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  • Organic Chemistry  (4)
  • cluster expansion  (1)
  • 1985-1989  (5)
  • 1
    Electronic Resource
    Electronic Resource
    m-Particle correlations in theN-particle McKean model (1989)
    Springer
    Journal of statistical physics 57 (1989), S. 267-288 
    Details
    ISSN: 1572-9613
    Keywords: BBGKY hierarchy ; correlations ; cluster expansion ; truncation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This work extends the comparison between exact and approximate solutions of the McKean model to finite particle numbers. We derive the coupled linear equations of motion for them-body densities (BBGKY hierarchy) and the corresponding nonlinear equations for them-body correlation functions. We calculate the stable fixed points and the subspace admitting a probabilistic interpretation for both descriptions of the model. Neglecting higher correlations withm〉n, we obtain approximate solutions, which are compared to the exact one. In this way various truncation effects can be studied, such as the appearance of saddle points and unphysical trajectories. Finally, we linearize the truncated equations for the correlations about the stable fixed point, and calculate the relaxation times up toO(N −1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01023643
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  • 2
    Electronic Resource
    Electronic Resource
    Synthese von trans-4-(ω-Cyanalkyl)cyclohexanolen (1987)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 329 (1987), S. 1123-1130 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Synthesis of trans-4-(ω-Cyanalkyl)-cyclohexanols
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19873290623
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  • 3
    Electronic Resource
    Electronic Resource
    Kristallinflüssige trans-4-(ω-Cyanalkyl)cyclohexylester und 4-(ω-Cyanalkyl)phenylester (1987)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 329 (1987), S. 963-974 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Liquid Crystalline trans-4-(ω-Cyanalkyl)cyclohexylester and 4-(ω-Cyanalkyl)phenylestersThe synthesis of the title esters 1 and 2a-e (n = 0 - 3) and their mesomorphic properties are described. When the alkyl-spacer n between the polar CN-group and the cyclohexane ring of cyanalkyl-cyclohexylesters 1 is increased the difference of the clearing points between the phenylesters 2 and the cyclohexylesters 1 decreases to nearly zero. The reason of higher clearing temperatures of 2 is a dynamic conformational effect of ring inversion of cyclohexane in the ester 1 with two polar substituents at the ring.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19873290604
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  • 4
    Electronic Resource
    Electronic Resource
    Conformational influences on the liquid-crystalline state of 1,4-disubstituted cyclohexanes. II. Applied Model Studies (1989)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 331 (1989), S. 171-174 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19893310129
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  • 5
    Electronic Resource
    Electronic Resource
    Synthesen in der Reihe der 1,4-Diazepine (1988)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1988 (1988), S. 799-801 
    Details
    ISSN: 0170-2041
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Synthesis of 1,4-Diazepines2,3-Diamino-1,4-naphthoquinone (1) reacts with variously substituted derivatives of diethyl malonate (2, 5, and 7) to yield the imidazole derivative 8, a tetraethyl tetracarboxylate of type 6, or substituted diaminonaphthoquinones 3. These react further in alkaline medium to give diazepines of type 4. Diazepine 9 reacts with aromatic aldehydes 10a-f to give 11a-f. Methylation of 11e-f yields 12a-b.
    Notes: 2,3-Diamino-1,4-naphthochinon (1) reagiert mit den Malonsäure-Derivaten 2,5 und 7 je nach deren Substituenten zum Imidazolderivat 8, zum Tetracarbonsäure-tetraethylester des Typs 6 oder zu substituierten Diaminonaphthochinonen 3, letztere reagieren im alkalischen Medium zu Diazepinen des Typs 4. Das Diazepin 9 setzt sich mit aromatischen Aldehyden 10a-f zu 11a-f um. Methylierung von 11e-f liefert 12a-b.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jlac.198819880816
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