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  • 1
    Electronic Resource
    Electronic Resource
    Fractal Modeling of Biological Structures (1987)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 504 (1987), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1987.tb48732.x
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  • 2
    Electronic Resource
    Electronic Resource
    Fractal functions and interpolation (1986)
    Springer
    Constructive approximation 2 (1986), S. 303-329 
    Details
    ISSN: 1432-0940
    Keywords: 26A ; 28A ; 41A ; 44A ; 60J ; Interpolation ; Fractals ; Moment theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let a data set {(x i,y i) ∈I×R;i=0,1,⋯,N} be given, whereI=[x 0,x N]⊂R. We introduce iterated function systems whose attractorsG are graphs of continuous functionsf∶I→R, which interpolate the data according tof(x i)=y i fori ε {0,1,⋯,N}. Results are presented on the existence, coding theory, functional equations and moment theory for such fractal interpolation functions. Applications to the approximation of naturally wiggly functions, which may show some kind of geometrical self-similarity under magnification, such as profiles of cloud tops and mountain ranges, are envisaged.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01893434
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  • 3
    Electronic Resource
    Electronic Resource
    Recurrent iterated function systems (1989)
    Springer
    Constructive approximation 5 (1989), S. 3-31 
    Details
    ISSN: 1432-0940
    Keywords: 28D99 ; 41A99 ; 58F11 ; 60F05 ; 60G10 ; 60J05 ; Iterated function systems ; Attractor ; Random maps ; Markov chain ; Ergodic ; Lyapunov exponent ; Fractal ; Dimension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recurrent iterated function systems generalize iterated function systems as introduced by Barnsley and Demko [BD] in that a Markov chain (typically with some zeros in the transition probability matrix) is used to drive a system of mapsw j :K →K,j=1, 2,⋯,N, whereK is a complete metric space. It is proved that under “average contractivity,” a convergence and ergodic theorem obtains, which extends the results of Barnsley and Elton [BE]. It is also proved that a Collage Theorem is true, which generalizes the main result of Barnsleyet al. [BEHL] and which broadens the class of images which can be encoded using iterated map techniques. The theory of fractal interpolation functions [B] is extended, and the fractal dimensions for certain attractors is derived, extending the technique of Hardin and Massopust [HM]. Applications to Julia set theory and to the study of the boundary of IFS attractors are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01889596
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  • 4
    Electronic Resource
    Electronic Resource
    Variational bounds on transition probabilities (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 479-487 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Complementary variational functionals are derived which impose upper and lower bounds on transition probabilities. These functionals are used to yield bounds in terms of sets of sum rules, and illustrative calculations are presented for hydrogen, helium and krypton atoms.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090310
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  • 5
    Electronic Resource
    Electronic Resource
    On the approximation of potential-energy functions for two-center systems (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 641-677 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Let E(R) be a potential-energy function for a neutral or ionic diatom in the Born-Oppenheimer approximation. Then the approximation of E(R) for 0 〈 R 〈 ∞ starting from finite and typically small sets of given information is considered. The approach is based on the fact that the scaled potential curves F(R) = R2E(R) derive from an eigenvalue problem which depends linearly on R. The nature of the curves F(R) is examined in detail. The results include the discovery of various approximants, some of which display rigorous bounding properties and others, closely related, whose behavior with respect to the approximated function appears to be predictable.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560130509
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