Monotony in interpolatory quadratures

Summary Let , be holomorphic in an open disc with the centrez ₀=0 and radiusr>1. LetQ _n (n=1, 2, ...) be interpolatory quadrature formulas approximating the integral . In this paper some classes of interpolatory quadratures are considered, which are based on the zeros of orthogonal polynomials corresponding to an even weight function. It is shown that the sequencesQ _n 9f] (n=1, 2, ...) are monotone. Especially we will prove monotony in Filippi's quadrature rule and with an additional assumption onf monotony in the Clenshaw-Curtis quadrature rule.     

Adams methods for neutral functional differential equations

Summary In this paper Adams type methods for the special case of neutral functional differential equations are examined. It is shown thatk-step methods maintain orderk+1 for sufficiently small step size in a sufficiently smooth situation. However, when these methods are applied to an equation with a non-smooth solution the order of convergence is only one. Some computational considerations are given and numerical experiments are presented.     

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.     

On the numerical treatment of a small divisor problem

Summary Quasiperiodic solutions of perturbed integrable Hamiltonian equations such as weakly coupled harmonic oscillators can be found by constructing an appropriate coordinate transformation which leads to a small divisor problem. However the numerical difficulties are not merely caused by the small divisors but rather by the appearence of ghost solutions, which appear in any reasonable discretization of the problem. Our numerical treatment, based on a Newton-type iteration, guarantees an approximation of the relevant solution of the nonlinear problem. Numerical solutions are found up to a critical value of the coupling constant, which is much larger than the coupling constants allowed by the existence theory available so far.     

Molecular structure and conformation of 2,3-dichloro-1-propene as determined by gas-phase electron diffraction

The molecular structure and conformation of 2,3-dichloro-1-propene have been determined by gas-phase electron diffraction at nozzle temperatures of 24, 90 and 273°C. The molecules exist as a mixture of two conformers with the chlorine atoms anti (torsion angle ∠φ = 0°) or gauche (∠φ = 109°) to each other and with the anti form the more stable. The composition (mole fraction) of the vapor with uncertainties estimated at 2σ was found to be 0.55 (0.08), 0.49 (0.08) and 0.41 (0.10) at 24, 90 and 273°, respectively. These values correspond to an energy difference with estimated standard deviation ΔE° = E°_g-E°_a = 0.7 ± 0.3 kcal mol^?1 and an entropy difference ΔS° = S°_g-S°_a = 0.6 ± 0.9 cal mol^?1 K^?1. Some of the diffraction results, together with spectroscopic observations, permit the evaluation of an approximate torsional potential function of the form 2V = V₁ (1 - cos φ) + V₂ (1 - cos 2φ) + V₃ (1 - cos 3φ); the results are V₁ = 4.4 ± 0.5, V₂ = ?2.9 ± 0.5 and V₃ = 4.8 ± 0.2, all in kcal mol^?1. The results at 24°C for the distance (r_a) and angle (∠_α) parameters, with estimated uncertainties of 2σ, are: r(C_sp²-H) = 1.098(0.020)Å, r(C_sp³-H) = 1.103(0.020)Å, r(CC) = 1.334(0.009)Å, r(C-C) = 1.504(0.013)Å, r(C_sp²-Cl) = 1.752(0.021)Å, r(C_sp³-Cl) = 1.776(0.020)Å, ∠C-CC = 127.6(1.1)°, ∠C_sp³-C_sp²-Cl = 110.2(1.0), ∠C_sp²-C_sp³-Cl = 113.1(1.2)°, ∠H-C_sp³-H = 109.5° (assumed), ∠CC-H = 120.0° (assumed) and ∠φ = 108.9(3.4)°.     

12-Membered crown ethers. Derivatives of benzo-and naphtho-12-crown-4 and their membrane electrode properties. Part II

A series of lipophilic derivatives of benzo-12-crown-4 and naphtho-12-crown-4 has been synthesized. The behavior of the prepared derivatives in membrane ion-selective electrodes has been studied. Selectivity changes dependent on the position and number of substituents have been observed.     

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.     

Li ion diffusion in Li4Ti5O12 thin film electrode prepared by PVP sol-gel method

Li₄Ti₅O₁₂ thin films for rechargeable lithium batteries were prepared by a sol-gel method with poly(vinylpyrrolidone). Interfacial properties of lithium insertion into Li₄Ti₅O₁₂ thin film were examined by cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), and potentiostatic intermittent titration technique (PITT). Redox peaks in CV were very sharp even at a fast scan rate of 50 mV s⁻¹, indicating that Li₄Ti₅O₁₂ thin film had a fast electrochemical response, and that an apparent chemical diffusion coefficient of Li⁺ ion was estimated to be 6.8×10⁻¹¹ cm² s⁻¹ from a dependence of peak current on sweep rates. From EIS, it can be seen that Li⁺ ions become more mobile at 1.55 V vs. Li/Li⁺, corresponding to a two-phase region, and the chemical diffusion coefficients of Li⁺ ion ranged from 10⁻¹⁰ to 10⁻¹² cm² s⁻¹ at various potentials. The chemical diffusion coefficients of Li⁺ ion in Li₄Ti₅O₁₂ were also estimated from PITT. They were in a range of 10⁻¹¹-10⁻¹² cm² s⁻¹.     

Growth and characterization of Mn- and Co-doped ZnO nanowires

A flow injection chemiluminescence method is proposed for the determination of cobalt, based on the strong catalytic effect of Cobalt(II) (1,10-phenanthroline)₃ complex on the lucigenin-periodate reaction in alkaline medium. Under the optimum experimental conditions, the chemiluminescence signal responded linearly to the concentration of cobalt(II) in the 1.0 × 10⁻⁹–3.0 × 10⁻⁷ g mL⁻¹ range with a detection limit of 4.4 × 10⁻¹⁰ g mL⁻¹ cobalt(II). The relative standard deviation for the determination of 5.0 × 10⁻⁸ g mL⁻¹ of cobalt was 2.3% in eleven replicated measurements. The method was successfully applied to the determination of cobalt(II) in pharmaceutical preparations.