Non-equilibrium gas-liquid transition model

A new rigorous mathematical model for evaporation/condensation, including boiling, has been proposed. A problem of phase transition and in particular evaporation/condensation is one of the most acute problems of modern technology with numerous applications in industry, such as: in refrigeration, distillation in chemical industry. It is very common to use equilibrium evaporation model, which assumes that concentrations of species in the gas phase is always at saturated condition. Such kind of approach can lead to significant errors, resulting in negative concentrations in complex computer simulations. In this work two analytical solution of simplified differential-algebraic system have been obtained. One of them was deduced using assumption that the process is isothermal and gas volume fraction is constant. In the second solution the assumption about gas volume fraction has been removed. The code for numerical solution of differential-algebraic system, using conservative scheme, has been developed. It was designed to solve both systems of equations with boiling and without. Numerical calculations of ammonia-water system with various initial conditions, which correspond to evaporation and/or condensation of both components, have been performed. It has been shown that, although system quickly evolves to quasi equilibrium state (the differences between current and equilibrium concentrations are small) it is necessary to use non-equilibrium evaporation model, to calculate accurately evaporation/condensation rates, and consequently all other dependent variables. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the existence of multiple solutions for a nonlocal BVP with vector-valued response

The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.     

Resonances inη-light nucleus systems

We locate resonances inη-light nucleus elastic scattering using the time delay method. We solve few-body equations within the finite rank approximation in order to calculate the t-matrices and hence the time delay for theη-³He andη-⁴He systems. We find a resonance very close to the threshold inη-³He elastic scattering, at about 0.5 MeV above threshold with a width of ∼2 MeV. The calculations also hint at the presence of sub-threshold states in both the cases     

Computer simulation of non-linear preparative chromatography processes

Summary A theory of non-linear chromatography based on the mass balance equation is presented. The model is a system of partial differential equations and it includes axial dispersion in the mobile phase, flow in the mobile phase and mass transfer between phases. In the case of the injection of a mixture competition between components for places in the stationary or the mobile phase is taken into account. In the paper are discussed: numerical calculations of concentration and volume overloading and the effect of the mutual influence of the components of the injected mixture on the process of mass transfer between phases. Additionally, results of experiments for convex and concave adsorption isotherms are presented. In both cases the results obtained qualitatively confirm the theoretical analyses.     

Semicommuting and Commuting Operators for the Heun Family

We derive the most general families of first- and second-order differential operators semicommuting with the Heun class differential operators. Among these families, we classify all the families that commute with the Heun class. In particular, we find that a certain generalized Heun equation commutes with the Heun differential operator, which allows constructing a general solution of a complicated fourth-order linear differential equation with variable coefficients whose solution cannot be obtained using Maple 16.     

Metal Exchange in the Interprotein ZnII-Binding Site of the Rad50 Hook Domain: Structural Insights into CdII-Induced DNA-Repair Inhibition

Cd^II is a major genotoxic agent that readily displaces Zn^II in a multitude of zinc proteins, abrogates redox homeostasis, and deregulates cellular metalloproteome. To date, this displacement has been described mostly for cysteine(Cys)-rich intraprotein binding sites in certain zinc finger domains and metallothioneins. To visualize how a Zn^II-to-Cd^II swap can affect the target protein's status and thus understand the molecular basis of Cd^II-induced genotoxicity an intermolecular Zn^II-binding site from the crucial DNA repair protein Rad50 and its zinc hook domain were examined. By using a length-varied peptide base, Zn^II-to-Cd^II displacement in Rad50’s hook domain is demonstrated to alter it in a bimodal fashion: 1) Cd^II induces around a two-orders-of-magnitude stabilization effect (log =20.8 vs. log =22.7), which defines an extremely high affinity of a peptide towards a metal ion, and 2) the displacement disrupts the overall assembly of the domain, as shown by NMR spectroscopic and anisotropy decay data. Based on the results, a new model explaining the molecular mechanism of Cd^II genotoxicity that underlines Cd^II’s impact on Rad50’s dimer stability and quaternary structure that could potentially result in abrogation of the major DNA damage response pathway is proposed.     

New indefinite integrals of Heun functions

We present a conspicuous number of indefinite integrals involving Heun functions and their products obtained by means of the Lagrangian formulation of a general homogeneous linear ordinary differential equation. As a by-product we also derive new indefinite integrals involving the Gauss hypergeometric function and products of hypergeometric functions with elliptic functions of the first kind. All integrals we obtained cannot be computed using Maple and Mathematica.     

Small cycle double covers of products I: Lexicographic product with paths and cycles

Bondy conjectured that every simple bridgeless graph has a small cycle double cover (SCDC). We show that this is the case for the lexicographic products of certain graphs and along the way for the Cartesian product as well. Specifically, if G does not have an isolated vertex then G □ P₂ and G □ C_2k have SCDCs. If G has an SCDC then so does G □ P_k, k > 2 and G □ C_{2k + 1}. We use these Cartesian results to show that P_2j[G] (j ≥ 1) and C_k[G] (k ≠ 3, 5, 7) have SCDCs. Also, if G has an SCDC then so does P_{2j + 1}[G] (j ≥ 4). The results for the lexicographic product are harder and, in addition to the Cartesian results, require certain decompositions of K_n,n into perfect matchings. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 99–123, 2008     

Anisotropy of diamagnetic susceptibility of alternant hydrocarbons

The anisotropy of diamagnetic susceptibility of several hydrocarbons has been calculated with the use of the SC LCAO MO method with the London theory. The results for 10 hydrocarbons are compared with experiment and other known theoretical approaches. It is found that the SC LCAO MO method leads to a best agreement with experiment.

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Zusammenfassung Die Anisotropie der diamagnetischen Suszeptibilität mehrerer Kohlenwasserstoffe wurde im Rahmen der Londonschen Theorie nach der SC LCAO MO-Methode berechnet. Für 10 Aromaten werden die Ergebnisse mit dem Experiment und anderweitig berechneten Werten verglichen. Die SC LCAO MO-Resultate zeigen die beste Übereinstimmung mit dem Experiment.

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Résumé L'anisotropie de la susceptibilité diamagnétique de plurieurs hydrocarbures a été calculée par la méthode SC LCAO dans le cadre de la théorie de London. Pour 10 hydrocarbures on compare les résultats à l'expérience et aux résultats d'autres théories. La méthode SC LCAO MO rend le meilleur accord avec l'expérience.