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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.
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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
    Electronic Resource
    Electronic Resource
    Springer
    Chromatographia 12 (1979), S. 790-798 
    ISSN: 1612-1112
    Keywords: Gas chromatography ; Dead-time ; log ts=f(C) ; Retention index calculation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung In der vorliegenden Arbeit wird eine Methode zur Retentionsindex-Bestimmung beschrieben, die von einem kubischen Zusammenhang zwischen Bruttoretentionszeit-Differenzen der Referenzhomologen und der Kohlenstoffzahl ausgeht. Hieraus ergeben sich direkt die Nettoretentionszeiten. Der Fehler der Totzeitbestimmung entfällt bei dieser Methode. Mit den so gewonnenen Nettoretentionszeiten erhält man über einen kubischen Zusammenhang zwischen 1g ts=f(C) die Retentionsindices. Extrapolationen und Interpolationen sind über 300 Retentionsindexeinheiten mit einem mittleren Fehler von ±0,02 Retentionsindexeinheiten möglich. Das Verfahren bietet sich für eine automatische Berechnung der I-Werte mittels on-line-Datenverarbeitung an.
    Notes: Summary The method for the calculation of retention indices described here is based on a third order relationship between the logarithm of differences of unadjusted retention times of homologues and the carbon number. From this adjusted retention times are directly calculated. A determination of the dead-time is not necessary thus avoiding the errors connected with this factor. A cubic equation for the logarithm of the adjusted retention time lg ts as a function of carbon number Cn is used for the retention index calculation. Extrapolations and interpolations can be done over a range of 300 index units with an average deviation of ±0.02 i.u.. The method offers the possibility of an automated on-line calculation of retention indices by computer merely on the basis of unadjusted retention times.
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  • 4
    ISSN: 1612-1112
    Keywords: Gas chromatography ; Retention index calculation ; lg ts=f(C) ; Dead-time ; Complex mixtures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Die bisher in der Literatur beschriebenen Verfahren zur Retentionsindex-Bestimmung beruhen auf einem linearen Zusammenhang zwischen dem Logarithmus der Nettoretentionszeit lg ts und der Kohlenstoffzahl C der n-Alkane. Wie genaue Meßwerte für Retentionszeiten zeigen, ist die Funkton lg ts=f(C) nicht streng linear. Die Krümmung des Funktionsbildes bedingt, daß lineare Regressionsmethoden, sowie auch die Methode nach Kovats, es nicht erlauben, extrapolativ sowie über weite Retentionsbereiche interpolativ I-Werte zu berechnen. In dieser Arbeit werden Retentionsindices aufgrund eines kubischen Zusammenhanges zwischen lg ts und der Kohlenstoffzahl ermittelt. Die hierzu notwendige Totzeit tm wird aus den Differenzen der Bruttoretentionszeiten der Referenzhomologen ermittelt.
    Notes: Summary Methods of retention index calculation described in the literature have been based on a linear relationship between the logarithm of the adjusted retention times lg ts and the carbon numbers C of n-alkanes. Exact measurements of the retention times of n-alkanes show that the relationship lg ts=f(C) is in fact not strictly linear. Correct extrapolative or interpolative calculations of retention indices over a wide retention range are therefore impossible when using the original formula as given by Kovats or methods based on a linear regression concept. The method of retention index calculation presented here is based on a cubic relationship between lg ts and carbon number allowing extrapolative or interpolative calculations. The hold-up time (tm) is calculated on the basis of differences of retention times of the reference homologues.
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