Time-discretization scheme for quasi-static Maxwell's equations with a non-linear boundary condition

We study a time dependent eddy current equation for the magnetic field H$\mathit{H}$ accompanied with a non-linear degenerate boundary condition (BC), which is a generalization of the classical Silver–Müller condition for a non-perfect conductor. More exactly, the relation between the normal components of electrical E$\mathit{E}$ and magnetic H$\mathit{H}$ fields obeys the following power law ν×E=ν×(|H×ν|^α-1H×ν)$\mathit{\nu }\times \mathit{E}=\mathit{\nu }\times (|\mathit{H}\times \mathit{\nu }{|}^{\alpha -1}\mathit{H}\times \mathit{\nu })$ for some α∈(0,1]$\alpha \in (0,1]$. We establish the existence and uniqueness of a weak solution in a suitable function space under the minimal regularity assumptions on the boundary Γ$\Gamma$ and the initial data _H0${\mathit{H}}_0$. We design a non-linear time discrete approximation scheme based on Rothe's method and prove convergence of the approximations to a weak solution. We also derive the error estimates for the time-discretization.     

Crystal structure, spectroscopic and magnetic properties, and antimicrobial activities of cobalt(II) 2-methylthionicotinate complexes with N-heterocyclic ligands

Synthesis and characterization of 10 new 2-methylthionicotinate (2-MeSnic) Co(II) complexes, namely, [Co(2-MeSnic)₂L₂(H₂O)₂] · nH₂O (L is N,N-diethylnicotinamide—Et₂nia, ethylnicotinate—Etnic, nicotinamide—nia, isonicotinamide—isonia, N-methylnicotinamide—N-Menia, furo[3,2-c]pyridine—fpy, 2,3-dimethylfuro[3,2-c]pyridine—Me₂fpy or benzo[4,5]furo[3,2-c]pyridine—Bfp; n is 0, 1 or 2) as well as [Co(2-MeSnic)₂L₂] (L is ronicol—ron or 2-methylfuro[3,2-c]pyridine—Mefpy), are reported. The characterizations were based on physico-chemical and spectroscopic methods. The crystal structure of one of the complexes has been determined. In the molecular complex [Co(2-MeSnic)₂(Me₂fpy)₂(H₂O)₂], the Co(II) central atom, located at a symmetry centre, is octahedrally coordinated by an oxygen atom of the unidentate 2-MeSnic carboxyl group, the nitrogen atom of the pyridine ring of Me₂fpy, a water molecule and the corresponding centrosymmetrically located atoms. Also, biological activity of the complexes against various strains of bacteria and filamentous fungi has been investigated. It is concluded that by complexation of these nicotinate derivatives their biological activities are elevated. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Vibrational spectra of the Cu(II) complexes of L-asparagine and L-glutamine

The infrared and Raman spectra of the copper(II) complexes [Cu(L-asn)2] and [Cu(L-gln)2] (L-asn=L-asparagine; L-gln=L-glutamine), were recorded and analyzed in relation to its structural peculiarities. Some comparisons between the spectra of these complexes and with those of related systems are made. The characteristics of the carboxylate and amide groups of the bonded ligands are discussed in detail.     

Synthesis of enantiomerically enriched α,α-disubstituted β,γ-epoxy esters using hydrolytic kinetic resolution catalyzed by salenCo(III)

Novel α,α-disubstituted epoxy esters were prepared in enantiopure form by hydrolytic kinetic resolution (HKR) of the corresponding racemic mixtures using chiral salenCo(III) as catalyst. The methodology provides a convenient route to enantioenriched β,γ-epoxy esters 2a, 2c and 2d.     

Structural peculiarities and electrical properties of multicomponent oxide crystals. Mixed anionic conductors

Electrical and dielectric properties, and ionic transport numbers of “pure” and rare earth elements doped Bi_5.8PO_11.2(BPO), and Bi₄Ge₃O₁₂(BGO) crystals are studied. Anisotropy of electrical properties in BPO is examined. Relations between the structure, physical properties, and transport mechanisms in BPO and BGO are discussed. Published in Russian in Elektrokhimiya, 2009, Vol. 45, No. 6, pp. 687–692. The article is published in the original. Published by report at IX Conference “Fundamental Problems of Solid State Ionics”, Chernogolovka, 2008.     

Synthesis,spectroscopic properties,crystal structure and biological activities of copper(II) 2-methylthionicotinate complexes with furopyridines

