Hyperfunctional Weights for Orthogonal Polynomials

The Chebychev polynomials associated to any given moments μ_{n ∞} ⁰ are formally orthogonal with respect to the formal δ-series $$w(x)= {\sum^\infty_0}(- 1)^{n}\mu_{{n}}\delta^{(n)}(x)/n!.$$ We show that this formal weight can be a true hyperfunctional weight if its Fourier transform is a slowly increasing holomorphic function in some tubular neighborhood of the real line. It provides a unifying treatment of real and complex orthogonality of Chebychev polynomials including all classical examples and characterizes Chebychev polynomials having Bessel type orthogonality.     

Semiconducting organic polymer from polyacrylamide–Cu++ chelate and iodine

Semiconducting organic polymer was obtained by the modification of polyacrylamide (PAAm)–Cu⁺⁺ chelate with iodine in acetone. Favorable conditions for preparing the chelate effective for the conduction were investigated. Surface resistivities were affected by the amounts of cupric salts and iodine, satisfactory results being given by about 25 wt % of the salts based on PAAm and more than 1 wt % of iodine on the chelate. The conductivity was also varied with the degree of neutralization of the chelate in solution, and optimal values were obtained by addition of about an equimolar amount of potassium hydroxide to cupric salts. Effective structures of the polymer chelate in solution were assumed on the basis of the visible and the NMR spectra and potentiometric titration.     

Structure of the asparagine-linked sugar chains of porcine kidney and human urine cerebroside sulfate activator protein

The specific sugar residues and their linkages in the oligosaccharides from pig kidney and human urine cerebroside sulfate activator proteins (saposin B), although previously hypothesized, have been unambiguously characterized. Exhaustive sequential exoglycosidase digestion of the trimethyl-p-aminophenyl derivatives, followed by either matrix-assisted laser desorption/ionization and/or mass spectrometry, was used to define the residues and their linkages. The oligosaccharides were enzymatically released from the proteins by treatment with peptidyl-N-glycosidase F and separated from the proteins by reversed-phase high-performance liquid chromatography (HPLC). Reducing termini were converted to the trimethyl-p-aminophenyl derivative and the samples were further purified by normal-phase HPLC. The derivatized carbohydrates were then treated sequentially with a series of exoglycosidases of defined specificity, and the products of each digestion were examined by mass spectrometry. The pentasaccharides from pig kidney and human urine protein were shown to be of the asparagine-linked complex type composed of mannose-alpha 1-6-mannose-beta 1-4-N-acetylglucosamine-N-acetylglucosamine(alpha 1-6-fucose). This highly degraded structure probably represents the final product of intra-lysosomal exoglycosidase digestion. Oligosaccharide sequencing by specific exoglycosidase degradation coupled with mass spectrometry is more rapid than conventional oligosaccharide sequencing. The procedures developed will be useful for sequencing other oligosaccharides including those from other members of the lipid-binding protein class to which cerebroside sulfate activator belongs. (c) 2000 John Wiley & Sons, Ltd.     

Pyranoxanthones from Calophyllum Inophyllum

Phytochemical investigation of the stem bark of Calophyllum inophyllum resulted in the isolation of a new dipyrenoxanthone, calophinone ( 1 ), together with four related xanthones ( 2–5 ). Identification of the isolated compounds was achieved through intensive studies of their spectral data, especially 2D NMR.     

Review of Directly Producing Light olefins via CO Hydrogenation

Directly making light olefins via CO hydrogenation is a promising process to obtain a nonpetroleum based supply of alkenes.Limited by the ASF distribution function of Fischer-Tropsch synthesis,the yield of light olefins (C2-C4) can not reach the desired levels,which is a great challenge to overcome.Beginning thermodynamic analysis,the ASF distribution function,the reaction performance of CO hydrogenation and slurry reactor studies.The problems currently faced by this research area are presented at the end of the article.     

Properties and Photoelectrocatalytic Behaviour of Sol-Gel Derived TiO2 Thin Films

Titanium dioxide (TiO₂) thin films have been prepared on indium doped tin oxide (ITO) glass by sol-gel dip-coating method. Properties of the films were determined as a function of heat-treatment by X-ray diffraction, scanning electron microscopy and photoelectrochemical tests. The films heat-treated at higher temperatures show better crystallinity and photoresponse. The microscopic structure on the film after heat-treatment is attributed to the incorporation of organic polymer into the precursor solution. The performance of the electrodes treated at different temperature on photoelectrocatalytic degradation of methyl orange was investigated. The effect of applied potential and the ability of the electrode to be repeatedly used in photoelectrocatalytic degradation were also evaluated.     

Topology evolution and gelation mechanism of agarose gel

Kinetics as well as the evolution of the agarose gel topology is discussed, and the agarose gelation mechanism is identified. Aqueous high melting (HM) agarose solution (0.5% w/v) is used as the model system. It is found that the gelation process can be clearly divided into three stages: induction stage, gelation stage, and pseudoequilibrium stage. The induction stage of the gelation mechanism is identified using an advanced rheological expansion system (ARES, Rheometric Scientific). When a quench rate as large as 30 deg C/min is applied, gelation seems to occur through a nucleation and growth mechanism with a well-defined induction time (time required for the formation of the critical nuclei which enable further growth). The relationship between the induction time and the driving force which is determined by the final setting temperature follows the 3D nucleation model. A schematic representation of the three stages of the gelation mechanism is given based on turbidity and rheological measurements. Aggregation of agarose chains is promoted in the polymer-rich phase and this effect is evident from the increasing mass/length ratio of the fiber bundles upon gelation. Continuously increasing pore size during gelation may be attributed to the coagulation of the local polymer-rich phase in order to achieve the global minimum of the free energy of the gelling system. The gel pore size determined using turbidity measurements has been verified by electrophoretic mobility measurements.     

Co-immobilization of polymeric luminol,iron(II) tris(5-aminophenanthroline) and glucose oxidase at an electrode surface,and its application as a glucose optrode

The anodic polymerization of 3-aminophthalhydrazide (luminol) and iron(II) tris 5-aminophenanthroline (Fe(phen-NH2)3(2+)) has been reported in this paper. A bilayer electrode was developed based on these polymers and the ITO conductive glass (denoted ITO[Fe(phen-NH2)3(2+)]luminol electrode). This electrode emitted light (lambdaem: 430 nm) as it was brought into contact with H2O2. At pH 10, the resulting electrochemiluminescence (ECL) showed a linear relationship with the concentration of H2O2 in the range of 10 microM(-1) mM. This bilayer electrode also showed an application potential for the detection of glucose after being further modified with glucose oxidase (denoted ITO[Fe(phen-NH2)3(2+)]luminol]GOx electrode). Although the resulting ECL decayed more rapidly in concentrated glucose solutions (e.g., I M) because of the consumption of luminol during use, the decay became less severe in diluted glucose solutions (e.g., 10 mM). According to the flow injection analysis, a linear relationship existed between the ECL and the concentration of glucose from 10(-5)-10(-3) M at pH 9. The detection limit could reach a level of 5 x 10(-5) M at this pH.