Inverse Problem for a Mathematical Model of Adsorption Dynamics

A mixed problem is considered for a system of partial differential equations modeling the process of adsorption dynamics. An existence and uniqueness theorem is proved for this problem, and the solution properties are investigated. The inverse problem is posed, involving the determination of the system coefficient given additional information about the solution. A uniqueness theorem is proved for the solution of the inverse problem.__________Translated from Prikladnaya Matematika i Informatika, No. 16, pp. 5 – 14, 2004.     

Experimental investigation and theoretical modeling of liquid entrainment in a horizontal tee with a vertical-up branch

This article describes a comprehensive literature review of liquid entrainment in horizontal pipes with vertical-up branches. Deficiencies in the available data and correlations were identified. The Air–water Test Loop for Advanced Thermal–hydraulic Studies (ATLATS) was constructed and entrainment onset and steady-state data were collected for a wide range of flow conditions. Using new insights gained from experimental testing, the authors developed a model for predicting the onset of entrainment and steady-state entrainment rate. Previously published correlations, along with the new model, are compared against all available data. The new model shows very good agreement with the onset data, but is not very good at predicting branch quality at high liquid flow rates.     

Liquid-liquid phase equilibria of aqueous two-phase systems containing salts and polyethylene glycol

Liquid-liquid phase equilibria of the ternary systems: (a) polyethylene glycol - ammonium sulfate- water and (b) polyethylene glycol - sodium carbonate -water have been determined experimentally at 15°, 25°, 35° and 45°C and for two different molecular weights of the polymer (Avg. M.W. 1000 and 2000). Details of the glass cell and of the equilibration and analytical procedures used are described. Equilibrium data along with phase diagrams are presented. Finally the effect of temperature and of the molecular weight of the polymer are also discussed.     

On Covariant Phase Space and the Variational Bicomplex

The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a generalization have appeared in the literature. In this paper We review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau's symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the modern geometric theory of differential equations and the variational bicomplex. As an elementary example, we construct a phase space for the Monge–Ampere equation.     

Volcanic monitoring for radon and chemical species in the soil and in spring water samples

Soil radon has been monitored at two fixed stations in the northern flank of Popocatepetl Volcano, a high risk volcano located 60 km SE from Mexico City. Water samples from three springs were also studied for radon as well as major and trace elements. Radon in the soil was recorded using track detectors. Radon in the water samples was evaluated using the liquid scintillation method and an Alphaguard. The major elements were determined through conventional chemical methods and trace elements using an ICP-MS equipment. Soil radon levels were low, indicating a moderate diffuse degassing through the flanks of the volcano. Groundwater radon had almost no relation with the eruptive stages. Water chemistry was stable in the reported time (2000–2002).     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

Wellposedness for the Navier–Stokes flow in the exterior of a rotating obstacle

In this paper we study the Navier–Stokes boundary‐initial value problem in the exterior of a rotating obstacle, in two and three spatial dimensions. We prove the local in time existence and uniqueness of strong solutions. Moreover, we show that the solutions are global in time, in two spatial dimensions. Copyright © 2005 John Wiley & Sons, Ltd.     

Unusual monodentate binding mode of 2,2'-dipyridylamine (L) in isomeric trans-(acac)2RuII(L)2, trans-[(acac)2RuIII(L)2]ClO4, and cis-(acac)2RuII(L)2 (acac = acetylacetonate). synthesis, structures, and spectroscopic, electrochemical, and magnetic aspects

The reaction of cis-Ru(acac)2(CH3CN)2 (acac = acetylacetonate) with 2,2'-dipyridylamine (L) in ethanolic medium resulted in facile one-pot synthesis of stable [(acac)2RuIII(L)]ClO4 ([1]ClO4), trans-[(acac)2RuII(L)2] (2), trans-[(acac)2RuIII)L)2]ClO4 ([2]ClO4), and cis-[(acac)2RuII(L)2] (3). The bivalent congener 1 was generated via electrochemical reduction of [1]ClO4. Although in [1]+ the dipyridylamine ligand (L) is bonded to the metal ion in usual bidentate fashion, in 2/[2]+ and 3, the unusual monodentate binding mode of L has been preferentially stabilized. Moreover, in 2/[2]+ and 3, two such monodentate L's have been oriented in the trans- and cis-configurations, respectively. The binding mode of L and the isomeric geometries of the complexes were established by their single-crystal X-ray structures. The redox stability of the Ru(II) state follows the order 1 < 2 < 3. In contrast to the magnetic moment obtained for [1]ClO4, mu = 1.84 muB at 298 K, typical for low-spin Ru(III) species, the compound [2]ClO4 exhibited an anomalous magnetic moment of 2.71 muB at 300 K in the solid state. The variable-temperature magnetic measurements showed a pronounced decrease of the magnetic moment with the temperature, and that dropped to 1.59 muB at 3 K. The experimental data can be fitted satisfactorily using eq 2 that considered nonquenched spin-orbit coupling and Weiss constant in addition to the temperature-independent paramagnetism. [1]ClO4 and [2]ClO4 displayed rhombic and axial EPR spectra, respectively, in both the solid and the solution states at 77 K.