Solvatochromic relationship: Prediction of distribution of ionic solutes in aqueous two-phase systems

Partition ratios of several ionic compounds in 20 different polymer/polymer aqueous two-phase systems (ATPS) containing 0.15 M NaCl in 0.01 M phosphate buffer, pH 7.4, were determined. The differences between the electrostatic properties of the phases in all the ATPS were estimated from partitioning of the homologous series of dinitrophenylated-amino acids. Also the solvatochromic solvent parameters characterizing the solvent dipolarity/polarizability (π*), solvent hydrogen-bond donor acidity (α), and solvent hydrogen-bond acceptor basicity (β) of aqueous media were measured in the coexisting phases of the ATPS. The solute-specific coefficients for the compounds examined were determined by the multiple linear regression analysis using the modified linear solvation energy relationship equation. The minimal number of ATPS necessary for determination of the coefficients was established and 10 ATPS were selected as a reference ATPS set. The solute-specific coefficients values obtained with this reference set of ATPS were used to predict the partition ratios for the compounds in 10 ATPS not included in the reference set. The predicted partition ratios values were compared to those determined experimentally and found to be in good agreement. It is concluded that the presented model of solute–solvent interactions as the driving force for solute partitioning in polymer/polymer ATPS describes experimental observations with 90–95% accuracy.     

Criteria for Balance in Abelian Gain Graphs, with Applications to Piecewise-Linear Geometry

Consider a gain graph with abelian gain group having no odd torsion. If there is a basis of the graph’s binary cycle space, each of whose members can be lifted to a closed walk whose gain is the identity, then the gain graph is balanced, provided that the graph is finite or the group has no non-trivial infinitely 2-divisible elements. We apply this theorem to deduce a result on the projective geometry of piecewise-linear realizations of cell-decompositions of manifolds.     

Formal Axiomatic Theories Based on a Three-Valued Logic

Formal axiomatic theories based on the three-valued logic of Lukasiewicz are considered. Main notions related to these theories, in particular, those of Luk-model, Luk-consistent theory, and Luk-complete theory are introduced. Logical calculuses that describe such theories are defined; counterparts of the classical compactness and completeness theorems are proved. Theories of arithmetic based on Lukasiewicz’s logic and on its constructive (intuitionistic) variant are investigated; the theorem on effective Luk-incompleteness is proved for a large class of arithmetic systems. This theorem is a three-valued counterpart of the famous Godel theorem on incompleteness of formal theories. Three-valued counterparts of Presburger’s arithmetic system are defined and proved to be Luk-complete but incomplete in the classical sense. Bibliography: 29 titles.__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 304, 2002, pp. 19–74.     

Analysis of the vibroacoustic field in an extended layer and in the layer–semispace structure

We analyze the acoustic field excited by dipole vibration sources in an extended layer. Two formulations of the problem are considered. In the first case, it is assumed that the layer boundaries are stiff in the normal direction, but the particles oscillating at the boundary may slip in the direction tangential to the walls. In another case, a rigid contact of a “patch” type takes place at the boundary with the host medium. A pattern of the space distribution of the field amplitude both inside and outside the layer is given. The vibration field of the sources operated in pulsed mode in the wave hodograph plane is presented. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 2, pp. 151–163, February 2009.     

Thermodynamically conditioned splitting schemes in combustion problems

Algorithms for solving the two-dimensional combustion problem for premixed flames are proposed and examined. The solution method is based on splitting into convective and diffusion parts according to the processes involved. A high-resolution explicit quasi-monotone scheme with flux correction is used for the hyperbolic part. For the parabolic part, the scheme is conservative and the source in the heat equation is set to be positive; i.e., the scheme ensures that the different thermodynamic consequences of the original equations hold; therefore, the scheme is thermodynamically conditioned. The applicability of the scheme to the full and purely gasdynamic problems is examined under various types of initial conditions and with various flux limiters. Numerical results are presented for one-and two-dimensional problems, including the Frank-Kamenetskii classical problem in two dimensions. The flame is shown to become turbulent in sufficiently wide pipes.     

Coupled oscillators with power-law interaction and their fractional dynamics analogues

A one-dimensional chain of coupled oscillators with the long-range power-law interactions is considered. Equations of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order α, when 0 < α < 2. The evolution of soliton-like and breather-like structures is obtained numerically and compared for two types of simulations: using the chain of oscillators and using the continuous medium equation with the fractional derivative.