Rückbezüge des Mathematikunterrichts und der Methodik des Mathematikunterrichts in der DDR auf historische Vorausentwicklungen

The author discusses at some examples exemplarily, how the pedagogy of mathematics education in the GDR from curricular and educational/psychological knowledge from the time before 1945 has developed scientifically.     

Time-scale and excitation energy partition in sequential binary decays induced by heavy-ion collisions at ≃6 MeV·A

We studied the sequential binary decay of the systems ³²S+⁴⁵Sc, ⁷⁶Ge, ⁸⁹Y, ⁵⁹Co, ⁶³Cu and ¹⁹F+⁶³Cu induced by collisions at ≃6 MeV·A. The two stages of the process have reaction-times compatible with the dynamics of different mechanisms. The study of the excitation energy partition shows that the reaction mechanism of the first step has influence on the de-excitation of the primary fragments producing two decay components which have different time scale. Received: 25 March 1997 / Revised version: 2 December 1997     

Atomic coherence effects in the ion-trap laser

The influence of atomic coherence effects on the statistical and spectral properties of the ion-trap laser is investigated. Various pump configurations are considered for a realistic level scheme using a Ca ion. Compared to previous suggestions, 50% more output is obtained.     

A193Ir Mössbauer study of Pt−Ir catalysts prepared by impregnantion of silica with H2MCl6

The state of iridium on Pt?Ir catalysts prepared by impregnation of amorphous silica with H₂IrCl₆ and H₂PtCl₆ was studied by¹⁹³Ir Mössbauer spectroscopy after different steps of preparation. The Ir is adsorbed in its trivalent state, presumably as [IrCl₆]^3?. Calcination in air at 450°C converts this to IrO₂. The metallic clusters formed by subsequent reduction in H₂ at 200°C show a strong tendency towards segregation of Ir and Pt and re-oxidize partially when exposed to air at ambient temperature. In both respects the behaviour is similar to that of samples prepared by co-exchange from [Ir(NH₃)₅Cl]Cl₂ and Pt(NH₃)₄Cl₂. H₂O.     

The complexity of many cells in arrangements of planes and related problems

We consider several problems involving points and planes in three dimensions. Our main results are: (i) The maximum number of faces boundingm distinct cells in an arrangement ofn planes isO(m ^2/3 n logn +n ²); we can calculatem such cells specified by a point in each, in worst-case timeO(m ^2/3 n log³ n+n ² logn). (ii) The maximum number of incidences betweenn planes andm vertices of their arrangement isO(m ^2/3 n logn+n ²), but this number is onlyO(m ^3/5– n ^4/5+2 +m+n logm), for any>0, for any collection of points no three of which are collinear. (iii) For an arbitrary collection ofm points, we can calculate the number of incidences between them andn planes by a randomized algorithm whose expected time complexity isO((m ^3/4– n ^3/4+3 +m) log² n+n logn logm) for any>0. (iv) Givenm points andn planes, we can find the plane lying immediately below each point in randomized expected timeO([m ^3/4– n ^3/4+3 +m] log² n+n logn logm) for any>0. (v) The maximum number of facets (i.e., (d–1)-dimensional faces) boundingm distinct cells in an arrangement ofn hyperplanes ind dimensions,d>3, isO(m ^2/3 n ^d/3 logn+n ^d–1). This is also an upper bound for the number of incidences betweenn hyperplanes ind dimensions andm vertices of their arrangement. The combinatorial bounds in (i) and (v) and the general bound in (ii) are almost tight.Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by NSF Grant CCR-8714565. Work by the third author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant DCR-82-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD—the Israeli National Council for Research and Development. An abstract of this paper has appeared in theProceedings of the 13th International Mathematical Programming Symposium, Tokyo, 1988, p. 147.