The Dunkl Oscillator in the Plane II: Representations of the Symmetry Algebra

The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations of the symmetry algebra of the system, called the Schwinger–Dunkl algebra sd(2), are investigated. The algebra sd(2) has six generators, including two involutions and a central element, and can be seen as a deformation of the Lie algebra \({\mathfrak{u}(2)}\) . Two of the symmetry generators, J ₃ and J ₂, are respectively associated to the separation of variables in Cartesian and polar coordinates. Using the parabosonic creation/annihilation operators, two bases for the representations of sd(2), the Cartesian and circular bases, are constructed. In the Cartesian basis, the operator J ₃ is diagonal and the operator J ₂ acts in a tridiagonal fashion. In the circular basis, the operator J ₂ is block upper-triangular with all blocks 2 × 2 and the operator J ₃ acts in a tridiagonal fashion. The expansion coefficients between the two bases are given by the Krawtchouk polynomials. In the general case, the eigenvectors of J ₂ in the circular basis are generated by the Heun polynomials, and their components are expressed in terms of the para-Krawtchouk polynomials. In the fully isotropic case, the eigenvectors of J ₂ are generated by little ?1 Jacobi or ordinary Jacobi polynomials. The basis in which the operator J ₂ is diagonal is considered. In this basis, the defining relations of the Schwinger–Dunkl algebra imply that J ₃ acts in a block tridiagonal fashion with all blocks 2 × 2. The matrix elements of J ₃ in this basis are given explicitly.     

Diffusion of small penetrant molecules in polybutadienes

The diffusion coefficient D in the dilute limit for three different penetrants – oxygen, water, and methanol – in three different conformations of polybutadiene (all cis-1,4, all trans-1,4, and a random copolymer containing 50% trans-1,4, 40% cis-1,4, and 10% vinyl-1,2 repeat units) has been computed using molecular dynamics simulations for temperatures in the range T?=?300–400?K. Simulation runs of 25 and 50?ns were made for each of the 45 combinations of penetrant, conformation, and temperature studied. Over this temperature range the density of the all-cis-1,4 conformation is higher than that of the all-trans-1,4 and random copolymer conformations, which are approximately equal. For all three conformations, D for oxygen and water are comparable and larger than that of methanol. However for a given penetrant, strong differences were observed in the rate of increase of D for the three conformations. We find that the activation barriers for the three penetrants are generally between 20 and 30?kJ?mol^?1, in agreement with experimental results. The magnitude of the activation energy is directly proportional to the size, rather than the mass, of the penetrant molecule.     

Preparation, characterization and thermal studies of some transition metal ternary complexes

Ternary complexes of Co(II), Ni(II), Cu(II) and Zn(II) with nitrilotriacetic acid as a primary ligand and glycine as secondary ligand were prepared in slightly acid medium. Their molecular masses were determined by acid-base titration against standard potassium hydroxide solution. Their molecular structures were found to be [M (HNTA)(glyH)(2H₂O)]. Thermogravimetric analysis confirmed this structure and that the water present is coordinated to the central metal atom. UV-Vis spectra showed that the complexes have octahedral symmetry. IR spectra suggested the presence of intermolecular hydrogen bonding. This phenomenon was supported by mass spectra. The ionization constants of these complexes, as diprotic acids, were determined.     

Synthesis and catalytic properties of novel ruthenium N-heterocyclic-carbene complexes

The reaction of [RuCl₂(p-cymene)]₂ with 1,3-dialkylimidazolinium salts 1a–f in the presence of a small excess of cesium carbonate yields chelated η⁶-arene, η¹-carbene ruthenium complexes 2a–f. All synthesised compounds were characterized by elemental analysis, NMR spectroscopy. The catalytic activity of RuCl₂(η⁶-arene, η¹-imidazolinylidene) complexes 2a–f was evaluated in the direct arylation of 2-phenylpyridine with chlorobenzene derivatives.     

Acutaxylines A and B, two novel triterpenes from Dysoxylum acutangulum

Two novel triterpenes, acutaxylines A (1) and B (2) consisting of a cyclopentenone side chain at C-17 and an oxepan-2-ol, were isolated from the leaves of Dysoxylum acutangulum. The relative stereochemistry of 1 and 2 was determined by NOESY correlations. Acutaxyline B showed moderate cytotoxicity against human blood premyelocytic leukemia cells.     

Adsorption Study of Immunoglobulin G Subclasses from Different Species by Pseudobioaffinity Separation on Histidyl–Bisoxirane–Sepharose

Adsorption chromatography is increasingly used for protein separations and biomedical applications. Therapeutic molecules such as antibodies, cytokines, therapeutic DNA, and plasma proteins must be purified before characterization and utilization. Use of immunoglobulins as immunodiagnostic and therapeutic tools has initiated many attempts to develop new adsorbents for their separation. Protein A and protein G are the affinity ligands most widely used for separation of immunoglobulins. These proteins are reliable, and have good selectivity and specificity, but are very expensive. Much attention has therefore been devoted to developing alternative methods for separation of immunoglobulins. Pseudobiospecific ligands, for example metal ions and amino acids, can be used for separation of a wide range of biological molecules. In this study, IgG₁, IgG₂, and IgG₃, three subclasses of human IgG, were separated from human serum using the amino acid histidine grafted on to bisoxirane-activated Sepharose, as pseudobiospecific adsorbent. Adsorption of IgG from different animal species on the same chromatographic adsorbent was also tested. The high recovery and purification on histidyl–bisoxirane–Sepharose gel of IgG from all the sources tested compared well with results obtained by use of protein A–Sepharose gel.     

On spaces in which countably compact sets are closed, and hereditary properties

A space X is called C-closed if every countably compact subset of X is closed in X. We study the properties of C-closed spaces. Among other results, it is shown that countably compact C-closed spaces have countable tightness and under Martin's Axiom or 2^ω0<2^ω1, C-closed is equivalent to sequential for compact Hausdorff spaces. Furthermore, every hereditarily quasi-k Hausdorff space is Fréchet-Urysohn, which generalizes a theorem of Arhangel'sk in [4]. Also every hereditarily q-space is hereditarily of pointwise countable type and contains an open dense first countable subspace.     

Preface

Preface

Preface     

Electrochemically Aided Control of Solid Phase Micro-Extraction (EASPME) Using Conducting Polymer-Coated Solid Substrates Applicable to Neutral Analytes

A method for the extraction and selective determination of the neutral species arsenobetaine (AsB) is proposed using electro-synthesized organic conducting polymer (OCP) films. The polymer films are used as solid phase micro-extraction (SPME) elements for the direct and specific extraction of trace levels of AsB. The separation and detection of the arsenic (As) species is attained using an HPLC-ICP-MS interfaced system. The selectivity of the method towards neutral AsB in the presence of other anionic As-species is explained in terms of the change in the hydrophobic nature of the film during the doping/undoping processes. The type of OCP, the thickness of the film, the applied potential during uptake and release of AsB are among the factors studied for the method. The uptake and release time/potential profiles are given, and a thermodynamic model is proposed. The performance of poly(3-octylthiophene), poly(3-dodecylthiophene), and poly(3-hexadecylthiophene) films were compared, with the best results obtained using poly(3-octylthiophene). The detection limit and linear dynamic range using this method are 14ngmL^–1 and 70–1200ngmL^–1, respectively. The method was validated using a standard reference material and tested for the determination of AsB in artificial environmental soil samples.