Interactions among special embed-solitons for the (3+1)-dimensional Burgers equation

With the help of a modified mapping method and a new mapping method, we re-study the (3+1)-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction.     

Local currents for the GL(N,C) self-dual Yang-Mills equation

By using a simple Bäcklund-like transformation which linearizes the GL(N, C) self-dual Yang-Mills equation, an infinite number of local conservation laws for this equation are constructed. In the SL(N, C) case, the currents become trivial, which explains why these currents are not found in SU(N) gauge theory.     

On the (3, N) Maurer-Cartan equation

Abstract

Deformations of the 3-differential of 3-differential graded algebras are controlled by the (3, N) Maurer-Cartan equation. We find explicit formulae for the coefficients appearing in that equation, introduce new geometric examples of N-differential graded algebras, and use these results to study N Lie algebroids.     

The microwave spectra of symmetric top polyacetylenes: 1,3,5-Heptatriyne,CH3(CC)3H and 1-cyano-2,4-pentadiyne,CH3(CC)2CN

The rotational spectra of 1,3,5-heptatriyne, CH₃(CC)₃H and 1-cyano-2,4-pentadiyne, CH₃(CC)₂CN have been studied in detail between 26.5 and 40.0 GHz. The molecules have long linear chains of heavy atoms and show characteristic C_3v symmetric top spectra consisting of groups of R-branch lines at regular intervals separated by approximately 2B₀. Six isotopic modifications of CH₃(CC)₂CN have been detected in natural abundance allowing r_s substitution structural data to be derived for this species. Long linear polyacetylenic chains are quite flexible and this dynamic property manifests itself in the appearance of extended sequences of complex vibrational satellites associated with the bending of the chain. The vibrational ground state spectra as well as several low frequency vibrational satellites have been analyzed yielding various vibration-rotation parameters. For CH₃(CC)₃H B₀ = 778.2445 ± 0.0007 and for CH₃(CC)₂CN B₀ = 778.040 ± 0.001 MHz.     

O(2)-symmetric bifurcation theory for convection rolls

The interaction of two steady state modes for the two-dimensional Benard problem with lateral periodic boundary conditions (p.b.c.) and free horizontal boundary conditions is considered. The p.b.c. generate an action of O(2) on the Navier-Stokes equations. The Boussinesq approximation induces an additional Z(2)-symmetry. The O(2) × Z(2) equivariant bifurcation equations are determined and two fifth order terms are identified. Two types of mixed mode solutions and a travelling wave solution are found. Using MACSYMA, the fifth order terms are calculated and the stability of the solutions to phase perturbations depending on the Prandtl number is determined.     

The Dbar-dressing method for the(2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation

In this work,the(2+1)-dimensional Date-Jimbo-Kashiwara-Miwa(DJKM)equation is studied by means of the(∂)-dressing method.A new(∂)problem has been constructed by analyzing the characteristic function and the Green's function of its Lax representation.Based on solving the(∂)equation and choosing the proper spectral transformation,the solution of the DJKM equation is constructed.Furthermore,the more general solution of the DJKM equation can be also obtained by ensuring the evolution of the time spectral data.     

The evans-vigier field,B (3): Derivation of the de Broglie matter-wave equation from the Hamilton-Jacobi equation

The emergence of the Evans-Vigier fieldB ⁽³⁾ of vacuum electromagnetism has been accompanied by a novel charge quantization condition inferred from 0(3) gauge theory. This finding is used to derive the de Broglie matter-wave equation from the classical Hamilton-Jacobi (HJ) equation of one electron in the electromagnetic field. The HJ equation is used with the charge quantization condition to show that, in a perfectly elastic photon-electron interaction, complete transfer of angular momentum occurs self-consistently, and the electron acquires the angular momentum of the photon. In this limit the electron travels infinitesimally near the speed of light, and its concomitant electromagnetic fields become indistinguishable from those of the uncharged photon. This result independently proves the validity of the charge quantization condition and demonstrates unequivocally the existence of the vacuum fieldB ⁽³⁾.     

