Eigenvalues of Hermite and Laguerre ensembles: large beta asymptotics

In this paper we examine the zero and first order eigenvalue fluctuations for the β-Hermite and β-Laguerre ensembles, using tridiagonal matrix models, in the limit as β→∞. We prove that the fluctuations are described by multivariate Gaussians of covariance O(1/β), centered at the roots of a corresponding Hermite (Laguerre) polynomial. The covariance matrix itself is expressed as combinations of Hermite or Laguerre polynomials respectively.We show that the approximations are of real value even for small β; we can use them to approximate the true functions even for the traditional β=1,2,4 values.     

The equations of a holomorphic subspace in a complex Finsler space

In [Mu1] we underlined the motifs of holomorphic subspaces in a complex Finsler space: induced nonlinear connection, coupling connections, and the induced tangent and normal connections. In the present paper we investigate the equations of Gauss, H-and A-Codazzi, and Ricci equations of a holomorphic subspace. We deduce the link between the holomorphic curvatures of the Chern-Finsler connection and its induced tangent connection. Conditions for totally geodesic holomorphic subspaces are obtained. Communicated by János Szenthe     

Multiple solutions of boundary value problems: an elementary approach via the shooting method

In this paper we derive the existence of multiple solutions for boundary value problems of the type $$u\prime \prime + f\left( {t,u} \right) = 0,u\left( 0 \right) = 0,u\left( \pi \right) = 0$$ , in terms of the behaviour of the ratiof(t,u)/u nearu=0 and near infinity. The nonlinear termf is assumed to be locally Lipschitz inu, so that the shooting method can be used. (AMS Subject Classification: 34B15).     

Preparation and characterisation of thermoresponsive poly[(N-isopropylacrylamide-co-acrylamide-co-(hydroxyethyl acrylate)] microspheres as a matrix for the pulsed release of drugs

Despite the large number of publications and patents concerning pH/thermoresponsive polymers, few data are available concerning the preparation of thermoresponsive cross-linked microspheres from preformed polymers. Therefore, N-isopropylacrylamide-co-acrylamide-co-(2-hydroxyethyl acrylate) copolymers were obtained as a new thermoresponsive material with a lower critical solution temperature (LCST) around 36 degrees C, in phosphate buffer at pH 7.4, and with a cross-linkable OH group in their structure. The LCST value was determined both by UV spectroscopy and microcalorimetric analysis. These copolymers were solubilised in acidified aqueous solution below their LCST, dispersed in mineral oil, and transformed into stable microspheres by cross-linking with glutaraldehyde. The thermoresponsive microspheres were characterised by optical and scanning electron microscopy, degree of swelling, and water retention. The pore dimensions of the microspheres and the retention volumes of some drugs and typical compounds were evaluated at different temperatures by liquid chromatography. Indomethacin, as a model drug, was included in the microspheres by the solvent evaporation method. Finally, the influence of temperature and of temperature cycling on drug release was investigated.     

Photometrische Bestimmung von Kohlenmonoxyd in der Luft

Zusammenfassung Es wird ein photometrisches Verfahren der CO-Bestimmung beschrieben, das auf der Absorption des Gases in einer alkalischen Lösung der Silberverbindung der p-Sulfamidbenzoesäure beruht. Die Silberverbindung wird zu metallischem Silber reduziert, das in kolloider Verteilung bleibt. Die Extinktion dieses Silbersols wird gemessen. Sie ist unter den Bedingungen der Arbeitsvorschrift im Bereich von 0,001–0,5% CO der Konzentration des Kohlenmonoxyds proportional. Bei Wellenlängen unterhalb 500 m nimmt die Extinktion stark zu. Die Messungen werden deshalb zweckmäßig im kurzwelligen Licht durchgeführt. Mit Zeiss-Filter S 42 wird z. B. nahezu die doppelte Meßempfindlichkeit erreicht wie mit Filter S 50. Die Durchführung der CO-Bestimmung wird genau beschrieben.     

Perturbational approach to the electron correlation cusp applied to helium‐like atoms

A recently proposed perturbational approach to the electron correlation cusp problem 1 is tested in the context of three spherically symmetrical two‐electron systems: helium atom, hydride anion, and a solvable model system. The interelectronic interaction is partitioned into long‐ and short‐range components. The long‐range interaction, lacking the singularities responsible for the electron correlation cusp, is included in the reference Hamiltonian. Accelerated convergence of orbital‐based methods for this smooth reference Hamiltonian is shown by a detailed partial wave analysis. Contracted orbital basis sets constructed from atomic natural orbitals are shown to be significantly better for the new Hamiltonian than standard basis sets of the same size. The short‐range component becomes the perturbation. The low‐order perturbation equations are solved variationally using basis sets of correlated Gaussian geminals. Variational energies and low‐order perturbation wave functions for the model system are shown to be in excellent agreement with highly accurate numerical solutions for that system. Approximations of the reference wave functions, described by fewer basis functions, are tested for use in the perturbation equations and shown to provide significant computational advantages with tolerable loss of accuracy. Lower bounds for the radius of convergence of the resulting perturbation expansions are estimated. The proposed method is capable of achieving sub‐μHartree accuracy for all systems considered here. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Chemoenzymatic synthesis of highly enantiomerically enriched secondary alcohols with a thiazolic core

Stereoselective preparative enzymatic acylation and hydrolysis/methanolysis of various C-substituted rac-thiazol-2-yl-methanols were achieved for the preparation of enantiopure or enantiomerically enriched, naturally occurring 2-hydroxymethylthiazoles. The absolute configurations of the resulting secondary alcohols were determined by a detailed ¹H NMR study of Mosher’s derivatives.     

Model-based sensitivity analysis of a fluidised-bed bioreactor for mercury uptake by immobilised Pseudomonas putida cells

A model-based sensitivity analysis was performed in order to evaluate the importance of the individual operating parameters of a three-phase fluidised-bed biological reactor used for removing mercury ions from wastewater. The parameters analysed involve the immobilised biomass load (bacteria P. putida) on alginate beads, particle size, inlet flow-rate, mercury ion loads in the fed wastewater, and the solid fraction in the reactor. Predictions were generated by using pseudo-first-order, Michaelis-Menten, or pseudo-Haldane kinetic models. The results highlight the major influence of the biomass/solid load and of the liquid residence time on the reactor efficiency. Also, the resultant significant differences in the model predictions underline the importance of using a more accurate kinetic model for process design and control purposes.     

The Vapor-Liquid Polycondensation of Cyclohexylphosphoric Dichloride with Hydroquinone

The vapor-liquid polycondensation of cyclohexylphosphoric dichloride with hydroquinone was investigated. The influence of the temperature, reaction time, base concentration, and molar ratio of reagents on the yield, inherent viscosity, and molecular weight of the obtained polymer was studied. Second order, central, composite, rotatable experimental design was used in order to carry out this work and to mark limits of the experimental field for optimal yields and high inherent viscosities.     

Geometrical and dynamical properties of general Euler top system

In this paper we present various geometrical and dynamical properties of the Euler top system in general form. Also the stability problem for the equilibrium states of them are discussed.