States on causal logic

Conserved currents are shown to define states on causal logic of Minkowski space.     

Colorimetric determination of the fluoride ion based on interference with extractability

Summary The sensitivity of colorimetric determinations based on reduction of extinction by complex-forming anions can be increased by measuring the change of absorbancy in the organic phase after shaking with a suitable solvent, i. e. by determining the interference of the anion with extractability. This principle has been applied to the determination of the fluoride ion.

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Zusammenfassung Die Empfindlichkeit kolorimetrischer Bestimmungen, die auf Herabsetzung der Extinktion durch komplexbildende Anionen beruhen, kann durch Messung der Absorptionsänderung in der organischen Phase nach Schütteln mit einem geeigneten Lösungsmittel, das heißt durch Bestimmung der durch das Anion verminderten Extrahierbarkeit, erhöht werden. Dieses Prinzip wurde auf die Bestimmung von Fluoridion angewendet.

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Résumé La sensibilité des déterminations colorimétriques basée sur l'effet de diminution d'extinction dû à des anions donnant lieu à la formation de complexes peut être accrue par la variation de l'absorption dans la phase organique après agitation avec un solvant approprié, ce qui revient à déterminer l'effet d'empêchement d'extraction dû à l'anion. Ce principe a été appliqué au dosage de l'ion fluorure.

     

Two-barrier detector

The paper describes the principle of a detector with two opposite surface barriers and the experimental verification of its functioning. The detector permits double the effective depth to be attained on the material with a given bias voltage. The principle of opposite barriers also permits a reduction in the system of dE/dx andE detectors to one detector.

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. . dE/dx E .

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The authors thank A. Irra for carefully preparing the plates, K. Putz and J. imková for very effective help in measuring on the cyclotron and the members of of the cyclotron staff for their cooperation.     

Thee + e −→¯nn cross section predicted remarkably larger than thee + e −→¯pp one

It is shown that all global analyses of nucleon electromagnetic form factor data predict the electron-positron annihilation into neutron-antineutron cross section (for which there are no data till now) to be in a finite energy region substantially larger than the electron-positron annihilation into the proton-antiproton one.Dedicated to the memory of M. Gmitro.     

Decomposability of matrix polynomials with coefficients possessing quasi-simple structure

The decomposability of matrix polynomials with commuting coefficients of quasi-simple structure into regular factors and the solvability of the corresponding matrix polynomial one-sided equations are investigated.Translated from Ukrainskii Matematicheskie Zhurnal, Vol. 44, No. 12, pp. 1716–1718, December, 1992.     

Die Lasker-Bedingung für Nicht Endlich Erzeugte Moduln

Ohne Zusammenfassung

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Behavior of integral curves in the neighborhood of optimal integral manifolds

We describe an explicit construction of optimal integral manifolds [1] for a quasilinear system of differential equations that uses the method of successive approximations. We study the behavior of integral curves in the neighborhood of optimal integral manifolds. We cite a numerical method of synthesis of optimal control and prove its justification.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1049–1060, August, 1992.     

Local error estimation for singly-implicit formulas by two-step Runge-Kutta methods

In this paper it is shown that the local discretization error ofs-stage singly-implicit methods of orderp can be estimated by embedding these methods intos-stage two-step Runge-Kutta methods of orderp+1, wherep=s orp=s+1. These error estimates do not require any extra evaluations of the right hand side of the differential equations. This is in contrast with the error estimation schemes based on embedded pairs of two singly-implicit methods proposed by Burrage.The work of A. Bellen and M. Zennaro was supported by the CNR and MPI. The work of Z. Jackiewicz was supported by the CNR and by the NSF under grant DMS-8520900.