Halogenated 3-pyridylketones

The oxidation of 2,6-dichloro-3-benzylpyridines and bis(2,6-dichloro-3-pyridyl)methanes, respectively, was accomplished using chromic trioxide in a highly acidic medium. The synthesis of several phenyl-3-(2,6-dichloropyridyl)ketones and of bis(2,6-dichloro-3-pyridyl)ketone are reported.     

Réactions d'addition-élmination à partir d'hétérocycles germaniés du type . III. Cas des diéthyl-2,2-germa-2-oxazolidines-1,3 (R = et; X = O; Y = NH,NMe)

Addition-elimination reactions from germanium heterocycles . III. 2,2-Diethyl-2-germa-1,-3-oxazolidines (R = Et; X = O; Y = NH, NMe) . The reactions of 2,2-diethyl-2-germa-1,3-oxazolidines with heterocumulenes (PhNCO, PhNCS, CS₂, CO₂, CH₂?C?O) and carbonyl compounds (aldehydes and ketones) are studied. Generally, monoinsertion derivatives are formed by addition of one molecule of the unsaturated compound accross the Ge? N bond. This bond is always the most reactive center of the molecule. In the case of the carbonyl compounds used, diinsertion may occur in a second step by a further addition across a Ge? O bond. Generally, this latter reaction is reversible. By thermal eliminat on of (Et₂GeO)_n or (Et₂GeS)₃ the monoaddition derivatives yield the corresponding oxazolidines and thiooxazolidines. The mechanisms of these reactions are discussed.     

Methylthiomethylierung von Anilinen und Phenolen, 3. Mitt.: Darstellung von N-Aryl-S,S-dialkylsulfimiden

Zusammenfassung Aus Anilinen, die im aromatischen Ring mit CH₃, CH₃SCH₂, CH₃O, Cl, Br oder NO₂ substituiert sind, und Sulfoxiden wird in Anwesenheit von P₄O₁₀ und Triäthylamin eine Reihe von N-Aryl-S,S-dialkylsulfimiden erhalten. Diese Reihe umfaßt Verbindungen mit CH₃-, C₂H₅- und –(CH₂)₄-Gruppen am Schwefelatom. Das Sulfimid aus Mesidin lagert sich—formal analog zu einerSommelet—Hauser-Umlagerung—zum 2,4,6-Trimethyl-2-methylthiomethylcyclohexa-3,5-dien-1-imin um.

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Methylthiomethylation of anilines and phenols, III: Preparation of N-aryl-S,S-dialkylsulfimides

The synthesis of a number of N-aryl-S,S-dialkylsulfimides by reaction of anilines with sulfoxides in presence of P₄O₁₀ and triethylamine is given. This series includes compounds with CH₃-, CH₃SCH₂-, CH₃O-, Cl-, Br- and nitro-groups attached to the aromatic nucleus, resp., and with CH₃-, C₂H₅-or–(CH₂)₄-groups on the sulfur atom. The sulfimide obtained from mesidine is rearranged in formal analogy to aSommelet-Hauser rearrangement to 2.4.6-trimethyl-2-methylthio-methylcyclohexa-3.5-dien-1-imine.

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Als 1. Mitt. soll gelten:P. Claus, Mh. Chem.99, 1034 (1968).

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2. Mitt.:P. Claus undW. Vycudilik, Tetrahedron Letters1968, 3607.     

On Anosov energy levels of hamiltonians on twisted cotangent bundles

LetT ^* M denote the cotangent bundle of a manifoldM endowed with a twisted symplectic structure [1]. We consider the Hamiltonian flow generated (with respect to that symplectic structure) by a convex HamiltonianH: T ^* M, and we consider a compact regular energy level ofH, on which this flow admits a continuous invariant Lagrangian subbundleE. When dimM3, it is known [9] that such energy level projects onto the whole manifoldM, and thatE is transversal to the vertical subbundle. Here we study the case dimM=2, proving that the projection property still holds, while the transversality property may fail. However, we prove that in the case whenE is the stable or unstable subbundle of an Anosov flow, both properties hold.     

Self and mutual admittance of slot antennas on a dielectric half-space

In this paper, an efficient implementation of the spectral domain moment technique is presented for computing the self and mutual coupling between slot antennas on a dielectric half-space. It is demonstrated that by the proper selection of the weighting functions in the method of moments, the analytic evaluation or simplification of the transverse moment integrals is enabled. This results into a significant reduction of the required computational labor. The method is then utilized in order to provide design data for the self and mutual admittances between two slot antennas on a dielectric substrate lens in the case of fused quartz ( _r =3.80), crystal quartz ( _r =4.53), silicon ( _r =11.9) and GaAs ( _r =12.8). The presented technique and associated results are useful when designing twin slot quasi-optical receivers, imaging arrays, phased arrays or power-combining arrays of slot elements at millimeter-wave frequencies.     

On the Haar measure of the quantumSU(N) group

We prove that the Haar state associated to the compact matrix quantum groupSU (N) is faithful for ]–1,1[,0, and anyN2.     

An exact homology sequences approach to the controllability of systems

Some results are given on the homology groups of the abstract simplicial complex associated to a multivariable control system, as an extension of the central result of J. Casti (J. Math. Anal. Appl.68 (1979), 347–370) to the multivariable case. The method used is “polyhedral dynamics” as termed by J. Casti, who introduced it. A given control system is mapped into a simplicial complex and then its homological structure is studied. These results, obtained in the multivariable case by the use of the Mayer-Vietoris homology sequence and of the relative homology sequence, present topological invariants for control systems thus creating the possibility of a new topological classification of multivariable systems. An example is given to clarify the approach.