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  • 1985-1989  (4)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 51 (1987), S. 103-122 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65L05, 58F08, 58F22 ; CR: G1.7
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We show that a one-step method as applied to a dynamical system with a hyperbolic periodic orbit, exhibits an invariant closed curve for sufficiently small step size. This invariant curve converges to the periodic orbit with the order of the method and it inherits the stability of the periodic orbit. The dynamics of the one-step method on the invariant curve can be described by the rotation number for which we derive an asymptotic expression. Our results complement those of [2, 3] where one-step methods were shown to create invariant curves if the dynamical system has a periodic orbit which is stable in either time direction or if the system undergoes a Hopf bifurcation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 65 (1989), S. 3983-3986 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The X-band electron-spin-resonance spectra of Fe-doped [Ca,Y](Ti,Al)O3 perovskite single crystals show five resonant lines. Two of the five lines have an inverse phase in the first-derivative curve. The possibility of emission transition of a paramagnetic ion in an anisotropic environment and/or in the presence of oscillating distortions is discussed in this paper.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 118 (1985), S. 1575-1579 
    ISSN: 0009-2940
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Thermal Rearrangement of cis- and trans-1-tert-Butyl-2-vinylphosphiranetrans-1-tert-Butyl-2-vinylphosphirane (2) isomerizes to 1-tert-butyl-3-phospholene (3) at 150°C. Thermolytic cleavage of cis-1-tert-butyl-2-vinylphosphirane (1) also yields 3 via 2. The kinetic data indicate that the rearrangement from 1 to 3 proceeds by two sequential first order reactions.
    Notes: trans-1-tert-Butyl-2-vinylphosphiran (2) lagert sich bei 150°C in 1-tert-Butyl-3-phospholen (3) um. Die Thermolyse der cis-Verbindung 1 führt über 2 ebenfalls zu 3. Die kinetischen Daten belegen, daß eine Reaktionsfolge mit 2 Schritten jeweils nach 1. Ordnung vorliegt.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 118 (1985), S. 97-106 
    ISSN: 0009-2940
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Reactions of Magnesium-Cyclooctatetraene with Dichlorophosphanes: Characterization and RearrangementsThe reaction of magnesium-cyclooctatetraene (MgCOT) with dichlorophosphanes RPCl2 (R = tert-butyl, cyclohexyl, menthyl) yields 9-phosphabicyclo[6.1.0]nonatrienes 1b-d, which thermally rearrange to syn-9-phosphabicyclo[4.2.1]nonatrienes 2b-d. However, 1b and c also rearrange via electrocyclic ring opening and intramolecular [4 + 2] cyclization to trans-dihydrophosphindoles 3b and c. The rearrangement of 1 in the presence of Ni0 catalysts or photochemically was found to give the corresponding epimeric products 4 of the thermally induced process. With RPCl2 (R = OR, NR2) and MgCOT, the syn-9-phosphabicyclo[4.2.1]nonatrienes 2e, f are obtained directly.
    Notes: Die Umsetzung von Magnesium-Cyclooctatetraen (MgCOT) mit Dichlorphosphanen RPCl2 (R = tert-Butyl, Cyclohexyl, Menthyl) liefert 9-Phosphabicyclo[6.1.0]nonatriene 1b-d, die thermisch zu syn-9-Phosphabicyclo[4.2.1]nonatrienen 2b-d umlagern. Zusätzlich lagern 1b und c nach elektrocyclischer Ringöffnung und intramolekularer [4 + 2]-Addition zu trans-Dihydrophosphindolen 3b und c um. In Gegenwart von Ni0-Verbindungen oder photochemisch lagern die Verbindungen 1 zu den zu 2 epimeren anti-Verbindungen 4 um. Mit RPCl2 (R = OR, NR2) und MgCOT erhält man die syn-9-Phosphabicyclo[4.2.1]nonatriene 2e und f unmittelbar.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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