On the Reactivity of Metal and Organometallic Halides and Pseudohalides Towards Stannosiloxane (Ph3Sn-O-SiPh3)

Abstract

Interactions of HgX₂ (X = Cl, Br, I, SCN, CN, NCO), SbCl₃, TeCl₄, and PhTeCl₃ with Ph₃Sn-O-SiPh₃ at room temperature have been found to proceed with the simultaneous cleavage of Sn-O and Si-O bonds, invariably yielding Ph₂SnO, Ph₃SiX, and the corresponding organo-mercury, -antimony, and -tellurium derivatives. The course of the reactions suggests the instability of the Sn-O-M (M = Hg, Sb, Te) system.

GRAPHICAL ABSTRACT      

Asymptotic Dual Conditions Characterizing Optimality for Infinite Convex Programs

Characterizations of optimality are presented for infinite-dimensional convex programming problems, where the number of constraints is not restricted to be finite and where no constraint qualification is assumed. The optimality conditions are given in asymptotic forms using subdifferentials and €-subdifferentials. They are obtained by employing a version of the Farkas lemma for systems involving convex functions. An extension of the results to problems with a semiconvex objective function is also given.     

Liberating the Subgradient Optimality Conditions from Constraint Qualifications

In convex optimization the significance of constraint qualifications is evidenced by the simple duality theory, and the elegant subgradient optimality conditions which completely characterize a minimizer. However, the constraint qualifications do not always hold even for finite dimensional optimization problems and frequently fail for infinite dimensional problems. In the present work we take a broader view of the subgradient optimality conditions by allowing them to depend on a sequence of ε-subgradients at a minimizer and then by letting them to hold in the limit. Liberating the optimality conditions in this way permits us to obtain a complete characterization of optimality without a constraint qualification. As an easy consequence of these results we obtain optimality conditions for conic convex optimization problems without a constraint qualification. We derive these conditions by applying a powerful combination of conjugate analysis and ε-subdifferential calculus. Numerical examples are discussed to illustrate the significance of the sequential conditions.     

Orlicz Figà – Talamanca Herz algebras and invariant means

The aim of this paper is to initiate a systematic study of the Orlicz Figà – Talamanca Herz algebras on locally compact groups. We also introduce and study invariant means on the dual of these algebras.     

Lipschitz continuity ofV-subdifferentials of convex operators

It is proved that theV-subdifferential of a convex operator is locally Lipschitzian on the set of points at which it is continuous and subdifferentiable.Proposition 2.2 was originally stated for Holder continuity ofV-subdifferentials. The author would like to thank J. P. Penot for a very helpful suggestion which led to the present form of this proposition.     

重复率气体火花开关绝缘恢复特性的实验研究

 在自行设计的气体火花开关上，利用双脉冲回路，对纳秒脉冲作用下N₂和H₂的绝缘恢复特性进行了实验研究。结果表明，在静态不吹气情况下，H₂的绝缘恢复时间明显比N₂短。在吹气情况下，适当的气流速度即可使绝缘恢复时间明显缩短。     

Synthesis of (−)-elemoxide,a commercially important fragrance compound

(?)-Elemoxide, a fragrant compound was synthesised using commercially available elemol in four steps with overall yield of 32%. The cyclic ether skeleton was constructed via intramolecular hydroalkoxylation using I₂ and PhSiH₃ catalytic system. Also, intramolecular oxymercuration-demercuration was employed as an alternate approach for cyclization. The various regioselective strategies involving epoxidation of alkene, reduction of epoxide and intramolecular cyclization were the highlights of the work. The key intermediate diol serves as a versatile intermediate for the synthesis of elemoxide and elemene.     

Dual conditions characterizing optimality for convex multi-objective programs

Received June 13, 1995 / Revised version received February 6, 1998 Published online August 18, 1998     

Geometry of rank 2 distributions with nonzero Wilczynski invariants

In the famous 1910 “cinq variables” paper Cartan showed in particular that for maximally nonholonomic rank 2 distributions in ?⁵ with non-zero covariant binary biquadratic form the dimension of the pseudo-group of local symmetries does not exceed 7 and among such distributions he described the one-parametric family of distributions for which this pseudo-group is exactly 7-dimensional. Using the novel interpretation of the Cartan covariant binary biquadratic form via the classical Wilczynski invariant of curves in projective spaces associated with abnormal extremals of the distributions [4, 27, 28] one can generalize this Cartan result to rank 2 distributions in ?ⁿ satisfying certain genericity assumption, called maximality of class, for arbitrary n ≥ 5.

In the present paper for any rank 2 distribution of maximal class with at least one nonvanishing generalized Wilczynski invariants we construct the canonical frame on a (2n — 3)-dimensional bundle and describe explicitly the moduli spaces of the most symmetric models. The relation of our results to the divergence equivalence of Lagrangians of higher order is given as well.