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  • 1
    Electronic Resource
    Electronic Resource
    Some convergence regions for continued fractions (1962)
    Springer
    Mathematische Zeitschrift 79 (1962), S. 376-380 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01193130
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Continued fraction approximation to functions (1965)
    Springer
    Numerische Mathematik 7 (1965), S. 292-309 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01436523
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  • 3
    Electronic Resource
    Electronic Resource
    The embedding problem for predistance matrices (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 769-796 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A fundamental problem in molecular biology is the determination of the conformation of macromolecules from NMR data. Several successful distance geometry programs have been developed for this purpose, for example DISGEO. A particularly difficult facet of these programs is the embedding problem, that is the problem of determining those conformations whose distances between atoms are nearest those measured by the NMR techniques. The embedding problem is the distance geometry equivalent of the multiple minima problem, which arises in energy minimization approaches to conformation determination. We show that the distance geometry approach has some nice geometry not associated with other methods that allows one to prove detailed results with regard to the location of local minima. We exploit this geometry to develop some algorithms which are faster and find more minima than the algorithms presently used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461553
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Representation theorems in reflexive Banach Spaces (1968)
    Springer
    Mathematische Zeitschrift 104 (1968), S. 405-406 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01110432
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  • 5
    Electronic Resource
    Electronic Resource
    Applications of weighting and chirality strategies for distance geometry algorithms to an enterotoxin peptide analog (1994)
    Springer
    Journal of mathematical chemistry 15 (1994), S. 353-366 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Significant improvements are made to a recent algorithm that finds molecular conformations using distance geometry on nuclear magnetic resonance data. Weighting factors for the nearest approximation of the distance matrix to a data matrix are allowed to vary between iterations of the algorithm. These changes are proportional to the error of the distance between atoms in the configuration and the nuclear magnetic resonance data bounds. The weight changes increase the rate of convergence by an order of magnitude. Penalty functions are proposed to ensure the correct chirality. Numerical results for these modifications and subsequent energy calculations using CHARMm are given for an analog of the heat stable (ST) enterotoxin peptide STh produced byE. coli in humans.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01277570
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  • 6
    Electronic Resource
    Electronic Resource
    Oscillation of differential equations in Banach spaces (1970)
    Springer
    Annali di matematica pura ed applicata 85 (1970), S. 383-394 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper some properties of solutions of the differential equation Y″(t)++P(t) Y(t)=0 in Banach spaces are investigated. In particular, conditions are given for some solutions of such equations to possess an infinite number of zeros as t → ∞ while another condition ensures some solutions possess only a finite number of zeros, Some examples and a theorem show the concept of an oscillatory solution of a differential equation in a Banach space involves pathologies not found in the case of finite dimensional spaces. Upon specialization of the Banach spaces involved the results reduce to known theorems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02413547
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  • 7
    Electronic Resource
    Electronic Resource
    Preconditioners for distance matrix algorithms (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 15 (1994), S. 227-232 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A recent gradient algorithm in nonlinear optimization uses a novel idea that avoids line searches. This so-called spectral gradient algorithm works well when the spectrum of the Hessian of the function to be minimized has a small range or is clustered. In this article, we find a general preconditioning method for this algorithm. The preconditioning method is applied to the stress function, which arises in many applications of distance geometry, from statistics to finding molecular conformations. The Hessian of stress is shown to have a nice block structure. This structure yields a preconditioner which decreases the amount of computation needed to minimize stress by the spectral gradient algorithm. © 1994 by John Wiley & Sons, Inc.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540150212
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    Paper (German National Licenses)
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