Asymptotic formula for a partition function of reversible coagulation-fragmentation processes

We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of the equilibrium measure for a wide class of parameter functions of the process. This formula proves the conjecture stated in [5] for the above class of processes. The method used goes back to A. Khintchine.     

On sums of subsets of a set of integers

Forr2 letp(n, r) denote the maximum cardinality of a subsetA ofN={1, 2,...,n} such that there are noBA and an integery with b=y ^r. It is shown that for any>0 andn>n(), (1+o(1))2^1/(r+1) n ^{(r–1)/(r+1)}p(n, r)n ^+2/3 for allr5, and that for every fixedr6,p(n, r)=(1+o(1))·2^1/(r+1) n ^{(r–1)/(r+1)} asn. Letf(n, m) denote the maximum cardinality of a subsetA ofN such that there is noBA the sum of whose elements ism. It is proved that for 3n ^6/3+mn ²/20 log² n andn>n(), f(n, m)=[n/s]+s–2, wheres is the smallest integer that does not dividem. A special case of this result establishes a conjecture of Erds and Graham.Research supported in part by Allon Fellowship, by a Bat-Sheva de Rothschild Grant and by the Fund for Basic Research administered by the Israel Academy of Sciences.     

Erratum to: Fusibility of Agricultural Plant Waste Ash under the Conditions of High-Temperature Processing

Russian Journal of Applied Chemistry - Erratum     

Laser Effect in the Explosion of Porous Silicon

JETP Letters - In the explosive reaction of composites based on porous silicon with perchlorate oxidizers, a new effect has been discovered: the intensity accompanying the explosive reaction...     

The oil ofThalictrum simplex

Summary Octadec-5-enoic acid, not found previously in other plant or animal oils and fats, has been found in the oil of slimtop meadowrue. The hydrocarbon fraction isolated contains n-dotriacontane and, apparently, other paraffinic hydrocarbons of similar composition. From its fatty-acid composition and its drying properties, the oil must be classed with thePapaveraceae group.Khimiya Prirodnykh Soedinenii, Vol. 1, No. 2, pp. 123–128, 1965     

On the measure of large values of the modulus of a trigonometric sum

We study the connection between the additive structure of a finite set A⊂Z$A\subset \mathbb{Z}$ and the measure of large values of the modulus of a trigonometric sum.     

Numerical analysis of the stress concentration near holes originating in previously loaded viscoelastic bodies at finite strains

The state of stress and strain of previously loaded viscoelastic bodies with holes originating in them, successively or simultaneously, is analyzed under finite plane deformations. The problem statement and solution are based on the theory of repeatedly superimposed large deformations. The material mechanical properties are described using integral relations of the convolution type over time with a weakly singular kernel. The problem solving is based on the finite-element method. To calculate the integral of the convolution type, a recurrence formula is used that can be obtained by approximating the initial kernel with a linear combination of exponential functions (the truncated Prony’s series). The nonlinear effects and the effect of the interaction between holes on the stress concentration are analyzed. For the dynamic problems, the results for incompressible and weakly compressible materials are compared.