L2 -cohomology of manifolds with flat ends

Geometric and Functional Analysis - We give a topological interpretation of the spaces of L2 -harmonic forms on manifolds with flat ends. We also prove a Chern-Gauss-Bonnet formula for the L2...     

The Huber theorem for non-compact conformally flat manifolds

It was proved in 1957 by Huber that any complete surface with integrable Gauss curvature is conformally equivalent to a compact surface with a finite number of points removed. Counterexamples show that the curvature assumption must necessarily be strengthened in order to get an analogous conclusion in higher dimensions. We show in this paper that any non compact Riemannian manifold with finite -norm of the Ricci curvature satisfies Huber-type conclusions if either it is a conformal domain with volume growth controlled from above in a compact Riemannian manifold or if it is conformally flat of dimension 4 and a natural Sobolev inequality together with a mild scalar curvature decay assumption hold. We also get partial results in other dimensions. Received: April 14, 2000; revised version: March 20, 2001     

Le saut en zéro de la fonction de décalage spectral

We give a formula for the jump at zero of the spectral shift function associated with Schrödinger operator on manifolds with conical ends. We show that, according to its decay, a zero energy resonant state has a non-integer contribution.     

New cis-clerodane diterpenoids from Croton schiedeanus

The acid fraction of extracts from the aerial part of Croton schiedeanus afforded six cis-clerodane type diterpenoids. Two of them (1 and 4) are new natural compounds. Structural elucidation was achieved on the basis of their spectral data.     

Ultrasmall Superparamagnetic Iron Oxide Nanoparticles with Europium(III) DO3A as a Bimodal Imaging Probe

A new prototype consisting of ultrasmall superparamagnetic iron oxide (USPIO) nanoparticles decorated with europium(III) ions encapsulated in a DO3A organic scaffold was designed as a platform for further development of bimodal contrast agents for MRI and optical imaging. The USPIO nanoparticles act as negative MRI contrast agents, whereas the europium(III) ion is a luminophore that is suitable for use in optical imaging detection. The functionalized USPIO nanoparticles were characterized by TEM, DLS, XRD, FTIR, and TXRF analysis, and a full investigation of the relaxometric and optical properties was conducted. The typical luminescence emission of europium(III) was observed and the main red emission wavelength was found at 614 nm. The relaxometric study of these ultrasmall nanoparticles showed r₂ values of 114.8 mm ^?1_Fes^?1 at 60 MHz, which is nearly double the r₂ relaxivity of Sinerem^®.     

Highly Enantioselective,Organocatalytic, and Scalable Synthesis of a Rare cis,cis-Tricyclic Diterpenoid

A highly enantioselective, organocatalytic, and scalable synthesis of a very unusual cis-decalin-cis-hydrindane tricyclic diterpenoid system has been achieved. Despite the prevalent pharmacological space that the related trans,trans and trans,cis-systems occupy, there have been no reports of an asymmetric synthesis of the cis,cis systems in the literature until now. We demonstrate the flexibility of our approach not only through access to a diverse range of products, all of which are attained in exceptionally high selectivities, but also by showing their easy conversion to the corresponding trans,cis-system and other derivatives.     

Synthesis and Antiviral Properties of Spirocyclic [1,2,3]‐Triazolooxazine Nucleosides

An efficient synthesis of spirocyclic triazolooxazine nucleosides is described. This was achieved by the conversion of β‐D ‐psicofuranose to the corresponding azido‐derivative, followed by alkylation of the primary alcohol with a range of propargyl bromides, obtained by Sonogashira chemistry. The products of these reactions underwent 1,3‐dipolar addition smoothly to generate the protected spirocyclic adducts. These were easily deprotected to give the corresponding ribose nucleosides. The library of compounds obtained was investigated for its antiviral activity using MHV (mouse hepatitis virus) as a model wherein derivative 3 f showed the most promising activity and tolerability.     

Variational approximations in a path integral description of potential scattering

Using a recent path integral representation for the T -matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables --over which one has to integrate functionally-- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading). We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to the variational result arising from a cumulant expansion is also evaluated. Comparison is made with exact partial-wave results for scattering from a Gaussian potential and better agreement is found at large scattering angles where the standard eikonal-type approximations fail.     

A Topological Criterion for the Existence of Half-Bound States

The following theorem is proved: if (M⁴ⁿ⁺¹,g) is a completeRiemannian manifold and M is an oriented hypersurface partitioningM and with non-zero signature, then the spectrum of the Hodge–deRhamLaplacian is [0,]. This result is obtained by a new Callias-typeindex. This new formula links half-bound harmonic forms (thatis, nearly L² but not in L²) with the signature of .