The Noncommutative Bispectral Problem for Operators of Order One

We study a noncommutative version of the bispectral problem and consider the corresponding ad-conditions in the case when both operators have order one. These terms are explained in an extended abstract given below.     

Geometric topology of generalized 3-manifolds

In this paper, we describe the history and the present status of one of the main classical problems in low-dimensional geometric topology—the recognition of topological 3-manifolds in the class of all generalized 3-manifolds (i.e., ANR homology 3-manifolds). This problem naturally splits into the cell-like resolution problem for 3-manifolds by means of homology 3-manifolds and the general-position problem for topological 3-manifolds. We have also included some open problems. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 71–84, 2005.     

Complément de Schur et sous-différentiel du second ordre d'une fonction convexe

Summary The Schur complement relative to the linear mappingA of a functionf is denotedAf and defined as the image off underA. In this paper we give some estimates for the second-order differential ofAf whenf is either a partially quadratic convex function or aC ² convex function with a nonsingular second-order differential. We then consider an arbitrary convex functionf and study the second-order differentiability ofAf in a more general sense.

     

Torsion-free covers and pure-injective envelopes over valuation domains

We describe the torsion-free covers of cyclic modules, the pure-injective envelopes of ideals, the maximal immediate extensions of localizations and the injective envelopes of cyclics over valuation domains. We study the relations among these modules. This paper generalizes some results of Banaschewski, Cheatham, Enochs and Nishi. Supported by Ministero della Pubblica Istruzione and GNSAGA (CNR).     

An improved synthesis of indazole-3-carboxylic acid

A new and efficient synthesis of indazole-3-carboxylic acid is reported. The method consists in reacting β-acetylphenylhydrazine with chloral hydrate and hydroxylamine hydrochloride in acidic medium to afford N-acetylaminoisonitrosoacetanilide which, in turn, is converted into the title compound by treatment with sulphuric acid.     

Synthesis,spectroscopic and magnetic characterization of some iron(III)-nucleotide compounds

Summary Magnetic moments and⁵⁷Fe M?ssbauer spectra at various temperatures of polycrystalline samples of some Fe^III-nucleotide compounds are described and have been characterized by u.v.-visible and fluorescence spectroscopy. Conclusions regarding the binding of iron(III) to nucleic acids are discussed.     

Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model

General boundary conditions (branes') for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morphisms and at the perturbative quantum level to the category of associative algebras (deforming algebras of functions on Poisson manifolds) with bimodules as morphisms. Possibly singular Poisson manifolds arising from reduction enter naturally into the picture and, in particular, the construction yields (under certain assumptions) their deformation quantization.     

Femtosecond dynamics of Co thin films on Si support

The ultrafast electron and spin dynamics of Co films was investigated using a femto-second pump-probe technique. The samples were magnetically characterized by means of magnetooptical Kerr effect and non-optical magnetometers, i.e. superconductive quantum interference device and alternating gradient field magnetometer. Time evolution of both, Kerr rotation and ellipticity, was measured at different points of the static hysteresis cycle. This allowed separating magnetic and non-magnetic contributions to the signal. The sample magnetization was found to drop within 200 fs, following the pulse cross-correlation trace, while the magnetization recovery time was found to last few picoseconds.     

On Af.Af* geometries

This paper is intended to be a first step towards the classification of finite flag-transitive geometries of rank 3 with affine planes and dual affine point-residues. We describe those of diameter 1. In the case of diameter > 1, we describe minimal quotients, assuming that the number of lines through two points is large enough.