基于群论的晶格扰动介质纳米孔阵列多重Fano共振机理及演变

基于全介质超构材料独特的电磁属性,提出了一种晶格扰动介质纳米孔阵列超构表面来激发近红外区域的多重Fano共振.结合群论深入探究了该超构表面在其原胞为方形晶格构型与方形晶格对称性被破坏两情况下多重Fano共振的形成机理及演变规律.研究表明,在方形晶格超构表面中,外部辐射连续体分别与由正入射平面波直接激发的双重简并模式共振干涉形成双重Fano共振,且该共振与原胞中是否含孔及孔的形状无关,在晶格扰动超构表面中,原本不耦合的非简并模式由正入射平面波激发出来并与外部辐射连续体干涉形成Q值更高的三重Fano共振.进一步探讨了正入射平面波的xy极化方向对上述五重Fano共振的影响,结果表明,双重简并模式Fano共振偏振无关,三重非简并模式Fano共振偏振依赖.本文将为利用方形晶格构型的超构表面实现多重Fano共振的激发及演变提供有效的理论参考.     

关于具有给定Sylow子群正规化子的有限群Ⅱ

本文在有限可解群中解决了：任意ｍ－秩≤２的子群闭的局部群系具有性质：“如果群Ｇ的非单位Ｓｙｌｏｗ子群的正规化子属于，则群Ｇ也属于的一个充分必要条件．     

运动水平平板上混合对流的群论分析

本文用变换群理论对运动水平平板混合对流边界层流动的动量、能量和浓度扩散方程进行了分析，得到了与X4/(7-5n)成正比的壁面温度分布和浓度分布，同时壁面运动速度正比于X(3-n)／(7-5n)时存在相似性解．导出了相似性解方程，用四阶Runge－Kutta方法进行了计算，给出了Pr＝0．72　和Sc，K1，K2，K3参数下的速度、温度和浓度分布，得出了各参数对流场、温度场的影响。     

转动喇曼散射截面的群论计算

本文利用群链U(4)U(3)O(3)描述双原子分子N_2和O_2振转谱的对称性质,并利用群论方法计算了N_2和O_2分子转动喇曼散射的跃迁矩阵元,给出了它们的转动喇曼散射的截面。结果与实验较好地符合。     

可解群的若干充分条件

A subgroup if of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|, |K|) - 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. In this paper, some sufficient conditions for a group to be solvable are obtained in terms of s-semipermutability.     

Integrated Groups and Smooth Distribution Groups

In this paper, we prove directly that α-times integrated groups define algebra homomorphisms. We also give a theorem of equivalence between smooth distribution groups and α-times integrated groups.     

一些部分差集和相对差集的构造

In this paper, we give a construction of RDS in Galois ring by using some bent function, and obtain the equivalent relationship between RDS and a kind of bent function. At the same time, its existence is demonstrated.     

On Two Theorems of Finite Solvable Groups

For a finite group G, let T（G） denote a set of primes such that a prime p belongs to T（G） if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions： （1） G has a p-complement for each p∈T（G）; （2）│T（G）│= 2： （3） the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T（G）; then G either is solvable or G/Sol（G）≌PSL（2, 7） where Sol（G） is the largest solvable normal subgroup of G.     

无限的可解SD_2-群

在本文里我们首先证明了:每真子群都是循环群的无限可解群或者是拟循环 p-群 Z(p~∞)或者是无限循环群,然后我们研究了这种群的自然推广.我们把每真子群都可以由二元生成的群叫做 SD_2-群,我们证明了:每个无限的可解SD_2-群或者是拟循环 p-群 Z(p~∞)或者它本身也是二元生成的,并且我们给出了无限的可解 SD_2-群的相当完整的结构.     

THE COMPLETE LANGLANDS PARAMETERS CORRESPONDING TO THE REPRESENTATIONS OF THE CLASSICAL GROUPS WITH INTEGRAL REGULAR INFINITESIMAL CHARACTERS

1.CompleteLanglandsParametersandL-PacketsInthissectionwereviewsomebasicfactsfrom[1].Wedenotethesetsofrealnumbers,complexnumbersandintegersbyR,CandZ,respectively.SupposethatGisaconnectedcomplexreductivealgebraicgroup.WehaveanextendedgrouPGrforG,andvGrisanE-groupforGr.WedenotethesetofLanglandsparametersandthesetofgeometricparametersforvGrbYp(vG')andX(VG'),respectively.ThereisanaturalmapfromP(VG')toX(vG').ItinducesabijectionfromequivalenceclassesofLanglandsparameterstogeometricparamet…