On the Integrability Conditions for Some Structures Related to Evolution Differential Equations

Using the result by D. Gessler, we show that any invariant variational bivector (resp., variational 2-form) on an evolution equation with nondegenerate right-hand side is Hamiltonian (resp., symplectic).     

Zur Darstellung von Imidazolidin-thionen-(4) und Imidazolin-(3)-thionen-(5)

Zusammenfassung 2,2,5-Trisubstituierte Imidazolidin-thione-(4) lassen sich mittels Schwefels mit guten Ausbeuten zu Imidazolin-(3)-thionen-(5) dehydrieren. Hierüber sowie über einige Verbesserungen der bisher bekannten Synthesen für insbesondere 2,2,5-trisubstituierte Imidazolidin-thione-(4) wird berichtet.

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Dehydration of 2.2.5-trisubstituted imidazolidine-(4)-thiones with elementary sulfur gives in good yields 3-imidazoline-(5)-thiones. This reaction and improved methods of the well known syntheses of especially 2.2.5-trisubstituted imidazolidine-(4)-thiones are described.

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Mitt.:F. Asinger, W. Schäfer undH. Triem, Mh. Chem.97, 1510 (1966).

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Teil der Dissertation vonH. Meisel, Techn. Hochschule Aachen, 1963.

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Teil der Dipl.-Arbeit vonHilde Kersten, Techn. Hochschule Aachen, 1963, und Teil der Dissertation vonHilde Kersten, Techn. Hochschule Aachen, 1965.     

Die Lösung der Prae-Maxwellschen Gleichungen mit Hilfe vollständiger Lösungssysteme

This paper deals with the Neumann problem of the pre-Maxwell partial differential equations for a vector field v defined in a region G ? R ³. We approximate its uniquely determined solution (integrability conditions assumed) uniformly on G by explicitly computable particular integrals and linear combinations of vector fields with a “fundamental” sequence of points .     

A constructive approximation theorem for the oblique derivative problem in potential theory

The (exterior) oblique derivative problem of potential theory is considered where l is a C^(1,λ)-vector field on a regular boundary ?G_e in Euclidean space R ³ and the direction l at any point of ?G_e forms with the outside normal n an angle ? (l, n) satisfying cos ? (l, n) ≥ c > 0. An approximation of the uniquely determined solution is given by use of trial functions {Φ_n}_n=0,1,… harmonic in some region containing G _e and suitable for numerical purpose (for instance: solid spherical harmonics, certain sequences of fundamental solutions). The system {l▽Φ_n+hΦ_n}_n=0,1,… defined on ?G_e is shown to be closed and complete in the pre-Hilbert space C^(0,λ)(?G_e) of λ-Hölder continuous functions.     

Artifacts in the Determination of Trace Metal Binding Forms in Anoxic Sediments by Sequential Extraction

Abstract

The binding forms of Co, Cd, Cu, Pb, and Zn in an anoxic, sulfide-bearing sediment were investigated by performing both thermodynamic equilibrium calculations and sequential extractions. Care was taken to maintain oxygen-free conditions during the whole experiment. The calculations suggested that trace metals were bound to sulfidic minerals. Sequential extraction results, however, showed increased importance of exchangeable and reducible fractions in the order Cu < Cd < Pb < Zn < Co. Thermodynamic equilibrium calculations of the chemical reactions during extraction showed that Cd, Co, Pb, and Zn sulfides are to a significant extent soluble in the acetate-exchangeable (step 1 + 2) and oxalate-reducible (step 3) fractions. Neglecting the dissolution of sulfide minerals would lead to a misinterpretation of the experimental results.