Verardi’s construction of special groups of prime exponent is generalized, and put into a context that helps to decide isomorphism problems and to determine the full group of automorphisms (or at least the corresponding orbit decomposition). The groups in question may be interpreted as groups of unitriangular matrices over suitable rings. Finiteness is not assumed.

In this paper we consider simultaneously triangularizable collections of compact operators and show that similarities of any finite subcollection can be made arbitrarily close to commuting normal operators. As a consequence, we obtain a variant of a theorem of G.-C. Rota. Also, we give some sufficient conditions for simultaneous triangularization of collections of compact operators. Finally, se...

A triangle is a lower triangular matrix with all principal diagonal entriesbeing nonzero. Given an almost increasing sequence {Xn} and a sequence {λn} satisfying certain conditions, we obtain sufficient conditions for the series ∑ anλn to be absolutely summable of order k ≥ 1 by a triangle T . As a corollary we obtain the corresponding result when T is a weighted mean matrix. Theorem 1 of this ...

Nakajima conjectured in [N] that the transition matrix between certain PBW-basis constructed in [LXZ] and the affine canonical basis is upper triangular with the diagonal entries equal to one and the upper diagonal entries in vZ[v]. In this paper, we show that the transition matrix between the PBW-basis in [LXZ] and the canonical basis is upper triangular with the diagonal entries equal to one ...

We consider the problem of completion of a matrix with a specified lower triangular part to a unitary matrix. In this paper we obtain the necessary and sufficient conditions of existence of a unitary completion without any additional constraints and give a general formula for this completion. The paper is mainly focused on matrices with the specified lower triangular part of a special form. For...

Thyroglossal duct cyst is a well-known congenital entity, and its embryonic development and clinical presentation are well understood. Very little can be added to the classic material found in the world literature. Rare cases of unusual clinical presentation have also been reported. Our case of endolaryngeal thyroglossal duct cyst is reported because of its unique endolaryngeal presentation...

Ejaculatory duct obstruction (EDO) underlies 1-5% of male infertility, although the diagnosis of EDO can be complex, treatment is well established and can be very effective. Part of reason that this condition probably is underdiagnosed, is because of its rarity, subtle presentation and the concomitantly low index of suspicion held by physicians. The causes of EDO are divided into congenital and...

A low-complexity multiple-input multiple-output (MIMO) subspace detection algorithm is proposed. It is based on decomposing a MIMO channel into multiple subsets of decoupled streams that can be detected separately. The new scheme employs triangular decomposition followed by elementary matrix operations to transform the channel into a generalized elementary matrix whose structure matches the sub...