Conditional Time Before Ruin of an Insurance Company

The statistical characteristics of conditional time before ruin of an insurance company, including the distribution function of conditional time and its moments are examined.     

Nematic LC to nematic glass phase transition in pores

The properties of a nematic liquid crystal in a porous matrix are discussed. On scales exceeding a certain characteristic scale the liquid crystal behaves as a nematic glass. Application of a weak magnetic field restores long-range orientational order. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 695–698 (10 May 1997)     

Unilaterally competitive games

The authors acknowledge valuable discussions with Jonathan Hamilton and Mamoru Kaneko as well as very detailed comments of two referees.     

Synthesis of 1,7-bis(4′-aminophenylamido)-m-carborane and 1,7-bis(4′-aminophenylcarboxy)-m-carborane

Conclusion 1,7-Bis(4-aminophenylamido)- and l,7-bis(4-aminophenylcarboxy)-m-carboranes were prepared and characterized.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2786–2787, December, 1986.     

Organomineral sorbents based on clinoptilolite-containing tuffs

The anion-exchange properties of a new organomineral sorbent obtained by modification of clinoptilolite-containing tuffs by polyhexamethyleneguanidine have been studied after different periods of storage (time after synthesis) and numbers of sorption-regeneration cycles. The sorbent can be used as a cation- and an anion-exchanger simultaneously. Selectivity coefficients (exchange constants) for F^–, SO₄ ^2–, and HPO₄ ^2– ionsvs. Cl^– ions on modified clinoptilolite-containing tuffs have been determined. The modification improves the mechanical properties of clinoptilolite tuffs.For part 1, see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1554–1556, September, 1994.     

Monolayer adsorption isotherms and a disordered medium model

A model of disordered medium is proposed to describe the monolayer adsorption isotherm on heterogeneous surfaces. The model is based on the premise that adsorption medium consists of separate regions in each of which there is a permanent local equilibrium constant, the character of the changes of which is determined by the disorder parameter of the medium. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 42, No. 3, pp. 189–193, May–June, 2006.     

Substitution reactions involving the 2,6-methyl groups of 1,4-dihydropyridines

4,4-Disubstituted 1,4-dihydropyridines (I) are brominated with bromine in chloroform to give 2,6-bis(bromomethyl)-4,4-disubstituted 1,4-dihydropyridines (II), whereas 2,6-bis(dibromomethyl)-4,4-disubstituted 1,4-dihydropyridines (III) are obtained in the case of bromination of I in acetic acid. The bromine atoms in II and III are labile and readily undergo nucleophilic substitution.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1519–1524, November, 1978.     

Step-by-step first order antiferroelectric-paraelectric transition induced by frustration and electric field

We show analytically that even not too strong frustrating next neighbor interaction strongly affects first order antiferroelectric-paraelectric transition in an external electric field. We apply mean-field Landau theory. In the electric field a single phase transition at T ₀ splits into a step-by-step staircase with a series of intermediate phases. Unexpectedly enough we found that the equilibrium structures of the phases differ substantially from structures formed at low temperature both without field and in field. Polarization of intermediate structures decreases with temperature in a stepwise manner. Similar step-by-step transitions can occur also in magnetic materials with frustrating interaction.     

Relationship between the nucleation and precrystallization liquid phase during homogeneous crystallization of metals

A comparative estimation of the size parameters of clusters of precrystallization liquid phase (PLP) of metals and critical crystalline nuclei has revealed the sizes of critical crystalline nuclei to be smaller than those of PLP clusters. Based on the results of estimation of the radii of critical crystalline nucleus by the methods of classical theory and molecular dynamics, it has been found for the first time that the radius of critical crystalline nucleus is about 0.2–0.4 of the PLP cluster radius. This fact confirmed the hypothesis of Ubellode et al. about the formation of a transition layer with a partially ordered structure between the solid and liquid phases. A scheme of the nucleation and growth of a crystalline nucleus under conditions of transition layer formation is proposed.

     

The Cauchy Transform of Certain Distributions with Application

We study boundary properties of the Cauchy transform of certain distributions with supports on non-rectifiable curves and apply these results for solution of the Riemann boundary value problem.