Convergence of multistep discretizations of DAEs

Standard ODE methods such as linear multistep methods encounter difficulties when applied to differential-algebraic equations (DAEs) of index greater than 1. In particular, previous results for index 2 DAEs have practically ruled out the use of all explicit methods and of implicit multistep methods other than backward difference formulas (BDFs) because of stability considerations. In this paper we embed known results for semi-explicit index 1 and 2 DAEs in a more comprehensive theory based on compound multistep and one-leg discretizations. This explains and characterizes the necessary requirements that a method must fulfill in order to be applicable to semi-explicit DAEs. Thus we conclude that the most useful discretizations are those that avoid discretization of the constraint. A freer use of e.g. explicit methods for the non-stiff differential part of the DAE is then possible.Dedicated to Germund Dahlquist on the occasion of his 70th birthdayThis author thanks the Centro de Estadística y Software Matemático de la Universidad Simón Bolivar (CESMa) for permitting her free use of its research facilities.Partial support by the Swedish Research Council for Engineering Sciences TFR under contract no. 222/91-405.     

A Study of Amorphous Precursors for PbZrO3-PbTiO3 Based Ceramic Materials

Amorphous precursors for PbZrO₃ and PbTiO₃ ceramics were prepared from lead acetate and the transition metaln-propoxide inn-propanol orn-butoxide inn-butanol and hydrolysed with an excess of water. According to GLC and TGA/EGA analyses, the type of alkoxide group influences distinctly the structure of heterometallic precursors, i.e., oxo or acetate bridging, and the amounts of hydroxyl and organic groups bound to the metal network. The local environments of metal atoms in the amorphous precursors were also studied by EXAFS. The analysis reveals that in Pb−Zr precursors alkoxide groups modify the coordination spheres of the zirconium atoms. Conversely, local environments of both lead and titanium atoms within the analysed range of 3.4 A depend weakly on the type of alkoxide used.     

Polar substituent effects in the bicyclo[1.1.1]pentane ring system: acidities of 3-substituted bicyclo[1.1.1]pentane-1-carboxylic acids

Experimental gas-phase acidities are reported for a series of 3-substituted (X) bicyclo [1.1.1]pent-1-yl carboxylic acids (1, Y = COOH). A comparison with available calculated data (MP2/6-311++G**// B3LYP/6-311+G**) reveals good agreement. The relative substituent effects are shown to be adequately described by a much lower level of theory (B3LYP/6-31+G*). Various correlations are presented which clearly point to polar field effects as being the origin of the relative acidities.     

Novel dye-attached macroporous films for cadmium, zinc and lead sorption: Alkali Blue 6B-attached macroporous poly(2-hydroxyethyl methacrylate)

Alkali Blue 6B-attached poly(2-hydroxyethyl methacrylate) (poly(HEMA)) microporous films were investigated as chelate forming sorbents for heavy metal removal. Poly(HEMA) microporous films were prepared by UV-initiated photo-polymerization of HEMA in the presence of an initiator (azobisisobutyronitrile (AIBN)). Alkali Blue 6B was attached covalently. These films with a swelling ratio of 58%, and carrying 14.8 mmol Alkali Blue 6B m(-2) which were then used in the removal of Cd(II), Zn(II) and Pb(II) from aqueous media. Adsorption rates were very high, equilibrium was achieved in about 30 min. The maximum adsorption of heavy metal ions onto the Alkali Blue 6B-attached films were 41.4 mmol m(-2) for Cd(II), 52.4 mmol m(-2) for Zn(II), and 64.5 mmol m(-2) for Pb(II). When the heavy metal ions competed during the adsorption from a mixture the adsorption values for Cd(II), Zn(II) and Pb(II) were quite close. Heavy metal ions were desorbed by using 0.1 M HNO(3). A significant amount of the adsorbed heavy metal ions (up to 95%) could be desorbed in 30 min. Repeated adsorption/desorption cycles showed the feasibility of these novel dye-attached microporous films for heavy metal removal.     

Intercalation of Cyclic Amines into α-Titanium Phosphate

The intercalation of some amines (aniline, benzylamine, cyclohexylamine,piperidine, pyridine, pyrazine and piperazine) into -titaniumphosphate, Ti(HPO₄)_2×H₂O,has been investigated by the batch method and/or by exposing the host to thevapour of the amines. The changes in the interlayer distance of the solidduring the intercalation process was followed by X-ray powder diffraction.The new intercalates were characterised by chemical and thermal analysis.Materials with a monolaminar and/or bilaminar arrangement of amine moleculesin the phosphate interlayer region are obtained depending on the nature ofthe amine. Due to steric hindrance, saturated phases are not obtained forall amines studied. The thermal decomposition of the intercalates (nitrogenatmosphere), takes place in three stages: dehydration, removal of amines andcondensation of the hydrogenphosphate to pyrophosphate groups.     

