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  • 1
    Electronic Resource
    Electronic Resource
    On theR-order of coupled sequences arising in single-step type methods (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 653-661 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H10 ; 15A48 ; CR: G1.5
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary As shown in preceding papers of the authors, the verification of anR-convergence order τ for sequences coupled by a system (1.1) of basic inequalities can be reduced to the positive solvability of system (3.3) of linear inequalities. Further, the bestR-order $$\bar \tau$$ implied by (1.1) is equal to the minimal spectral radius of certain matrices composed from the exponents occuring in (1.1). Now, these results are proven in a unified and essentially simpler way. Moreover, they are somewhat extended in order to facilitate applications to concrete methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397134
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  • 2
    Electronic Resource
    Electronic Resource
    Calibration and Application of an X-ray Image Intensifier/ Charge-Coupled Device Detector for Monochromatic Macromolecular Crystallography (1997)
    Chester : International Union of Crystallography (IUCr)
    Journal of synchrotron radiation 4 (1997), S. 67-77 
    Details
    ISSN: 1600-5775
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Charge-coupled device (CCD)-based X-ray detectors allow data to be collected much more quickly ( ̃10 times) than with current on-line imaging-plate systems. At the ESRF, X-ray image intensifier/CCD detector systems have been developed. These have great potential as fast read-out detectors for macromolecular and other forms of crystallography. They are relatively large sensitive X-ray detectors but have two inherent weaknesses: convex detection surfaces leading to spatial distortion and non-uniformity of intensity response, and susceptibility to small changes in magnetic fields. A large improvement has been made to the accuracy obtained by non-uniformity of response calibration and correction, using fluorescence from doped lithium borate glasses. Monochromatic macromolecular crystallography demonstration experiments with external user groups have shown that high-quality results may be obtained under real experimental conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0909049596015087
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  • 3
    Electronic Resource
    Electronic Resource
    ID14 `Quadriga', a Beamline for Protein Crystallography at the ESRF (1998)
    Chester : International Union of Crystallography (IUCr)
    Journal of synchrotron radiation 5 (1998), S. 215-221 
    Details
    ISSN: 1600-5775
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The ESRF undulator beamline ID14 `Quadriga' is dedicated to monochromatic macromolecular crystallography. Using two undulators with 23 mm and 42 mm periods and a minimum gap of 16 mm installed on a high-β section, it will provide high-brilliance X-ray beams at around 13.5 keV, as well as a wide tuneability between 6.8 and 40 keV. Based on the Troika concept, this beamline has four simultaneously operating experimental stations: three side stations, EH1, EH2 and EH3, using thin diamond crystals, and an end station, EH4, with a fast-scan double-crystal monochromator. Station EH3 has a κ-diffractometer, and an off-line Weissenberg camera with a large 80 × 80 cm active area combined with a 2048 × 2048 CCD detector. During data collection the image plates are placed and removed by a robot located inside the hutch using a cassette system. After data collection the image plates are scanned with an off-line drum scanner. Station EH4 is designed for MAD applications, including Xe K-edge anomalous experiments, and is equipped with a 2048 × 2048 CCD detector on a pseudo 2θ arm. A common graphical user interface and a database will be available to cover all aspects of data collection, including strategy optimization. First results on the performance of the optics elements and initial crystallographic results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0909049597018785
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  • 4
    Electronic Resource
    Electronic Resource
    Optimal interval enclosing of certain sets of matrices, with application to monotone enclosing of square roots (1980)
    Springer
    Computing 25 (1980), S. 283-295 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden zwei Halbordnungen für symmetrische Matrizen zueinander in Beziehung gesetzt, nämlich die durch den KegelK der elementweise nichtnegativen Matrizen definierte natürliche Halbordnung ≤ und die durch den KegelK D der nichtnegativ definiten Matrizen erzeugte definite Halbordnung $$ \leqslant \cdot$$ . Als Hauptresultat der Arbeit wird gezeigt, wie ein Matrixintervall im Sinne der definiten Halbordnung in optimale Schranken bezüglich der natürlichen Halbordnung eingeschlossen werden kann. Mit diesem Ergebnis ist es möglich, aus einer Lösungseinschließung mit der definite Halbordnung eine numerisch verwendbare Einschließung auf der Basis der natürlichen Halbordnung zu berechnen. Insbesondere kann auf diesem Wege ein stets und überdies quadratisch konvergentes Verfahren zur elementweisen monotonen Einschließung der Quadratwurzel einer symmetrischen, positiv definiten Matrix angegeben werden.
