On Orthogonal Double Covers of Graphs

An orthogonal double cover (ODC) is a collection of n spanning subgraphs(pages) of the complete graph K _n such that they cover every edge of the completegraph twice and the intersection of any two of them contains exactly one edge. If all the pages are isomorphic tosome graph G, we speak of an ODC by G. ODCs have been studied for almost 25 years, and existenceresults have been derived for many graph classes. We present an overview of the current state of research alongwith some new results and generalizations. As will be obvious, progress made in the last 10 years is in many waysrelated to the work of Ron Mullin. So it is natural and with pleasure that we dedicate this article to Ron, on theoccasion of his 65th birthday.     

Applications of Category Theory to the Area of Algebraic Specification in Computer Science

The theory of algebraic specifications – one of the most important mathematical approaches to the specification of abstract data types and software systems – is reviewed from a mathematical and a computer science point of view. The important role of category theory in this area is discussed and it is shown how the following selected problems are treated using category theory: First, a unified framework for specification logics, second compositional semantics, third partial algebras and their specification, and fourth specifications and models for concurrent systems. For the solution of two of the problems classifying categories are used. They allow to present categories of algebras as functor categories and to derive a number of important properties from well known results for functor categories.     

From crystalline boryl-substituted and boryl-coupled 2,2,4,4,6,6-hexamethyl-cyclotrisilazanes to β-SiC and BN

[Me₂SiNBFN(SiMe₃)₂]₃ (1) is synthesized in the reaction of trilithiated hexamethylcyclotrisilazane with F₂BN(SiMe₃)₂. The mono- and dilithium derivatives of the six-membered ring (Me₂SiNH)₂ Me₂SiNSiFMe₂ react with the F₂B-substituted cyclotrisilazane F₂B(NSiMe₂)₃(SiFMe₂)₂ in the molar ratio 1:1 or 1:2 to give the BF-coupled rings 2 and 3. The crystal structure analysis of 1 and 3 and pyrolysis of 1 and 3 with formation of silicon boron carbonitride and its crystallisation to composite powders at very high temperatures are reported.     

Die bildung von thiirenen

Photochemical nitrogen elimination of 1,2,3-thiadiazoles leads to primary fragments ( 1 , X = S), which are able to cyclize to thiirenes ( 2 , X = S). An exception is found for bicyclic systems like 4 . These results, gained by isotope labelling experiments are related to the oxirene formation of α-oxocarbenes.     

Continuous Linear Extension of Ultradifferentiable Functions of Beurling Type

For a weight function ω and a closed set A ? ?^N let ?_(ω)(A) denote the space of all ω-Whitney jets of Beurling type on A. It is shown that for each closed set A ? ?^N there exists an ω-extension operator EA: ?_(ω)(A) → ?_(ω)(?^N) if and only if ω is a (DN)-function (see MEISE and TAYLOR [18], 3.3). Moreover for a fixed compact set K ? ?^N there exists an ω-extension operator E_K: ?_(ω)(K) → ?_(ω)(?^N) if and only if the Fréchet space ?_(ω)(K) satisfies the property (DN) (see Vogt [29], 1.1.).