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  • 1
    Monograph available for loan
    Monograph available for loan
    Fehler in numerischen Prozessen; 65 (1985)
    Berlin : Akad.-Verl.
    Associated volumes
    Details Availability
    Call number: MOP B 18120
    In: Mathematische Lehrbücher und Monographien
    Type of Medium: Monograph available for loan
    Pages: 244 S. : graph. Darst.
    Series Statement: Mathematische Lehrbücher und Monographien : II Abt., Mathematische Monographien 65
    Location: MOP - must be ordered
    Branch Library: GFZ Library
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  • 2
    Electronic Resource
    Electronic Resource
    Synthesis and epoxidation of cis-enriched polydeltacyclene (1990)
    s.l. : American Chemical Society
    Macromolecules 23 (1990), S. 2819-2821 
    Details
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ma00212a038
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  • 3
    Electronic Resource
    Electronic Resource
    Spline collocation for singular integro-differential equations over (0.1) (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 337-352 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65R20 ; CR: G1.9
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper analyses the convergence of spline collocation methods for singular integro-differential equations over the interval (0.1). As trial functions we utilize smooth polynomial splines the degree of which coincides with the order of the equation. Depending on the choice of collocation points we obtain sufficient and even necessary conditions for the convergence in sobolev norms. We give asymptotic error estimates and some numerical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390710
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  • 4
    Electronic Resource
    Electronic Resource
    Boundary element discretization of Poincar\'e--Steklov operators (1994)
    Springer
    Numerische Mathematik 69 (1994), S. 83-101 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65N38, 65N12, 65N55, 65N30, 31A10, 31B10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. The construction of a discretization of Poincar\'e--Steklov operators with the boundary element method is given providing the same mapping properties as the finite element discretization of these operators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050081
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  • 5
    Electronic Resource
    Electronic Resource
    Shock waves of a continuous model of traffic flow (1972)
    Springer
    Computing 9 (1972), S. 365-381 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Zusammenfassung Ziel dieser Untersuchung ist die Entwicklung eines Programms zum Zeichnen der Stromlinienbilder von Verkehrsflüssen unter Verwendung eines kontinuierlichen Modells vonLighthill. Es handelt sich dabei um eindimensionale Strömungen mit geschwindigkeitsabhängiger Dichte ρ(v). Die Kontinuitätsgleichung führt zu der quasilinearen partiellen Differentialgleichung $$v_t + v_x \cdot (v + \rho (v)/\rho '(v)) = 0$$ . In [3] sind geeignete Randbedingungen dafür angegeben, und es wird gezeigt, daß man aus dem Fahrverhaltenx=x (t; 0) des Führungsfahrzeugs einer Kolonne die Trajektorienx=x (t; c), also das Fahrverhalten der folgenden Fahrzeuge, explizit erhalten kann. Hier wird die Theorie der Verdichtungslinien entwickelt. Bei einem Spezialfall des kontinuierlichen Modells, beimP-Modell, lassen sich die Verdichtungslinien explizit bestimmen. DasP-Modell kann man für eine approximative Behandlung allgemeinerer Fälle verwenden. Zum Abschluß wird eine Standardaufgabe der Simulation von Verkehrsflüssen, die durch eine Folge von Verkehrsampeln geregelt sind, formuliert und ein Programm beschrieben, das anhand des kontinuierlichen Modells Stromlinienbilder davon errechnet.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02241610
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  • 6
    Electronic Resource
    Electronic Resource
    Boundary layer approximate approximations and cubature of potentials in domains (1999)
    Springer
    Advances in computational mathematics 10 (1999), S. 311-342 
    Details
    ISSN: 1572-9044
    Keywords: volume potentials ; semi‐analytic cubature formulae ; approximate approximations ; approximate multi‐resolution ; 65D32 ; 65D15 ; 65N38
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this article we present a new approach to the computation of volume potentials over bounded domains, which is based on the quasi‐interpolation of the density by almost locally supported basis functions for which the corresponding volume potentials are known. The quasi‐interpolant is a linear combination of the basis function with shifted and scaled arguments and with coefficients explicitly given by the point values of the density. Thus, the approach results in semi‐analytic cubature formulae for volume potentials, which prove to be high order approximations of the integrals. It is based on multi‐resolution schemes for accurate approximations up to the boundary by applying approximate refinement equations of the basis functions and iterative approximations on finer grids. We obtain asymptotic error estimates for the quasi‐interpolation and corresponding cubature formulae and provide some numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018990918531
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  • 7
    Electronic Resource
    Electronic Resource
    Describing semantic domains with sprouts (1989)
    Springer
    Acta informatica 27 (1989), S. 217-245 
    Details
    ISSN: 1432-0525
