Multinuclear magnetic resonance study of some mesoionic oxatriazoles containing nitrogenous exocyclic groups

¹H,¹³C,¹⁴N and¹⁵N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N^– H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995.     

Microlocal study of topological Radon transforms and real projective duality

Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.     

Limit cycles and Lie symmetries

Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a prescribed number of hyperbolic limit cycles. Finally we show how this procedure solves the problem of the hyperbolicity of periodic orbits in problems where other criteria, like the classical one of the divergence, fail.     

Proof of semialgebraic covering mapping cylinder conjecture with semialgebraic covering homotopy theorem

In this paper we prove the semialgebraic version of Palais' covering homotopy theorem, and use this to prove Bredon's covering mapping cylinder conjecture positively in the semialgebraic category. Bredon's conjecture was originally stated in the topological category, and a topological version of our semialgebraic proof of the conjecture answers the original topological conjecture for topological G-spaces over “simplicial” mapping cylinders.     

Krichever-Novikov algebras for more than two points

Krichever-Novikov algebras of meromorphic vector fields with more than two poles on higher genus Riemann surfaces are introduced. The structure of these algebras and their induced modules of forms of weight 14u5886/xxlarge955.gif" alt="lambda" align="BASELINE" BORDER="0"> is studied.     

Complex surfaces polarized by an ample and spanned line bundle of genus three

Let X be a complex connected projective nonsingular algebraic surface endowed with an ample line bundle L, which is spanned by its global sections. Pairs (X, L) as above, with sectional genus g(X, L)=1+(L·(K _X L))/2=3 are classified by means of the main techniques of adjunction theory.     

大环二萜类化合物的研究(Ⅳ)——Isosarcophytol—A前体化合物的合成

Isosarcophytol-A(1)是1982年首次从澳大利亚软珊瑚(Nephthea brassica)中分离鉴定的西松烷型(Cembrane)大环二萜类化合物,其结构为6,10,14-三甲基-3-异丙基-3E,5E,9E,13E-环十四碳四烯-1-醇,是Sarcophytol—A(2)的异构体,但有关1的生物活性试验和全合成研究尚未见报道.我们在前文报道了以低价钛诱导的分子内二羰基偶联为环化方法,完成了天然大环二萜类化合物Cembrene—C的全合成和Sarcophytol—A(2)苄醚衍生物(3)的合成.本文报道以天然法呢醇4为起始原料,经区域选择性氧化、羟醛缩合等六步反应,合成了1的前体化合物11.合成路线如下:     

In search of 1,3-disila/germa/stannabicyclo[1.1.1]pentanes with short bridgehead-bridgehead distances and low ring strain energies

The strain energies and through-space distances between the two bridgehead E atoms of a selection of 1,3-dimethyl-1,3-ditetrelbicyclo[1.1.1]pentanes (tetrel E = Si, Ge or Sn) were examined by quantum chemical calculations at MP2 and B3LYP levels. The aim is to identify which bridges lead to short through-space E,E distances, and simultaneously, to as low strain as possible. A short E,E distance should improve through-space interaction, and a low strain should promote the thermal stability and possibly also facilitate their synthesis. The bridges examined included CH₂, CMe₂, CtBu₂, C(CH₂)n (n = 2–4), O, NMe, S, PMe, SiMe₂, GeMe₂, and SnMe₂. The calculations indicate that the phospha bridge is a good compromise providing reasonably low strain as well as E,E through-space distances which are only longer than normal E–E single bonds by factors of 1.06–1.10. This paper is dedicated to Professor Mitsuo Kira in recognition of his stimulating Si chemistry and his 2005 Wacker Award.