    Notes: Abstract In this paper, two kinds of partial ordering for symmetric matrices are related to each other, namely, the natural partial ordering ≤ generated by the coneK of elementwise nonnegative matrices, and the definite partial ordering $$ \leqslant \cdot$$ generated by the coneK D of nonnegative definite matrices. The main result of this paper shows how a matrix interval in the sense of the definite partial ordering can be enclosed between optimal bounds with respect to the natural partial ordering. By means of this result, it is possible to compute a numerically practicable inclusion based on the natural partial ordering from a given inclusion of some matrix with the definite partial ordering. In this way, an always and moreover quadratically convergent method of elementwise enclosing the square root of a positive definite, symmetric matrix can be constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02242005
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  • 5
    Electronic Resource
    Electronic Resource
    A strict bound to the condition number of bordered positive definite matrices (1988)
    Springer
    Computing 40 (1988), S. 181-183 
    Details
    ISSN: 1436-5057
    Keywords: 65F05 ; Condition number ; positive definite matrices ; bordered matrices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine leicht berechenbare scharfe Schranke für dieL 2-Konditionszahl in berandeten positiv-definiten Matrizen hergeleitet.
    Notes: Abstract An easily computable strict bound is derived for the condition number in theL 2 norm of bordered positive definite matrices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02247946
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  • 6
    Electronic Resource
    Electronic Resource
    On the R-order of coupled sequences II (1982)
    Springer
    Computing 29 (1982), S. 73-81 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Bestimmung der R-Ordnung τ von Folgen {x n, i ∼, die über ein System (3) von Ungleichungen miteinander verkoppelt sind, wird wie in der vorangegangenen Arbeit [3] auf die nichtnegative Lösbarkeit des Systems (4) von linearen Ungleichungen zurückgeführt. Weiterhin wird gezeigt, daß die beste R-Ordnung τ, welche sich aus (3) herleiten läßt, gleich dem Spektralradius einer bestimmten Matrix ist, welche aus in (3) auftretenden Exponenten gebildet wird.
    Notes: Abstract As in the preceding paper [3], the question whether some of the sequences {x n, i } coupled by a system (3) of inequalities converge at least with a certain R-order τ is reduced to the nonnegative solvability of the system (4) of linear inequalities. Further, the optimal R-order τ implied by (3) is characterized as the spectral radius of a certain matrix composed of exponents appearing in (3).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02254852
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  • 7
    Electronic Resource
    Electronic Resource
    On the R-order of coupled sequences III (1983)
    Springer
    Computing 30 (1983), S. 157-169 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 15A48 ; Iterative parallel processes ; best individualR-orders ; ordered positive decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für konvergente Folgen {x n,1 },...,{x n,s }, welche über ein System (2) von Ungleichungen miteinander verkoppelt sind, werden die besten individuellenR-Ordnungen τ1,...,τ s bestimmt. Dazu wird gezeigt, daß diese gleich den Spektralradien von bestimmten Matrizen sind, welche aus Exponenten in (2) gebildet werden.
