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  • 1
    Electronic Resource
    Electronic Resource
    A Method of Electron Diffraction Intensity Correction in Combination with High-Resolution Electron Microscopy (1996)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 152-157 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An empirical method is proposed for partially correcting the distortion of electron diffraction intensity caused by Ewald-sphere curvature, crystal bending, thickness inhomogeneity etc. The method is based on the combination of electron diffraction and high-resolution electron microscopy. It has been tested with a crystal of high-temperature superconducting oxide YBa2Cu3O7−x and shown to be effective.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767395012682
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On Interacting Systems of Hilbert-Space-Valued Diffusions (1998)
    Springer
    Applied mathematics & optimization 37 (1998), S. 151-188 
    Details
    ISSN: 1432-0606
    Keywords: Key words. Martingale problem, Nuclear, Interacting Hilbert-space-valued diffusions, McKean—Vlasov equation, Propagation of chaos. AMS Classification. Primary 60J60, Secondary 60B10.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. A nonlinear Hilbert-space-valued stochastic differential equation where L -1 (L being the generator of the evolution semigroup) is not nuclear is investigated in this paper. Under the assumption of nuclearity of L -1 , the existence of a unique solution lying in the Hilbert space H has been shown by Dawson in an early paper. When L -1 is not nuclear, a solution in most cases lies not in H but in a larger Hilbert, Banach, or nuclear space. Part of the motivation of this paper is to prove under suitable conditions that a unique strong solution can still be found to lie in the space H itself. Uniqueness of the weak solution is proved without moment assumptions on the initial random variable. A second problem considered is the asymptotic behavior of the sequence of empirical measures determined by the solutions of an interacting system of H -valued diffusions. It is shown that the sequence converges in probability to the unique solution Λ 0 of the martingale problem posed by the corresponding McKean—Vlasov equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002459900072
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Exponential Convergence for a System of Conuclear Space-Valued Diffusions with Mean-Field Interaction (1999)
    Springer
    Applied mathematics & optimization 39 (1999), S. 281-307 
    Details
    ISSN: 1432-0606
    Keywords: Key words. Exponential convergence rate, Exponential tightness, Measure-valued process, Stochastic differential equation. AMS Classification. Primary 60F10, Secondary 60H10, 60J60.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We consider an interacting system of n diffusion processes X n j (t): t∈[0,1] , j=1,2,. . ., n , taking values in a conuclear space Φ' . Let ζ n t =(1/n)Σ n j=1 δ Xnj(t) be the empirical process. It has been proved that ζ n , as n→∞ , converges to a deterministic measure-valued process which is the unique solution of a nonlinear differential equation. In this paper we show that, under suitable conditions, ζ n converges to ζ at an exponential rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002459900107
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    Paper (German National Licenses)
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