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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 95 (1994), S. 101-111 
    ISSN: 1434-6036
    Keywords: 05.40.+j ; 02.50.+s
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Starting from the deformed commutation relationsa q (t) a † q (s)−q a † q (s) a q (t)=Γ(t−s)1, −1≦q≦1 with a covariance Γ(t−s) and a parameterq varying between −1 and 1, a stochastic process is constructed which continuously deforms the classical Gaussian and classical compound Poisson process. The moments of these distinguished stochastic processes are identified with the Hilbert space vacuum expectation values of products of $$\hat \omega _q (t) = \gamma (a_q (t) + a_q^\dag (t)) + \xi a_q^\dag (t)a_q (t)$$ with fixed parametersq, γ and ξ. Thereby we can interpolate between dichotomic, random matrix and classical Gaussian and compound Poisson processes. The spectra of Hamiltonians with single-site dynamical disorder are calculated for an exponential covariance (coloured noise) by means of the time convolution generalized master equation formalism (TC-GME) and the partial cumulants technique. The final result for the spectral function is given as aq-dependent infinite continued fraction. In the case of the random matrix processes the infinite continued fraction can be summed up yielding a self-consistent equation for the one-particle Green function.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 92 (1993), S. 399-407 
    ISSN: 1434-6036
    Keywords: 05.40.+j ; 02.50.+s
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Generalized master equations correspond to different kinds of cumulants. Here, we discuss the recently introduced non-crossing cumulants from a physical point of view and propose the corresponding integro-differential master equation as a new type of equation for a self-consistent treatment of memory effects. We prove the cluster property of the non-crossing cumulants, and show that the Gaussian approximation of our equation is given by a random matrix process. As an instructive example for our expansion formula we treat the random frequency-modulated oscillator.
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  • 3
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A series of bridged calix [4] arenes (5-10 methylene groups in the bridge) were synthesized and transformed into their tetraester derivatives by reaction with ethyl bromoacetate. The stability constants for complexes of the tetraester derivatives with sodium, potassium and silver cations, determined in methanol by spectroscopic or potentiometric techniques, show a drastic decrease (more than 105 for Na +) for the shorter methylene chains. 1H NMR studies demonstrate a conformational rearrangement of the calixarene part to fourfold symmetry to be necessary for the complexation of a cation, which is prevented by the shorter chains. This is further confirmed by the X-ray structure of a tetraester derivative with a CH2CH2COCH2CH2 bridge; crystals were monoclinic, space group P21/c,a = 11.847(2), b = 39.773(5), c = 12 · 127(2) Å, β = 109.24(1), V = 5395.1 Å3, Z = 4, Dx = 1.186 Mg m-3.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 5 (1992), S. 496-501 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The effect of chemical modifications on the lower rim of calix [n] arenes is analysed with respect to the cation binding ability of the receptor. Extraction data and stability constants of the complexes are discussed. Three main factors are investigated: the size of the calixarene, the conformation of the calixarene and the nature of the ligating group attached to the phenolic oxygen. The work concentrates on esters, ketones, amides, thioamides and carboxylic acids. Some data concern chemically modified tetrahomodioxacalix [4] arene esters.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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