Lie point symmetry algebras and finite transformation groups of the general Broer--Kaup system

Using a new symmetry group theory, the transformation groups and symmetries of the general Broer--Kaup system are obtained. The results are much simpler than those obtained via the standard approaches.     

Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation

In this paper, the Lie symmetry algebra of the coupled Kadomtsev--Petviashvili (cKP) equation is obtained by the classical Lie group method and this algebra is shown to have a Kac--Moody--Virasoro loop algebra structure. Then the general symmetry groups of the cKP equation is also obtained by the symmetry group direct method which is proposed by Lou et al。 From the general symmetry groups, the Lie symmetry group can be recovered and a group of discrete transformations can be derived simultaneously. Lastly, from a known simple solution of the cKP equation, we can easily obtain two new solutions by the general symmetry groups.     

A ‘tree’ for generation and identification of the colour symmetry point groups

A flow chart (inverted ‘tree’) for generating and identifying the 58 magnetic and 18 polychromatic point groups using a classification for the 32 generating crystallographic point groups is suggested. The idea of colour generator is explored for generating the colour symmetry point groups. The advantages in presenting the identification of colour groups through a tree are discussed.     

点群乘法表和对称操作规定间的关系

导出了C3v群在不同对称操作规定下的两个乘法表,说明点群的乘法表在不同规定下有不同形式;并以C3v群为例给出Cnv群中Cnm操作与Cnn-m操作共轭的一个直观的解释.     

Surface harmonics for pentagonal point groups

Surface harmonics for the seven pentagonal point groups 5(C₅), {ie859-1}(S₁₀), {ie859-2}(C_5h ), {ie859-3}m2(D_5h ), {ie859-4} 2(D₅), 5m(C_5v ) and 5 2m(D_5d ) that represent the symmetries of quasicrystals in two and three dimensions are obtained, employing the projection operator method [11] and the simplified (authors) method. The results obtained are tabulated and are briefly discussed.     

Broken relativistic symmetry groups,toroidal moments and superconductivity in magnetoelectric crystals

Summary A connection between the creation of toroidal moments and the breaking of the relativistic crystalline group associated to a given crystal is presented in this paper. Indeed, if magnetoelectric effects exist, the interaction between electrons and elementary magnetic cells appears in such a way that the resulting local polarization and magnetization break the local relativistic crystalline symmetry. Therefore, a Goldstone boson responsible for the production of toroidal moments is created and, consequently toroidal phases arise in the crystal. The list of the Shubnikov groups compatible with this kind of phases is given and possible consequences in superconductor theory in magnetoelectric crystals are examined.     

晶格不具备五度及六度以上对称轴的双轴证明是正确的

指出晶格不具备五度及六度以上对称轴的双轴证明是正确的     

New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein--Maxwell theory with $p$ Abelian gauge fields (EM-$p$ theory, for short). Two EHC structural Riemann--Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-$p$ theory. This symmetry group is verified to have the structure of semidirect product of Kac--Moody group $\widehat{SU(p+1,1)}$ and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme. This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.     

碳纳米管中的群论及一系列新点群

在讨论了碳纳米管的几何结构的基础上，对齿型和椅型碳纳米管的对称性进行了分析并将这些对称元进行了抽象和总结.对齿型和椅型碳纳米管的对称元所属的群Dnh点群进行了讨论. 关键词： 点群 碳纳米管 几何结构 对称性     

Piezoelectricity in quasicrystals: A group-theoretical study

Group-theoretical methods have been accepted as exact and reliable tools in studying the physical properties of crystals and quasicrystalline materials. By group representation theory, the maximum number of non-vanishing and independent second-order piezoelectric coefficients required by the seven pentagonal and two icosahedral point groups — that describe the quasicrystal symmetry groups in two and three dimensions — is determined. The schemes of non-vanishing and independent second-order piezoelectric tensor components needed by the nine point groups with five-fold rotations are identified and tabulated employing a compact notation. The results of this group-theoretical study are briefly discussed.      

<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.     

From two mesons and (V-A) weak currents to the standard model of quark and lepton interactions

This retrospective paper traces the conceptual evolution of two theories in which the author was involved—the two-meson theory (with H A Bethe) in 1947 and the universal (V-A) theory of weak interactions (with E C G Sudarshan) in 1957—into the present-day standard model of particle interactions. Part 1 is entitled ‘From the pion to QCD and pseudo-Goldstone bosons” and Part 2 “From the muon and neutrino to QFD and chiral anomalies’. Adapted from two lectures delivered at the University of Rochester in October, 1987.     

Lower excited states of 7-azaindole dimer with a C2h(M) symmetry

The title subjects (in the vapor phase) were assessed to be in the weak-coupling limit as Frenkel-type excitons of a L_a-type excited state, by examining reported data on these systems: (1) L_b/L_a interconversion by dimerization (in the solution) just like what happens in the monomer by the change of solvent polarity, e.g., from 3-methylpentane to ethanol. (2) Good correspondence between the monophotonic excitation spectrum of the tautomer fluorescence (after excited-state double proton-transfer reaction of the dimer) and mass-selected (2 + 2) photoionization spectrum of the dimer, as is predicted theoretically. (3) Potential minima for locally excited configurations, as were predicted by ab initio calculations. Comments on the current controversy about the mechanism of its excited-state tautomerization, i.e., whether it is of one step or two steps, are made as well.