Lattice gas state functions

State equations for simple lattice systems are constructed by extending the Gibbs method to a non-equilibrium system.In memory of D. N. Zubarev, teacher and scientist, whose advice and attention are gratefully remembered.The idea of constructing such a model (on the basis of the vacancy model of condensed matter proposed by the author) belongs to D. N. Zubarev.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 3, pp. 478–490, December, 1995.     

Annihilation of ultra low energy antiprotons

The p interaction at ultra low energies is considered taking into account the Coulomb interaction. It is shown that Coulomb effects dramatically modify the usual behaviour of the annihilation cross section. A possibility to extract the scattering length from experimental data is discussed.     

On a Lemma Arising in the Solution of Waring’s Problem

Siberian Mathematical Journal - We give a simple proof of one assertion used in solving Waring’s problem.     

Invariant functionals for random matrices

A new approach to the study of the Lyapunov exponents of random matrices is presented. It is proved that, under general assumptions, any family of nonnegative matrices possesses a continuous concave positively homogeneous invariant functional (“antinorm”) on ℝ₊^d. Moreover, the coefficient corresponding to an invariant antinorm equals the largest Lyapunov exponent. All conditions imposed on the matrices are shown to be essential. As a corollary, a sharp estimate for the asymptotics of the mathematical expectation for logarithms of norms of matrix products and of their spectral radii is derived. New upper and lower bounds for Lyapunov exponents are obtained. This leads to an algorithm for computing Lyapunov exponents. The proofs of the main results are outlined.     

Magnetometer Based on a Structure Consisting of High-Temperature Superconductor and Epitaxial Iron-Garnet Film

Technical Physics - A scheme for construction of a magnetometer based on periodic spatial modulation of magnetic flux density by a multielement HTS structure is proposed and physically...     

Spaces of Dyadic Distributions

Functional Analysis and Its Applications - This paper studies spaces of distributions on a dyadic half-line, which is the positive half-line equipped with bitwise binary addition and Lebesgue...     

Asymmetric decompositions of abelian groups

A subsetA of an Abelian groupG is said to be asymmetric ifg+S⊄A for any elementg∈G and any infinite symmetric subsetS⊂G (S=−S). The minimal cardinality of a decomposition of the groupG into asymmetric sets is denoted by ν(G). for any Abelian groupG, the cardinal number ν(G is expressed via the following cardinal invariants: the free rank, the 2-rank, and the cardinality of the group. In particular, . Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 10–19, July, 1999.     

Determination of the Coefficient of Laser Radiation Reflection from Dielectric Targets in Vacuum

We present the results of experimental determination of the coefficients of laser radiation reflection (₁ 10.6 m and ₂ 1.06 m) from dielectric targets of complex chemical composition in vacuum with allowance for a regime of developed plasma formation.     

Energy efficiency of femtosecond laser ablation of refractory metals

We present the results of an experimental study of the ablation energy thresholds and ablated mass for a number of refractory metals (Ti, Zr, Nb, Mo) by femtosecond (τ _0.5 = 45–70 fs) exposed to laser pulses in the ultraviolet — near infrared range (λ = 266, 400, 800 nm) under atmospheric conditions and under vacuum (p ~ 10^–2 Pa). We have analyzed the ablation efficiency (mass yield per unit energy of the acting coherent radiation) and ablation energy thresholds vs. the laser pulse duration and photon energy.