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  • 34D30  (1)
  • Baker-Venkataraman rearrangement  (1)
  • Continuous spiking oscillations  (1)
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Years
Keywords
  • 1
    Electronic Resource
    Electronic Resource
    Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells (1999)
    Springer
    Journal of mathematical biology 38 (1999), S. 21-78 
    Details
    ISSN: 1432-1416
    Keywords: Key words: Bursting-spiking oscillations ; Continuous spiking oscillations ; Kneading sequence ; Period-doubling cascade ; Turning point ; Junction point ; Junction-fold point ; Slow manifold ; Stable and unstable foliations ; Poincaré map ; Asymptotic expansion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract  In the presence of stimulatory concentrations of glucose, the membrane potential of pancreatic β-cells may experience a transition from periods of rapid spike-like oscillations alternating with a pseudo-steady state to spike-only oscillations. Insulin secretion from β-cells closely correlates the periods of spike-like oscillations. The purpose of this paper is to study the mathematical structure which underlines this transitional stage in a pancreatic β-cell model. It is demonstrated that the transition can be chaotic but becomes more and more regular with increase in glucose. In particular, the system undergoes a reversed period-doubling cascade leading to the spike-only oscillations as the glucose concentration crosses a threshold. The transition interval in glucose concentration is estimated to be extremely small in terms of the rate of change for the calcium dynamics in the β-cells. The methods are based on the theory of unimodal maps and the geometric and asymptotic theories of singular perturbations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002850050141
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Homoclinic twisting bifurcations and cusp horseshoe maps (1993)
    Springer
    Journal of dynamics and differential equations 5 (1993), S. 417-467 
    Details
    ISSN: 1572-9222
    Keywords: Strong inclination property ; neutrally twisted homoclinic orbits ; cusp horseshoe maps ; quotient symbolic systems ; singular perturbations ; 00A71 ; 34A34 ; 34C28 ; 34D30 ; 58F12 ; 58F13 ; 58F14 ; 58F40
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Chaotic dynamics arises when the unstable manifold of a hyperbolic equilibrium point changes its twist type along a homoclinic orbit as some generic parameter is varied. Such bifurcation points occur naturally in singularly perturbed systems. Some quotient symbolic systems induced from the Bernoulli symbolic system on two symbols are proved to be characteristic for this new mechanism of chaos generation. Combination of geometrical and analytical methods is proved to be more fruitful.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053531
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A Practical Synthesis of 3-Methoxyflavones (1997)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1997 (1997), S. 2169-2175 
    Details
    ISSN: 0947-3440
    Keywords: Baker-Venkataraman rearrangement ; 3-Methoxyflavones ; Phase-transfer catalysis ; Catalytic transfer hydrogenation ; Transesterifications ; Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Some 3-methoxyflavones were known to possess antipicornavirus properties. In order to study the structure-activity relationship, attempts to prepare 3-methoxyflavone by literature methods were unsuccessful. We have modified the Baker-Venkataraman rearrangement, using a solid base and a phase-transfer catalyst. After searching optimal reaction conditions and a study of the intermediate formed in a model reaction, good yields were obtained for the 3-methoxyflavones 7, 21-32. Further some of the corresponding 7-O-n-butyl derivatives 4, 33-37 could be isolated as side products.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jlac.199719971020
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    Paper (German National Licenses)
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