The synthesis and characterization of six new 2-methylthionicotinate (2-MeSnic) copper(II) monomeric complexes [Cu(2-MeSnic)₂L₂] (L is furo[3,2-c]pyridine—fpy, 2-methylfuro[3,2-c]pyridine—Mefpy, 2,3-dimethylfuro[3,2-c]pyridine—Me₂fpy or benzo[4,5]furo[3,2-c]pyridine—Bfp), [Cu(2-MeSnic)₂(fpy)₂(H₂O)], as well as [Cu(2-MeSnic)₂(CF₃Phfpy)₂(H₂O)₂] (CF₃Phfpy is 2-(3-trifluoromethylphenyl)furo[3,2-c]pyridine) are reported. The characterizations were based on elemental analysis, infrared, electronic and EPR spectra. The crystal structure of one of the complexes has been determined. The Cu^II atoms of [Cu(2-MeSnic)₂(fpy)₂(H₂O)] are six-coordinated in a highly distorted tetragonal–bipyramidal arrangement by two nitrogen atoms, one from each fpy, in trans-positions, by three oxygen atoms of the carboxyl groups of 2-MeSnic ligands (one monodentate, one asymmetrically bidentate), one axial position being occupied by the oxygen of a water molecule. The antimicrobial effects have been tested on various strains of bacteria, yeasts and filamentous fungi. A comparison of the IC₅₀ and MIC values has shown a decrease of inhibition activities of tested compounds in the order: [Cu(2-MeSnic)₂(Bfp)₂] > Bfp > [Cu(2-MeSnic)₂(CF₃Phfpy)₂(H₂O)₂] > [Cu(2-MeSnic)₂(Me₂fpy)₂] > CF₃Phfpy > [Cu(2-MeSnic)₂(Mefpy)₂] > Me₂fpy > [Cu(2-MeSnic)₂(fpy)₂(H₂O)] > [Cu(2-MeSnic)₂(H₂O)]₂ > Mefpy > fpy = 2-MeSnicH = CuSO₄. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Determination of a material constant in the impedance boundary condition for electromagnetic fields

We study a recovery problem for an unknown boundary data at the boundary part in static electromagnetism. Our computational area is a bounded domain Ω⊂Rⁿ with a Lipschitz continuous boundary. The problem for determining the coefficient λ is considered. This coefficient represents one of the ferromagnetic material characteristics occupying this domain. The existence and uniqueness of a weak solution are proved and a numerical method for its recovery is supported by numerical experiments.     

Electrical and dielectric properties of glass system NaPO3–KHSO4

Glass samples have been prepared in the NaPO₃–KHSO₄ binary system with the classical melting, casting and annealing steps. Electrical and dielectrical properties of glass samples were studied. Measurements of DC and AC conductivity and complex electrical permittivity of xNaPO₃–(100 ? x)KHSO₄ glass system were carried out at temperatures ranging from room temperature to temperature located 15 °C below glass transition temperature T_g. Results showed that changes of NaPO₃ concentration considerably affect values of observed parameters. DC conductivity of glass increases as NaPO₃ concentration grows until concentration x = 60. However, beyond this value a sharp decrease of DC conductivity was observed. In addition relaxation times showed abrupt changes at concentration x = 60, corresponding to the lowest relaxation times at the temperature 90 °C.     

Benzylammonium,imidazolium and pyridinium polyvanadates — Synthesis and characterization

Summary From the reaction systems,B-V₂O₅-HClO₄-H₂O andB-V₂O₅-H₂O, whereB is benzylamine (Bz), imidazole (Im) or pyridine (Py), eight new compounds were synthesized: at 20°C, the metavanadate and decavanadates of composition (BzH)VO₃, (BzH)₆V₁₀O₂₈·3H₂O, (ImH)₆V₁₀O₂₈·2H₂O, (PyH)₆V₁₀O₂₈·2H₂O, (ImH)₄H₂V₁₀O₂₈·2H₂O and (PyH)₄H₂V₁₀O₂₈·3H₂O, and at 60°C, the hexavanadates of composition (ImH)₂V₆O₁₆·H₂O and (PyH)₂V₆O₁₆·H₂O. ThepH ranges of solutions the polyvanadates can be isolated from, were estimated. The compounds prepared were characterized by chemical analysis and IR spectroscopy. The synthesis of deuterated analogues allowed to assign the IR bands corresponding to vibrations of water in the spectra of deca- and dihydrogendecavanadates and to V-OH vibrations in the spectra of dihydrogendecavanadates.

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Benzylammonium-, Imidazolium- und Pyridinium-Polyvanadate. Synthese und Charakterisierung

Zusammenfassung Aus dem ReaktionssystemB-V₂O₅-HClO₄-H₂O undB-V₂O₅-H₂O [B=Benzylamin (Bz), Imidazol (Im) oder Pyridin (Py)] wurden acht neue Verbindungen synthetisiert: bei 20°C entstanden die Metavanadate und Decavanadate der Zusammensetzung (BzH)VO₃, (BzH)₆V₁₀O₂₈·3H₂O, (ImH)₆V₁₀O₂₈·2H₂O, (PyH)₆V₁₀O₂₈·2H₂O, (ImH)₄H₂V₁₀O₂₈·2H₂O und (PyH)₄H₂V₁₀O₂₈·3H₂O, bei 60°C entstanden die Hexavanadate (ImH)₂V₆O₁₆·H₂O und (PyH)₂V₆O₁₆·H₂O. DiepH-Bereiche, innerhalb derer Polyvanadate isoliert werden können, wurden abgeschätzt. Die Verbindungen wurden mittels chemischer Analyse und IR-Spektroskopie charakterisiert, wobei die Synthese deuterierter Analoga die Zuordnung von Banden unterstützte.