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.     

基于谱间线性滤波的高光谱图像压缩感知

根据高光谱图像较强的谱间相关性,提出一种基于谱间线性滤波的高光谱图像压缩感知方法.高光谱图像进行压缩重构时,利用相邻波谱的谱间相关性,对重构的当前帧与前一谱段的重构图像进行谱间线性滤波,降低了重构帧的噪音信息,纠正了重构帧的轮廓信息,从而提高重构质量.在进行谱间线性滤波时,保留重构帧的低频系数,高频系数与前一波谱重构图像的高频小波变换系数进行线性加权求和,达到滤波的效果.通过实验表明,该方法能够有效提升图像重构质量,并降低重构时间.     

Oscillation of even order partial differential equations with distributed deviating arguments

Some Kamenev-type oscillation criteria are established for a class of boundary value problems associated with even-order partial differential equations with distributed deviating arguments. Our approach is to reduce the high-dimensional oscillation problem to a one-dimensional oscillation one, and the general means developed by Philos and Wong is used as the main tool. The results obtained here extend and improve some known results in the literature.     

Fe-Co-Ni合金纳米线有序阵列的模板合成与磁性

以二次阳极氧化的氧化铝膜为模板，用电化学沉积的方法成功地合成了Fe-Co-Ni三组份有序纳米线阵列.扫描电子显微镜（SEM）和透射电子显微镜(TEM)观察表明纳米线表面光滑、有序、高长径比；磁性测量表明,其矫顽力较同组份的膜材料有较大的提高.将样品在惰性气体氛围中不同温度下退火，随着退火温度增加，其纵向矫顽力有一个极值，而对应的横向矫顽力没有类似的变化，关于这一现象的机理,本文进行了初步的讨论. 图5参15     

Influence of anodizing voltage mode on the nanostructure of TiO2 nanotubes

The nanostructure of self-ordered porous anodic TiO₂ nanotubes (PATNTs) has extraordinary influence on their physical and chemical properties. For this reason, extensive attention has been paid on pulse anodization to regulate the nanostructure of PATNT. However, the relationships between the nanostructures and current curves still remain unclear. Based on the traditional potentiostatic and pulse anodizations, five different modes (i.e., potentiostatic, pulse, triangle wave, decrease, and increase step by step) of applied voltage and their influences on the nanostructures of PATNT have been investigated in detail. The growing rates of the nanotubes anodized under five different modes were compared for the first time. The results show that the growing rate of pulse voltage anodization is the fastest, reaching 116.4 nm min^?1. The slowest is triangle wave voltage anodization, only 59.3 nm min^?1. When the applied voltage decreases step-by-step, branched nanotubes can be formed in the bottom of PATNT. Yet, when the applied voltage increases step-by-step, triple-layer nanotubes with different diameters are formed, and the forming mechanism of this special nanostructure is discussed. The present results may be helpful to understand the mechanism of PATNT and facilitate the assembling diverse nanostructures for extensive applications in photocatalysis, dye-sensitized solar cells, and biomedical devices.