Synthesis of N,N'-Diacyl-1,2-di-(4-pyridyl)ethylenedianiines

Reaction of N-(4-pyridylmethyl)benzamide N-oxides with acetic anhydride yielded dimerization compounds. This dimerization occurs at the atom attached to the pyridine ring. These compounds so obtained were evaluated for analgesic and antiinflammatory activity.     

On the Hilbert Evolution Algebras of a Graph

Evolution algebras are a special class of nonassociative algebras exhibiting connections with various fields of mathematics. Hilbert evolution algebras generalize the concept in the framework of Hilbert spaces. This allows us to deal with a wide class of infinite-dimensional spaces. We study Hilbert evolution algebras associated to a graph. Inspired by the definitions of evolution algebras we define the Hilbert evolution algebra that is associated to a given graph and the Hilbert evolution algebra that is associated to the symmetric random walk on a graph. For a given graph, we provide the conditions for these structures to be or not to be isomorphic. Our definitions and results extend to the graphs with infinitely many vertices. We also develop a similar theory for the evolution algebras associated to finite graphs.

     

Bernstein-Type Inequalities for Rational Functions with Prescribed Poles

We establish Bernstein-type inequalities for rational functionswith prescribed poles in the Chebyshev norm on the unit circlein the complex plane. Generalizations of polynomial inequalitiesof Erds-Lax and Turán are also obtained for such rational functions with restricted zeros.