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  • 1
    Electronic Resource
    Electronic Resource
    High dimensional polynomial interpolation on sparse grids (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 273-288 
    Details
    ISSN: 1572-9044
    Keywords: multivariate polynomial interpolation ; sparse grids ; least solution ; universal method ; tractability ; 41A05 ; 41A63 ; 65D05 ; 41A25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study polynomial interpolation on a d-dimensional cube, where d is large. We suggest to use the least solution at sparse grids with the extrema of the Chebyshev polynomials. The polynomial exactness of this method is almost optimal. Our error bounds show that the method is universal, i.e., almost optimal for many different function spaces. We report on numerical experiments for d = 10 using up to 652 065 interpolation points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018977404843
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  • 2
    Electronic Resource
    Electronic Resource
    High dimensional integration of smooth functions over cubes (1996)
    Springer
    Numerische Mathematik 75 (1996), S. 79-97 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 41A55, 41A63, 65D30, 65Y20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We construct a new algorithm for the numerical integration of functions that are defined on a $d$ -dimensional cube. It is based on the Clenshaw-Curtis rule for $d=1$ and on Smolyak's construction. This way we make the best use of the smoothness properties of any (nonperiodic) function. We prove error bounds showing that our algorithm is almost optimal (up to logarithmic factors) for different classes of functions with bounded mixed derivative. Numerical results show that the new method is very competitive, in particular for smooth integrands and $d \ge 8$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050231
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  • 3
    Electronic Resource
    Electronic Resource
    Über das Verhalten des Organismus bei Einwirkung verschiedener Weichmacher (1956)
    Springer
    European food research and technology 103 (1956), S. 413-424 
    Details
    ISSN: 1438-2385
    Source: Springer Online Journal Archives 1860-2000
    Topics: Process Engineering, Biotechnology, Nutrition Technology
    Notes: Zusammenfassung Umfangreiche akute, subakute und chronische Versuche über die Toxieität der Weichmacher Benzyloctyladipinat, Dibutylphthalat, Mesamoll, Dicyclohexylphthalat und Polymerweichmacher PW 63/51 ergaben, daß alle geprüften Substanzen wenig giftig sind. Es spricht aber manches dafür, daß Mesamoll und PW 63/51 eine besonders günstige Beurteilung hinsichtlich der Unbedenklichkeit ihrer Verwendung auch in Folien, die zur Verpackung von Lebensmitteln gebraucht werden sollen, verdienen. Vor dem Einsatz von Dibutylphthalat zu dem genannten Zweck werden weitere Versuche für nötig gehalten.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01683646
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  • 4
    Electronic Resource
    Electronic Resource
    Stoffwechselwirkungen appetitvermindernder Substanzen (1957)
    Springer
    Journal of molecular medicine 35 (1957), S. 638-641 
    Details
    ISSN: 1432-1440
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Zusammenfassung 1. Preludin, Ritalin, Eventin und Ephedrin steigerten den Sauerstoffverbrauch von Ratten; Pesomin beeinflußte ihn nicht. Diese Steigerung war nur unter bestimmten Bedingungen nachweisbar. 2. Bei wiederholter chronischer Zufuhr von Eventin nahm die stoffwechselsteigernde Wirkung rasch ab; Ritalin und Ephedrin zeigten diese Gewöhnung nur angedeutet, Preludin nicht. 3. Die untersuchten „Appetitzügler“ beeinflußten den Glykogengehalt der Leber und den Blutzuckerspiegel nur wenig oder gar nicht; allenfalls verursachten sie gelegentlich eine mäßige Verringerung des Leberglykogengehaltes und einen geringen Blutzuckeranstieg. 4. Die Glykogenolyse in Leberschnitten wurde von den untersuchtenSubstanzen praktisch nicht beeinflußt. 5. Von allen geprüften „Appetitzüglern“ veränderte nur Pesomin das histologische Bild der Schilddrüse, und zwar im Sinne vermehrter Aktivität.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01481044
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  • 5
    Electronic Resource
    Electronic Resource
    Allgemeinstoffwechsel und Trijodthyronin (1955)
    Springer
    Journal of molecular medicine 33 (1955), S. 743-745 
    Details
    ISSN: 1432-1440
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Zusammenfassung Es wird über Versuche berichtet, in denen die Wirkung von Trijodthyronin und Thyroxin auf den Allgemeinstoffwechsel bei normalen Ratten vergleichend untersucht wird. Dabei ergab sich: 1. Auf den Sauerstoffverbrauch wirkt Trijodthyronin anregend und steigert die Stoffwechselvorgänge mindestens 4mal so stark wie das jodreichere Thyroxin. Der Wirkungsunterschied tritt noch deutlicher bei fraktionierter oder mehrfacher Verabfolgung wirksamer Mengen hervor. 2. Bei Berücksichtigung der Wirkungsstärke lassen sich Unterschiede in der Latenz zwischen Trijodthyronin und Thyroxin nicht feststellen. 3. Auch hinsichtlich der Wirkungsdauer scheint zwischen beiden nach einmaliger Verabfolgung Übereinstimmung zu bestehen. 4. Oral verabfolgt wirkt Trijodthyronin zuverlässig; offenbar wird es vollständiger resorbiert als Thyroxin.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01473510
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  • 6
    Electronic Resource
    Electronic Resource
    Studien zur Stoffwechselwirkung eines Phenothiazinabkömmlings („Megaphen“) (1954)
    Springer
    Journal of molecular medicine 32 (1954), S. 265-266 
    Details
    ISSN: 1432-1440
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Zusammenfassung Der Sauerstoffverbrauch von Ratten wird bei einmaliger oraler Zufuhr von „Megaphen“ vorübergehend herabgesetzt. Bei wiederholter Verabreichung läßt sich keine bleibende Stoffwechselsenkung erkennen, auch wenn die Dosen gesteigert werden.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01466814
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Methods of conjugate directions versus quasi-Newton methods (1972)
    Springer
    Mathematical programming 3 (1972), S. 101-116 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is shown that algorithms for minimizing an unconstrained functionF(x), x ∈ E n , which are solely methods of conjugate directions can be expected to exhibit only ann or (n−1) step superlinear rate of convergence to an isolated local minimizer. This is contrasted with quasi-Newton methods which can be expected to exhibit every step superlinear convergence. Similar statements about a quadratic rate of convergence hold when a Lipschitz condition is placed on the second derivatives ofF(x).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584978
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    A superlinearly convergent method for minimization problems with linear inequality constraints (1973)
    Springer
    Mathematical programming 4 (1973), S. 44-71 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A method is described for minimizing a continuously differentiable functionF(x) ofn variables subject to linear inequality constraints. It can be applied under the same general assumptions as any method of feasible directions. IfF(x) is twice continuously differentiable and the Hessian matrix ofF(x) has certain properties, then the algorithm generates a sequence of points which converges superlinearly to the unique minimizer ofF(x). No computation of secondorder derivatives is required.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584646
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  • 9
    Electronic Resource
    Electronic Resource
    On the rate of superlinear convergence of a class of variable metric methods (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 293-313 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS) ; 90C30 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper considers a class of variable metric methods for unconstrained minimization. Without requiring exact line searches each algorithm in this class converges globally and superlinearly on convex functions. Various results on the rate of the superlinear convergence are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396414
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Average errors for zero finding: Lower bounds for smooth or monotone functions (1994)
    Springer
    Aequationes mathematicae 47 (1994), S. 120-120 
    Details
    ISSN: 1420-8903
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01838149
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