Self-association of daunomycin antibiotic in various buffer solutions

The self-association of an antitumor antibiotic, daunomycin (DAU), in various buffer solutions, including water-salt solutions, phosphate buffer, HEPES, and TRIS, was studied by 1D and 2D ¹H NMR spectroscopy at 500 MHz. The two-dimensional NOESY spectra and the concentration and temperature dependences of the chemical shifts of antibiotic protons in the solvents studied showed that the self-association parameters of DAU were independent of the type of buffer solutions. The most probable two spatial structures of the dimer of DAU in solution were constructed by the method of molecular mechanics. The mutual orientation of the chromophores was parallel in one structure and antiparallel in the other.     

Equilibrium States of Random Economies with Locally Interacting Agents and Solutions to Stochastic Variational Inequalities in 〈L1,L∞〉

We study a stochastic model of an economy with locally interacting agents. The basis of the study is a deterministic model of dynamic economic equilibrium proposed by Polterovich. We generalize Polterovich's theory, in particular, in two respects. We introduce stochastics and consider a version of the model with local interactions between the agents. The structure of the interactions is described in terms of random fields on a directed graph. Equilibrium states of the system are solutions to certain variational inequalities in spaces of random vectors. By analyzing these inequalities, we establish an existence theorem for equilibrium, which generalizes and refines a number of previous results.     

Influence of thermal conductivity on the heating of a substance by a high-intensity ion beam

Relations describing the process of heat transfer from the energy-dissipation region of a monoenergetic ion beam in an obstructing target within the pulse duration are derived on the basis of an analysis of the fundamental laws governing the interaction of a high-intensity ion beam with condensed media and the solution of the heat-conduction equation. The proposed analytical expressions can be used to assess the feasibility of neglecting thermal conductivity and calculating the temperature fields in the target without solving the heat-conduction boundary-value problem, namely on the basis of the characteristics of a heat-release source approximating the real source.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 16–20, June, 1986.     

Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset

This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study of local stability of the wealth dynamics through the application of recent results on the linearization and stability of random dynamical systems (Evstigneev et al. Proc Am Math Soc 139:1061–1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary stability. A locally evolutionarily stable investment strategy in the evolutionary model with a risk-free asset is derived, extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial dynamic models involving randomness.     

Complete solution of the problem of one-dimensional non-covalent non-cooperative self-assembly in two-component systems

Equations for the mass conservation law and the molecular parameters observed in spectroscopic experiments have been derived for non-covalent, non-cooperative, one-dimensional self-assembly in systems containing two types of interacting molecules (hetero-association), taking into account "reflected" complexes and "edge effects."     

1H NMR study of the hetero-association of flavin-mononucleotide with mutagenic dyes: ethidium bromide and proflavine

The hetero-association of the vitamin B₂ derivative, flavin-mononucleotide (FMN), with a mutagenic dye, ethidium bromide (EB) or proflavine (PF), has been studied by 1D and 2D 500?MHz ¹H NMR spectroscopy. The variations of proton chemical shifts of both the vitamin and dye as a function of concentration and temperature were analysed in terms of the structural and thermodynamical properties of the FMN–EB and FMN–PF complexes in solution. The structures of the complexes were also investigated by observed intermolecular ROE contacts and molecular mechanics calculations. The results show that the 1?:?1 hetero-association complexes in solution are more stable than the self-association complexes, which is consistent with formation of an intermolecular hydrogen-bond in the hetero-complexes of FMN–EB and FMN–PF. Hence it is possible that the toxicity of aromatic molecules such as EB and PF may be reduced in vitro by the presence of FMN, partly because of the known antimutagenic action of FMN and partly because it has been shown in this work that there is an effective intermolecular association between the mutagens and the vitamin.