Rhodium(III)‐Catalyzed Selective ortho‐Olefinations of N‐Acyl and N‐Aroyl Sulfoximines by CH Bond Activation

Two new rhodium‐catalyzed oxidative couplings between sulfoximine derivatives and alkenes by regioselective C?H activation, affording ortho‐olefinated (Heck‐type) products, are reported. A synthetic application of the ortho‐alkenylated products into the corresponding cyclic derivatives has been demonstrated, and a mechanistic rational for the rhodium catalysis is presented.     

Matroidal games

The theory ofmatriods consists of generalization of basic notions oflinear algebra likedependence, basis andspan. In this paper we point out that every non-trivial matroid represents a simple game though the converse need not be true. The class of simple games which possess the matroidal structure is designated asmatroidal games. In matroidal games, we have a generalization of the concept of complete exchangeability of players observed in purely size dependent games. Invoking the well developed theory of matroids, we study the combinatorial structure of matroidal games.     

Quantum analogues of a coherent family of modules at roots of unity: A 3

To a given coherent family of virtual representations of a complex semiesimple Lie algebra we associate elsewhere a coherent family of virtual representations of the corresponding quantum group at roots of unity. We also proposed a conjecture there that under some hyptoheses the members of the family in a certain positive cone are actually modules (and not just a virtual module, i.e., a difference of two modules). The validity of this conjecture for A ₂ and B ₂ has been verified by the author. In this paper we solve the problem for A ₃.     

LipschitzianQ-matrices areP-matrices

In this note, we show that LipschitzianQ-matrices areP-matrices by obtaining a necessary condition on LipschitzianQ ₀-matrices. The sufficiency of this condition has also been established by the first two authors along with another coauthor (Murthy, Parthasarathy and Sriparna, 1995). This work was done while I visited ISI, Delhi Center during March–April, 1994. I want to express my sincere thanks for their kind hospitality.     

Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae

An analysis of Feynman-Kac formulae reveals that, typically, the unperturbed semigroup is expressed as the expectation of a random unitary evolution and the perturbed semigroup is the expectation of a perturbation of this evolution in which the latter perturbation is effected by a cocycle with certain covariance properties with respect to the group of translations and reflections of the line. We consider generalisations of the classical commutative formalism in which the probabilistic properties are described in terms of non-commutative probability theory based on von Neumann algebras. Examples of this type are generated, by means of second quantisation, from a unitary dilation of a given self-adjoint contraction semigroup, called the time orthogonal unitary dilation, whose key feature is that the dilation operators corresponding to disjoint time intervals act nontrivially only in mutually orthogonal supplementary Hilbert spaces.Parts of this work were carried out when the first author was a participant in the Sonderforschungsbereich 123 (Stochastische Mathematische Modelle) of the Deutsche-Forschungsgemeinschaft and when the third author was Visiting Fellow at the University of Warwick     

High-Pressure Mössbauer Measurements on Nanocrystalline Perovskite (La,Sr)(Mn,Fe)O3

We report here the Mössbauer measurements on nanocrystalline perovskite structured manganite La_0.8Sr_0.2Mn_0.8Fe_0.19 ⁵⁷Fe_0.01O₃ as a function of pressure up to 10 GPa at room temperature. The nanocrystalline sample, prepared by sol–gel technique found to have crystallite sizes of ∼138 ± 10 Å. Zero-field electrical resistivity measurements with temperature support the nanocrystalline nature. At ambient pressure, Fe³⁺ as well as Fe⁴⁺ ions are distributed in two different environments – Fe³⁺ in low symmetric site surrounded by Mn³⁺ ions only while Fe⁴⁺ in high symmetric site with at least one Mn³⁺ ion. Pressure seems to affect the higher symmetric site. A sudden increase in isomer shift at 0.52 GPa indicates the first order phase transition representing the transformation of Fe⁴⁺ to Fe³⁺. Another transition at 3.7 GPa, represents the presence of Fe³⁺ in single kind of environment. Pressure dependence of electrical resistivity measurements verifies the transitions attributing the first order transition to the cross over of localized-electron to band magnetism.