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.     

Analytic Functions in Local Shift-Invariant Spaces and Analytic Limits of Level Dependent Subdivision

Journal of Fourier Analysis and Applications - We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ( $$SG$$ ), which is a fractal set that can be viewed as a limit...     

Comparative Safety Assessment of Packaged Mineral Waters

Russian Journal of General Chemistry - The technical legal acts that regulate the quality and safety parameters of mineral waters out were analyzed. Seven samples of mineral waters produced in...     

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.     

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.