The kernel theorem for Cauchy ultradistribution

Kernel theorems for spaces of Cauchy ultradistribution, supported by an n-dimensional tube and cone of the product type, are investigated.     

Unexpected cycloadducts from 1,3-dipolar cycloaddition of 3,4-dehydromorpholine N-oxide to N-cinnamoyl piperidines—first report of the novel formation of 2:1 cycloadducts

A series of unexpected cycloadducts along with normal cycloadducts have been isolated from the 1,3-dipolar cycloaddition of 3,4-dehydromorpholine N-oxide to piperidides of cinnamic acid and para-substituted cinnamic acids and these were analyzed by X-ray crystallography to reveal novel solid-state structures. At first, 1:1 cycloadducts were formed which underwent in situ nucleophilic attack by another reduced nitrone moiety. A plausible iminium-oxonium ion mechanism has been proposed.     

Kinetics of the oxidation of phosphinic,phenylphosphinic, and phosphorous acids by N-bromoacetamide

The oxidation of phosphinic, phenylphosphinic, and phosphorous acids by N-bromoacetamide (NBA) in acid solution, results in the formation of corresponding higher oxyacids of phosphorus. The reaction is first order with respect to NBA, second order in the oxyacid and inverse first in hydrogen ions. The oxidation of deuteriated phosphorus oxyacids showed the presence of a substantial primary kinetic isotope effect. The reaction failed to induce polymerization of acrylonitrile. Added acetamide has no effect on the reaction rate. It has been shown that the ‘inactive’ tautomer of the phosphorus oxyacids, RHP(O)OH, participates in the oxidation process. A rate-determining step involving transfer of a hydride ion from the P? H bond to the oxidant has been proposed.     

Creation or destruction of sourceless abelian gauge strings in a Robertson-Walker universe

Following Morris’s [5] consideration of a sourceless abelian gauge string in a Robertson-Walker universe with flat space sections we have generalized the treatment to the case of arbitrary spatial curvature. We find that creation or destruction of the gauge string is not possible if the spatial curvature is nonzero.     

Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications

We present here a comprehensive account of the formulation and pilot applications of the second‐order perturbative analogue of the recently proposed unitary group adapted state‐specific multireference coupled cluster theory (UGA‐SSMRCC), which we call as the UGA‐SSMRPT2. We also discuss the essential similarities and differences between the UGA‐SSMRPT2 and the allied SA‐SSMRPT2. Our theory, like its parent UGA‐SSMRCC formalism, is size‐extensive. However, because of the noninvariance of the theory with respect to the transformation among the active orbitals, it requires the use of localized orbitals to ensure size‐consistency. We have demonstrated the performance of the formalism with a set of pilot applications, exploring (a) the accuracy of the potential energy surface (PES) of a set of small prototypical difficult molecules in their various low‐lying states, using natural, pseudocanonical and localized orbitals and compared the respective nonparallelity errors (NPE) and the mean average deviations (MAD) vis‐a‐vis the full CI results with the same basis; (b) the efficacy of localized active orbitals to ensure and demonstrate manifest size‐consistency with respect to fragmentation. We found that natural orbitals lead to the best overall PES, as evidenced by the NPE and MAD values. The MRMP2 results for individual states and of the MCQDPT2 for multiple states displaying avoided curve crossings are uniformly poorer as compared with the UGA‐SSMRPT2 results. The striking aspect of the size‐consistency check is the complete insensitivity of the sum of fragment energies with given fragment spin‐multiplicities, which are obtained as the asymptotic limit of super‐molecules with different coupled spins. © 2015 Wiley Periodicals, Inc.     

A competent pot and atom-efficient synthesis of Betti bases over nanocrystalline MgO involving a modified Mannich type reaction

A simple, efficient, and eco-friendly method for the synthesis of 1-(α-aminoalkyl) naphthols, the Betti bases, has been carried out over a basic nanocrystalline MgO catalyst in aqueous condition. The method has been applied for the synthesis of a range of compounds with variable functionalities in excellent yield and selectivity.     

A convenient palladium catalyzed synthesis of symmetric biaryls, biheterocycles and biaryl chiral diamides

A series of symmetrical diamido biaryls has been synthesized in good yield by direct homocoupling of iodoarylbenzamides by palladium-catalysis. No cross product has been isolated from the reaction mixture of two different iodoarylbenzamides under similar conditions. However, only in the case of 2-iodo-N-phenylbenzamide, the intramolecularly coupled product phenanthridone has been isolated as a minor product along with the major intermolecularly coupled product. Biphenyl chiral diamides have been synthesized by this coupling method. This coupling reaction also works well with the reductive dimerization of functionalized heterocyclic compounds. Thus 6,6′-dipivaloylamino-3,3′-bipyridine and 6,6′-dimethyl-2,2′-bipyridine have been efficiently synthesized. In two cases, the X-ray crystal structures have been solved to establish the structures of symmetrical and chiral diamido biaryls and their supramolecular networks.     

Recent advances in the chemistry of lignans

The recent literature on the chemistry of simple lignans has been comprehensively reviewed.     

Axially symmetric electrovac solutions

Two classes of electrovac solutions are obtained in oblate spheroidal coordinates, which are the electromagnetic analogs of Zipoy's monopole and dipole solutions. The asymptotic behavior of the solutions is studied to gain some insight into the nature of the source of the gravitational and electromagnetic fields. A similar stationary solution of the pure gravitational field is found to belong to Papapetrou's class.