A geometric approach to time evolution operators of Lie quantum systems

Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain certain ad hoc methods used in previous papers in order to obtain exact solutions. Finally, several instances of time-dependent quadratic Hamiltonian are solved.Comment: Accepted for publication in the International Journal of Theoretical Physic

Isolation of pregnancy-associated glycoproteins (PAG) from water buffalo (Bubalus bubalis) placenta by use of Vicia villosa bound agarose affinity chromatography

The present study describes the isolation and characterisation of new PAG molecules extracted from mid- and late-pregnancy placentas in the water buffalo (Bubalis bubalis). After extraction, acid and ammonium sulphate precipitation and DEAE chromatography water buffalo PAG (wbPAG) were enriched by Vicia villosa agarose (VVA) affininity chromatography. As determined by Western blotting with anti-PAG-sera, apparent molecular masses of immunoreactive bands from VVA peaks ranged from 59.5 to 75.8 kDa and from 57.8 to 80.9 kDa in the mid- and late- pregnancy placenta respectively. Aminoterminal microsequencing of proteins allowed the identification of three distinct wbPAG sequences wich have ben deposed in the SwissProt database: RGSXLTIHPLRNIRDFFYUG (Acc. n. P85048), RGSXLTILPLRNIID (P85049) and RGSXLTHLPLRNI (P85050). Their comparison to those previously identified revealed that two of them were new since they have not been described yet. Our results confirm the suitability of VVA chromatography in enrichment of multiple PAG molecules expressed in buffalo placenta. Productions of specific antisera can be very useful in immonoistochemical and immunocyitochemical studies of PAG expression in fetomaternal interfaces. Purified native PAG are also required for development on specific immoassays (RIA/ELISA) currently used for pregnancy diagnosis and physiological investigation in farm animal

Supercoherent States, Super K\"ahler Geometry and Geometric Quantization

Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view is extended to the supersymmetric context, through the study of the OSp(2/2) coherent states. These are explicitly constructed starting from the known abstract typical and atypical representations of osp(2/2). Their underlying geometries turn out to be those of supersymplectic OSp(2/2) homogeneous spaces. Moment maps identifying the latter with coadjoint orbits of OSp(2/2) are exhibited via Berezin's symbols. When considered within Rothstein's general paradigm, these results lead to a natural general definition of a super K\"ahler supermanifold, the supergeometry of which is determined in terms of the usual geometry of holomorphic Hermitian vector bundles over K\"ahler manifolds. In particular, the supergeometry of the above orbits is interpreted in terms of the geometry of Einstein-Hermitian vector bundles. In the second part, an extension of the full geometric quantization procedure is applied to the same coadjoint orbits. Thanks to the super K\"ahler character of the latter, this procedure leads to explicit super unitary irreducible representations of OSp(2/2) in super Hilbert spaces of $L^2$ superholomorphic sections of prequantum bundles of the Kostant type. This work lays the foundations of a program aimed at classifying Lie supergroups' coadjoint orbits and their associated irreducible representations, ultimately leading to harmonic superanalysis. For this purpose a set of consistent conventions is exhibited.Comment: 53 pages, AMS-LaTeX (or LaTeX+AMSfonts

Variations in plasma matrix metalloproteinases and placental pregnancy - associated glycoproteins during gestation in rabbits

[EN] Adaptation to pregnancy involves major maternal anatomical, physiological and metabolic modifications to support the mother's metabolic needs and those of the growing foetus. Invasion of embryonic territories and implantation in humans and other mammals is the result of an active biochemical process. The invasive faculty of cytotrophoblastic cells depends on their capacity to secrete proteolytic enzymes such as matrix metalloproteinases (MMPs). Many studies have addressed the variations in MMPs in placental tissues, but few have reported on their measurements in plasma. Furthermore, the Pregnancy-Associated Glycoproteins (PAGs), which are synthesized in the syncytiotrophoblast and used as early markers of pregnancy in domestic and wild animals, have not yet been studied in rabbits. In this study, we attempt to purify PAGs from rabbit placenta using a previously described methodology and to measure their concentrations as well as those of MMP-2 and MMP-9 in the plasma throughout pregnancy. In the course of the work, we noted certain modifications of the biochemical parameters in plasma during gestation, essentially in glycemia and lipemia. We detected proteins immunologically-related to PAGs in placental extracts between D14 to D21. Until now, it has been impossible to develop a homologous RIA in order to measure PAGs in rabbit plasma, as the recovery of PAGs during the purification procedure was very low and PAGs were undetectable in rabbit plasma using heterologous RIAs. Finally, we demonstrated a rise in MMP-2 and -9 at the middle and the end of the gestation. However, the small variations presented by these matrix metalloproteinases preclude the use of plasma levels of these enzymes as early markers of pregnancy progress in the rabbit.Financial support for this study was obtained from DRS and INSERM (accord INSERM-DRS) and the authors wish to thank Mary Osbone-Pellegrin for editing the manuscript.Othmani-Mecif, K.; Benazzoug, Y.; Jacob, M.; Beckers, J. (2006). Variations in plasma matrix metalloproteinases and placental pregnancy - associated glycoproteins during gestation in rabbits. World Rabbit Science. 14(1). doi:10.4995/wrs.2006.542SWORD14

Traitements hormonaux repetes : prudence

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