Stability and accuracy of time discretizations for initial value problems

Summary This paper continues earlier work by the same authors concerning the shape and size of the stability regions of general linear discretization methods for initial value problems. Here the treatment is extended to cover also implicit schemes, and by placing the accuracy of the schemes into a more central position in the discussion general method-free statements are again obtained. More specialized results are additionally given for linear multistep methods and for the Taylor series method.This research has been supported by Swiss National Foundation, Grant No. 82-524.077This research has been supported by the Heinrich-Hertz-Stiftung, B 32 No. 203/79     

Finite elements for parabolic equations backwards in time

Summary Several regularization methods for parabolic equations backwards in time together with the usual additional constraints for their solution are considered. The error of the regularization is estimated from above and below. For a boundary value problem in time-method, finite elements as well as a time discretization are introduced and the error with respect to the regularized solution is estimated, thus giving an overall error of the discrete regularized problem. The algorithm is tested in simple numerical examples.     

The finite element method with non-uniform mesh sizes applied to the exterior Helmholtz problem

Summary The finite element method with non-uniform mesh sizes is employed to approximately solve Helmholtz type equations in unbounded domains. The given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary. This approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases. This results in a great reduction in the number of equations to be solved. It is proved that optimal error estimates hold inL ²,H ¹ andL , provided that certain relationships hold between the frequency, mesh size and outer radius.     

Fractionation and purification of antioxidant peptides from Chinese sturgeon (Acipenser sinensis) protein hydrolysates prepared using papain and alcalase 2.4L

Protein hydrolysates have the potential to be natural and safer sources of bioactive peptides. In this study, two proteases were used to hydrolyze Chinese sturgeon (Acipenser sinensis) protein, and the hydrolysates were then purified to yield antioxidant peptides. The degree of hydrolysis of 23.56 % and 18.14 % was obtained using papain and alcalase 2.4L, respectivly, and hydrolysates had 96.80 % and 87.24 % total amino acid content, respectivly. The papain hydrolysate (PH) and alcalase 2.4L hydrolysate (AH) showed good antioxidant activity against DPPH^? (IC₅₀ of 3.64 and 3.15 mg/mL) and ABTS^?+ (IC₅₀ of 1.92 and 1.58 mg/mL), respectively. The low-molecular-weight (<1000 Da) fraction of both hydrolysates demonstrated the highest antiradical activity (IC₅₀ of 2.59 and 2.31 mg/mL, DPPH) and (IC₅₀ of 1.54 and 1.36 mg/mL, ABTS), respectively. Nine peptides were separated from both hydrolysates using reverse phase high performance liquid chromatography (RP-HPLC). The IC₅₀ for ABTS^?+ scavenging activity of peptide P5 with valine, glycine and asparagine (MW of 282.13 Da) from PH, and peptide P3 with histidine, glycine and alanine (MW of 302.74 Da) from AH was 0.89 and 0.72 mg/mL, respectively. The fractions and purified peptides obtained from Chinese sturgeon hydrolysates could be utilized as natural antioxidant substitutes in pharmaceuticals and food products.     

Determination of trace metals in industrial boron carbide by solid sampling optical emission spectrometry. Optimization of DC arc excitation (current, atmosphere and chemical modifier)

Graphite arc emission spectrometry has become possible as a result of the invention of novel types of optical spectrometers with Echelle-optics and semiconductor array detectors, and by the application of electronically controlled, high current arc generators. An optimization of the excitation parameters to boron carbide analysis is reported here, measuring background corrected line intensities that were integrated for the time of total evaporation of 5 mg boron carbide sample with or without added chemical modifiers. The following set of experimental conditions were compared with respect of analytical sensitivity and precision: (A) no modifier, Ar + O₂ (20%), 16 A; (B) sample + graphite powder (1 + 1), Ar + O₂ (20%), 16 A; (C) sample + CaF₂ (1 + 1), Ar, 25 A; (D) sample + CaF₂ + graphite powder (1 + 1 + 1), Ar, 25 A. The graphite powder modifier resulted in improved precision in general, and the CaF₂ was effective as a plasma ionization buffer and fluorinating agent. The best compromise was found under conditions B, when oxygen was present in the discharge atmosphere. This is likely due to the stepwise conversion of the boron carbide matrix to the more volatile boron oxide. Under conditions B, detection limits in the ranges of 0.3–9 μg g⁻¹ for Al, Ca, Cr, Cu, Fe, Mg, Mn and Si and that of 18–38 μg g⁻¹ for Ti, W, and Zr were attained. Average RSDs of 10.2 and 9.7% were found, respectively, without and with internal referencing to boron.     

