infinite families are regular balanced Cayley maps on the groups Z4p , Z22 × Zp and D4p .     

非紧集上不连续函数的Ky Fan不等式及其等价形式和应用

证明了非紧集上不具有任何连续性的函数弱Ky Fan点的存在性,给出了在函数只具非常弱的连续性和凸性条件下非紧集上Ky Fan不等式解的存在性,并给出它的两种等价形式.作为应用:(1)得到Ky Fan截口定理和Fan-Browder不动点定理的推广;(2)应用于博弈理论,得到几个新的Nash平衡存在性定理.     

图的上可嵌入性与独立顶点的新度和

Let G be a k(k ≤3)-edge connected simple graph with minimal degree ≥ 3,girth g,r=g12.For any independent set {a1,a2 , . . . , a 6/(4 k)} of G,if,then G is up-embeddable.     

Dynamics of a general non-autonomous stochastic Lotka-Volterra model with delays

In this paper, a general non-autonomous n-species Lotka-Volterra model with delays and stochastic perturbation is investigated. For this model, sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The influences of the stochastic noises to the properties of the stochastic model are discussed. The property permanence for the model is preserved with the sufficiently small noise and sufficiently large noise may cause extinction of the model. The critical value between weak persistence and extinction is obtained. Finally, numerical simulations are given to support the theoretical analysis results.     

氧化石墨烯纳米剪裁方法

石墨烯纳米剪裁先进方法的研究对于基于石墨烯的电子和光学设备非常重要。本文利用模板法制作反蛋白石结构,并借助反蛋白石纳米网结构,利用光催化还原氧化石墨烯,对氧化石墨烯进行纳米剪裁,形成具有纳米尺度的石墨烯。对还原后的氧化石墨烯表面进行扫描电子显微镜表征和红外光谱表征,并研究剪裁后石墨烯的电学性质。实验表明,反应时间、胶粒大小都会对剪裁后氧化石墨烯的周期和颈宽有影响,进而影响还原后氧化石墨烯的电学性质。利用纳米网状结构对石墨烯进行纳米剪裁是一种可行的方法,通过控制模板尺寸和反应条件可以控制裁剪后的性质。