Symmetrized Chebyshev polynomials

We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves alternate) result that their coefficients are non-negative. As a corollary we find that and are positive definite functions. We further show that a Central Limit Theorem holds for the coefficients of our polynomials.

     

Load-Carrying Capacity of Circular Plates Made of a Fiber-Reinforced Composite

The load-carrying capacity of circular plates made of a fiber-reinforced composite and loaded with axisymmetric transverse forces under axisymmetric boundary conditions is investigated. The plates can be freely supported or clamped along their contour. To the known yield condition used, in the plane of main bending moments, there correspond irregular hexagons, which depend on the mechanical properties of composite constituents and some characteristic geometrical parameters. It is shown that, depending on the ratio of ultimate radial and circumferential bending moments, in the plastic state, the circular plates (the central part of the clamped plates) take the form of a cone or a frustum of cone. For each of the cases, the limit load is found, which is a function of the above-mentioned mechanical parameters. The statically allowable fields of bending moments and the corresponding allowable fields of deflection rates are determined. The solutions found are exact. Special cases for the freely supported plates are analyzed, and the results obtained are presented in the form of graphs.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 177–192, March–April, 2005.     

基于智能手机和Matlab的居家悬滴法表面张力测量实验

本文基于智能手机和Matlab软件设计了一种居家环境下可实现的悬滴法水滴表面张力测量实验.借助智能手机拍照功能获得水滴图像,利用Matlab进行边缘检测及计算,从而得出表面张力系数.对于不同清晰度的情况提出了对应的分析和处理方法,实验结果表明该方法稳定可靠.为后疫情时代开展居家大学物理实验教学提供了一个典型案例.     

Recent Advances in Common Transition Metal-Based Single-Atom Nanozymes and Their Applications in Pollutant Detection and Degradation

Nanozymes can be used as favorable substitutes for natural enzymes because of their strong catalytic activity and good stability. At the same time, research on single-atom catalysts (SACs) with isolated metal atoms as active centers is also in full swing, showing excellent performance in a variety of catalytic reactions. With the in-depth study of SACs, people have a comprehensive understanding of them and put forward the concept of single-atom nanozymes (SAzymes) by combining nanozymes with SACs. As a new type of nanomaterial, SAzymes have attracted great interest due to their remarkable catalytic activity and rapid energy conversion. However, most applications of SAzymes are mainly in the fields of biomedicine and biosensing, and less research has been done in the field of the environment. Based on the amazing ability of nanozymes to detect and degrade pollutants, SAzymes are also used in the environmental field, and even they will show better capabilities. This review mainly analyses common transition metal-based SAzymes and describes their applications in the field of environmental pollutants.     

方位远探测声波测井仪数据采集控制软件设计*

方位远探测声波测井技术在近年来得到了快速发展,数据采集控制软件是测井仪器系统的重要功能模块,其主要功能是完成地面采集控制平台与井下仪器的实时命令控制与数据传输。方位远探测声波测井仪数据采集控制软件模块以仪器库的形式挂接到成像测井系统,软件主要由仪器初始化、数据采集、数据分析及处理、仪器参数设置、下发命令封装、文件操作、实时波形绘图显示、实时波形处理、数据回放、帮助系统等部分组成。在程序设计中采用了多线程编程技术,提高与测井主控平台进行交互的时效性以及程序的响应速度。实验室及现场测试表明,方位远探测声波测井仪数据采集控制软件的总体及各个功能模块运行稳定,能够完成现场应用过程中对仪器的控制、数据读取、数据分析及处理、文件记录以及与现场测井采集控制平台的数据接口等需求,为仪器的进一步功能优化升级和现场应用提供了基础。     

基于电光调制提高静态傅里叶干涉具光谱分辨率的研究

在静态干涉系统中,采用电光调制可变折射率晶体LiNbO₃做静态傅里叶干涉具的材料,两侧分别加载相位相反的调制信号,从而在不改变静态傅里叶干涉具尺寸的条件下提高光谱分辨率。通过推导光程差函数与折射率调制度的函数关系,计算得在折射率调制度为0.030的条件下,比同尺寸干涉具光谱分辨率提高了16.7倍,达到2.836 cm-1。仿真结果表明折射率调制度会因波长增大而减小,光程差函数会随干涉位置的增大而产生偏大的现象。实际探测过程中,由于光谱范围500～1 100 nm相对较窄,波长变化造成的光谱探测失真不大,可以通过标定补偿,所以应用该方法可以有效地提高静态干涉系统的光谱分辨率。     

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本文在{ξi}为强混合样本,{ani}是实三角阵列下,得到了一个新的关于线性和n∑i=1aniξi的中心极限定理.并利用该中心极限定理,进一步建立了线性过程部分和的中心极限定理.     

Internal cancellation of spikes using two avalanche photodiodes in series for single photon detection

<正>We propose a method of improving the performance of InGaAs/InP avalanche photodiodes by using two avalanche photodiodes in series as single photon detectors for 1550-nm wavelength.In this method,the raw single photon avalanche signals are not attenuated,thus a high signal-to-noise ratio can be obtained compared with the existing results.The performance of the scheme is investigated and the ratio of the dark count rate to the detection efficiency is obtained to be 1.3×10~(-4) at 213 K.     

基于探测器模型的MPPC标定方法

探测器的光子数分辨能力是精确描述多光子态的突破口,近年来受到广泛的关注。光子数可分辨探测器有望被进一步应用于量子光学基础研究、量子成像、量子计算、量子通讯以及远距离激光测距等领域。基于空间复用原理的多像素光子计数器具有常温下稳定高效的光子数可分辨探测能力,加上尺寸和成本上的优势使得它成为光子数可分辨探测应用的首选。针对多像素光子计数器,我们通过建模给出了能描述探测器量子特性的标准矫正方法,系统地考虑了探测器量子效率、噪声、各像素点感光面的光子入射效率对量子特性的影响,给出了不同光子数态的正定算子估值测量和魏格纳函数。     

基于零拍探测和压缩真空光输入增强Sagnac效应

利用量子技术增强Sagnac效应提高陀螺输出精度具有重要的研究意义, 是实现全自主导航的重要途径. 以相干态激光作为输入光源的光学陀螺因真空零点波动使其输出精度限制于散粒噪声极限而难以提高. 为减小真空波动的影响, 提出在激光输入的分束器的另一输入端输入压缩真空光并结合平衡零拍探测技术的方法增强Sagnac效应. 理论分析表明Sagnac效应性能得到有效提升: 干涉输出的灵敏度检测极限和动态范围均随着压缩程度的增加而呈指数级增长. 该方法只需对经典光学陀螺做少量改动就可实现, 是提高光学陀螺输出精度的一种新方法.