Inhomogeneous electron liquid due to encapsulated atoms in C60 compounds: dynamic polarisability induced in the outer C60 shell

The work of Amusia and Baltenkov (Phys. Lett. A 360, 294, (2006)) on the possibility of considering the fullerene shell C₆₀ as a conducting sphere is briefly reviewed.     

Fingerprints of antiaromaticity in the negative ion (Li3Al4)− via an ab initio quantum-chemical study of the equilibrium structure of the inhomogeneous electron liquid

Fingerprints of antiaromaticity in the negative ion (Li₃Al₄)^?, this species being realisable via a laser vaporisation technique, are revealed by means of an ab initio quantum-chemical investigation. First, the ground-state equilibrium geometry of this ion is predicted. Also, for the corresponding inhomogeneous electron liquid, the characteristics of the HOMO are studied, both for the square and the rectangular Al₄ geometry in two low-lying isomers of the negative ion. There is no particular sensitivity to the change in geometry of the Al₄ configuration. Therefore, we have calculated theoretically nucleus-independent chemical shifts (NICS), which contain remarkable fingerprints of antiaromaticity. As to future directions, some comments are added in relation to the Shannon entropy.     

Oscillatory hyper-Hilbert transform along curves on modulation spaces

We consider the boundedness of the n-dimension oscillatory hyper-Hilbert transform along homogeneous curves on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces. The main theorems signicantly improve some known results.     

径向非均匀压电介质中圆孔对SH波的散射

利用复变函数理论对SH波作用下含圆孔径向非均匀压电介质的反平面动力特性进行了研究。压电介质的密度沿径向按幂函数形式变化,但压电参数、弹性参数、介电参数均为常数。利用变量替换法将非均匀压电介质的变系数波动方程组转化为标准的Helmholtz方程组,得到了满足边界条件的波函数解析表达式。通过数值算例分析了入射角度、入射波频率、幂次等对应力集中系数和电场强度集中系数的影响,并与已有文献进行比较。结果表明,某些参数组合下,动应力集中系数与电场强度集中系数均随幂次增大而增大。     

Rainbow Scattering by an Inhomogeneous Cylinder with an Off-Axis Gaussian Beam Incidence at Normal

The problem of an off-axis Gaussian beam incident perpendicular on an infinitely long multi-layered cylinder is investigated. The efficient and accurate recursive algorithm for computing the scattering field is discussed. The stability of the numerical scheme allows us to extend the feasible range of computations, both in size parameter and in number of layers for a given size. Particular attention is paid to rainbow scattering of homogeneous and inhomogeneous fibers.     

随机结构系统的一般实矩阵特征值问题的概率分析

由于工程实际结构的复杂性和所用材料在统计上的离散性以及测量、加工、制造误差的存在，必然导致具有随机参数的随机结构振动系统，按结构参数的性质来划分，随机振动问题包括两方面内容：(1)确定结构问题；(2)随机结构问题。本文以现代数学理论为依托，研究了随机结构系统的一般实矩阵的特征值问题。根据Kronecker代数、向量值和矩阵值函数的灵敏度分析、一般二阶矩法和概率摄动技术给出了计算随机结构系统的一般实矩阵的特征值和特征向量的数值方法，可以有效地得出随机结构系统的一般实矩阵的特征向量的统计量，发展了2D矩阵值函数的随机结构系统的特征值问题概率分析理论。     

Classification of polymer structures by graph theory

Compact polymers such as proteins obtain their unique conformation by appropriate nonbonded interactions among their monomer residues. Innumerable nonnative compact conformations are also possible, and it is essential to distinguish the native from the nonnative conformations. Toward this goal we have used graph‐theoretic methods to classify polymer structures formed by noncovalent interactions. All compact structures on a 4×4 two‐dimensional lattice and a few conformations on 3×3×3 cubic lattice have been investigated. The 69 compact conformations in 4×4 two‐dimensional lattice are classified into 12 groups based on the highest eigenvalue and eigenvector. The complex graphs obtained for polymers in a 3×3×3 lattice space are analyzed. Their eigenvalues and eigenvector components are correlated with the branching structure and the center of the graph. The method has application in classifying real polymers such as proteins into their substructures, cluster, and domains. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 349–356, 1999     

A General Framework for Localization of Classical Waves: I. Inhomogeneous Media and Defect Eigenmodes

We introduce a general framework for studying the localization of classical waves in inhomogeneous media, which encompasses acoustic waves with position dependent compressibility and mass density, elastic waves with position dependent Lamé moduli and mass density, and electromagnetic waves with position dependent magnetic permeability and dielectric constant. We also allow for anisotropy. We develop mathematical methods to study wave localization in inhomogeneous media. We show localization for local perturbations (defects) of media with a spectral gap, and study midgap eigenmodes.     

Density Profiles in a Classical Coulomb Fluid Near a Dielectric Wall. II. Weak-Coupling Systematic Expansions

In the framework of the grand-canonical ensemble of statistical mechanics, we give an exact diagrammatic representation of the density profiles in a classical multicomponent plasma near a dielectric wall. By a reorganization of Mayer diagrams for the fugacity expansions of the densities, we exhibit how the long-range of both the self-energy and pair interaction are exponentially screened at large distances from the wall. However, the self-energy due to Coulomb interaction with images still diverges in the vicinity of the dielectric wall and the variation of the density is drastically different at short or large distances from the wall. This variation is involved in the inhomogeneous Debye–Hückel equation obeyed by the screened pair potential. Then the main difficulty lies in the determination of the latter potential at every distance. We solve this problem by devising a systematic expansion with respect to the ratio of the fundamental length scales involved in the two coulombic effects at stake. (The application of this method to a plasma confined between two ideally conducting plates and to a quantum plasma will be presented elsewhere). As a result we derive the exact analytical perturbative expressions for the density profiles up to first order in the coupling between charges. The mean-field approach displayed in Paper I is then justified.     

Using Laplacian Eigenvalues and Eigenvectors in the Analysis of Frequency Assignment Problems

A Frequency Assignment Problem (FAP) is the problem that arises when frequencies have to be assigned to a given set of transmitters so that spectrum is used efficiently and the interference between the transmitters is minimal. In this paper we see the frequency assignment problem as a generalised graph colouring problem, where transmitters are presented by vertices and interaction between two transmitters by a weighted edge. We generalise some properties of Laplacian matrices that hold for simple graphs. We investigate the use of Laplacian eigenvalues and eigenvectors as tools in the analysis of properties of a FAP and its generalised chromatic number (the so-called span).