Analysis of S-SEED''s characteristics in optical switch

This article introduces the basic structure of a symmetric self-electrooptic effect device （S-SEED）, and applies the Kirchoff＇ s current law and a purely equivalent capacitive model, to analyze S-SEED＇s switch characteristics. Linear approximation and N-segment approximation are utilized to obtain S-SEED＇s voltage-time （V-T） and characteristics. Theoretical analysis is verified by simulations, and the results demonstrate that the precision of S-SEED＇s switch time can satisfy the requirement in applications with linear approximation. Moreover, the simulations compare S-SEED＇s switch characteristics with different input powers and input contrast ratios, which reveal that increasing input contrast ratio is an effective way to improve S-SEED＇s switch characteristics.     

STM tunneling spectroscopy on high Tc superconductors

STM tunneling spectroscopy has been performed on the bulk single crystals of BiSrCaCuO (BSCCO) and the epitaxial thin films of YBaCuO (YBCO) at cryogenic temperatures. The STM images and tunneling spectra observed on the (001) surfaces can be classified into three cases; 1) Atomic image is visible. However, the tunneling spectrum shows semiconducting or smeared superconducting gap structures, depending on the tip-sample distance. 2) Clear atomic image can not be obtained. But, the tunneling spectrum shows flat bottom region with quite low zero bias conductance. 3) Tunneling spectra demonstrate gapless behavior, independent of the tip-sample separation. These observations support the quasi-2D electronic picture in whichs-wave like 2D superconducting layers are coupled with each other through the Josephson effect.     

最大重迭对称性分子轨道和分子几何参数计算

建立了AMl级别的最大重迭对称性分子轨道计算方案(MOSMO)。采用通常的半经验分子轨道方法AMl级别中完全相同的参数，计算了各种分子的几何参数等。所得计算结果与实验值及HF／6-31G*从头算方法计算结果相符，说明提出的计算方案是可行的。同时，由于提出的计算方案过程简单，更易推广使用到从头算方法难以解决的大分子体系和超分子体系的结构和性质研究。     

Electronic Kaleidoscopes for the Mind

The goal ofthis article is to present an informal introduction and tutorial on aestheticallypleasing kaleidoscopic images. The article is intended for the non-mathematical reader interested in computer art. Simple generating formulas and recipes are included.     

新型Ag_mCu_nHgI_4可逆热致变色颜料的研究

将Cu(NO3 ) 2 和AgNO3 溶液以不同比例同时加入K2 HgI4水溶液中合成了系列AgmCunHgI4(m +n =2 )可逆热致变色颜料。研究发现 :随着Ag和Cu比例的改变 ,颜料变色温度呈现出一定的变化规律 ;当m和n的比例接近 1∶1时 ,变色温度达到最低 35℃ ;降低环境温度 ,可以缩短产品的复色时间 ;差示扫描量热分析 (DSC)图谱中颜料的相变温度与目测变色温度表现出相同的规律性。在分析AgmCunHgI4颜料变色机理的基础上 ,结合晶体微观结构 ,推测得出晶体的微观对称性越低 ,颜料的变色温度越低的结论     

FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

Detecting symmetries of rational plane and space curves

This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space curves, our method finds the involutions in all cases, and all the rotation symmetries in the particular case of Pythagorean-hodograph curves. Our algorithms solve these problems without converting to implicit form. Instead, we make use of a relationship between two proper parametrizations of the same curve, which leads to algorithms that involve only univariate polynomials. These algorithms have been implemented and tested in the Sage system.     

Analysis of heregulin symmetry by weighted evolutionary tracing

Heregulins are members of the protein family of EGF-like growthand differentiation factors. The primary cell-surface targetsof heregulins are heterodimers of the EGF-receptor homolog HER2with either HER3 or HER4. We used a weighted evolutionary traceanalysis to identify structural features that distinguish theEGF-like domain (hrg) of heregulins from other members of theEGF family. In this analysis, each amino acid sequence is weightedaccording to its uniqueness and the variability in each positionis assigned by an amino acid substitution matrix. Conservedresidues in heregulin that are variable in other EGF-like domainsare considered possible specificity-conferring residues. Thisanalysis identifies two clusters of residues at the foot ofthe boot-shaped hrg domain. The residues in one cluster arerecruited from the N-terminus; those in the other are from the-loop region and show a weak sequence similarity to the N-terminalresidues at the opposite side of the boot. The remaining residueswith high conservation scores distribute themselves into thesetwo distinct surfaces on hrg. This pseudo-twofold symmetry andthe presence of two distinct interfaces may reflect the preferenceof hrg for heterodimeric versus homodimeric HER complexes.     

M序列的对称性变换及对称群

n级M序列是由n级非线性回馈移位寄存器产生的周期为2n的二元序列,也称为de Bruijn序列。该文将讨论M序列的对称性变换,提出了一类新的对称性变换——"与/或"逻辑对称性变换,并研究了基于对称性变换的对称群。     

框架的行置换和列置换——处理复杂系统的新思维系列之四

本系列论文基于《多边矩阵理论》,由东方整体性思维所启迪,试图提供并完善一套从整体到局部处理复杂系统多指标问题、非均匀性问题、非线性问题的强有力的数学工具,并对其进行严格的理论推导和证明。本文利用群论的相关概念和结论,将其和框架的剖分运算相结合,引入了导出框架和对称框架的定义,证明了框架的行置换等价于列置换的结论,从而以后可以统一地处理指标间的置换问题。