Character of the thermal motion of water molecules according to the data on quasielastic incoherent scattering of slow neutrons

The paper discusses the applicability of quasi-crystalline approximation to describing the thermal motion of water molecules in their normal and supercooled states. The problem is subjected to the critical analysis of experimental data on incoherent scattering of slow neutrons based on theories developed by Singwi-Sjolander [1] and Oskotsky [2] modified to duly take into account the limited applicability range of diffusion approximation. The applicability conditions of quasi-crystalline approximation are shown to be consistently satisfied only when water is in supercooled state and within a narrow temperature range above the melting temperature.     

Controlling the diffusion process via time-variable diffusion coefficient

The establishment of the steady-state dopant profile in a medium with a time-variable diffusion coefficient is considered within the approach proposed previously for estimating mass-and heat-transfer time characteristics. It is shown that the time it takes for the equilibrium concentration to set in may be increased or decreased by appropriately choosing the law of variation of the diffusion coefficient.     

ΓD‐convergence for a class of quasilinear elliptic equations in thin structures

We study the asymptotic behaviour of the solution of a stationary quasilinear elliptic problem posed in a domain Ω^(ε) of asymptotically degenerating measure, i.e. meas Ω^(ε) → 0 as ε → 0, where ε is the parameter that characterizes the scale of the microstructure. We obtain the convergence of the solution and the homogenized model of the problem is constructed using the notion of convergence in domains of degenerating measure. Proofs are given using the method of local characteristics of the medium Ω^(ε) associated with our problem in a variational form. Copyright © 2005 John Wiley & Sons, Ltd.     

Multinomial permutations on a circle

Multinomial permutations on a circle are considered in the framework of combinatorics. Different cases are presented and shown to agree with previously derived formula for the number of cyclic necklaces. Two applied examples are discussed with a view to illustrate the implications of derived formulas. Copyright © 2006 John Wiley & Sons, Ltd.     

Gromov's K-area and symplectic rigidity

Supported by the United States-Israel Binational Science Foundation grant 94-00302     

Enumerating disjunctions and conjunctions of paths and cuts in reliability theory

Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of source-sink pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. Furthermore, under the assumption that P consists of all pairs within a given vertex set, we also give incremental polynomial time algorithm for enumerating all minimal path disjunctions and cut conjunctions. For directed graphs, the enumeration problem for cut disjunction is known to be NP-complete. We extend this result to path conjunctions and path disjunctions, leaving open the complexity of the enumeration of cut conjunctions. Finally, we give a polynomial delay algorithm for enumerating all minimal sets of arcs connecting two given nodes s₁ and s₂ to, respectively, a given vertex t₁, and each vertex of a given subset of vertices T₂.     

Quantum-Chemical Evaluation of the Protolytic Properties of Thiophenols

The enthalpies and free energies of proton affinity (PA) were calculated by the PM3 method for 27 thiophenoxide anions. For thiophenols, linear correlation has been found between the PAs and the values of pK _a measured by different authors in aqueous acetone, aqueous ethanol, and methanol media. The dependences found permit one to predict a priori the protolytic properties of thiophenols. The differential effects of aqueous ethanol media with different ethanol contents on thiophenol acidity were evaluated based on quantum-chemical data.Original Russian Text Copyright © 2004 by A. N. Pankratov and A. V. Shalabai__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 800–806, September–October, 2004.     

The asymptotic behavior of the solutions of variational problems in domain with “accumulators”

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 54, pp. 97–105, 1990.