Parameter Estimation for Multiscale Diffusions

We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized single-scale model to such multiscale data. We demonstrate, numerically and analytically, that if the data is sampled too finely then the parameter fit will fail, in that the correct parameters in the homogenized model are not identified. We also show, numerically and analytically, that if the data is subsampled at an appropriate rate then it is possible to estimate the coefficients of the homogenized model correctly. The ideas are studied in the context of thermally activated motion in a two-scale potential. However the ideas may be expected to transfer to other situations where it is desirable to fit an averaged or homogenized equation to multiscale data.     

(2 + 1)D exotic Newton-Hooke symmetry, duality and projective phase

A particle system with a (2 + 1)D exotic Newton-Hooke symmetry is constructed by the method of nonlinear realization. It has three essentially different phases depending on the values of the two central charges. The subcritical and supercritical phases (describing 2D isotropic ordinary and exotic oscillators) are separated by the critical phase (one-mode oscillator), and are related by a duality transformation. In the flat limit, the system transforms into a free Galilean exotic particle on the noncommutative plane. The wave equations carrying projective representations of the exotic Newton-Hooke symmetry are constructed.     

Tuning spin-filtering,rectifying, and negative differential resistance by hydrogenation on topological edge defects of zigzag silicene nanoribbons

By first-principles calculations, we propose three heterojunction nanodevices based on zigzag silicene nanoribbons with different edge-hydrogenated topological line defects. The devices all present excellent spin-filtering properties with 100% spin polarization as well as remarkable rectifying effect (with rectification ratio around 10²) and negative differential resistance behaviors. Our findings shed new light on the design of silicon-based nanodevices with intriguing spintronic applications.     

Hidden Symmetries for Thermodynamics and Emergence of Relativity

Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity. Though this is a beautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many other problems. In this article I will comment on some of the problems of Verlinde＇s proposal with special emphasis on the thermodynamical origin of the principle of relativity. It is found that there is a large group of hidden symmetries of thermodynamics, which contains the Poincare group of the spacetime for which space is emergent. This explains the thermodynamic origin of the principle of relativity.     

Spectrum-Generating Symmetries for the Superpotentials Acot θ and Btanh y

The hierarchy of supersymmetric partner Schrödinger equations for the superpotentials Acot?θ and Btanh?y with A and B as half-integer and negative integer numbers are solved. The number of bound states for given trigonometric and hyperbolic potentials are infinite and finite, respectively. In addition to the spectrum-generating corresponding to the standard supersymmetry which is based on shifting potential parameter, there exist three other different methods for generating the spectrum. The first method is based on supersymmetrizing two given models via infinite and finite number of their bound states. This is realized by the ladder operators which shift only quantum numbers. The second and third methods are based on supersymmetrizing any of the models via all bound states corresponding to hierarchy of their partner potentials. They are respectively realized via simultaneous increasing or decreasing of quantum number and the potential parameter, and also, increasing one of them while decreasing the other. Any of the second and third methods leads to introducing two different classes of the algebraic solutions for both models.     

在“画法几何及机械制图”课程教学中如何培养学生的能力

本文从高等教育必须加强学生各种能力培养的观点出发，阐述了在“画法几何及机械制图”课程教学活动中如何培养大学生的自学能力、空间想象能力、逻辑思维能力、读图和绘图能力的途径和方法上所作的探索和体会。     

高氯酸二水邻菲咯啉合铜配合物的合成和晶体结构

Crystal structure of the title compound， Cu(phen)(H₂O)₂·ClO₄(phen=1，10-phenanthroline)， was deter-mined by X-ray crystallography. It crystallizes in the monoclinic system， space group C2/c with lattice parameters a=1.49071(4)nm， b=1.38594(4)nm， c=0.70292(1)nm， β=108.509(1)° and Z=4; The Cu(Ⅰ) ion is chelated by a phen ligand and two aqua ligands in cis arrangement and assumes a C2 symmetric square-planar geometry with the CuN₂O₂ core. Eight Cu(phen)(H₂O)₂·ClO₄ molecules are interconnected by strong hydrogen bonds between coordinated water molecules and uncoordinated perchlorate anions to form a molecular scale cavities along c axis. The bond distances of Cu-N and Cu-O are 0.2003(4)nm and 0.1973(3)nm， respectively. CCDC： 197600.     

优化几何构型对高级别从头算能量的影响

对《ＣＲＣ物理与化学手册》（第７７版）中第三周期以前的无机双原子分子,当其理论优化构型的相对误差大于２％时,分别在实验构型和最大偏差的理论构型下,计算了ＱＣＩＳＤ（Ｔ）／６－３１１＋Ｇ（３ｄｆ,２ｐ）能量并作了比较。结果表明,大多数能量的差别在４．２ｋＪ．ｍｏｌ＾－１以内。由此说明,目前一般采用的构型优化理论方法,多数情况下不至于明显影响单点高级别从头算的计算精度。同时还发现,Ｇ２（ＱＣＩ）的高级     

干涉型光纤法布里-珀罗传感系统抗噪方法的实验研究

对于干涉型光纤法布里-珀罗(FFP)传感系统,外界环境对解调干涉仪的扰动是其主要噪声源之一.在光纤布拉格光栅构成的FFP传感系统中,对比分析了采用参考传感器和参考光源两种抗噪方法.实验结果表明,对于单频和宽带干扰,两种方法均可提高信噪比到40 dB.而且由于采用窄线宽光纤激光器作为参考光源的噪声水平较低,其差分探测结果具有更好的抗噪效果.     

磺胺二甲嘧啶钠的二阶导数差示脉冲极谱法定量研究

建立了磺酸二甲嘧啶钠的二阶导数差示脉冲极谱定量分析方法,磺胺二甲嘧啶钠在乙醇－（硼酸－氯化钾缓冲液）－水（体积比７０：２：２８）的底液中,于－１．５６０Ｖ（ｖｓ．Ａｇ／ＡｇＣｌ）处出现一良好的二阶导数差示脉冲极谱峰,磺胺二甲嘧啶钠浓度与其峰幅值在０．０６～０．６ｍｍｏｌ．Ｌ＾－１范围内呈非常显著的线性关系（Ｐ〈０．０１）,检出限为９．２ｎｍｏｌ．Ｌ＾－１,已用于注射液中磺酸二甲嘧啶钠的测定。