Embedding complex networks in a low dimensional Euclidean space based on vertex dissimilarities

We propose a method for representing vertices of a complex network as points in a Euclidean space of an appropriate dimension. To this end, we first adopt two widely used quantities as the measures for the dissimilarity between vertices. The dissimilarity is then transformed into its corresponding distance in a Euclidean space via the non-metric multidimensional scaling. We applied the proposed method to real-world as well as models of complex networks. We empirically found that real-world complex networks were embedded in a Euclidean space of relatively lower dimensions and the configuration of vertices in the space was mostly characterized by the self-similarity of a multifractal. In contrast, by applying the same scheme to the network models, we found that, in general, higher dimensions were needed to embed the networks into a Euclidean space and the embedding results usually did not exhibit the self-similar property. From the analysis, we learn that the proposed method serves a way not only to visualize the complex networks in a Euclidean space but to characterize the complex networks in a different manner from conventional ways.     

A new integral equation for the radial distribution function of a hard sphere fluid

Based on a proposal by Shinomoto, a new integral equation is derived for the radial distribution function of a hard-sphere fluid using mainly geometric arguments. This integral equation is solved by a perturbation expansion in the density of the fluid, and the results obtained are compared with those from molecular dynamics simulations and from the Born-Green-Yvon (BGY) and Percus-Yevick (PY) theories. The present theory provides results for the radial distribution function which are intermediate in accuracy between those obtained from the BGY and from the PY theories.     

A new information dimension of complex networks

The fractal and self-similarity properties are revealed in many complex networks. The classical information dimension is an important method to study fractal and self-similarity properties of planar networks. However, it is not practical for real complex networks. In this Letter, a new information dimension of complex networks is proposed. The nodes number in each box is considered by using the box-covering algorithm of complex networks. The proposed method is applied to calculate the fractal dimensions of some real networks. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks.     

积分球技术在高能激光能量测量中的应用

 介绍了一种采用积分球技术对高能激光能量测试的有效方法,给出了其工作原理、设计要求和误差分析。     

Effect of varying lanthanide local coordination sphere on luminescence properties illustrated by selected inorganic and organic rare earth complexes synthesized in sol-gel host glasses

Inorganic and organic ligands were carefully selected to illustrate the effect of modifications in the local field environment around the rare earth lanthanide (III) on its emission properties. In this article two strategies were employed to enhance emission of lanthanides encapsulated in sol-gel glass. (i) Changing the symmetry around the lanthanide, which was diagnosed by changing the local environment around the lanthanide using different inorganic counter ions (acetate, nitrate and chloride) these ligands differ in their affinity toward the lanthanide first coordination sphere. The ligand that penetrates the lanthanide more results in more asymmetric environment and thus results in higher emission. The aim of this part was to demonstrate the change of symmetry on emission in the absence of energy transfer. Our results indicate that the acetate ion has the highest affinity toward the first coordination sphere followed by the nitrate while the chloride showed the lowest affinity. Penetration by the ligands ofthe lanthanide also results in removing OH quenchers surrounding the lanthanide and this further explains the boost in emission. (ii) A bulky organic ligand that forms a complex with the lanthanide is used. The organic ligand separates the lanthanide ion from inner O-H oscillators. In this case the chelating organic chromophore with suitable photophysical properties was employed to sensitize the lanthanide and thus energy transfer occurs via the antenna effect. The organic ligand absorbs UV light, then energy is transferred to the lanthanide and finally the lanthanide emits in the visible region. The first coordination environment surrounding europium was controlled by the ligand selection and the outer sphere was modified by doping the synthesized complexes in an optically transparent sol-gel glass host. The glass network carefully prepared by sol-gel process is effective in preventing free oxygen and water from attacking lanthanide -complexes without loss of luminescence. Emission spectroscopy measurements of the doped silica specimens confirmed the variation of Eu (III) emission depending on the first coordination sphere surrounding the europium ion. The encapsulation of the europium complexes was performed for two reasons: (i) to improve the stability of red phosphor with efficient and high color-purity characteristics under ultraviolet excitation and (ii) this work provides a framework for preparing transparent composite glasses that are robust hosts to study the fundamental interactions between nano-materials and light.     

广义线性量子变换在相空间的新表示

用坐标和动量算子作为基本算子给出广义线性量子变换在相位空间的新表示,具体包括变换关系式、变换算子的幺正条件、变换算子的普通表达形式和正、反正规乘积形式.     

积分球技术在高能激光能量测量中的应用

介绍了一种采用积分球技术对高能激光能量测试的有效方法,给出了其工作原理、设计要求和误差分析。     

A note on the spheroidal modes vibration of an elastic sphere in linear viscoelastic fluid

Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing, and also to investigate materials mechanical properties. An analytical approach based on the exact theory has been developed in this paper, to establish a new accurate and simple generalized frequency equation to predict spheroidal vibration of an elastic nanosphere, in a compressible viscoelastic fluid using linear Maxwell fluid model. To demonstrate the accuracy of the present approach, a comparison is made with the published theoretical results in the literature in some particular cases, which shows a very good agreement. Thus, the obtained frequency equation can be very useful to interpret the experimental measurements of vibrational dynamics of nanospheres and can serve as benchmark solution in design of liquid sensors.     

