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。     

改进型LOG算子在偏振片绝对角度中的应用

光学成像系统自身通常都具有一定的偏振效应,严重影响仪器偏振测量精度,而提高仪器中偏振片绝对角度精度能提高偏振定标精度,对校正光学系统自身的偏振特性具有重要的意义。对偏振片直线透光轴Raw图像高精度边缘定位和直线检测是偏振片绝对角度计算的关键步骤。针对传统LOG算子各向同性及虚假边缘与边缘定位精度相矛盾的缺陷,提出改进型一阶导阈值旋转式椭圆对称LOG算子。该算子不仅保留了经典LOG算子的优点,还具有对不同角度的边缘更加有效地进行检测,在保持边缘定位精度下,减少虚假边缘的特点。在处理得到的边缘二值图像上,进行直线检测求出偏振片绝对角度,通过对比分析最小二乘法线性拟合和霍夫变换的直线检测效果,得出霍夫变换能精确计算出偏振片绝对角度。实验证明改进型LOG算子与霍夫变换相结合提高了偏振片绝对角度测量精度,对偏振定标精度具有很大的提高。     

特征线坐标系下柱对称超音速流膨胀波计算方法研究

在静压圆盘止推气体轴承柱对称超音速流膨胀波系的计算中,借鉴Liepmann的特征线坐标系与自然坐标系变换理论和Liepmann引入两个黎曼不变量的方法,使得边界条件的处理更为直观和简便。采用特征线坐标系下的特征线法,推导计算该膨胀波系所用到的基本计算公式,将其应用于 P-M 流动并与 P-M 流动理论解进行比较。结果表明,数值计算结果与P-M流动理论解吻合,该计算方法可行。     

La–Mg–Ni ternary hydrogen storage alloys with Ce2Ni7-type and Gd2Co7-type structure as negative electrodes for Ni/Mh batteries

Hydrogen strorage alloys with formula La_1.5Mg_0.5Ni₇ were prepared by induction melting followed by different annealing treatments (1073, 1123 and 1173 K) for 24 h. The alloy composition, alloy microstructure and electrochemical properties were investigated, respectively. The results showed that the multi-phase structure of as-cast alloy was converted into a double-phase structure (Gd₂Co₇-type phase and Ce₂Ni₇-type phase) through annealing treatments. Mg atoms were mainly located in Laves unit of Gd₂Co₇-type unit cell and Ce₂Ni₇-type unit cell. The electrochemical capacity of alloy electrodes after annealing treatment could be up to 390 mAh/g. The cyclic stability of alloy electrodes was significantly improved by annealing treatments; After 150 charge/discharge cycles, the capacity retention ratio of alloy annealed at 1173 K was the highest (81.9%). The high rate dischargeability of alloy electrodes was also improved due to annealing treatment.