A sharp Sobolev inequality on Riemannian manifoldsUne inégalité de Sobolev optimale sur les varietés riemanniennes

We outline our results in [11] concerning some sharp Sobolev inequalities on Riemannian manifolds. Our inequalities emphasize the role of scalar curvature in this context. To cite this article: Y.Y. Li, T. Ricciardi, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 519–524.     

Model calculations of a two-step reaction scheme for the production of neutron-rich secondary beams

A two-step reaction scheme for the production of extremely neutron-rich radioactive beams, fission followed by cold fragmentation, is considered. The cross-sections of the second step, the cold fragmentation of neutron-rich fission fragments, are estimated with different computer codes. Discrepancies between an empirical systematics and nuclear-reaction codes are found. Received: 27 January 2003 / Accepted: 6 March 2003 / Published online: 27 May 2003     

Synthesis of porphyrazines bearing thioalkylthiol tethers: useful building blocks for supramolecular chemistry

A simple and substantially inexpensive method is proposed for the synthesis of a porphyrazine macrocycle symmetrically functionalized with eight bromoalkylthio pendants and its conversion in the S-acetyl protected thiol-hexylthio-substituted analog.     

Vortices in the Maxwell‐Chern‐Simons theory

Our aim is to prove rigorously that the Chern‐Simons model of Hong, Kim, and Pac [13] and Jackiw and Weinberg [14] (the CS model) and the Abelian Higgs model of Ginzburg and Landau (the AH model, see [15]) are unified by the Maxwell‐Chern‐Simons theory introduced by Lee, Lee, and Min in [16] (MCS model). In [16] the authors give a formal argument that shows how to recover both the CS and AH models out of their theory by taking special limits for the values of the physical parameters involved. To make this argument rigorous, we consider the existence and multiplicity of periodic vortex solutions for the MCS model and analyze their asymptotic behavior as the physical parameters approach these limiting values. We show that, indeed, the given vortices approach (in a strong sense) vortices for the CS and AH models, respectively. For this purpose, we are led to analyze a system of two elliptic PDEs with exponential nonlinearities on a flat torus. © 2000 John Wiley & Sons, Inc.     

A DFT/TDDFT interpretation of the ground and excited states of porphyrin and porphyrazine complexes

A comprehensive treatment is given of the electronic excitation spectra of Mg, Zn and Ni complexes of porphyrin and porphyrazine using time-dependent density functional theory (TDDFT). It is emphasized that the Kohn–Sham (KS) molecular orbital (MO) method, which is the basis for the TDDFT calculations, affords a MO interpretation of the ground state electronic structure and of the nature of the excitations. This implies that a direct connection can be made to many previous MO treatments of the title compounds. We discuss in particular, how the original explanations of the intensity distribution over the lowest excitations (the Q and B bands) in terms of a cyclic polyene model, or even a free-electron model, can be reconciled with the actual molecular and electronic structure of these compounds being much more complicated than these simple models. A fragment approach is used, building the porphyrin ring from pyrrole rings and CH or N bridges. This leads directly to a simple interpretation of the orbitals of Gouterman's four-orbital model, which are responsible for the Q and B bands. It also leads to additional occupied π-orbitals which are absent in the cyclic polyene model and which need to be invoked to understand other features of the electronic spectra such as the origin of the N, L and M bands. Considerable attention is given to the intensities of the various transitions, explaining why the transitions within the so-called four-orbital model of Gouterman have large transition dipoles, why transitions from additional occupied π-orbitals have relatively small transition dipoles.     

Tetra-2,3-pyrazinoporphyrazines with externally appended pyridine rings. 1. Tetrakis-2,3-[5,6-di(2-pyridyl)pyrazino]porphyrazine: a new macrocycle with remarkable electron-deficient properties

A new pyrazinoporphyrazine macrocycle carrying externally appended pyridine rings, tetrakis-2,3-[5,6-di(2-pyridyl)pyrazino]porphyrazine (hydrated), [Py(8)TPyzPzH(2)].2H(2)O, was prepared in high yield by direct cyclotetramerization of the precursor, 2,3-dicyano-5,6-di(2-pyridyl)-1,4-pyrazine, [(CN)(2)Py(2)Pyz], in the presence of 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU). The single-crystal X-ray structure of [(CN)(2)Py(2)Pyz] shows a noncoplanar positioning of the pyrazine and pyridine rings in the two slightly different independent molecular units present in the crystal. UV-vis spectra of [Py(8)TPyzPzH(2)] were measured in two nondonor solvents (CHCl(3), CH(2)Cl(2)), a slightly basic solvent (pyridine), and an acidic solvent (CH(3)COOH). In all cases, the spectral changes are consistent with the occurrence of molecular aggregation and colloidal dispersions which break up with time to give clear solutions containing exclusively the monomeric form of the macrocycle, either neutral [Py(8)TPyzPzH(2)] (in CHCl(3), CH(2)Cl(2), and CH(3)COOH) or dianionic [Py(8)TPyzPz](2)(-) (in pyridine). A spectrally monitored titration of [Py(8)TPyzPzH(2)] in CH(2)Cl(2) with TBA(OH) shows the loss of two protons from the macrocyclic core and quantitative conversion of [Py(8)TPyzPzH(2)] to [Py(8)TPyzPz](2)(-). Cyclic voltammetry and thin-layer spectroelectrochemical measurements show that [Py(8)TPyzPzH(2)] is present in CH(2)Cl(2) while [Py(8)TPyzPz](2)(-) is present in pyridine, but both forms of the compound exhibit identical electrochemical behavior, consistent with a conversion of the dianion to the neutral porphyrazine in pyridine prior to electroreduction via four reversible one-electron transfer steps. No oxidations of the macrocycle are observed in either solvent containing 0.1 M tetrabuthylammonium perchlorate (TBAP). A comparison of the electrochemical behavior for [Py(8)TPyzPzH(2)] with what is reported for related phthalocyanine and porphyrazine analogues highlights the remarkable electron-accepting properties of the presently investigated free-base macrocycle.     

