On the Automorphism Groups of Cayley Graphs of Finite Simple Groups

Let G be a finite nonabelian simple group and let be a connectedundirected Cayley graph for G. The possible structures for thefull automorphism group Aut are specified. Then, for certainfinite simple groups G, a sufficient condition is given underwhich G is a normal subgroup of Aut. Finally, as an applicationof these results, several new half-transitive graphs are constructed.Some of these involve the sporadic simple groups G = J₁, J₄,Ly and BM, while others fall into two infinite families andinvolve the Ree simple groups and alternating groups. The twoinfinite families contain examples of half-transitive graphsof arbitrarily large valency.     

基于碳纳米管分子封装的一维电子波函数扫描

利用第一性原理,设计并研究了一类基于单臂碳纳米管的分子封装的分子体系．计算表明,半环葫芦脲类化合物可有效封装碳纳米管,引入微弱的分子间相互作用,对碳纳米管的电子态能级结构分布 仅带来微弱影响．半环葫芦脲分子与碳纳米管在管径方向的一维电子态波函数充分耦合,进而有效改变了一些前沿分子轨道的波函数在管径两头的分布以及相应的电子布居浓度．基于电子输运的模拟,发现半环葫芦脲分子在碳纳米管一维方向滑动时的某个电压下的电导变化可准确反映电子态波函数在相应分子导电通道上的一维分布信息．     

基于创新思维培育的大学物理实验教学平台建设与实践简

大学物理实验是激发学生学习大学物理兴趣、培养学生创新思维的有效手段。文中调研了国内外大学物理实验教学现状,基于地方本科院校的实际,从教学方法、教学模式和教学管理三个方面阐述了大学物理演示实验教学,着重分析了如何利用大学物理实验平台激发大学生的创新思维。     

财经类院校数学建模的教学与实践

针对经济、管理类专业学生的特点 ,介绍了在财经类院校开展数学建模活动的意义、方法和步骤 ,总结了开展数学建模竞赛的经验 .     

The Riemann–Hilbert analysis to the Pollaczek–Jacobi type orthogonal polynomials

In this paper, we study polynomials orthogonal with respect to a Pollaczek–Jacobi type weight The uniform asymptotic expansions for the monic orthogonal polynomials on the interval (0,1) and outside this interval are obtained. Moreover, near , the uniform asymptotic expansion involves Airy function as , and Bessel function of order α as in the neighborhood of , the uniform asymptotic expansion is associated with Bessel function of order β as . The recurrence coefficients and leading coefficient of the orthogonal polynomials are expressed in terms of a particular Painlevé III transcendent. We also obtain the limit of the kernel in the bulk of the spectrum. The double scaled logarithmic derivative of the Hankel determinant satisfies a σ‐form Painlevé III equation. The asymptotic analysis is based on the Deift and Zhou's steepest descent method.     

Isometric Extension Problem Between Strictly Convex Two-dimensional Normed Spaces

In this paper, based on the smooth point of the unit ball and its support linear functional,we show two equivalent formulations of the isometric extension problem between the unit spheres of strictly convex two-dimensional normed spaces. We prove that these equivalent formulations have a positive answer in a special case.     

Surface Gravity on the Horizon of η- ξ Spacetime

We investigate the two methods of defining the surface gravity ,κ on the horizon, which are the metric definition and the definition given by the spacetime conformal method. It is found that the latter is of greater generality. By this method, we find that ,κ of η- ξ spacetime is equal to the exponent factor α in the coordinate transformation, which confirms the argument that η- ξ spacetime can be considered as the background spacetime for finitetemperature field theories. The reasons why the metric definition of ,κ can not be applied in η- ξ spacetime are presented.     

光声池径向共振模式耦合系数理论分析

光声光谱法是基于红外吸收光谱原理的一种高灵敏度的微量气体探测技术。它使用声共振腔来实现微弱声信号的共振放大。通过调节激光的调制频率,当它等于腔的某个共振频率时,在腔内形成声驻波,而腔本身的作用相当于一声放大器。共振腔的放大作用取决于当前被激活的共振模式、腔的品质因素、声传感器的状态以及电磁辐射与腔共振模式的耦合作用。值得关注的是,红外激光相对于声共振腔的入射方位不同则激励产生的光声信号幅值也不同。采用理论推导与数值计算相结合的方法,以圆柱形光声池为例,研究了径向共振模式下耦合系数受激光入射方位的影响。研究表明,激光入射角在0～π/2范围变化时耦合系数存在2个零点和2个极大值：入射角为0或tan-1(0.859 2×2R/L)时,耦合系数为零而径向共振失效;入射角为tan-1(0.556 8×2R/L)或tan-1(2R/L)时,耦合系数极大而径向共振最强。此处R为池径而L为池长。结果可用于指导光声池结构优化设计与安装调试,增强光声法检测微量气体的信号幅值,提高检测灵敏度。     

Linear convergence analysis of the use of gradient projection methods on total variation problems

Optimization problems using total variation frequently appear in image analysis models, in which the sharp edges of images are preserved. Direct gradient descent methods usually yield very slow convergence when used for such optimization problems. Recently, many duality-based gradient projection methods have been proposed to accelerate the speed of convergence. In this dual formulation, the cost function of the optimization problem is singular, and the constraint set is not a polyhedral set. In this paper, we establish two inequalities related to projected gradients and show that, under some non-degeneracy conditions, the rate of convergence is linear.     

A characterization of almost simple K 3-groups

It is a well-known fact that characters of a finite group can give important information about the group's structure. Also it was proved by the third author of this article that a finite simple group can be uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite almost simple group by using less information of its character table, and successfully characterize the almost simple K₃-groups by their orders and at most three irreducible character degrees of their character tables.