Tail asymptotics for the fundamental period in the MAP/G/1 queue

This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802–813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions. I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.     

Dark matter annihilation in the Galaxy

The awaited dark matter (DM) neutralino annihilation signal from the galactic halo crucially depends on the presence of small-scale clumps. A mass function of the DM small-scale clumps is calculated in the standard cosmological scenario. The final distribution of clumps in the Galaxy is influenced by their tidal destruction. The basic sources of clump destruction are (i) clumps of larger scales, (ii) the gravitational field of the galactic disk, (iii) the stars in the galactic bulge, and (iv) the stars in the galactic halo. The destruction of clumps due to their mutual tidal interactions is important at earl stages of hierarchical clustering and the galactic halo formation. The clumps surviving through the hierarchical clustering are continuously destroyed by interactions with the galactic disk and stars. It is shown that, among the Moon or Earth mass DM clumps surviving through the hierarchical clustering, only 20% will further survive near the Sun’s position mainly because of the tidal destruction by the galactic disk. This reduction of DM clump density significantly diminishes the expected DM annihilation signal from the galactic halo. The text was submitted by the authors in English.     

Control of the temperature hysteresis and diffuse dielectric anomaly in the temperature range of the ferroelectric-antiferroelectric phase transition in PbZr1 − x TixO3 (0.03 ≤ x ≤ 0.05) ceramics

The magnitudes of the temperature hysteresis and diffuse dielectric anomaly corresponding to the transition from the antiferroelectric phase to the ferroelectric phase in PbZr_{1 ? x} Ti_xO₃ (0.03 ≤ x ≤ 0.05) ceramics can be reversibly changed by varying the temperatures of heating and cooling in the course of thermocycling. The results obtained indicate that the antiferroelectric-ferroelectric transition in the PbZr_{1 ? x} Ti_xO₃ ceramics materials is a smeared first-order phase transition.     

Experimental and theoretical investigation into the effect of the electron velocity distribution on chaotic oscillations in an electron beam under virtual cathode formation conditions

The effect of the electron transverse and longitudinal velocity spread at the entrance to the interaction space on wide-band chaotic oscillations in intense multiple-velocity beams is studied theoretically and numerically under the conditions of formation of a virtual cathode. It is found that an increase in the electron velocity spread causes chaotization of virtual cathode oscillations. An insight into physical processes taking place in a virtual-cathode multiple-velocity beam is gained by numerical simulation. The chaotization of the oscillations is shown to be associated with additional electron structures, which were separated out by constructing charged particle distribution functions.     

Laser spectroscopy of high spin isomers – a review

This review summarizes the experimental data on charge radii differences among ground state and high spin isomeric states determined by high-resolution laser spectroscopic methods. A comparison is presented between radii changes obtained from the isomeric shifts in the atomic spectra and from the quadrupole moments of both ground and isomeric states under the assumption that the radii changes are determined by the difference of the quadrupole deformations. Special attention is paid to isomers arising from the break-up of nucleon pairs and isomers of odd–odd nuclei. The characteristic features of the radii changes for isomeric states of different origin are discussed.     

Noether analysis of zilch conservation laws and their generalization for the electromagnetic field. II. Use of poincaré-invariant formulation of the principle of least action

Uzhgorod Branch, Institute of Nuclear Research, Ukrainian SSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 80, No. 3, pp. 340–352, September, 1989.     

Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle-focus and Saddle Under Reversible Condition

In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-homoclinic orbits to the saddle and 2-homoclinic orbits to the saddle-focus is shown. And it is also proved that, corresponding to each 1-homoclinic （resp. 2-homoclinic） orbit F, there is a spiral segment such that the associated orbits starting from the segment are all reversible 1-periodic （resp. 2-periodic） and accumulate onto F. Moreover, each 2-homoclinic orbit may be also accumulated by a sequence of reversible 4-homoclinic orbits.     

Second order Runge–Kutta methods for Stratonovich stochastic differential equations

The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly. AMS subject classification (2000)  65C30, 65L06, 60H35, 60H10     

Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25     

A Partial Differential Inequality in Geological Models

Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation.This limiter happens to satisfy a stationary scalar hyperbolic inequality,within a constraint,for which the authors prove the existence and the uniqueness of the solution.Actually,this solution is shown to be the maximal element of a convenient convex set of functions.The existence proof is obtained thanks to the use of a numerical scheme.