Maximal Contractive Tuples

Maximality of a contractive tuple of operators is considered. A characterization for a contractive tuple to be maximal is obtained. The notion of maximality for a submodule of the Drury–Arveson module on the \(d\) -dimensional unit ball \({\mathbb {B}}_d\) is defined. For \(d=1\) , it is shown that every submodule of the Hardy module over the unit disc is maximal. But for \(d\ge 2\) we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of maximal submodules is obtained.     

A unified approach to the integrals of Mellin–Barnes–Hecke type

In this paper, we provide a unified approach to a family of integrals of Mellin–Barnes type using distribution theory and Fourier transforms. Interesting features arise in many of the cases which call for the application of pull-backs of distributions via smooth submersive maps defined by Hörmander. We derive by this method the integrals of Hecke and Sonine related to various types of Bessel functions which have found applications in analytic and algebraic number theory.     

A simple efficient sequential one-pot intermolecular aza-Michael addition and intramolecular Buchwald–Hartwig α-arylation of amines: synthesis of functionalized tetrahydroisoquinolines

An efficient one-pot sequential intermolecular aza-Michael addition and Pd-catalyzed intramolecular Buchwald–Hartwig α-arylation of secondary amines have been investigated, for the synthesis of tetrahydroisoquinolines. This method is simple and furnished products in very good yield and also successfully applied for the synthesis of novel aza-spirotricylcic ethers.     

An eco-safe approach to benzopyranopyrimidines and 4H-chromenes in ionic liquid at room temperature

An environmentally benign, ionic liquid promoted multicomponent protocol to benzopyrano(2,3-d)pyrimidines and 4H-chromenes has been developed at room temperature. Results of the reaction depend on the nature of the nucleophile used in the reaction. Secondary amines result in the formation of benzopyrano(2,3-d)pyrimidines, whereas thiols give rise to 4H-chromenes under the same set of reaction conditions.     

New Chromogenic Spray Reagent for Detection and Identification of Carbosulfan

JPC – Journal of Planar Chromatography – Modern TLC - A new chromogenic spray reagent has been used for detection and identification of carbosulfan in HPTLC. Alkaline hydrolysis of...     

Molecular conformation and liquid structure of 2-propanol through neutron diffraction

The neutron diffraction data analysis of deuterated liquid 2-propanol at room temperature to define its molecular conformation is presented. 2-Propanol being a large molecule with twelve atomic sites, the conformation analysis is tricky and an improved method of data analysis is given. The intermolecular structural correlations, i.e., hydrogen-bonded liquid structure, can be modelled accurately to extract the nature of the average hydrogen-bonded molecular association in liquid state at room temperature. Like other alcohols these are mostly hexamer ring chain (HRC) clusters. The cluster analysis of recent X-ray data available in the literature also support the same liquid structure.     

Lasing without population inversion in molecules

We have described here the physical basis for lasing without population inversion (LWOPI). This type of amplification is obtained basically by two mechanisms: (i) one is based on atomic interference and (ii) the other is based on Fano-type interference. We have shown here, in H₂ molecules, amplification without population inversion is feasible by considering both the mechanisms.