Microwave‐Assisted Dibromoolefination of Aromatic and Heteroaromatic Aldehydes and Ketones

Microwave (MW) irradiation was successfully employed to convert aromatic and heteroaromatic aldehydes and ketones efficiently to the corresponding dibromoolefins. Exemplified by the successful dibromoolefination of traditionally inert pyridyl‐flanked carbonyls, MW activation significantly broadens the scope of this valuable transformation, although some limitations especially with electron‐rich aromatic ketone derivatives remain.     

The Palladium Way to N‐Heteroacenes

Novel synthetic methodologies allow increasingly efficient access to known organic materials, as well as the preparation of otherwise inaccessible species. Pd‐catalyzed coupling of aromatic dihalides to ortho‐diaminoarenes furnishes embedded stable N,N′‐dihydropyrazines expediently and in often excellent yields. The embedded N,N′‐dihydropyrazines can then be oxidized by MnO₂ to give substituted azatetracenes, azapentacenes, azahexacenes, and azaheptacenes, which are soluble, processable, and stable. This powerful Pd‐catalyzed methodology allows the preparation of azaacenes, including diaza‐, tetraaza‐ and hexaazaacenes. In combination with a suitable Pd precursor, Buchwald‐type biarylphosphines have been shown to give excellent results. Activated dihalides such as 2,3‐dihaloquinoxalines are coupled easily under simplified conditions, whereas 2,3‐dibromoacenes require more stringent conditions and advanced catalyst precursors. Pd catalysts effect the assembly of azaacenes with otherwise difficult to obtain substitution patterns. High yields and flexibility make this method most attractive.     

Formation of substituted 2-iminooxazolidines via intermolecular 1,2-addition/intramolecular N-vinylation using 3-substituted-2-bromo-2-propen-1-ols as substrates

The Cu₂O-catalyzed reaction between equimolar amounts of easily available 3-substituted-2-bromo-2-propen-1-ols and dicyclohexyl carbodiimide in DMSO at 100?°C using K₃PO₄ as the base and in the absence of any additive exclusively delivers substituted 2-iminooxazolidines with yields up to 80%. The highly selective transformation is assumed to start with an intermolecular 1,2-addition, which is followed by an intramolecular N-vinylation. The products can also be obtained in the absence of Cu₂O, albeit in lower yields.     

Supernode processing of mixed-integer models

This paper discusses processing software for large scale mixed-integer optimization models. The software is part of the Mathematical OPtimization System MOPS [18] which contains algorithms for solving large-scale LP and mixed-integer programs. The processing techniques are implemented in such a way that they can be applied not only initially but also during the branch-and-bound algorithm.This paper discusses only a subset of the processing techniques included in MOPS. Algorithmic and software design aspects of the branch-and-bound process are not part of this paper.Dedicated to Professor George B. Dantzig on the occasion of his eightieth birthday.     

Approximations to permutation and exchangeable processes

We obtain weighted approximations by a Brownian bridge to permutation and exchangeable processes and to appropriately defined inverse processes. Our results provide as special cases useful weighted approximations to the uniform empirical and quantile processes and to generalized bootstrapped versions of these processes. A number of other applications are discussed. Our approach is based on the Skorokhod embedding for martingales.     

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.