Online preconcentration system for determining ultratrace amounts of Cd in vegetal samples using thermospray flame furnace atomic absorption spectrometry

A system has been developed for online preconcentration and determination of Cd using thermospray flame furnace atomic absorption spectrometry (TS-FF-AAS). It is based on the solid-phase extraction of Cd in an Amberlite XAD-2 minicolumn loaded with 2-(2-thiazolylazo)-5-dimethylaminophenol (TAM), and the metal ion is eluted with 1 mol L⁻¹ hydrochloridric acid, followed by its determination. The online system allows determining Cd with a detection limit of 8.0 ng L⁻¹ and a quantification limit of 25.0 ng L⁻¹. The precision (repeatability), calculated as the relative standard deviation (% RSD) in sample solutions containing 0.5 and 3.0 μg L⁻¹ of Cd, was 6.1 and 4.5%, respectively. The preconcentration factor obtained was 24. The system’s accuracy was confirmed by analyzing the following certified reference materials (CRMs): Rice flour NIES 10b, Apple leaves NIST 1515 and Orchard leaves NBS 1571. This procedure was applied to the determination of Cd in cabbage and powdered guarana samples.     

Determination of trace amounts of cadmium and copper by atomic absorption spectrometry after simultaneous extraction and preconcentration using a new water-soluble polyacrylic acid/alumina sorbent

An analytical method using alumina modified with water-soluble polyacrylic acid polymer for the simultaneous separation and preconcentration of trace Cu and Cd in a column system, and their determination by flame atomic absorption spectrometry was developed. The conditions for coating Al₂O₃ with polyacrylic acid were optimized, then the column was packed with 50 mg of this sorbent. Cd and Cu solution was passed through a glass column at pH 4.5, and elution was carried out with 5 mL of 0.05 M HCl at a flow rate of 1 mL min⁻¹. A sorption capacity of 10 mg Cu and 12 mg Cd was obtained for 1 g sorbent. The detection limit was calculated as 4.5 μg L⁻¹ for Cu and 1.54 μg L⁻¹ for Cd in the final solution. Enrichment factors of 300 for Cd and 400 for Cu were obtained.     

The coulometric titration of bromate with cuprous copper

A coulometric procedure has been developed by which 18 to 240 μg quantities of bromate may be determined to within 0.3 μg. The bromate is allowed to react with bromide in an acid solution and electrolytically generated cuprous copper is used for the titration. A dual platinum electrode indicator system is used in an amperometric end-point procedure     

Wavelength-modulated,continuum-source excited atomic fluorescence spectrometric system for wear metals in jet engine lubricating oils using electrothermal atomization

A system for measuring atomic fluorescence of atoms produced via an electrically-heated graphite filament in a flame (acetylene/air or acetylene/nitrous oxide) and excited with a 300-W Eimac xenon are lamp is described. The experimental system also included wavelength modulation for background emission/fluorescence/scatter correction and an optically-triggered electronic integrator for efficient monitoring of the analyte fluorescence signal. Copper, aluminum and molybdenum were determined in jet engine lubricating oil samples (1 μl) with no pretreatment. The determinations are evaluated with respect to the accuracy and repeatability criteria of the U.S. Joint Oil Analysis Program.     

Anthill Earth as a Gold Occurrence Indicator,and Gold Determination by Solid Sampling Flame Atomic Absorption Spectrometry

With the aim of avoiding cumbersome sample treatment, we present a device for the introduction of solid soil samples into AAS-flames for gold determination, as well as the proposition of earth from anthills as a gold occurrence indicator. A previous ground sample of anthill earth (0.50 mg) was weighed directly into a small recipient of polyethylene which was then connected to a sampling boronsilicate glass chamber. The sample was carried by an airflow (5 L min⁻¹) to a quartz cell positioned between the burner top and the optical beam. The generated atomic vapor produced a transient signal which was totally integrated in three seconds. The performance was compared with conventional flame atomic absorption spectrometry after proper sample digestion. No significant differences were observed between both procedures (mean deviation ±1.90%), and a LOQ of 0.03 μg Au was achieved using the proposed method. The anthill earth was found to be very suitable for indication of gold occurrence in soils and related materials.