Magneto-electrogyration in cubic Sr(NO3)2, Ba(NO3)2, and Pb(NO3)2

The simultaneous application of electric and magnetic fields on single crystals of Sr-, Ba-and Pb-dinitrate yields an additional term to the pure electrogyration and Faraday effect. The symmetric part of the fourth-rank tensor of this magneto-electrogyration has been completely determined with the aid of a high-resolution computer-aided polarimetric device. In Pb(NO₃)₂ a maximum magneto-electrogyration of about 10% of the magnitude of electrogyration is observed when a magnetic field of 1000 kA/m (1.2 Tesla) is applied along [111]. The effects in Sr(NO₃)₂ and Ba(NO₃)₂ are much smaller. Index of refraction, electrogyration, Faraday effect, and the new magneto-electrogyration obey the same sequence: Pb(NO₃)₂ > Ba(NO₃)₂ > Sr(NO₃)₂.     

The E(2)Sigma(+) --> C(2)Pi Transition of NO and Term Values for the A, D, E, and C Lowest Rydberg Levels

The E(2)Sigma(+) --> C(2)Pi Rydberg-Rydberg transition of (14)N(16)O near 8492 cm(-1) has been studied by Fourier transform spectrometry in the emission from a dc excited supersonic jet expansion and from a dc discharge under equilibrium conditions. The same transition has also been observed in laser-induced stimulated emission. Line wavenumbers of the 0-0, 1-1, and 2-2 bands, together with data for previously published near-infrared transitions, have been reduced to consistent sets of rovibronic term values for v = 0, 1, and 2 of the A(2)Sigma(+), D(2)Sigma(+), E(2)Sigma(+), and C(2)Pi states which frequently serve as intermediates in the multiphoton excitation of higher Rydberg levels of NO. Copyright 2000 Academic Press.     

一类简化Lang-Kobayashi方程的Hopf分岔及其稳定性

讨论了一类简化Lang-Kobayashi方程的Hopf 分岔的性质.根据分岔理论,给出了系统产生Hopf 分岔的临界时滞条件,然后利用中心流形定理和规范型理论得到了确定Hopf分岔方向和分岔周期解的稳定性计算公式.最后,用数值模拟对理论结果进行了验证. 关键词： Lang-Kobayashi方程 时滞 Hopf分岔 稳定性     

C20分子与C20(1-)、C20(2-)离子的特性分析与比较

应用密度范函理论（DTF）的B3LYP方法,在6-31G*基组水平上对CI对称C20富勒烯分子及 C20(1-)、C20(2-)离子进行了几何结构的全局优化、频率以及自然键轨道分析计算（NBO）,然后对三者的几何构型、稳定性、振动光谱等做了分析和比较。研究表明：离子的键长普遍比分子的键长长, C20(1-)离子的稳定性最高。 C20(2-)离子的红外峰值较大,C20(1-)离子的拉曼光谱峰值较大,振动光谱可以用来作为区分三者的手段。     

Interpretation of the ionization spectra of the cyanomethanes: CH3CN,CH2(CN)2 and C(CN)4

The valence ionization spectra of the mono-, di- and tetra-cyanomethane molecules are computed by Green function methods. As previously experienced on other cyano-derivatives of organic molecules, a hole-mixing effect is found. A partial reassignment of the spectrum is possible in the case of CH₂(CN)₂, whereas, due to the compactness of the spectrum and to the limitation of the basis set, an unambiguous assignment is not possible for C(CN)₄. The Koopmans ordering of the IP's is modified in two cases by the many-body perturbation.     

一个(3+1)维孤子方程的周期解

利用Hirota方法及Riemann theta函数得到了一个(3+1)维孤子方程的周期解.在极限情况下,该周期解退化为孤子解.另外,利用计算机技术和Mathematica绘制了解的三维曲面图.     

Electron impact ionization cross-section of C2, C3, Si2, Si3, SiC,SiC2 and Si2C

Total ionization cross-sections for C₂, C₃, Si₂, Si₃, SiC, SiC₂ and Si₂C molecules have been calculated by electron impact. Spherical complex optical potential formalism has been employed for obtaining the inelastic cross-sections for these molecules. Then by applying complex scattering potential-ionization contribution method, total ionization cross-sections are derived. These cross-sections are calculated in the energy range from ionization threshold to 2?keV. There are no measurements available in the literature to the best of our knowledge with which our results can be compared. The results show a linear relationship between maximum ionization cross-section and square root of the ratio of polarizability to ionization potential, depending on its atomicity. This gives a confirmation for the consistency of the data reported here. Present work is a maiden attempt to find electron impact ionization cross-section for these molecules, except for C₂ and C₃.