    Notes: Abstract For convergent sequences {x n,1 },...{x n,s } coupled by a system (2) of inequalities the optimal individualR-orders τ1,...,τ s are determined as the spectral radii of certain matrices composed of exponents appearing in (2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02280786
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  • 8
    Electronic Resource
    Electronic Resource
    Determination of the cone radius for positive concave operators (1984)
    Springer
    Computing 33 (1984), S. 37-49 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 90C30 ; 15A48 ; Iterative processes ; bestR-orders ; cone radius of concave operators ; spectral radii ; partial ordering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Berechnung der bestenR-Ordnung von Folgen aus iterativen Näherungsverfahren führt auf die Ermittlung des hier eingeführten Kegelradius bestimmter konkaver Operatoren. Das Hauptergebnis der Arbeit ist die Darstellung des Kegelradius als Infimum der Spektralradien aller den konkaven Operator majorisierenden linearen Operatoren. Diese Charakterisierung ist von numerischem Intersse.
    Notes: Abstract The computation of bestR-orders of sequences produced by iterative methods leads to the determination of the cone radius of certain concave operators. The main result of the paper is the representation of the cone radius as the infimum of spectral radii of all linear operators majorizing the concave operator. This characterization is of numerical interest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243074
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  • 9
    Electronic Resource
    Electronic Resource
    Convex spline interpolants with minimal curvature (1985)
    Springer
    Computing 35 (1985), S. 219-229 
    Details
    ISSN: 1436-5057
    Keywords: 65K05 ; 65D07 ; 90C20 ; 41A15 ; Existence conditions ; quadratic programming ; dual optimization problem ; tridiagonal Hessian ; Newton's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das Problem, konvexe Interpolationssplines mit minimaler mittlerer Krümmung zu ermitteln, führt auf eine speziell strukturierte quadratische Optimierungsaufgabe. In der vorliegenden Note wird eine zugehörige duale Aufgabe aufgestellt, die ohne Nebenbedingungen auskommt, deren Zielfunktion stückweise quadratisch ist und die daher eine effektive numerische Behandlung erlaubt.
    Notes: Abstract The problem of finding convex spline interpolants with minimal mean curvature leads to a quadratic optimization problem of special structure. In the present note a corresponding dual problem without constraints is derived. Its objective function is piecewise quadratic and therefore admits an effective numerical treatment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02260507
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  • 10
    Electronic Resource
    Electronic Resource
    Vitamin-D-Sterole in Frauenmilch, Kuhmilch und Säuglingsnahrung (1985)
    Springer
    European journal of nutrition 24 (1985), S. 44-53 
    Details
    ISSN: 1436-6215
    Keywords: Vitamin D ; Vitamin-D-Metaboliten ; Frauenmilch ; Kuhmilch ; Säuglingsnahrung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary A review is given of the results of vitamin D determinations in human and cow's milk using physico-chemical methods. Thereby only parent vitamin D is determined. Further, the results obtained with protein-binding assays are discussed in detail. With the aid of these newer methods the concentrations of hydroxylated vitamin D derivatives can also be measured. A comparison of the concentration of these vitamin D metabolites in human milk and infant formulas based upon cow's milk suggests that the higher anti-rachitic activity of human milk is connected with its higher concentration of 25-hydroxy-vitamin D.
    Notes: Zusammenfassung Nach einer übersicht der Untersuchungen von Frauenmilch und Kuhmilch, die mit biologischen und physikalisch-chemischen Methoden durchgeführt worden sind und die nur das native Vitamin D erfassen, werden die Ergebnisse, die mit neueren Nachweisverfahren gewonnen wurden, ausführlich diskutiert. Die Anwendung von Proteinbindungsassays ermöglicht auch eine Bestimmung von hydroxylierten Vitamin-D-Metaboliten. Ein Vergleich der Konzentrationen von Frauenmilch und Säuglingsformulae auf Kuhmilchbasis deutet darauf hin, daß die günstigere antirachitische Aktivität von Frauenmilch vor allem auf den höheren Gehalt an 25-Hydroxy-Vitamin D zurückzuführen ist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02023894
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