The semigroup generated by a unitary orbit of a singular matrix

We investigate the structure of the multiplicative semigroup generated by the set of matrices that are unitarily equivalent to a given singular matrix A. In particular, we give necessary and sufficient conditions, in terms of the singular values of A, for such a semigroup to consist of all matrices of rank not exceeding the rank of A.     

Posner and herstein theorems for derivations of 3-prime near-rings

The analog of Posner's theorem on the composition of two derivations in prime rings is proved for 3-prime near-rings. It is shown that if d is a nonzero derivation of a 2-torsionfree 3-prime near-ring N and an element a ? N is such that ax^d = x^da for all x ? N, then a is a central element. As a consequence it is shown that if d\ and d₂ are nonzero derivations of a 2-torsionfree 3-prime near-ring N and x^d1y^d2 = y^d2x^d1 for all x, y ? N, then N is a commutative ring. Thus two theorems of Herstein are generalized     

The coexponent of a regular p -group

A sharp bound is derived for the nilpotency class of a regular p-group in terms of its coexponent, and is used to show that the number of groups of order pⁿ with a given fixed coexponent, is independent of n, for p and n sufficiently large. Explicit formulae are calculated in the case of coexponent 3.     

Approaches to primary tert-alkyl amines as building blocks

Primary tert-alkyl amines include analogues of amantadine, a fragment commonly linked to pharmacophoric groups to enhance biological activity. The preparation of primary tert-alkyl amines is considered to be a difficult problem. Four synthetic procedures, some of which have been previously reported for the synthesis of amines with primary (RCH₂NH₂) or secondary (RR'CHNH₂) alkyl and/or aryl groups, were tested for the synthesis of primary tert-alkyl amines (RR′R″CNH₂) in aliphatic series including adamantane adducts. These procedures included the formation and reduction of tert-alkyl azides, the Ritter reaction in standard and modified conditions, the addition of organometallic reagents to N-tert-butyl sulfinyl ketimines and one-pot reactions between nitriles and organometallic reagents in the presence of a Lewis acid, Τi(iPrO)₄ or CeCl_3. These synthetic routes are unexplored for primary tert-alkyl amines. Studies on the synthetic routes for primary tert-alkyl amines are currently lacking. The reaction conditions and substrate limitations were studied for each procedure, with the first procedure being the most general and applicable also for compounds bearing bulky adducts.     

Hofmann rearrangement of primary carboxamides and cyclic imides using DCDMH and application to the synthesis of gabapentin and its potential peptide prodrugs

Two protocols for the efficient transformation of aromatic as well as aliphatic primary carboxamides to the corresponding carbamates and aromatic as well as aliphatic cyclic imides to the corresponding anthranilic acid derivatives & amino acid derivatives, respectively, are described. We also developed a novel methodology to the multigram scale synthesis of gabapentin and (S)-pregabalin. The gabapentin methyl carbamate was converted to novel potential peptide prodrugs of gabapentin.     

Reductive Amination of Carbonyl Compounds with Ammonia and Hydrogenation of Nitriles to Primary Amines with Heterogeneous Cobalt Catalysts

Reductive amination of aldehydes/ketones with aqueous NH3 and hydrogenation of nitriles to primary amines with Co catalysts were reported. Co@NC-700 exhibited remarkable activity and high selectivity for the reductive amination of aldehydes/ketones with aqueous NH3 and the hydrogenation of nitriles to primary amines. Several primary amines can be obtained with good to excellent yields via the reductive amination of aldehydes/ketones and the hydrogenation of nitriles. The nitrogen-doped carbon(C)-supported Co@NC-700 metal catalyst was prepared via the pyrolysis of bioMOF Co/adenine in activated C. Co@NC-700 can be reused five times without evident loss of activity.     

Lee–Yang Problems and the Geometry of Multivariate Polynomials

We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by Pólya–Schur for univariate real polynomials and provides a natural framework for dealing in a uniform way with Lee–Yang type problems in statistical mechanics, combinatorics, and geometric function theory.