Markov chains on a matrix group

The limiting behavior of a sequence of products of random matrices is investigated. Certain well-known results concerning independent identically distributed matrices are translated to the case of discrete-time Markov processes.Translated from Matematicheskie Zametki, Vol. 10, No. 2, pp. 181–186, August, 1971.     

Iterations of homogeneous polynomial transformations with positive coefficients

A study is made of the behavior as k of the iterations T^k(x) of a homogeneous polynomial transformation T acting from Rⁿ to Rⁿ according to the formula (T(x))_i=Q_i (x), i=1, 2,..., n, where Q_i(x) is a homogeneous polynomial of degree m>1 with positive coefficients.Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 411–416, October, 1969.In conclusion I should like to thank S. A. Molchanov for proposing the topic and S. M. Natanzon for his help with the paper.     

Sharing Nonconvex Costs

The paper analyzes cooperative games with side payments. Each player faces a possibly non-convex optimization problem, interpreted as production planning, constrained by his resources or technology. Coalitions can aggregate (or pool) members' contributions. We discuss instances where such aggregation eliminates or reduces the lack of convexity. Core solutions are computed or approximated via dual programs associated to the grand coalition.     

Almost sure Nash equilibrium strategies in evolutionary models of asset markets

We consider a stochastic model of a financial market with long-lived dividend-paying assets and endogenous asset prices. The model was initially developed and analyzed in the context of evolutionary finance, with the main focus on questions of “survival and extinction” of investment strategies. In this paper we view the model from a different, game-theoretic, perspective and examine Nash equilibrium strategies, satisfying equilibrium conditions with probability one.     

Evolutionary finance and dynamic games

The paper examines a game-theoretic evolutionary model of an asset market with endogenous equilibrium asset prices. Assets pay dividends that are partially consumed and partially reinvested. The investors use general, adaptive strategies (portfolio rules), distributing their wealth between assets, depending on the exogenous states of the world and the observed history of the game. The main objective of the work is to identify strategies, allowing an investor to “survive”, i.e. to possess a positive, bounded away from zero, share of market wealth over the whole infinite time horizon. This work brings together recent studies on evolutionary finance with the classical topic of non-cooperative market games.     

A revised treatment of the non-electrostatic contribution to the solvation free energy of DNA-binding ligands

A revised magnitude of the microscopic surface tension coefficient, γ_vdW, is suggested to account for the van der Waals solvation energy, ΔG_vdW^solv, in the standard expression ΔG_vdW^solv = γ_vdW ⋅ ΔA, where ?A is the change in solvent accessible surface area on complexation. The revised value of γ_vdW = − 0.063(± 0.008) kcal/mol/Ų is based on the decomposition of the Gibbs free energy for 49 reactions of non-covalent bimolecular ligand-DNA and ligand-ligand complexation, involving 20 DNA-binding molecules that differ in structure and charge state. The total non-electrostatic contribution to the solvation free energy can also be calculated from the standard equation ΔG_nel^solv = γ_nel ⋅ ΔA with the revised coefficient γ_nel = − 0.013(± 0.008) kcal/mol/Ų. It is proposed that these results may be utilized for analysis of any ligand-DNA or ligand-ligand interaction, if the structure and other physical properties of the interacting molecules do not change on complexation.     

Structure of porous permeable materials in a titanium-aluminum-carbon-alloy-component system obtained by self-propagating high-temperature synthesis

A study is made of the structure of porous permeable materials obtained by the method of self-propagating high-temperature synthesis on the basis of the titanium-aluminum-carbon system and the same system with the introduction of alloy components: metals and nonmetals. It is shown that the structure of the skeleton of the unalloyed material includes a matrix on the basis of intermetallides and a solid solution with disperse titanium carbides distributed in its volume. It is established that depending on the mechanism by which the alloy components influence the structure of the skeleton of the material, they can be subdivided into those that do and do not give rise to carbides. Introducing elements of one of the groups into the reaction mixture, one can have a directed influence on the parameters of both the matrix and carbide components of the obtained material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 9–13, January, 1992.     

H NMR investigation of the self-association of ethidium homodimer and its complexation with propidium iodide in aqueous solution

The self-association of a bis-intercalator, ethidium homodimer (EBH), and its hetero-association with phenanthridine dye, propidium iodide (PI), have been studied by 1D and 2D ¹H NMR spectroscopy using the analysis of proton chemical shifts changes in aqueous solution as a function of concentration and temperature. Experimental results have shown that dynamic equilibrium in solution includes different conformational states of EBH molecules: folded (F) and unfolded (U) forms, a dimer form (F₂) where an aromatic chromophore of one of EBH molecules is inserted (intercalated) between the linked chromophores of the other homodimer molecule and a trimer complex (F₃) with two partitially intercalated aromatic chromophores between the chromophores of the folded EBH molecule. It has been found that EBH associates with propidium iodide forming 1:1 complex, where PI is inserted between the chromophores of the folded form, and 1:2 complex resulting from intercalation of PI into F₂ EBH dimer. Thermodynamical parameters of EBH self-association and complexation between EBH and PI have been determined and conclusions about the nature of the physical forces responsible for the formation of intermolecular complexes have been made.     

Force dependence of transition rates in atomic friction

The lateral forces during stick-slip motion of an atomic force microscope cantilever on highly oriented pyrolytic graphite are measured and analyzed. We identify the regimes where thermally activated interstitial hopping of the cantilever tip proceeds according to a single-step reaction scheme and extract the corresponding force-dependent transition rates directly from the experimental data. We find that such a single-step reaction scenario is valid only at relatively high velocities, while at slower pulling speeds, a more complicated hopping mechanism must be at work. We suggest formation of multiple bonds of the tip-sample contact as a possible candidate for this mechanism.     

1H NMR Study of Heteroassociation of Daunomycin and Propidium Iodide in Aqueous Solution

Heteroassociation of an anthracycline antibiotic Daunomycin (DAU) and phenanthridine dye Propidium iodide (PI) in aqueous solution was studied by ¹H NMR spectroscopy. The complex PI-DAU is stabilized mainly by dispersion van der Waals interactions and hydrogen bond between the 3(8)-amino group of the dye and 9-acetyl group of DAU. This conclusion follows from comparison of parameters of DAU-PI heteroassociation and complex formation of DAU with aromatic dyes, Proflavine and Ethidium bromide, under the same conditions.