Sels de N-alcoxyquinoléinium et de N-alcoxyisoquinoléinium porteurs d'une fonction ester dans leur chaine alcoxyle: Synthèse et réactivité vis-a-vis des ions cyanure

Reaction of ethyal α-bromoisobutyrate on quinoline 1-oxide and isoquinoline 2-oxide in the presence of silver perchlorate leads to the corresponding N-alkoxyl salts 1 and 2 . On treatment with potassium cyanide, these salts are converted into 2-cyanoquinoline and 1-cyanoise-quinoline according to mode B of the Katritzky' s classification concerning the reaction of nucliophiles on N-alkoxypyridinium salts. When the reaction of cyanide ions were performed on salt 1 at 0° in aqueous solution the dihydro aromatic 4 was isolated. This result confirms the addition-elimination mechanism of the reaction studied.     

Regularity and intersections of bracket powers

Czechoslovak Mathematical Journal - Among reduced Noetherian prime characteristic commutative rings, we prove that a regular ring is precisely that where the finite intersection of ideals commutes...     

The set of mapsF_{a,b} :x \mapsto x + a + \tfrac{b}{{2\pi }} sin(2πx) with any given rotation interval is contractiblewith any given rotation interval is contractible

Consider the two-parameter family of real analytic maps $F_{a,b} :x \mapsto x + a + \tfrac{b}{{2\pi }}$ sin(2πx) which are lifts of degree one endomorphisms of the circle. The purpose of this paper is to provide a proof that for any closed intervalI, the set of mapsF _a,b whose rotation interval isI, form a contractible set.     

BΛF theory and flat spacetimes

We propose a reduced constrained Hamiltonian formalism for the exactly solubleBF theory of flat connections and closed two-forms over manifolds with topology ³ × (0,1). The reduced phase space variables are the holonomies of a flat connection for loops which form a basis of the first homotopy group ₁( ³), and elements of the second cohomology group of ³ with value in the Lie algebraL(G). WhenG=SO(3,1), and if the two-form can be expressed asB=ee, for some vierbein fielde, then the variables represent a flat spacetime. This is not always possible: We show that the solutions of the theory generally represent spacetimes with global torsion. We describe the dynamical evolution of spacetimes with and without global torsion, and classify the flat spacetimes which admit a locally homogeneous foliations, following thurston's classification of geometric structures.This research is supported in part by the National Science Foundation, Grant No. PHY 89-04035, by CONACyT Grant No. 400349-1714E (Mexico), and by the Association Générale pour la Coopération et le Développement (Belgium).