Matrix perturbation theory for driven three‐level systems with damping

We investigate the dynamics of the Λ system driven by two resonant laser fields in presence of dissipation for coupling strengths where the rotating‐wave approximation starts to break down. This regime is characterised by Rabi frequencies being approximately equal or smaller than the field frequencies. A systematic procedure to obtain an expansion for the solution of the Bloch evolution equations of the system is presented. The lowest contribution results to be the well‐known rotating‐wave approximation. The method is based on a semi‐classical treatment of the problem, and its predictions are interpreted fully quantum mechanically. The theory is illustrated by a detailed study of the disappearance of coherent population trapping as the intensities of the fields increase.     

Dirac Optical Potential of p-^14Be and Pronounced “Long-Tail” Shape

The Dirac optical potential for p-^14 Be elastic scattering is evaluated by the relativistic impulse approximation. Each of the real part and the imaginary part of the potential shows a pronounced “long tail” for the proton elastic scattering from halo nucleus ^14Be compared with the potentials for proton scattering from its adjacent nuclei ^12C and ^16O, which do not have halo structures.This kind of “long tail” phenomenon suggests another signature for halo nuclei.     

Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application

Different versions of the Darboux–Weinstein theorem guarantee the existence of action–angle-type variables and the harmonic-oscillator variables in a neighborhood of isotropic tori in the phase space. The procedure for constructing these variables is reduced to solving a rather complicated system of partial differential equations. We show that this system can be integrated in quadratures, which permits reducing the problem of constructing these variables to solving a system of quadratic equations. We discuss several applications of this purely geometric fact in problems of classical and quantum mechanics.     

Skew-Hermitian Triangular Splitting Iteration Methods for Non-Hermitian Positive Definite Linear Systems of Strong Skew-Hermitian Parts

By further generalizing the skew-symmetric triangular splitting iteration method studied by Krukier, Chikina and Belokon (Applied Numerical Mathematics, 41 (2002), pp. 89–105), in this paper, we present a new iteration scheme, called the modified skew-Hermitian triangular splitting iteration method, for solving the strongly non-Hermitian systems of linear equations with positive definite coefficient matrices. We discuss the convergence property and the optimal parameters of this new method in depth. Moreover, when it is applied to precondition the Krylov subspace methods like GMRES, the preconditioning property of the modified skew-Hermitian triangular splitting iteration is analyzed in detail. Numerical results show that, as both solver and preconditioner, the modified skew-Hermitian triangular splitting iteration method is very effective for solving large sparse positive definite systems of linear equations of strong skew-Hermitian parts.     

具有开发的非自治单种群生态系统研究

研究了具有开发的单种群非自治周期系统．利用非自治微分方程理论．以及变分法理论和泛函极值的Euler方程方法,得到了该开发系统的持续生存性．周期解存在性，全局渐近稳定性．研究了在开发情况下的最大收获量问题，以及取得最大经济效益下的收获问题等．     

Equilibrium in Queueing Systems with Complementary Products

We study a model of a queueing system with two complementary products/services. In our model, there is one M/M/1 system and another facility that provides instantaneous service. The two services are complementary and the customer has no benefit from obtaining just one of them. We investigate the model under various price structures and ownership assumptions.AMS subject classification: 90B22, 91A10The authors are equal in their contribution to this paper. This paper is submitted by the first author to the Tokyo Institute of Technology as partial fulfillment of the requirements for the Ph.D. program in the Department of Value and Decision Sciences, and the order of names was chosen in compliance with program conditions. This research was supported by the Israel Science Foundation (grant No. 237/02).     

T 1 theorem for Besov spaces on nonhomogeneous spaces

Suppose μ is a Radon measure on ℝ ^d , which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀>0 such that for all x∈supp(μ) and r>0, μ(B(x, r))⪯C₀rⁿ, where 0<n⪯d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa’s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

The semi‐iterative method applied to the hyper‐power iteration

The semi‐iterative method (SIM) is applied to the hyper‐power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi‐iterative–hyper‐power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd.     

Generalized lattice model of liquid state and its relation to Ginzburg–Landau theory

Basic principles of the generalized lattice model of multicomponent condensed systems are formulated. Short-range parts of interatomic interactions are taken into account by means of the geometric constraints method. Long-range parts of the interactions are taken into account in mean field approximation. The expression for Helmholtz free energy is obtained. A system of integral equations for the equilibrium distributions of components is derived. The asymptotic properties of its solutions are investigated. Moment expansion of interatomic interactions and localization of integral terms in free energy is obtained. A Ginzburg–Landau-like functional of free energy is derived.     

LocalH-theorem for a kinetic variational theory

A localH-theorem is derived for a recently proposed extension of Enskog kinetic theory to a dense model fluid composed of particles with interactions extending beyond a hard core.On leave from: Katedra Fizyki, Uniwersytetu Szczecinskiego, 70-451 Szczecin, Poland.