Solution of boundary and eigenvalue problems for second‐order elliptic operators in the plane using pseudoanalytic formal powers

We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D = div p grad + qin the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q with the aid of pseudoanalytic function theory a complete system of null solutions of the operator can be constructed following a simple algorithm consisting in recursive integration. This system of solutions is used for solving boundary value and spectral problems for the operator D in bounded simply connected domains. We study theoretical and numerical aspects of the method. Copyright © 2010 John Wiley & Sons, Ltd.     

Transparent Fourier transform spectrometer

We realized a transparent Fourier transform spectrometer and investigated its operating principle. The spectrometer consists of a low-reflectivity Fabry-Perot interferometer and a partially transparent photodetector, which allows for the operation of the spectrometer in transmission. By changing the distance between the low-reflectivity mirrors of the Fabry-Perot interferometer, the light intensity that reaches the partially transparent photodetector is modulated and the spectral information of the incident light is determined by the Fourier transform of the generated photocurrent. This transparent Fourier transform spectrometer allows easy miniaturization and integration into any kind of optical system.     

A critical evaluation of the 0.05 M EDTA extraction of Pb from forest soils

Among many single-step extraction procedures proposed, 0.05 M EDTA (ethylenediaminetetraacetic acid) extraction is widely used. Although it has been often criticised, this protocol remains an effective and simple approach for a fast determination of the potential availability of several metals (e.g., Pb, Cd, Cu, Zn, etc.). However, other metallic elements present in soils at high concentrations such as Ca and Fe can possibly influence the extraction of the target metal due to competition for the EDTA ligand. The aim of this study was to evaluate the role of these metals during the 0.05 M EDTA extraction procedure. Furthermore, sequential extraction and Pb isotope analyses (^206/207Pb) were used in order to obtain more detailed information. The results of this study showed that especially the concentration and crystallinity of Fe play a very important role during the extraction of the target metals from low to moderately contaminated soils and this fact should be taken into account during result interpretation.     

A simple and convenient synthesis of 4-methyl-3-nitro-2-trihalomethyl-2H-chromenes from N-unsubstituted imines of 2-hydroxyacetophenones and trichloro(trifluoro)ethylidene nitromethanes

The reaction of N-unsubstituted imines of 2-hydroxyacetophenones with trichloro(trifluoro)ethylidene nitromethanes in the presence of DABCO proceeds via tandem oxa-Michael/aza-Henry additions (in dichloromethane) or aza-Michael addition (in benzene) to give 4-methyl-3-nitro-2-trichloro(trifluoro)methyl-2H-chromenes or 1,1,1-trichloro(trifluoro)-3-nitro-N-[1-(2-hydroxyaryl)ethylidene]propan-2-amines, respectively.     

Spectrometric study of tautomeric and protonation equilibria of o-vanillin Schiff base derivatives and their complexes with Cu(II)

Electronic absorption and emission properties of a series of Schiff bases derived from 2-hydroxy-3-methoxybenzaldehyde and 2-aminopyridine, 2,3-diaminopyridine, 2,6-diaminopyridine, or 3-aminomethylpyridine were studied in solvents of different polarities. The interconversion of the enolimine to the ketoamine tautomeric form was observed for compound 1, 6-methoxy-2-(3-pyridylmethyliminomethyl)phenol, and the corresponding equilibrium constant was estimated in several solvents. Protonation constants of all the investigated compounds were determined spectrophotometrically in the methanol/water 1/4 system. The effect of copper(II) ions on absorption and on the emission spectra of these ligands was examined in the buffered dioxane/water 1/1 system (pH 5.8). Strong complexation of Cu(II) and formation of a 1:1 complex were observed for the bis-Schiff base derived from 2,3-diaminopyridine. The complex of copper(II) with compound 1 was isolated and characterized by elemental analysis, magnetic susceptibility measurement, UV-vis and IR spectrometry.     

Vibrational analysis of N-acetyl-alpha-D-glucosamine and beta-D-glucuronic acid

Infrared spectra of solid and aqueous solutions of N-acetyl-alpha-D-glucosamine and beta-D-glucuronic acid have been investigated by means of Fourier transform infrared (FT-IR) spectroscopy and quantum chemical density functional theory (DFT) calculations. The errors of the computed harmonic force field were corrected according to the scaled quantum mechanical (SQM) method of Pulay, with scale factors partly from the literature and partly developed here. Scale factors for the hydrogen-bonded OH groups were determined by SQM treatment of ethylene glycol. The IR spectra and test computations revealed that beta-D-glucuronic acid is present as a dimer, formed by hydrogen-bonding between the COOH groups, in the solid phase. On the basis of the calculated results, 64 and 56 bands in the 4000-50 cm(-1) range of the FT-IR spectra have been assigned for N-acetyl-alpha-D-glucosamine and beta-D-glucuronic acid, respectively.     

