The Calogero–Bogoyavlenskii–Schiff Equation in 2+1 Dimensions

We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.     

Universality and summability of trigonometric polynomials and trigonometric series

Periodica Mathematica Hungarica -     

R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

Two Stage Solid Phase Extraction with Subsequent HPLC Isolation for Structure Elucidation of Major Metabolites of (+)-(R)-2-{3-(benzo[1,4]dioxan-2-yl-methylamino)-1-propyl}-3(2H)-pyridazinone (GYKI-16084)

GYKI-16084 – (+)-(R)-2-{3-(benzo[1,4]dioxan-2-yl-methylamino)-1-propyl}-3(2H)-pyridazinone hydrochloride – is a new drug candidate for the treatment of benign prostatic hyperplasia. In our study the major metabolites formed in the rat and dog were isolated from dog and rat urine, then their structures were elucidated by means of MS and NMR. A two stage solid phase extraction (SPE) procedure and a semi-preparative HPLC method were developed utilizing various mechanisms of separation. The major metabolites proved to be isomeric glucuronides of the benzodioxane moiety hydroxylated at positions 6 or 7 and {2-(2-carboxyethyl)-3(2H)-pyridazinone}.     

Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary

We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions.     

Simultaneous Determination of Carbamate and Organophosphorus Pesticides in Honeybees by Liquid Chromatography-Mass Spectrometry

Summary The potential of liquid chromatography-mass spectrometry (LC-MS) has been studied for the simultaneous determination of sixteen carbamate and organophosphorus pesticides in honeybees using a traditional sample preparation protocol based on acetone extraction and dichloromethane partitioning. The performances of both atmospheric pressure chemical ionization (APCI) and electrospray (ES) interfaces were compared. APCI offered better sensitivity and specificity for a higher range of pesticides. Limits of quantification were from 0.01 to 0.17 mg kg^–1, at which recoveries obtained were between 64 and 93%, except for pirimicarb that was at 13%, with relative standard deviations ranging from 7 to 20%. Fenitrothion, fenoxycarb, methiocarb and phoxim were found in bees from Valencian Community beehives at concentrations between 0.03 and 3.75 mg kg^–1.     

Pattern forming precipitation in gels due to coupling of chemical reactions with diffusion

Precipitate-forming chemical reactions have been studied in chemically cross-linked poly(vinyl alcohol) gel medium. One of the reactive components was incorporated into the gel, the other was allowed to diffuse into it. Depending on the experimental conditions the reaction-diffusion process often results in patterns of different type. Experiments performed in tubes and in thin layers were carried out in order to investigate the effects of various factors (cross-linking density, swelling degree as well as the concentrations of the outer and inner electrolytes) on the morphologies of the precipitate patterns. It was found that precipitation occurs not only in the Liesegang bands, but also between bands. Beside Liesegang-type structures, tree-like patterns have been observed, showing a characteristic periodicity in the density profile obtained by digitalized image analyses.