共轴均匀带电薄圆盘间的相互作用力

本文利用静电场的高斯定律和环路定律巧妙地求出了均匀带电圆盘在空间任一点所产生的电场 ,进而计算出了共轴均匀带电薄圆盘之间的相互作用力     

Symmetry specified enumeration of substituted derivatives: an easy solution to the complex problem

Several sophisticated methods to solution of symmetry specified enumeration problems are available in the modern literature. In this paper we propose a simple technique that allows one to manually compute the exact numbers of fixed-symmetry derivatives for a given structure either with inclusion or ignoring the substitution patterns. The basic idea of the method suggested consists in the derivation of Pólya-like cycle indices for the automorphism groups of specially constructed orbit partition graphs; the expansion of these indices and subsequent simple calculations result in the desired numbers of substituted derivatives with achiral substituents. Limitations of the new technique (and a method suggested earlier) depend on the relevance of the orbit partitions for particular subgroups of the point symmetry group. For illustration purposes, the results obtained for the prismane (D _3h ) and adamantane (T _d ) structures are discussed. In the former case the numbers of substituted derivatives can be found for all subgroups of the D _3h group, whereas in the latter case these numbers can be determined for eight out of eleven subgroups of the T _d point symmetry group. This work is based on the text of the lecture presented by the authors at the 5th All-Russia Conference on Molecular Modeling (Moscow, April 2007). The paper deals with the methodology and detailed treatment of applied aspects related to solution of enumeration problems for substituted derivatives with prescribed symmetry groups. Unlike the known methods of symmetry specified enumeration, the technique suggested is simple enough and may be regarded as generalization of the Pólya methodology, which is widely used by chemists. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 227–245, February, 2008.     

非保守力和非完整约束对Hamilton系统Lie对称性的影响

研究非保守力和非完整约束对Hamilton系统的Lie对称性和守恒量的影响.分别研究了Hamilt on系统受到非保守力和非完整约束作用时，系统的Lie对称性保持不变的条件，同时给出了 系统的结构方程和守恒量保持不变的条件.以著名的Emden方程和Appell-Hamel模型为例进行 了分析讨论. 关键词： 分析力学 Hamilton系统 非保守力 非完整约束 对称性 守恒量     

Four‐dimensional couplings among BF and matter theories from BRST cohomology

The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a “free” model that describes a generic matter theory and an abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.     

A Reality Proof in PT-Symmetric Quantum Mechanics

We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral equivalences inspired by the correspondence are also discussed.     

Isospin symmetry violation, meson production and η-nucleus interaction studies

We have studied isospin symmetry violation in nuclear reactions by measuring simultaneously the cross-section of the following two reactionsp +d →³H π⁺ andp +d →³He π⁰. The experiment was perfomed at the cooler synchrotron accelerator COSY, Jülich at several beam energies close to the correspondingη production threshold. We also have ongoing programmes onη-nucleus final-state interaction studies viap+⁶ Li →⁷ Be +η reactions, high resolution search for dibaryonic resonances and lambda-proton final state interaction studies. The experimental details and results obtained so far are presented here     

布里渊区内能带E(k)=E(-k)的对称性

说明了布里渊区内能带Ｅ（ｋ）＝Ｅ（－ｋ）的对称性是时间反演对称性的结果，而与晶体的空间对称性无关．并且证明了当晶体具有中心反演对称性时，布里渊区内能带是二重简并的．     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

Structure,Chirality, and Formation of Giant Icosahedral Fullerenes and Spherical Graphitic Onions

We describe the topology, structure, and stability of giant fullerenes exhibiting various symmetries (I, I _h , D _2h , T). Our results demonstrate that it is possible to create two new families of nested chiral icosahedral (I) fullerenes namely C₂₆₀@C₅₆₀@C₉₈₀@C₁₅₂₀@, ...,and C₁₄₀@C₃₈₀@C₇₄₀@C₁₂₂₀@ ..., which exhibit interlayer separations of ca. 3.4 Å. These chiral fullerenes are thought to possess metalliclike conduction properties. We discuss in detail the transformation of polyhedral graphitic particles into quasispherical nested giant fullerenes by reorganization of carbon atoms, which result in the formation of additional pentagonal and heptagonal carbon rings. These spherical structures are metastable and we believe they could be formed under extreme conditions, such as those produced by high-energy electron irradiation. There is circumstantial experimental evidence for the presence of heptagonal rings within these spherical fullerenes.