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In this paper, sufficient and necessary maximum conditions are established for a class of mathematical programming problems with an infinite set of restrictions, which is described by a finite number of inequalities. The criteria may be applied to nonlinear approximation problems and to the numerical solution of boundary value problems.

Extending papers of Pólya and Schoenberg we get a remainder theorem for the quasi hermitian interpolation problem. Since extrapolation for discretization methods can be viewed as such a problem we can deduce some remainder formulas for extrapolation methods., In Erweiterung von Arbeiten von Pólya und Schoenberg wird eine Restglieddarstellung für die quasihermitesche Interpolationsaufgabe gewonnen. Da die Extrapolation bei Diskretisierungsverfahren als eine solche Aufgabe gedeutet werden kann, gelingt auf diesem Wege die Herleitung einiger Fehlerdarstellungen bei Extrapolationsaufgaben.

1. Lorenz, F.: Quadratische Formen uber Korpern. Lecture notes Math. 130. Berlin-Heidelberg-New York: Springer 1970. 2. Scharlau, W.: Quadratic forms. Queen's papers on pure and applied math. No. 22, Queen's University, Kingston, Ontario (1969). 3. Springer, T. A.: Sur les formes quadratiques d'indice zero. C.R.Acad. Sei. 234, 1517-1519(1952). 4. Witt, E.: Verschiedene Bemerkungen zur Theorie der quadratischen Formen uber einem Korper. Colloque d'Algebre Superieure, Bruxelles, 245-250 (1956). Manfred Knebusch Mathematisches Institut der Universitat BRD-6600 Saarbrucken 15 Deutschland

In the present paper we consider the emission of light quanta by an atom using the methods of non-relativistic quantum theory. The differential equations occurring there are solved using a Laplace transformation. By means of an analytic continuation and a displacement of the integration path we get exact solutions whose approximations lead to the usual formulae for the intensity distribution and for the natural line width.