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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Acta applicandae mathematicae 6 (1986), S. 19-45 
    ISSN: 1572-9036
    Schlagwort(e): 20C35 ; 81G20 ; Harmonic analysis ; stochastic quantum mechanics ; systems of covariance
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The spectral resolution of phase space representations of the Galilei group is achieved by deriving all possible decompositions into irreducible representations corresponding to reproducing kernel Hilbert spaces. Spectral syntheses in terms of eigenfunction expansions, as well as in terms of continuous resolutions of the identity, are achieved. For the latter, the existence, uniqueness and other basic properties of resolution generators are established. This is shown to lead to systems of covariance related to measurements of stochastic phase space values performed with extended quantum test particles, whose proper wavefunctions are the aforementioned resolution generators.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Acta applicandae mathematicae 6 (1986), S. 1-18 
    ISSN: 1572-9036
    Schlagwort(e): 20C35 ; 81G20 ; 83A05 ; POV measures ; systems of covariance ; phase space representations of kinematical groups ; stochastic geometries
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper we review the mathematical methods and problems that are specific to the programme of stochastic quantum mechanics and quantum spacetime. The physical origin of these problems is explained, and then the mathematical models are developed. Three notions emerge as central to the programme: positive operator-valued (POV) measures on a Hilbert space, reproducing kernel Hilbert spaces, and fibre bundle formulations of quantum geometries. A close connection between the first two notions is shown to exist, which provides a natural setting for introducing a fibration on the associated overcomplete family of vectors. The introduction of group covariance leads to an extended version of harmonic analysis on phase space. It also yields a theory of induced group representations, which extends the results of Mackey on imprimitivity systems for locally compact groups to the more general case of systems of covariance. Quantum geometries emerge as fibre bundles whose base spaces are manifolds of mean stochastic locations for quantum test particles (i.e., spacetime excitons) that display a phase space structure, and whose fibres and structure groups contain, respectively, the aforementioned overcomplete families of vectors and unitary group representations of phase space systems of covariance.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Calcified tissue international 56 (1995), S. 118-122 
    ISSN: 1432-0827
    Schlagwort(e): Osteogenesis imperfecta ; Mineral ; Composition ; Microanalysis
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Medizin , Physik
    Notizen: Abstract A semiquantitative electron probe X-ray microan-alytical (XRMA) technique, in conjunction with transmission electron microscopy, was used to compare the calcium to phosphorus (Ca/P) molar ratios in calcium phosphate standards of known composition, in normal bone and in bone from patients with osteogenesis imperfecta (OI). Using a modified routine processing and resin embedding schedule, the measured Ca/P molar ratio of calcium phosphates standards of known composition were found to correlate well with the Ca/P molar ratio based on their respective chemical formulae. This technique was then used to compare the Ca/P molar ratio in normal human bone and in OI bone. The Ca/P ratio values for normal bone (Ca/P=1.631) correlated well with those for chemically prepared hydroxyapatite (Ca/P=1.602), but in bone from OI patients, the Ca/P molar ratio was significantly lower (Ca/P=1.488). This study has shown that there is a lower Ca/P molar ratio in OI bone compared with normal, matched bone. This suggests that the mineral deviates from the carbanoapatite usually found in bone. Isomorphous substitutions in the carbanoapatite lattice could account for this although this study has neither proved nor disproved this. The altered bone mineral is an-other factor that could contribute to the increased fracture rate observed in OI.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    ISSN: 1435-5604
    Schlagwort(e): Key words Osteogenesis imperfecta ; Mineral ; Composition ; FTIR ; 31P-NMR
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Medizin
    Notizen: Abstract Fourier transform infrared spectroscopy and 31P solid-state nuclear magnetic resonance spectroscopy were used to determine if any structural or compositional differences in osteogenesis imperfecta (OI) bone mineral could be detected that might help to explain the bone fragility observed in this disease. A previous study by Cassella et al. used an electron probe X-ray microanalytical technique to compare the calcium to phosphorus (Ca/P) molar ratios in normal bone and bone from patients with OI. It was demonstrated that bone from OI patients had a lower Ca/P molar ratio. This study demonstrated that OI bone mineral had a general hydroxyapatite structure and that isomorphous substitutions in the carbanoapatite lattice could account for the low Ca/P molar ratio.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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