Topological analysis of some special graphs. III. Regular polyhedra

A regular polyhedron is isomorphic to a cluster on which every face has same number of bonds and every atom has an equal number of coordinating atoms. A general strategy for generating the eigenvectors and the eigenvalues of regular polyhedra is given. Net sign analyses are also performed on the eigenvectors of regular polyhedra. The results provide us a quick way to grasp the topological feature of the electronic structure of clusters having interesting topology.     

On the inhomogeneous deformation of rubber-elastic polymers

Measurements in a gas dilatometer on carbon-black filled rubber cross-linked with sulfur show a large pressure drop in the specimen chamber, which to a large extent cannot be explained by a volume change of the specimen. The extension ratio at which the pressure starts to fall depends on the carbon-black content. Comparative measurements in a deformation calorimeter show that crystallisation always begins first at higher strains. It is assumed that the investigated specimens are inhomogeneously deformed even at small strains, depending on the carbon-black content, and that internal voids are formed, onto the surfaces of which gas molecules are deposited. This gas adsorption causes the pressure drop measured in the dilatometer; it is dependent on the nature of the gas. Argon shows no interaction with internal surfaces in the specimen; for measurements in an argon atmosphere, volume increases and strain-induced crystallisation can be properly determined. It is presumed that strain-induced crystallisation sets in earlier for specimens with larger carbonblack content, corresponding to the more inhomogeneous character of the deformation.Dedicated to Prof. Dr. R. Bonart on the occasion of his 60th birthday     

与双调和方程相关的连续模和Heinz-Schwarz型不等式

对于给定的两个正整数n ≥ 2和m ≥ 1，假设函数f满足如下条件：（1）在Bⁿ内满足非齐次双调和方程△（△f）=g（g ∈ C（Bⁿ，R^m））；（2）在S^n-1上满足f=ψ₁（ψ₁ ∈ C（S^n-1，R^m）），以及∂f/∂n=ψ₂（ψ₂ ∈ C（S^n-1，R^m）），其中∂/∂n表示内法线方向导数，Bⁿ表示Rⁿ中的单位球以及S^n-1表示Bⁿ的边界.本文主要研究f的连续模和Heinz-Schwarz型不等式.     

Yang-Baxter algebra and generation of quantum integrable models

We discover an operator-deformed quantum algebra using the quantum Yang-Baxter equation with the trigonometric R-matrix. This novel Hopf algebra together with its q→1 limit seems the most general Yang-Baxter algebra underlying quantum integrable systems. We identify three different directions for applying this algebra in integrable systems depending on different sets of values of the deforming operators. Fixed values on the whole lattice yield subalgebras linked to standard quantum integrable models, and the associated Lax operators generate and classify them in a unified way. Variable values yield a new series of quantum integrable inhomogeneous models. Fixed but different values at different lattice sites can produce a novel class of integrable hybrid models including integrable matter-radiation models and quantum field models with defects, in particular, a new quantum integrable sine-Gordon model with defect. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 470–485, June, 2007.     

Resonant excitation of single-pulse nuclear spin echo in magnetically ordered media

An analytical expression for a single-pulse nuclear echo signal in magnetically ordered materials has been obtained taking into account inhomogeneous broadening of the spectroscopic transition and non-uniform distribution of the enhancement factor. The signal has been shown to result from superimposing the nuclear magnetic moment oscillations of the same amplitude and phase that arise upon termination of a radio-frequency pulse. The cause for the effective suppression of oscillations of nuclear magnetic moments in the initial phase of the free precession signal has been determined analytically. The single-pulse echo signal amplitude has been found as a function of the external variable magnetic field strength, the exciting pulse duration, the inhomogeneous NMR line broadening, and the distribution width of the enhancement factor. The results have been compared with experimental data observed in a Co₂MnSi ferromagnetic polycrystalline sample. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 387–394, May–June, 2009.     

Near-surface instability of composites weakly reinforced with short fibers

The paper is concerned with loss of stability near the free flat surface of a weakly short-fiber-reinforced composite material under compression along the fibers. Emphasis is on the effect of the mechanical and geometrical parameters of the composite and the distance between fibers and to the free surface on the critical strains. The piecewise-homogeneous medium model and the rigorous three-dimensional linearized theory of stability of deformable bodies are used __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 28–35, June 2008.     

Decomposition of variables and duality in non-Abelian models

We consider inhomogeneous current states in low-dimensional systems characterized by spatial separation of phase states with ordered spin and charge degrees of freedom. We show that near the self-duality point in the Ginzburg-Landau spinor model, the inhomogeneity degree of non-Abelian states is higher than that of states with an Abelian distribution of degrees of freedom. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 510–517, June, 2007.     

Spectral analysis of nonselfadjoint Schr(o)dinger problem with eigenparameter in the boundary condition

In this paper we consider the nonselfadjoint (dissipative) Schr(o)dinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator,and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schr(o)dinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schr(o)dinger boundary value problem are given.     

常系数线性非齐次微分方程的简单解法

简化了文[1]中结论的证明,得到了求n阶常系数非齐次线性微分方程一般解更方便的方法,以及几种特殊情形解的表达式.     

Distributions of transverse relaxation times for soft-solids measured in strongly inhomogeneous magnetic fields

The single-sided NMR-MOUSE sensor that operates in highly inhomogeneous magnetic fields is used to record a CPMG ¹H transverse relaxation decay by CPMG echo trains for a series of cross-linked natural rubber samples. Effective transverse relaxation rates 1/T_2,short and 1/T_2,long were determined by a bi-exponential fit. A linear dependence of transverse relaxation rates on cross-link density is observed for medium to large values of cross-link density. As an alternative to multi-exponential fits the possibility to analyze the dynamics of soft polymer network in terms of multi-exponential decays via the inverse Laplace transformation was studied. The transient regime and the effect of the T₁/T₂ ratio in inhomogeneous static and radiofrequency magnetic fields on the CPMG decays were studied numerically using a dedicated C++ program to simulate the temporal and spatial dependence of the CPMG response. A correction factor T₂/T_2,eff is derived as a function of the T₁/T₂ ratio from numerical simulations and compared with earlier results from two different well logging devices. High-resolution T₁–T₂ correlations maps are obtained by two-dimensional Laplace inversion of CPMG detected saturation recovery curves. The T₁–T₂ experimental correlations maps were corrected for the T₁/T₂ effect using the derived T₂/T_2,eff correction factor.