Wall Rational Functions and Khrushchev’s Formula for Orthogonal Rational Functions

The Nevalinna–Pick algorithm yields a continued fraction expansion of every Schur function, whose approximants are identified. These approximants are quotients of rational functions which can be understood as the rational analogs of the Wall polynomials. The properties of these Wall rational functions and the corresponding approximants permit us to obtain a Khrushchev’s formula for orthogonal rational functions. An introduction to the convergence of the Wall approximants in the indeterminate case is presented. This work was partially realized during two stays of the second author at the Norwegian University of Science and Technology (NTNU) financed respectively by Secretaría de Estado de Universidades e Investigación from the Ministry of Education and Science of Spain and by the Department of Mathematical Sciences of NTNU. The work of the second author was also partially supported by the Spanish grants from the Ministry of Education and Science, project code MTM2005-08648-C02-01, and the Ministry of Science and Innovation, project code MTM2008-06689-C02-01, and by Project E-64 of Diputación General de Aragón (Spain).     

Surface properties of inclusion complexes between alpha-cyclodextrin and poly(ethylene oxide)

The surface properties of the supramolecular inclusion complex (IC) obtained from the threading of alpha-cyclodextrin (alpha-CD) onto poly(ethylene oxide) (PEO) free in solution are studied. The complexes were characterized by IR, (1)H NMR spectroscopy, and thermal analysis. The variation of the interfacial tension, gamma(int), with inclusion complex (IC) concentration and temperature were determined. The results were compared with those found for PEO under the same conditions. alpha-CD does not present surface activity. To quantify the adsorption process of IC and PEO in aqueous medium, the Gibbs equation was used. The driving force for adsorption of IC at the air/aqueous interface seems to arise from an enthalpic contribution. The wettability of the alpha-CD, PEO, and IC films with two liquids was determined by static contact angle measurements. The hydrophobicity degree was estimated. IC is more hydrophobic than PEO and alpha-CD.     

2-(5-Bromo-2-pyridylazo)-5-diethylaminophenol as a reagent for the spectrophotometric determination of La(III), Y(III), and Ce(III)

The complexes of the reagent 5-Br-PADAP with the metal ions La(III), Ce(III), and Y(III) have been studied.The composition and stability of these complexes have been determined. A sensitive spectrophotometric procedure for the determination of the metal ions La(III), Ce(III), and Y(III) has been proposed. The limitations of this procedure and the effect of other ions have been studied.     

Electrostatic pull-in instability for tweezer architectures

Meccanica - The work investigates the static pull-in instability of electrostatically actuated tweezers with tubular electrodes. At a critical voltage, named pull-in voltage, the attraction force...     

A method for the solution of the mass transport equation in a free burning d.c. arc

A method is developed for the solution of a general form of the mass transport equation for a free burning d.c. arc. The spatial particle density distribution function is represented in form of a linear combination of appropriate basis functions in which the expansion coefficients are calculated using the variation principle. The method allows calculation of particle distribution at various levels of approximation, and also includes cases in which both radial and axial dependences of the diffusion coefficient as well as the directed transport velocity are taken into account. The results of some simple test calculations are presented.     

Asymptotics for Szegö polynomial zeros

The Wiener-Levinson method and algorithm, formulated here in terms of Szegö polynomials _n ( _N,I ;z) orthogonal on the unit circle, is used to find unknown frequencies _j from anN-sample of a discrete time signal consisting of the superposition of sinusoidal waves with frequencies ₁,...,₁. In a recent paper the authors (and W.J. Thron) have shown that zerosz(j, n, N, I) of _n ( _N,I ;z) converge asN to the critical points ,j=1, 2,...,I, providednn ₀ (I)=2I+L, whereL is 0 or 1. The present paper gives results on the convergence of zerosz(j, n, N, I) to some of the for the case in whichnn ₀ (I), wheren is the degree of _n ( _N,I ;z).Research supported in part by the United States Educational Foundation in Norway (Fulbright Grant), the Norwegian Research Council (NAVF) and the US National Science Foundation under Grant No. DMS-9103141.     

