Alkylation of 4,5-dichloropyridazin-6-one with α,ω-dibromoalkanes or 4,5-dichloro-1-(ω-bromoalkyl)pyridazin-6-ones

Alkylations of 4,5-dichloropyridazin-6-one (1) with dibromoalkanes 2 or 3 in the presence of potassium carbonate or tetrabutylammonium bromide/potassium hydroxide were investigated under restricted condition. Reactions of 1 with 2 or 3, except for 2b and 3b , in the presence of potassium carbonate or tetrabutylammonium bromide/potassium hydroxide gave only the N-alkylation products 3 and/or 4. Alkylation of 1 with 2b or 3b in the presence of potassium carbonate yielded the N-alkylation products 3b and/or 4b and the O-alkylation product 5 as the main product, whereas treatment of 1 with 2b or 3b in the presence of tetrabutylammonium bromide/potassium hydroxide afforded selectively the N-alkylation products 3b and/or 4b.     

Generalized fundamental equations on the submanifolds of a manifoldESX n

A connection which is both Einstein and semisymmetric is called anES connection, and a generalizedn-dimensional Riemannian manifold on which the differential geometric structure is imposed by a unified field tensorg through anES connection is called ann-dimensionalES manifold and denoted byESX _n . We investigate some necessary and sufficient conditions for submanifolds ofESX _n to be also Einstein and derive the generalized fundamental equations on various submanifolds ofESX _n , such as generalized Gauss formulas, generalized Weingarten equations, and generalized Gauss-Codazzi equations. We employ the useful and powerful concept ofC-nonholonomic frame of reference, introduced in earlier work.