Dioxygen Activation by Siloxide Complexes of Chromium(II) and Chromium(IV)

The reaction of a tripodal trisilanol with n‐butyllithium and CrCl₂ results in a dinuclear Cr^II complex ( 1 ), which is capable of cleaving O₂ to yield in a unique complex ( 2 ) with an asymmetric diamond core composed of two Cr^IV?O units. Magnetic susceptibility data reveal significant exchange coupling of Cr^II (S=2) in 1 and large zero‐field splitting for Cr^IV (S=1) in 2 owing to strong spin–orbit coupling of the ground state. The Cr^IV?O compound can also be generated using PhIO, and evidence was gathered that although it is the stable product isolated after excessive O₂ treatment, it further activates O₂ to yield an intermediate species that oxidizes THF or Me‐THF. By extensive ¹⁸O labeling studies we were able to show, that in the course of this process ¹⁸O₂ exchanges its label with siloxide O atoms of the ligand via terminal oxido ligands.     

Measurements of edge-uncolorability

Cubic bridgeless graphs with chromatic index four are called uncolorable. We introduce parameters measuring the uncolorability of those graphs and relate them to each other. For k=2,3, let c_k be the maximum size of a k-colorable subgraph of a cubic graph G=(V,E). We consider r₃=|E|−c₃ and . We show that on one side r₃ and r₂ bound each other, but on the other side that the difference between them can be arbitrarily large. We also compare them to the oddness ω of G, the smallest possible number of odd circuits in a 2-factor of G. We construct cyclically 5-edge connected cubic graphs where r₃ and ω are arbitrarily far apart, and show that for each 1c<2 there is a cubic graph such that ωcr₃. For k=2,3, let ζ_k denote the largest fraction of edges that can be k-colored. We give best possible bounds for these parameters, and relate them to each other.     

KamiWaAI – interactive 3D sketching with Java based on Cl(4, 1) conformal model of Euclidean space

This paper introduces the new interactive Java sketching software KamiWaAi, recently developed at the University of Fukui. Its graphical user interface enables the user without any knowledge of both mathematics or computer science, to do full three dimensional “drawings” on the screen. The resulting constructions can be reshaped interactively by dragging its points over the screen. The programming approach is new. KamiWaAi implements geometric objects like points, lines, circles, spheres, etc. directly as software objects (Java classes) of the same name. These software objects are geometric entities mathematically defined and manipulated in a conformal geometric algebra, combining the five dimensions of origin, three space and infinity. Simple geometric products in this algebra represent geometric unions, intersections, arbitrary rotations and translations, projections, distance, etc. To ease the coordinate free and matrix free implementation of this fundamental geometric product, a new algebraic three level approach is presented. Finally details about the Java classes of the new GeometricAlgebra software package and their associated methods are given. KamiWaAi is available for free internet download.     

Learning with classroom videos: conception and first results of an online teacher-training program

Within the framework of a yearlong teacher education program we examined the conditions and effectiveness of learning with classroom videos. In online phases and face-to-face sessions (blended learning), 20 teachers from two different countries. (Germany and Switzerland) analyzed videos of their own mathlessons and math-lessons of other teachers. Using different instruments, the training program was evaluated from a scientific perspective. The evaluation aimed to obtain information about processes within the training, about the acceptance of the training by the teachers and the patterns of perception of teaching processes of the teachers.     

Den starken Einflu? der dritten Komponenten bei der spektrographischen Analyse von Messing

Ohne Zusammenfassung     

Die analytische Charakteristik des k?uflichen und des gereinigten Schwefels

Ohne ZusammenfassungVortrag, gehalten auf der Tagung der Gesellschaft Deutscher Chemiker — Fachgruppe Analytische Chemie — am 25. Oktober 1958 in Marburg/Lahn.Dissertation, Chemisches Institut der Universität Köln.     

Eisen

Ohne Zusammenfassung     

Eine polarographische Methode zur Bestimmung von Chrom, Nickel und Zinn in Zirkonium und seinen Legierungen

Ohne Zusammenfassung