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Summary In denotational semantics the meaning of a construct of a programming language is modelled by an element of a (semantic) domain. Domains are essentially ordered sets, in which every element may be approximated by a directed set of compact elements. We propose a new approach to domain construction using directed systems of certain finite subsets of a domain called sprouts. Every element of the domain can be considered as growing out from the sprouts, i.e., it can be uniquely approximated by an element of any given sprout. Sprouts consist only of compact elements and every compact element is contained in some of the sprouts. The directed system of sprouts fits neatly to the usual domain constructions, so we are able to describe the approximations of an element of a composed domain by the corresponding approximations in the component domains very exactly. Furthermore, we get a constructive and less abstract description of profinite domains than given by C. Gunter with one added feature: Given a domain functional τ, the inverse limit of the retraction sequence1, τ[1,], τ2[1,], ... is indeed the least of a certain subset of fixed points of τ, namely of those being the vertex of a cone that is “definable” in some sense.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00572989
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  • 8
    Electronic Resource
    Electronic Resource
    Regionalisierung der Durchlässigkeitsbeiwerte mit unscharfen (fuzzy) Zahlen: Der Natur näher? (1997)
    Springer
    Grundwasser 2 (1997), S. 3-10 
    Details
    ISSN: 1432-1165
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Geosciences
    Description / Table of Contents: Abstract This article demonstrates an application of fuzzy geostatistics in spatial regionalization of imprecise hydrogeological data. The regionalization was carried out for hydraulic condictivity values of a major aquifer in northwestern Germany. The original data set consists of 557 borehole points with known (crisp) hydraulic conductivities. This data set was supplemented by 30 additional data points, placed in areas with lowest borehole density. At these points, hydraulic conductivities were estimated based on subjective expert knowledge of regional geology, and entered the regionalization procedure as fuzzy (imprecise) numbers. By utilizing the expert knowledge, which cannot be implemented in conventional geostatistics, the reliability of regionalization has been improved. The imprecision of fuzzy-regionalization is fully quantifiable, so that it can be easily accounted for when evaluating the results.
    Notes: Kurzfassung In vorliegender Arbeit wird eine Anwendung der Fuzzy-Geostatistik bei der räumlichen Regionalisierung von unscharfen hydrogeologischen Daten vorgestellt. Regionalisiert wurden Durchlässigkeitsbeiwerte eines Hauptgrundwasserleiters in Nordwest-Deutschland. Der ursprüngliche Datensatz besteht aus 557 Bohrungen mit bekannten (scharfen) Durchlässigkeitsbeiwerten. Dieser Datensatz wurde um 30 zusätzliche Punkte in Bereichen mit geringster Bohrlochdichte erweitert. An diesen Punkten wurden die Durchlässigkeitsbeiwerte anhand des subjektiven Expertenwissens der regionalen Geologie abgeschätzt und flossen in das Regionalisierungsverfahren als unscharfe (fuzzy) Zahlen ein. Durch die Anwendung des Expertenwissens, die in konventioneller Geostatistik nicht vorgesehen ist, erhöhte sich die Aussagekraft der Regionalisierung. Die Unschärfe der Fuzzy-Regionalisierung ist völlig quantifizierbar, so daß sie bei der Betrachtung der Ergebnisse objektiv berücksichtigt werden kann.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s767-1997-8507-1
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  • 9
    Electronic Resource
    Electronic Resource
    Asymmetric Control in the Pictet-Spengler Reaction by Means of N-Protected Amino Acids as Chiral Auxiliary Groups (1996)
    Weinheim : Wiley-Blackwell
    Chemistry - A European Journal 2 (1996), S. 1566-1571 
    Details
    ISSN: 0947-6539
    Keywords: amino acids ; asymmetric syntheses ; carbolines ; chiral auxiliaries ; Pictet-Spengler reaction ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Aromatic and aliphatic Schiff bases of tryptamine react with Fmoc- or phthaloyl-protected amino acid chlorides to form N-acyliminium intermediates, which, in the presence of titanium alkoxides at room temperature, undergo Pictet-Spengler reactions to give tetrahydro-β-carbolines with diastereomeric ratios of up to 99:1. The chiral auxiliary can be removed from the Pictet-Spengler adducts by means of a simple reduction. To rationalize the observed stereoselectivity a transition-state model is proposed in which the titanium atom coordinates both the carbonyl group of the N-acyliminium ion and the amino acid protecting group.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/chem.19960021215
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  • 10
    Electronic Resource
    Electronic Resource
    Asymmetrische Pictet-Spengler-Reaktionen mit N,N-Phthaloyl-Aminosäuren als chiralen HilfsgruppenProfessor Ivar Ugi zum 65. Geburtstag gewidmetDiese Arbeit wurde von der Deutschen Forschungsgemeinschaft und vom Fonds der Chemischen Industrie unterstützt. Wir danken der Degussa AG für die Bereitstellung von Aminosäuren. (1995)
    Weinheim : Wiley-Blackwell
    Zeitschrift für die chemische Industrie 107 (1995), S. 2608-2610 
    Details
    ISSN: 0044-8249
    Keywords: Aminosäuren ; Asymmetrisch Synthesen ; Chirale Hilfsstoffe ; Pictet-Spengler-Reaktionen ; Tetrahydrocarboline ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/ange.19951072127
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