On the efficiency of data representation on the modeling and characterization of complex networks

Specific choices about how to represent complex networks can have a substantial impact on the execution time required for the respective construction and analysis of those structures. In this work we report a comparison of the effects of representing complex networks statically by adjacency matrices or dynamically by adjacency lists. Three theoretical models of complex networks are considered: two types of Erd?s-Rényi as well as the Barabási-Albert model. We investigated the effect of the different representations with respect to the construction and measurement of several topological properties (i.e. degree, clustering coefficient, shortest path length, and betweenness centrality). We found that different forms of representation generally have a substantial effect on the execution time, with the sparse representation frequently resulting in remarkably superior performance.     

A non-standard auxiliary integrating sphere and correction method for the realization of diffuse reflectance

To realize spectral diffuse reflectance scale in 0/d geometric condition at National Institute of Metrology in China (NIM), a facility based on a non-standard auxiliary integrating sphere method with special structure has been built up and a correction method for the influence on the thickness of PTFE (polytetrafluoroethylene) coating at the port of auxiliary integrating sphere is mainly discussed. The uncertainty of spectral diffuse reflectance in NIM is approximately 0.25% (k = 2) in 380–800 nm. This facility has been used to establish China diffuse reflectance scales in the VIS–NIR part of the spectrum. This system and correction method presented in this paper can be easily implemented on most commercial spectrophotometers with a lower cost.     

A new procedure for obtaining the Voigt function dependent upon the complex error function

This work proposes a new method for obtaining the differential equation of the Voigt function and, from this equation, expressing the Voigt function as dependent upon the complex error function. In addition, the integral expression of the successive derivatives of the Voigt function is given, and from this a method is generalized which permits the representation, also, of other functions depending on the complex error function. This enables us to simplify other functions which are the convolution of a Gaussian function with rational polynomial functions. Moreover, the relationship between the Lorentzian (w_L), Gaussian (w_G) and Voigt (w_V) widths at half maximum for the function is given, which is of great interest in diverse branches of physics, such as plasma spectroscopy, astrophysics, nuclear magnetic resonance, etc.     

Mixed polarization in determining the film thickness of a silicon sphere by spectroscopic ellipsometry

The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed, and a method to eliminate this effect is proposed. Based on the simulation result of the SE measurement on a silicon sphere by ray tracking, we find that the sphere makes the parallel incident beam of the SE be divergent after reflection, and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory. By settling an aperture in front of the detector of the SE, we can almost eliminate the error. For the silicon sphere with a diameter of 94 mm used in the Avogadro project, the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method. The principle of the method and the results of the experimental verification are presented.     

Applications of the Poincaré sphere in polarization metrology

The Poincaré sphere representation of polarization states is used to derive two auxiliary equations for phase retardance measurements. These equations, in addition to another two previously derived equations, allow for extending the range of validity of a model for calibrating phase plates in pairs. In another application, the sphere is used to explain a new method for identifying the principal axes of two birefringent phase plates during their calibration.     

Mixed polarization in determining the film thickness of a silicon sphere by spectroscopic ellipsometry

The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed,and a method to eliminate this effect is proposed.Based on the simulation result of the SE measurement on a silicon sphere by ray tracking,we find that the sphere makes the parallel incident beam of the SE be divergent after reflection,and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory.By settling an aperture in front of the detector of the SE,we can almost eliminate the error.For the silicon sphere with a diameter of 94 mm used in the Avogadro project,the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method.The principle of the method and the results of the experimental verification are presented.     

An extension of a characterization of the automorphisms of Hilbert space effect algebras

The aim of this paper is to show that if an order preserving bijective transformation of the Hilbert space effect algebra also preserves the probability with respect to a fixed pair of mixed states, then it is an ortho-order automorphism. A similar result for the orthomodular lattice of all sharp effects (i.e., projections) is also presented.     

超短脉冲贝塞尔-高斯光束在自由空间的传输特性

 使用复解析信号法研究了束宽与频率无关的超短脉冲贝塞尔-高斯光束在自由空间的传输特性。研究表明：在无衍射长度内,超短脉冲贝塞尔-高斯光束的横向光强分布几乎不变并集中在传输轴附近,轴上脉冲随传输距离增加而展宽。在无衍射长度外,横向光强分布显著扩展。随传输距离增加,轴上光谱蓝移先增加,达到极大值后逐渐减小,最后在远场趋于一渐近值。对单周期的超短脉冲贝塞尔-高斯光束的轴上光谱蓝移先增加,达到极大值0.50 fs^-1。然后逐渐减小,在远场蓝移趋于渐近值0.16 fs^-1。     

一种空间超紫外望远镜在轨指向标定方法

介绍了一种不同波段的超紫外望远镜在轨指向的标定方法。此方法利用四个波段(13.0,17.1,19.5,30.4nm)的超紫外望远镜均有较高的光谱响应和能够对较强的太阳辐射光谱成像的特点,根据由不同的望远镜所获得的太阳的四个图像的变化,计算出了四个望远镜间的指向偏差。根据四个不同波段的超紫外望远镜的光学性能和太阳紫外辐射谱线的亮度优化出了具体的太阳辐射谱线,并对所选用的标定谱线的可行性进行了分析。该方法的在轨标定精度为0.1″。