Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous magnetic moment

We show that the point spectrum of the standard Coulomb-Dirac operator H₀ is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment H_a as the anomaly parameter tends to 0. For negative angular momentum quantum number κ, this holds for all Coulomb coupling constants c for which H₀ has a distinguished self-adjoint realisation. For positive κ, however, there are some exceptional values for c, and in general an index shift between the eigenvalues of H₀ and the limits of eigenvalues of H_a appears, accompanied with additional oscillations of the eigenfunctions of H_a very close to the origin.     

ROBUSTNESS OF AN UPWIND FINITE DIFFERENCE SCHEME FOR SEMILINEAR CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY TURNING POINTS

We consider a singularly perturbed semilinear convection-diffusion problem with a boundary layer of attractive turning-point type. It is shown that its solution can be decomposed into a regular solution component and a layer component. This decomposi-tion is used to analyse the convergence of an upwinded finite difference scheme on Shishkin meshes.     

Three Types of Expression in Dark-Soliton Perturbation Theory Based on Squared Jost Solutions

Three types of expression in the dark-soliton perturbation theory based on squared Jost solutions are invesgigaged in ghis paper. It is shown that there are three formally different results about the effects of perturbagion on a dark soliton, and it is proved by means of a transformation between two integral variables that they are essentially equivalent.     

New results for virial coefficients of hard spheres inD dimensions

We present new results for the virial coefficientsB _k for κ<- 10 for hard spheres in dimensionsD = 2,..., 8.     

Eigenvalues of the antiplane-shear crack problem for a power-law material

This paper discusses the problem of finding the eigenvalue spectrum in determining the stress and strain fields at the tip of an antiplane-shear crack in a power-law material. It is shown that the perturbation method provides an analytical dependence of the eigenvalue on the material nonlinearity parameter and the eigenvalue of the linear problem. Thus, it is possible to find the entire spectrum of eigenvalues and not only the eigenvalue of the Hutchinson-Rice-Rosengren problem. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 173–180, January–February, 2008.     

ON OPTIMAL BACKWARD PERTURBATION ANALYSIS FOR THE LINEAR SYSTEM WITH BLOCK CYCLIC COEFFICIENT MATRIX

Based on the block style spectral decomposition, this paper deals with the optimal backward perturbation analysis for the linear system with block cyclic coefficient matrix.     

Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters

We study a model linear convection-diffusion-reaction problem where both the diffusion term and the convection term are multiplied by small parameters ε_d and ε_c, respectively. Depending on the size of the parameters the solution of the problem may exhibit exponential layers at both end points of the domain. Sharp bounds for the derivatives of the solution are derived using a barrier-function technique. These bounds are applied in the analysis of a simple upwind-difference scheme on Shishkin meshes. This method is established to be almost first-order convergent, independently of the parameters ε_d and ε_c.     

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators. This revised version was published online in June 2006 with corrections to the Cover Date.     

Higher-order radiative perturbation theory

As a computationally effective tool, the first-order term of the radiative perturbation theory has been computed successfully, and has been applied in a number of areas. In this article, we develop the computational expressions for the higher-order terms of the perturbation expansion in a plane parallel atmosphere. These expressions are then implemented, and numerical results for some typical cases are presented. These results indicate that the computation is successful and that the higher-order terms are essential in cases where the first-order term alone cannot predict the perturbation with sufficient accuracy.     

Predicting vibration signals of automobile engine using chaos theory

Condition monitoring and life prediction of the vehicle engine is an important and urgent problem during the vehicle development process. The vibration signals that are closely associated with the engine running condition and its development trend are complex and nonlinear. The chaos theory is used to treat the nonlinear dynamical system recently. A novel chaos method in conjunction with SVD (singular value decomposition)denoising skill are used to predict the vibration time series. Two types of time series and their prediction errors are provided to illustrate the practical utility of the method.