An approach to numerical solution of multipoint boundary-value problems

An approach is proposed to solving multipoint boundary-value problems for linear differential equation of w-th order, based on reduction to two-point boundary-value problems. The two-point problems are solved by the stable discrete orthogonalization method. Some numerical examples are considered.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 36–45, 1986.     

A Parabolic Spline on a Nonuniform Grid

We obtain estimates for errors of interpolation on a nonuniform grid for a parabolic nonperiodic spline of defect 1.     

Two-dimensional Numerical Simulation of the Beam-Plasma-Discharge

A two-dimensional self consistent model of the Beam-Plasma-Discharge (BPD) has been developed to calculate the discharge ignition of a bandlike electron beam in a discharge chamber. The discharge was considered in Argon with an initial concentration of 10¹⁴ cm^?3. The model allows calculation of the time evolution of perpendicular profiles of electron density, temperature and the potential.     

Book reviews

Ohne Zusammenfassung

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Book reviews

     

Kinetics and mechanism of oxidation of indigo carmine by hypohalites

Kinetics of oxidation of indigo carmine (IC) by sodium hypohalites, NaOX (X ? Cl or Br), in alkaline buffer of pH 9–11 has been studied spectrophotometrically at λ = 610 nm. The experimental rate law obtained is ?d[IC]/dt = k[OX^?][IC][OH^?]^x where x <1. Variation of ionic strength or dielectric constant of the medium had no effect on the reaction rate while the addition of halide ions slightly retarded the rate. A most plausible mechanism proposed on the basis of experimental results involves the formation of isatin sulphonate which undergoes further oxidation to anthranilate. Activation parameters have been evaluated.     

On the structure of solutions of a system of singularly perturbed differential equations with nondiagonalizable limit operator

We construct uniform asymptotics of a solution of a heterogeneous system of singularly perturbed differential equations in the case of nondiagonalizable limit operator. We consider the case where the spectrum of the limit operator contains an unstable element at the point x = 0. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 867–876, July, 1998.     

Some remarks on operator ranges

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 53, pp. 69–70, 1990.     

Mössbauer studies on some new magnetic oxides

Three new magnetic oxides have been synthesised, viz., Li₂Fe₃VO₈, YFe₃TiO₈ and CaFe₃VO₈. XRD studies show that the first compound has a cubic symmetry of spinel type while the latter two show orthorhombic symmetry. All the three compounds are magnetic at room temperature, however, the first compound shows a large magnetic moment as compared to the other two. Their Mössbauer spectra at room temperature show distinct hyperfine split spectral lines. The present preliminary investigation indicates that the long range order is ferrimagnetic in Li₂Fe₃VO₈ and CaFe₃VO₈ while in YFe₃TiO₈ it is more likely to be canted antiferromagnetic.