Cytotoxic properties of platinum(IV) and dinuclear platinum(II) complexes and their ligand substitution reactions with guanosine-5′-monophosphate

The substitution reaction of the Pt(IV) complex [PtCl₄(bipy)] with guanosine-5??-monophosphate (5??-GMP) was studied by UV?CVis spectrophotometry. This reaction was investigated under pseudo-first-order conditions at 37?°C in 25?mM Hepes buffer (pH?=?7.2) in the presence of 10?mM NaCl to prevent the hydrolysis of the complex. The substitution of chlorides in [{trans-Pt(NH₃)₂Cl}₂(??-1,2-bis(4-pyridyl)ethane)](ClO₄)₂ (Pt3) complex by 5??-GMP was followed by ¹H NMR spectroscopy under second-order conditions. Very similar values for the rate constants of both substitution steps were obtained. The Pt(IV) complexes, [PtCl₄(bipy)] and [PtCl₄(dach)], as well as dinuclaer Pt(II) [{trans-Pt(NH₃)₂Cl}₂(??-pyrazine)](ClO₄)₂ (Pt1), [{trans-Pt(NH₃)₂Cl}₂(??-4,4??-bipyridyl)](ClO₄)₂?·?DMF (Pt2) and [{trans-Pt(NH₃)₂Cl}₂(??-1,2-bis(4-pyridyl)ethane)](ClO₄)₂ (Pt3) complexes, displayed potent cytotoxic activity against human ovarium carcinoma cell line TOV21G and lower activity toward human colon carcinoma HCT116 cell line at the same concentrations. Our data indicate that these platinum complexes could be explored further, as potential therapeutic agents for ovarian cancer.     

An Integrated approach (thermodynamic, structural, and computational) to the study of complexation of alkali-metal cations by a lower-rim calix[4]arene amide derivative in acetonitrile

The calix[4]arene secondary-amide derivative L was synthesized, and its complexation with alkali-metal cations in acetonitrile (MeCN) was studied by means of spectrophotometric, NMR, conductometric, and microcalorimetric titrations at 25 °C. The stability constants of the 1:1 (metal/ligand) complexes determined by different methods were in excellent agreement. For the complexation of M(+) (M = Li, Na, K) with L, both enthalpic and entropic contributions were favorable, with their values and mutual relations being quite strongly dependent on the cation. The enthalpic and overall stability was the largest in the case of the sodium complex. Molecular and crystal structures of free L, its methanol and MeCN solvates, the sodium complex, and its MeCN solvate were determined by single-crystal X-ray diffraction. The inclusion of a MeCN molecule in the calixarene hydrophobic cavity was observed both in solution and in the solid state. This specific interaction was found to be stronger in the case of metal complexes compared to the free ligand because of the better preorganization of the hydrophobic cone to accept the solvent molecule. Density functional theory calculations showed that the flattened cone conformation (C(2) point group) of L was generally more favorable than the square cone conformation (C(4) point group). In the complex with Na(+), L was in square cone conformation, whereas in its adduct with MeCN, the conformation was slightly distorted from the full symmetry. These conformations were in agreement with those observed in the solid state. The classical molecular dynamics simulations indicated that the MeCN molecule enters the L hydrophobic cavity of both the free ligand and its alkali-metal complexes. The inclusion of MeCN in the cone of free L was accompanied by the conformational change from C(2) to C(4) symmetry. As in solution studies, in the case of ML(+) complexes, an allosteric effect was observed: the ligand was already in the appropriate square cone conformation to bind the solvent molecule, allowing it to more easily and faster enter the calixarene cavity.     

Divergent-flow isoelectric focusing for separation and preparative analysis of peptides

A divergent-flow isoelectric focusing (DF IEF) technique has been applied for the separation and preparative analysis of peptides. The parameters of the developed DF IEF device such as dimension and shape of the separation bed, selection of nonwoven material of the channel, and separation conditions were optimized. The DF IEF device was tested by the separation of a peptide mixture originating from the tryptic digestion of BSA, cytochrome c, and myoglobin. The pH gradient of DF IEF was created by the autofocusing of tryptic peptides themselves without any addition of carrier ampholytes. The focusing process was monitored visually using colored pI markers, and the obtained fractions were analyzed by RP-HPLC and ESI/TOF-MS. DF IEF operating in the autofocusing mode provides an efficient preseparation of peptides, which is comparable with a commercially available MicroRotofor multicompartment electrolyzer and significantly improves sequence coverage of analyzed proteins. The potential of the DF IEF device as an efficient tool for the preparative scale separations was demonstrated by the isolation of caseinomacropeptide (CMP) from a crude whey solution.     

Synthesis of isoxazolopyrroloisoquinolines by intramolecular cyclizations of 5-(2-arylethyl)-6-hydroxytetrahydro-4H-pyrrolo[3,4-d]isoxazol-4-ones

5,8a,11a,11b-Tetrahydroisoxazolo[5′,4′:3,4]pyrrolo[2,1-a]isoquinolin-8(6H)-ones were prepared by intramolecular cyclization of 5-(2-arylethyl)-6-hydroxytetrahydro-4H-pyrrolo[3,4-d]isoxazol-4-ones in the presence of boron trifluoride diethyl etherate.