Electrochemical and Spectroscopic Studies on the Interaction of Gatifloxacin,Moxifloxacin and Sparfloxacin with DNA and Their Analytical Applications

The electrochemical oxidation of the three fluoroquinolone drugs FQs: gatifloxacin GTF, moxifloxacin MXF and sparfloxacin SPF, at the bare and DNA‐modified glassy carbon electrodes has been studied by voltammetric techniques. The three FQs showed one irreversible oxidation peak at potential range 0.85–0.91 V vs. Ag‐AgCl, in phosphate buffer of pH 7.0. Differential pulse voltammetry (DPV) and UV‐absorption spectroscopic techniques were employed to probe the interaction between the FQs and calf thymus double stranded deoxyribonucleic acid (ds CT‐DNA). From electrochemical data, the binding constant between DNA and the gatifloxacin, moxifloxacin and sparfloxacin are calculated to be 3228, 2596 and 2857 M^?1 respectively. Based on electrochemical and spectroscopic results, the mode of binding of fluoroquinolone to DNA through combined effect of intercalation and electrostatic interaction was concluded. A detection scheme based on a preconcentration and differential pulse voltammetric (DPV) determination at dsDNA modified glassy carbon electrode (DNA/GCE) was proposed for the trace determination of the studied analytes. The developed method was successfully applied to the determination of the FQs in pharmaceutical formulations.     

Molecularly Imprinted Electrochemical Sensor for the Detection of Organophosphorus Pesticide Profenofos

The presence of profenofos (PFF) in food has been strictly limited by legislation due to its genotoxic and toxic effects on health. It is therefore very important to establish simple and rapid analytical methods to detect traces of this insecticide. A reusable molecularly imprinted polypyrrole MIP(O-PPy) on a glassy carbon electrode (GCE) has been developed to measure PFF. The PPy was polymerized by cyclic voltammetry (CV) in the presence of template molecules (PFF) in an acidic solution on a GCE. The various experimental parameters such as film thickness, analyte/monomer ratio, and removal/rebinding requirements were examined and optimized. The signal of the redox probe (ferrocyanide/ferrocyanide) was used for the electrochemical detections. All steps of the sensor manufacturing, removal/rebinding of template molecules, and response to different PFF concentrations were tested by cyclic voltammetry (CV), differential pulse voltammetry (DPV), and electrochemical impedance spectroscopy (EIS). The MIP sensor was able to detect PFF in the linear ranges of 1.0×10⁻⁹ to 1.0×10⁻⁶ M and 1.0×10⁻⁹ to 5.0×10⁻⁶ M, with detection limits, a signal-to-noise ratio (S/N) of three was used to estimate LOD, of about 1 nM using DPV and EIS, respectively. The MIP (PPy) GCE provided excellent PFF recognition performance and was successfully used to quantify PFF in sweet pepper samples, yielding recoveries not greater than 108 %.     

Simultaneous detection of ascorbate and uric acid using a selectively catalytic surface

The direct and selective detection of ascorbate at conventional carbon or metal electrodes is difficult due to its large overpotential and fouling by oxidation products. Electrode modification by electrochemical reduction of diazonium salts of different aryl derivatives is useful for catalytic, analytical and biotechnological applications. A monolayer of o-aminophenol (o-AP) was grafted on a glassy carbon electrode (GCE) via the electrochemical reduction of its in situ prepared diazonium salts in aqueous solution. The o-aminophenol confined surface was characterized by cyclic voltammetry. The grafted film demonstrated an excellent electrocatalytic activity towards the oxidation of ascorbate in phosphate buffer of pH 7.0 shifting the overpotential from +462 to +263 mV versus Ag/AgCl. Cyclic voltammetry and d.c. amperometric measurements were carried out for the quantitative determination of ascorbate and uric acid. The catalytic oxidation peak current was linearly dependent on the ascorbate concentration and a linear calibration curve was obtained using d.c. amperometry in the range of 2-20 μM of ascorbate with a correlation coefficient 0.9998, and limit of detection 0.3 μM. The effect of H₂O₂ on the electrocatalytic oxidation of ascorbate at o-aminophenol modified GC electrode has been studied, the half-life time and rate constant was estimated as 270 s, and 2.57 × 10⁻³ s⁻¹, respectively. The catalytically selective electrode was applied to the simultaneous detection of ascorbate and uric acid, and used for their determination in real urine samples. This o-AP/GCE showed high stability with time, and was used as a simple and precise amperometric sensor for the selective determination of ascorbate.