Trace Theorems for Anisotropic Weighted SOBOLEV Spaces in a Corner

In this paper, we prove a trace theorem for anisotropic weighted Sobolev spaces in a cube Q naturally associated to a class of degenerate elliptic operators. The fundamental property of this class is the existence of a suitable metric d which is “natural” for the operators. The basic tool of the proof is a representation formula obtained via suitable non-euclidean translations closely fitting the geometry of the d-balls. In a more particular situation, we construct a right inverse of the trace operator and we describe the compatibility conditions on the edges of Q.     

Weighted Poincaré inequalities for Hörmander vector fields and local regularity for a class of degenerate elliptic equations

In this note we state weighted Poincaré inequalities associated with a family of vector fields satisfying Hörmander rank condition. Then, applications are given to relative isoperimetric inequalities and to local regularity (Harnack's inequality) for a class of degenerate elliptic equations with measurable coefficients.     

Mono- and dinuclear bioxazoline-palladium complexes for the stereocontrolled synthesis of CO/styrene polyketones

The coordination chemistry of the chiral bioxazoline ligand (4S,4'S)-2,2'-bis(4-isopropyl-4,5-dihydrooxazole) to Pd(II) provides evidence that the ligand bonding can occur either through chelation of one Pd(II) ion leading to a mononuclear species with the expected cis geometry, or by double bridging of two Pd(II) ions giving a dinuclear complex with trans geometry. The species in solution are identified by 1H NMR spectroscopy. Both the mononuclear and the dinuclear complexes promote the CO/styrene copolymerization, yielding the corresponding polyketone with a fully or a predominantly isotactic microstructure, depending on the reaction medium. The nature of the anion present in the palladium precatalysts affects the polyketone stereochemistry. MALDI-TOF analysis of the copolymers synthesized reveals the presence of p-hydroxyphenolic end-groups, thus confirming and explaining the role of 1,4-hydroquinone as a molecular weight regulator.     

A finite element approximation for a class of degenerate elliptic equations

In this paper we exhibit a finite element method fitting a suitable geometry naturally associated with a class of degenerate elliptic equations (usually called Grushin type equations) in a plane region, and we discuss the related error estimates.

     

Synthesis and characterization of a persistent paramagnetic rotaxane based on α-cyclodextrin and α,ω-alkyl disulfides

A new synthetic strategy for the preparation of persistent paramagnetic cyclodextrin-based rotaxanes is described. The method consists in the formation of inclusion complexes between α-cyclodextrin (α-CD) and α,ω-dithiols containing an octamethylene chain covalently trapped by bulky stoppers composed of 2,2,6,6-tetramethylpiperidine-N-oxyl (TEMPO) radical fragments. Interaction of α-CD (the bead) and 1,8-octanedithiol (the thread) occurs in aqueous alkaline media and encapsulation is obtained by nucleophilic substitution at both termini of the linear component with a bulky paramagnetic iodide [2,2,6,6-tetramethyl-4-(2-iodoacetamide)piperidine-N-oxyl]. Structure determination of the new [2]rotaxane by ¹H NMR is reported and the spectroscopic data are discussed.     

Asymptotic Singular Homology of a Complete Hyperbolic 3-Manifold of Finite Volume

Let V be a complete connected hyperbolic 3-manifold of finitevolume, with Liouville measure m, geodesic flow _t and Brownianmotion Z_t. Let be a smooth 1-form, closed in the cusps of V.Then the limit laws as t of under m and of are calculated, and seen to be Gaussian, and equal. The geodesic flow case isstudied via the Brownian case. 1991 Mathematics Subject Classification:60J65, 58F17, 51M10.     

Investigation of lacidipine,a new 1,4-dihydropyridine antihypertensive agent and three chemically related compounds by means of chemical ionization,mass spectrometry and collision-induced dissociation

Chemical ionization of two 1,4-dihydropyridines, lacidipine and its Z-isomer, and their corresponding pyridines in three different reagent gases and the collision-induced dissociation (CID) of their respective mass-selected protonated molecular ions in the collision energy range 10–200 eV were performed on a multiple quadrupole instrument. The weakness of the Breasted acid NH₄⁺ as a protonating agent is clearly manifested in one of the ammonia positive-ion chemical ionization (CI⁺) mass spectra which displays the addition ion, [M + NH₄]⁺, as the favoured reaction channel. The stereochemistry of the precursor molecules, the exothermicity of the protonation process and the threshold of certain dissociation channels as a function of the collision energy are among the arguments invoked to explain some of the observed differences between the CI⁺ mass spectra and the CID data of the different isomers investigated. In an attempt to present a more comprehensive study, some high-performance liquid chromatographic retention times and resolutions are also given.     

Biological fixation of endosseous implants

Primary implant stability is ensured by a mechanical fixation of implants. However, during implant healing a biological anchorage is necessary to achieve final osseointegration.

Aim of this study was to investigate the histological aspects of biological fixation around titanium screws.

Forty-eight titanium screws with different surfaces (smooth, plasma sprayed, sand blasted) were inserted in tibiae and femura of sheep and analyzed by light microscope and SEM 1 hour, 14 and 90 days after implantation.

One hour after implantation the implant-bone gap was filled with a blood clot and host bone chips arising from burr surgical preparation or friction during implant insertion. Fourteen days after implantation new trabecular bone and enveloped bone chips were observed in the gap: no osteogenesis developed where implant threads were in contact with host bone. Ninety days after surgery all trabecular bone and most of the bone chips were substituted by a mature lamellar bone with few marrow spaces.

Our results suggest that the trabecular bone and bone chips represent a three-dimensional network ensuring a biological implant fixation in all different implant surfaces 2 weeks after surgery. Host bone chips could favour the peri-implant osteogenesis. Inter-trabecular and implant-trabecular marrow spaces of both trabecular and lamellar bone may favour the peri-implant bone turnover.