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.     

A versatile protocol for the preparation of substituted 1- and 2-naphthyl piperazines from aminonaphthols

Aminonaphthols are easily transformed into a variety of 1- and 2-naphthyl piperazines using a sequence of diazotization, iodide substitution and Pd(0) catalyzed coupling reactions.     

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.     

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).     

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.     

Carbon fiber cylindrical microelectrode-based detector for the determination of antithyroid drugs

An amperometric flow-injection method for the determination of antithyroid drugs such as 6-methyl-2-thiouracil (MTU) using a carbon fiber cylindrical microelectrode-based detector is reported. A home-made flow-cell specially adapted for working with cylindrical microelectrodes ranging between 4 and 10 mm in length was used for this purpose. Methanol containing 0.05 mol l(-1) tetrabutylammonium perchlorate as the supporting electrolyte was employed, and a potential of +1.6 V was selected for the amperometric detection of MTU. No cleaning or electrode surface regeneration of the fiber was necessary during the whole working day. A limit of detection of 2.6x10(-7) mol l(-1) (37 mug MTU l(-1)) was achieved. The method was applied to the determination of MTU in spiked feed samples (peas and corn flour), at the 142 mug g(-1) level. The procedure involved the extraction of the drug in methanol, a clean-up step using Florisil cartridges and the use of the standard additions method. Recoveries of 81+/-6 and 85+/-8% were obtained for peas and corn flour, respectively.     

Second-generation mimics of ganglioside GM1 oligosaccharide: a three-dimensional view of their interactions with bacterial enterotoxins by NMR and computational methods

As a step to delineate a strategy of ligand design for cholera toxin (CT), NMR studies were performed on several mimics of the GM1 ganglioside oligosaccharide. The conformation of these analogues was investigated first in solution and then upon binding to cholera toxin by transferred nuclear Overhauser effect (TR-NOE) measurements. It was demonstrated that CT selects a conformation similar to the global minima of the free saccharides from the ensemble of presented conformations. No evidence of major conformational distortions was obtained, but one or two of the available conformers of the hydroxyacid side chain appear to be selected in the bound state. The NMR data were interpreted with the aid of computer models, generated and analyzed by using a combination of different approaches (MacroModels' MC/EM and MC/SD, Autodock, and GRID). Analysis of the NMR data supported by computational studies allowed us to interpret the experimental observations and to derive workable models of the ligand:toxin complexes. These models suggest that the higher affinity of the (R)-lactic acid derivative 3 may stem from lipophilic interactions with a hydrophobic area in the toxin binding site located in the vicinity of the sialic acid side chain binding region of the CT:GM1 complex, and formed by the side chain of Ile-58 and Lys-34. Thus, the models obtained have allowed us to make useful design suggestions for the improvement of ligand affinity.