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  • 1
    Electronic Resource
    Electronic Resource
    Derivation of closed analytical expressions for Rosen–Morse Franck–Condon factors (1998)
    Springer
    Journal of mathematical chemistry 24 (1998), S. 39-60 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The expressions for Rosen–Morse Franck–Condon factors derived previously yield a double sum with alternating terms. For higher values of the quantum number the numerical calculation of the Franck–Condon factors by electronic computers using these expressions leads to numerical overflow inspite of the use of double-precision (32 digits) arithmetic. High values for the quantum number in the final ground state of the Rosen–Morse potential occur in molecular nonradiative rate calculations. Furthermore, the expressions show a lack of clearness with respect to the parameters of the potential. For out-of-plane modes exact closed form expressions and exact recurrence relations are derived. Asymptotic expressions for the matrix elements are calculated. Exact closed form expressions for matrix elements with quantum numbers which correspond to regions close to the dissociation barrier are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019154115691
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Neural Networks in Non-Euclidean Spaces (1999)
    Springer
    Neural processing letters 10 (1999), S. 201-210 
    Details
    ISSN: 1573-773X
    Keywords: neural networks ; learning ; minimal distance methods ; similarity-based methods ; machine learning ; interpretation of neural functions ; classification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons providing decision borders using combinations of soft hyperplanes. The weighted fun-in activation function may be replaced by a distance function between the inputs and the weights, offering a natural generalization of the standard MLP model. Non-Euclidean distance functions may also be introduced by normalization of the input vectors into an extended feature space. Both approaches influence the shapes of decision borders dramatically. An illustrative example showing these changes is provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018728407584
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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