Oxygen-17 NMR chemical shifts of esters

The ¹⁷O NMR spectra of some esters are discussed and are correlated with ¹³C NMR chemical shift and IR carbonyl streching band data.     

Four-manifolds with π<Subscript>1</Subscript>–free second homotopy

 We study the homotopy type of closed connected orientable topological 4–manifolds M with Λ–free second homotopy group, where Λ is the integral group ring of π₁(M). This is related with problem N.4.53 of [23], and extends some results proved for the class of closed 4–manifolds with free fundamental group [10][11]. Other applications on special classes of closed topological manifolds complete the paper. Received: 27 November 2001 / Revised version: 28 October 2002 Published online: 19 May 2003 Work performed under the auspices of the GNSAGA of the CNR of Italy and partially supported by Ministero per la Ricerca Scientifica e Tecnologica of Italy within the project Proprietà Geometriche delle Varietà Reali e Complesse, and by a research grant of the University of Modena and Reggio Emilia. Mathematics Subject Classification (2000): Primary: 57 N 65, 57 R 67; Secondary: 57 Q 10, 57 R 80     

BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces

This paper is devoted to real valued backward stochastic differential equations (BSDEs for short) with generators which satisfy a stochastic Lipschitz condition involving BMO martingales. This framework arises naturally when looking at the BSDE satisfied by the gradient of the solution to a BSDE with quadratic growth in Z$Z$. We first prove an existence and uniqueness result from which we deduce the differentiability with respect to parameters of solutions to quadratic BSDEs. Finally, we apply these results to prove the existence and uniqueness of a mild solution to a parabolic partial differential equation in Hilbert space with nonlinearity having quadratic growth in the gradient of the solution.     

On the homotopy type of Poincaré spaces

We study the homotopy type of finite-oriented Poincaré spaces (and, in particular, of closed topological manifolds) in even dimension. Our results relate polarized homotopy types over a stage of the Postnikov tower with the concept of CW-tower of categories due to Baues. This fact allows us to obtain a new formula for the top-dimensional obstruction for extending maps to homotopy equivalences. Then we complete the paper with an algebraic characterization of high-dimensional handlebodies. Received: April 14, 1999?Published online: October 2, 2001     

The combinatorics of some tetrahedron manifolds

We study a family of closed connected orientable 3-manifolds (which are examples of tetrahedron manifolds) obtained by pairwise identifications of the boundary faces of a standard tetrahedron. These manifolds generalize those considered in previous papers due to Grasselli, Piccarreta, Molnár and Sieradski. Then we completely describe our tetrahedron manifolds in terms of Seifert fibered spaces, and determine their Seifert invariants. Moreover, we obtain different representations of our manifolds as 2-fold coverings, and give examples of non-equivalent knots with the same tetrahedron manifold as 2-fold branched covering space.