An efficient and environmental-friendly synthetic route to 1,8-dioxodecahydroacridines derivatives have been developed via multi-component one-pot Hantzsch reaction of various aldehydes and ammonium acetate with 2 equivalents dimedone in the presence of Phosphorus pentoxide supported on aluminaas catalyst under solvent-free conditions. The present approach offersseveral advantages such as short...

An efficient and environmentally friendly procedure for one-pot synthesis of 13-acetyl-9-methyl-11-ox-8-oxa-10,12-diazatricyclo [7.3.1. ] trideca-2,4,6-triene from salicylaldehyde, acetylaceton and urea via Biginelli condensation and intramolecular Michael-addition by using magnesium bromide as an expensive and easily available catalyst under solvent-free condition is desired. The structural el...

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean eld type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translationinvariant interactions of nite range. In the spe...

In this paper we prove that a free product of conjugacy separable groups A and B, amalgamating a cyclic subgroup, is conjugacy separable if A and B are subgroup separable, cyclic conjugacy separable, 2-free, and residually p-finite, for all prime numbers p. The following result is an example of the applications we obtain as consequences of our main theorem. Let A and B each be a free product of...

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translationinvariant interactions of finite range. In the...

In this work, we calculate the limit distribution of the total cost incurred by splitting a tree selected at random from the set of all finite free trees. This total cost is considered to be an additive functional induced by a toll equal to the square of the size of tree. The main tools used are the recent results connecting the asymptotics of generating functions with the asymptotics of...

An efficient and environmental-friendly synthetic route to 1,8-dioxodecahydroacridines derivatives have been developed via multi-component one-pot Hantzsch reaction of various aldehydes and ammonium acetate with 2 equivalents dimedone in the presence of Phosphorus pentoxide supported on aluminaas catalyst under solvent-free conditions. The present approach offersseveral advantages such as s...

An efficient and environmental-friendly synthetic route to 1,8-dioxodecahydroacridines derivatives have been developed via multi-component one-pot Hantzsch reaction of various aldehydes and ammonium acetate with 2 equivalents dimedone in the presence of Phosphorus pentoxide supported on aluminaas catalyst under solvent-free conditions. The present approach offersseveral advantages such as s...

Let A be the collection of groups which can be assembled from infinite cyclic groups using the binary operations free and direct product. These groups can be described in several ways by graphs. The group (Z ∗Z)×(Z ∗Z) has been shown by [1] to have a rich subgroup structure. In this article we examine subgroups of A–groups. DefineA to be the smallest class of groups which contains the infinite ...