Magnetic resonance of the weak organic magnet TDAE-C60

The charge transfer compound TDAE-C₆₀ (TDAE — tetrakis-dimethylamino-ethylene) is so far the only known C₆₀ based molecular ferromagnet. The ESR spectra of TDAE-C₆₀ single crystals demonstrate that freshly grown regularly shaped single crystals show at first an AFM (antiferromagnetic)-like behavior which changes upon annealing at room temperature in vacuum to a FM (ferromagnetic) one. It thus seems that annealing induces a change in the relative orientation of the distorted C ₆₀ ^? ions resulting in a change in the sign of the effective magnetic interactions between neighboring C ₆₀ ^? ions. A structural transition in the TDAE methyl protons at 250 K seems to be connected with this process. Here we review the structure, the ESR spectra, the proton NMR spectra and the¹³C NMR spectra of TDAE-C₆₀.     

Electrocatalytic Properties of a Novel Poly‐1‐Naphthylamine‐Modified Electrode Using Ascorbic Acid as Molecule Probe

A glassy carbon electrode was modified with an electropolymerized film of 1‐naphthylamine in aqueous solution. The electrocatalytic properties of this modified electrode (ME) were investigated using ascorbic acid (AA) as probe molecule. The electrochemical behavior of AA in buffer solution was examined by voltammetry and amperometry. The results showed that the ME exhibited good electrocatalytic activity towards the oxidation of AA, as a consequence, it can be used as amperometric sensor of this analyte in a flow injection system with good sensitivity. Calibration curves were linear over the concentration range 0.05–1.50 mM with a phosphate buffer solution pH 3 as the carrier, the detection limit was 1 ppm (S/N=3). The methods were applied to the determination of AA in beverages and pharmaceutical products. A good correlation with a reference method was attained.     

Surface properties of Reactive Yellow 2 immobilised pHEMA and HEMA/chitosan membranes: characterisation of their selectivity to different proteins

Poly(hydroxyethyl methacrylate), pHEMA, and a composite pHEMA/chitosan networks were synthesized in the membrane form via UV initiated photo-polymerisation in the presence of an initiator ,′-azoisobutyronitrile. Reactive Yellow 2 (RY-2) was covalently immobilised as a dye–ligand onto both membranes. The polarity and surface energy of the investigated membranes were determined by contact angle measurement. The incorporation of chitosan in the pHEMA networks produced more hydrophilic surface, as indicated by contact angle analysis. The binding characteristics of lysozyme, γ-globulins, human serum albumin (HSA) and bovine serum albumin (BSA) to pHEMA-RY-2 and pHEMA/chitosan-RY-2 affinity membranes have been investigated from aqueous solution and their dye–ligand free forms were used as control systems. When chitosan was incorporated in the pHEMA network as a cationic polymer led to higher adsorption capacity for the lysozyme. Selective adsorption behaviour was also observed in the case of pHEMA/chitosan-RY-2 membrane for the lysozyme. The non-specific adsorptions of the lysozyme on the pHEMA and pHEMA/chitosan membranes were about 1.9 and 7.2 mg/ml, respectively. These were negligible for all others investigated proteins. The lysozyme adsorption data was analysed using the first-order and the second-order models. The first-order equation in both affinity membrane systems is the most appropriate equation to predict the adsorption capacities of the adsorbents. The adsorption isotherms well fitted the combined Langmuir–Freundlich model. A theoretical analysis has been conducted to estimate the thermodynamic contributions (changes in enthalpy, entropy and Gibbs free energy) for the adsorption of lysozyme to both dye–ligand immobilised membranes. The adsorption capacities of both dye–ligand immobilised membranes increased with increasing the temperature while decreased with increasing the NaCl concentration. Both affinity membranes are stable when subjected to sanitization with sodium hydroxide after repeated separation–elution cycles.     

Concanavalin a immobilized affinity adsorbents for reversible use in yeast invertase adsorption

Concanavalin A (Con A) immobilized poly(2-hydroxyethyl methacrylate) (PHEMA) beads were investigated for specific adsorption of yeast invertase from aqueous solutions. PHEMA beads were prepared by a suspension polymerization technique with an average size of 150-200 microm, and activated by epichlorohydrin. Con A was then immobilized by covalent binding onto these beads. The maximum Con A immobilization was found to be 10 mg/g. The invertase-loading capability of the PHEMA/Con A beads was 107 mg/g. The maximum invertase adsorption capacity on the PHEMA/Con A adsorbents was observed at pH 5.0. The values of the Michaelis constant K(m) of invertase were significantly larger upon adsorption, indicating decreased affinity by the enzyme for its substrate, whereas V(max) was smaller for the adsorbed invertase. Adsorption improved the pH stability of the enzyme as well as its temperature stability. Thermal stability was found to increase with adsorption. The adsorbed enzyme activity was found to be quite stable in repeated experiments. Storage stability of adsorbed invertase.