Numerical solution of delay differential equations by uniform corrections to an implicit Runge-Kutta method

Summary In this paper we develop a class of numerical methods to approximate the solutions of delay differential equations. They are essentially based on a modified version, in a predictor-corrector mode, of the one-step collocation method atn Gaussian points. These methods, applied to ODE's, provide a continuous approximate solution which is accurate of order 2n at the nodes and of ordern+1 uniformly in the whole interval. In order to extend the methods to delay differential equations, the uniform accuracy is raised to the order 2n by some a posteriori corrections. Numerical tests and comparisons with other methods are made on real-life problems.This work was supported by CNR within the Progetto Finalizzato Informatica-Sottopr. P1-SOFMAT     

Hydrogen sulphide doping of GaAs and AlxGa1−xAs grown by molecular beam epitaxy (MBE)

H₂S gas has been used during molecular beam epitaxy (MBE) growth of GaAs and Al _x Ga_1–x As as sulphur vector forn-type doping. Doping efficiencies are less than 10^–3 at usual growth temperatures, and are limited by an incorporation competitive surface process, probably 2Ga+H₂SGa₂S+H₂. In Al_xGa_1–x As forx0.2 the doping efficiency is further reduced by carrier freeze-out at deep levels. Measured thermal activation energies depend on growth conditions and remain relatively low even up to the direct-indirect bandgap crossover for substrate temperatures in the 585–645 C range.     

Spectrophotometric study of bismuth with N-(2-acetamido)iminodiacetic acid (ADA): Determination of bismuth in pharmaceutical formulations

A new method for the Spectrophotometric determination of bismuth using N-(2-acetamido)iminodiacetic acid as complexometric agent is proposed. The complex is formed in a wide pH range, 5.5–7.5, and has a maximum absorption at 265 nm. Beer's law is obeyed in the interval 3.8–17.9 μg of bismuth(III)/ml, with a minimum photometric error of 2.3. The molar absorptivity is 9.1 × 10³ liters/cm mol. The stoichiometry of the reaction takes place in the metal-to-ligand ratio 1:2. The interferences produced by the more common ions are studied. The method has been successfully applied to the determination of bismuth in pharmaceutical formulations.     

A 13C and 31P N.M.R. Investigation of restricted rotation in [Pt(η3-allyl){P(cyclohexyl)3}2]+ [PF6]- and related compounds

The dynamic behaviour of [Pt(/gh³-allyl){P(cyclohexyl)₃}₂]⁺[PF₆]^- has been reinvestigated, and the earlier interpretation of restricted rotation about the Pt—P endorsed. The activation parameters were obtained. [Pt(/gh³-allyl)(PPrⁱ₃)₂]⁺[PF₆]^- behaves similarly, while it has not prove possible to stop the rotation in [Pt(/gh³-allyl){P(CH₂Ph)₃}₂]⁺[PF₆]^-.     

On the mechanism of electroluminescence emission by porous silicon layers

The analytical treatment of a model considering the electrooxidation of p-porous silicon layers under galvanostatic conditions is able to give account of experimental facts such as the shape and location of the electroluminescence peak as well as of the spectral shift of the electroluminescence peak produced by oxidation. The proposed model considers electroluminescence to be the result of electron injection into the conduction band by an adsorbed intermediate produced by electrooxidation of the surface coverage with hydrogen or siloxene of the silicon nanocrystallites. The access of holes to the surface is made possible by low accumulation layer conditions and is the rate determining step in the electroluminescence mechanism. In this way it is possible to give a satisfactory explanation to the shift towards the blue experimented by the electroluminiscence emission maximum as a consequence of electrooxidation.     

The effect of packing density of cellulose plugs on streaming potential phenomena

An experimental investigation on streaming potentials of porous plugs of cellulose in both the linear and the non-linear range is described. The variation of the electrokinetic coefficients as a function of fibre concentration in the porous pad has been studied, using solutions of different concentration of Congo Red dye as a permeant. The trend observed for changes of both linear electrokinetic coefficientL ₂₁ and non-linear coefficientL ₂₁₁ as packing density,c _F, increases, is somewhat analogous, the similarity suggesting some proportionality between both coefficients. The electroviscous effect accounts for the decrease ofL ₂₁₁ with the increase ofc _F. The coefficientL ₂₂₁ was found to be always negative and, in absolute value, to decrease with increasingc _F. Second-order coefficients have been interpreted in terms of modifications of “generalized conductivities” produced by the changes of thermodynamic forces.     

Alkylation of β-diketones through their co(II), co(III) and zn(II) complexes. 1-Bromoadamantane as alkylating agent.

α-(1-adamantyl)-β-diketones are now accessible by the alkylation of Co(II) complexes of β-diketones with 1-bromoadamantane. The intermediacy of adamantyl cation is proposed. Co(II), Co(III) and Zn(II) complexes of pentane-2,4-dione react with alkyl halides precursors of stabilized carbenium ions, to give 3-alkylpentane-2,4-diones.     

Monitoring of the metal displacement from the recombinant mouse liver metallothionein Zn(7)-complex by capillary zone electrophoresis with electrospray MS detection

A solution of a Zn-complex of recombinant mouse MT-1 isoform (Zn(7)-MT-1) was prepared and titrated with Cd(2+) ions. A method based on the coupling of capillary zone electrophoresis (CZE) with electrospray MS detection was developed for the analysis of the stoichiometry of the species formed during the titration. The method offered the possibility of the on-line removal of up to 100 mM Tris or phosphate buffer solutions that would otherwise suppress the electrospray signal. By allowing the determination of the metal stoichiometry of the complex species present in solution the method was shown to be complementary to circular dichroism and UV-VIS spectrophotometry conventionally used for similar studies. The titration of the Zn(7)-MT complex with Cd(II) showed the sequential displacement of the Zn by Cd. The unusually high stability of the Cd(6)Zn(1)-MT species was observed which suggests a structural role of the remaining Zn(II) ion.     

Baeyer-Villiger oxidation with potassium peroxomonosulfate supported on acidic silica gel

[reaction: see text] Potassium peroxomonosulfate deposited onto silica SiO2 x KHSO5 efficiently reacts with ketones in dichloromethane at room temperature to give the corresponding esters or lactones in quantitative yields. This method avoids hydrolysis of the reaction products. The Baeyer-Villiger reaction is catalyzed by potassium hydrogensulfate present in the supported reagent.