Non-leptonic decays of charmed and beautiful particles

By fitting simultaneously the values of ζ-1/N _c and α _s (m _c ² ) on the inclusive rates of the Cabibbo allowed decaysD, F→PP andD→PV, which are independent of the final state interactions, we find ζ=0 and α _s (m _c ² )=0.44. This value for ζ is the same found by other authors [1, 4]. In order to explain the rescattering of the final states produced in the non-leptonic decays of charmedD-particles and to make theoretical predictions for all the exclusive channels, we propose a rescattering model based on the production of resonances inSU(3)-symmetry. In thePP sector we predict a new multiplet of meson resonances 0⁺ which allows us, with few free parameters, to obtain a satisfactory agreement between theoretical predictions and experimental data. Unfortunately, such an agreement cannot be obtained in thePV sector, for which the presence of other rescattering effects is needed to balance the exotic channelD ⁺→PV. In thePV sector we do not use any free parameter. Finally, we also make predictions for the Cabibbo allowed decay channelsB→PP, PV, without considering in this case the final state interactions, because of the high energy of the decay products.     

Modelling Pressurized Water Reactor cores in terms of porous media

The aim of this study is to develop a tractable model of a nuclear reactor core taking the complexity of the structure (including its nonlinear behaviour) and fluid flow coupling into account. The mechanical behaviour modelling includes the dynamics of both the fuel assemblies and the fluid. Each rod bundle is modelled in the form of a deformable porous medium; then, the velocity field of the fluid and the displacement field of the structure are defined over the whole domain. The fluid and the structure are first modelled separately, before being linked together. The equations of motion for the structure are obtained using a Lagrangian approach and, to be able to link up the fluid and the structure, the equations of motion for the fluid are obtained using an arbitrary Lagragian Eulerian approach. The finite element method is applied to spatially discretize the equations. Simulations are performed to analyse the effects of the characteristics of the fluid and of the structure. Finally, the model is validated with a test involving two fuel assemblies, showing good agreement with the experimental data.     

Electronic structure,chemical bond,and optical spectra of metal bis(porphyrin) complexes: a DFT/TDDFT study of the bis(porphyrin)M(IV) (M = Zr,Ce, Th) series

The electronic absorption spectra of the bis(porphyrin) sandwich complexes of the metals Zr, Ce, and Th are studied with time-dependent density functional theory (TDDFT). A ground-state electronic structure analysis reveals that the highest occupied one-electron levels are, as expected, composed of the porphyrin a(1u) and a(2u) highest occupied orbitals (the Gouterman orbitals), but the level pattern is not simply a pair of low-lying nearly degenerate in-phase combinations and a pair of high-lying approximately degenerate antibonding combinations. Instead, the a(1u) split strongly and the a(2u) do not. Since the calculated spectrum agrees very well with experiment, the assignment leaves little doubt that although the experimental spectrum has porphyrin-like features, such as the well-known Q and B bands, the actual composition of the states is rather different from that in porphyrin. In particular the strong mixing of a(1u) --> e(g) and a(2u) --> e(g) is absent, there is mixing with excitations of non-Gouterman type, and, in Ce, ring to metal charge-transfer transitions play an important role. The composition of the states as calculated in this work does not lead to a classification of the excitations as purely "excitonic" or "charge-resonance".     

Measurement of a complete set of nuclides, cross sections, and kinetic energies in spallation of 238U 1A GeV with protons

Spallation residues and fission fragments from 1A GeV 238U projectiles irradiating a liquid hydrogen target were investigated by using the fragment separator at GSI for magnetic selection of reaction products including ray-tracing, energy-loss and time-of-flight techniques. The longitudinal-momentum spectra of identified fragments were analyzed, and evaporation residues and fission fragments could be separated. For 1385 nuclides, production cross sections down to values of 10 microb with a mean accuracy of 15%, velocities in the uranium rest frame and kinetic energies were determined. In the reaction all elements from uranium to nitrogen were found, each with a large number of isotopes.