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  • Articles  (6)
  • 41  (4)
  • Phosphate
  • Striation pattern
  • Springer  (6)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerical algorithms 3 (1992), S. 201-209 
    ISSN: 1572-9265
    Keywords: AMS 15 ; 41 ; Orthogonal polynomials ; Laurent polynomials ; T-fractions ; Padé approximants
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper is concerned with double sequencesC={C n} n =−∞/∞ of Hermitian matrices with complex entriesC n ∈M s×s ) and formal Laurent seriesL 0(z)=−Σ k=1 ∞ C −k z k andL ∞(z)=Σ k=0 ∞ C k z −k . Making use of a Favard-type theorem for certain sequences of matrix Laurent polynomials which was obtained previously in [1] we can establish the relation between the matrix counterpart of the so-calledT-fractions and matrix orthogonal Laurent polynomials. The connection with two-point Padé approximants to the pair (L 0,L ∞) is also exhibited proving that such approximants are Hermitian too. Finally, error formulas are also given.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Advances in computational mathematics 5 (1996), S. 297-328 
    ISSN: 1572-9044
    Keywords: Distribution functions ; integration rules ; interpolation nodes ; Szegö polynomials ; 41 ; 65D
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, quadrature formulas on the unit circle are considered. Algebraic properties are given and results concerning error and convergence established. Finally, numerical experiments are carried out.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Calcified tissue international 10 (1972), S. 113-127 
    ISSN: 1432-0827
    Keywords: Calcium ; Phosphate ; Fluoride ; Tooth ; Enamel ; Kinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé Les surfaces d'émail dentaire sont confrontées avec des solutions de calcium et phosphate, qui y recirculent. Les réactions cinétiques au niveau des surfaces en calcium, phosphate, fluorure et ions hydrogène sont déterminées dans des solutions à concentrations en ions fluor constantes (0.012, 0.025, 0.050, 0.250 ou 0.500 mM/l) et/ou à pH constant (6.8, 7.0, 7.2 ou 7.4). Les vitesses de réactions des ions calcium, phosphate, hydrogène et fluorures augmentent dans les conditions suivantes: 1) augmentation de la surface d'émail, 2) augmentation des vitesses d'écoulement au niveau des surfaces, 3) augmentation du pH de la solution et 4) augmentation de la concentration en ion fluorure. Les vitesses presque proportionnelles des réactions mesurées simultanément indiquent la formation de minéraux apatitiques à la surface de l'émail pendant tout le temps de contact solide-solution.
    Abstract: Zusammenfassung Oberflächen von Zahnschmelz wurden mit konstant zirkulierenden Lösungen, welche Calcium und Phosphate enthielten, equilibriert. Die kinetischen Oberflächenreaktionen von Calcium-, Phosphat-, Fluori- und Wasserstoff-Ionen wurden in Lösungen mit konstanten Fluoridkonzentrationen (0,012, 0,025, 0,050, 0,250 oder 0,500 mM/l) und/oder konstantem pH (6,8, 7,0, 7,2 oder 7,4) bestimmt. Die Reaktionsgeschwindigkeiten dieser Ionen an der Grenze zwischen fester und flüssiger Phase erhöhten sich unter folgenden Bedingungen: 1. Vergrößerung der Schmelzoberfläche; 2. Erhöhung der Geschwindigkeit der der Oberfläche zugeführten Lösungen; 3. Erhöhung des pH der Lösung; 4. Erhöhung der Fluoridionenkonzentration in der Lösung. Die beinahe proportionalen Geschwindigkeiten der gleichzeitig gemessenen Reaktionen deuteten darauf hin, daß auf den Schmelzoberflächen während der ganzen Equilibrierungszeit Apatitminerale gebildet wurden.
    Notes: Abstract Surfaces of tooth enamel were interfaced with recirculating solutions containing calcium and phosphate. The kinetic interfacial reactions of calcium, phosphate, fluoride, and hydrogen ions were determined in solutions of constant fluoride ion concentrations (0.012, 0.025, 0.050, 0.250, or 0.500 mM/l) and /or constant pH (6.8, 7.0, 7.2, or 7.4). The rates of the calcium, phosphate, fluoride, and hydrogen ion reactions at the solid-solution interface increased under the following conditions: (1) increase of the enamel surface area; (2) increase of the rates of solution flow to the interface; (3) increase of solution pH; and (4) increase of the solution fluoride ion concentration. The nearly proportional rates of the concurrently measured reactions indicated the formation of apatitic minerals on the enamel surfaces throughout the time of solid-solution interface.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Cell & tissue research 129 (1972), S. 11-19 
    ISSN: 1432-0878
    Keywords: Muscle ; Invertebrates ; Sabellastarte magnifica ; Striation pattern ; Electron microscopy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Summary As described in other invertebrate muscles, most thick myofilaments of the dorsal longitudinal muscle of Sabellastarte magnifica appear to be obliquely arranged with respect to the longitudinal axis of the myofibrils. Some sections, however, show long bundles of myofilaments parallel to the longitudinal axis of the myofibrils. Since the oblique striation concept cannot account for such images, a different (longitudinal) arrangement is proposed for Sabellastarte which can account for all observed images. A wax and threads model built according to this arrangement has been used to demonstrate that by oblique sectioning the longitudinal model can generate a false appearance of filament obliquity.
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  • 5
    Electronic Resource
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    Springer
    Numerical algorithms 15 (1997), S. 167-192 
    ISSN: 1572-9265
    Keywords: Matrix Padé Approximation ; rationality ; minimum degrees ; uniqueness ; 65 ; 41 ; 15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In many applications it is of major interest to decide whether a given formal power series with matrix-valued coefficients of arbitrary dimensions results from a matrix-valued rational function. As the main result of this paper we provide an answer to this question in terms of Matrix Padé Approximants of the given power series. Furthermore, given a matrix rational function, the “smallest” degrees of the matrix polynomials which represent it are not necessarily unique. Therefore we study a certain minimality-type, that is, minimum degrees. We aim to obtain all the minimum degrees for the polynomials which represent the function as equivalents. In addition, given that the rational representation of the function for the same pair of degrees need not be unique, we have obtained conditions to study the uniqueness of said representation. All the results obtained are presented graphically in tables setting out the above information. They lead to a number of properties concerning special structures, staired blocks, in the Padé Table.
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  • 6
    ISSN: 1572-9265
    Keywords: Transfer-function model ; Padé approximation ; ε-algorithm ; 41 ; 62 ; 65 ; 90
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The aim of this paper is to apply an algorithm related to the rational approximation for the identification of the lag structure in a transfer-function model. In fact, we apply the ε-algorithm proposed by Berlinet [3–5] to determine the polynomial orders in univariate and multivariate ARMA models. Furthermore, it has been proposed by Berlinet [5], González and Cano [13, 14] and González et al. [15] for a transfer-function model with one input and multiple inputs, respectively. The main contribution in this paper concerns the study of the relative significance of the elements in the ε-algorithm table, in the same way as that given by Berlinet and Francq [7] for ARMA models, to confirm the pattern used to specify the model. Two examples will be considered, namely, the sales series M [8] and a simulated model [20]. A comparison is also made between the results of the ε-algorithm and the corner method generally used in the econometric literature. Although the ε-algorithm requires a more advanced theory in Numerical Analysis, it can be applied in a more simple way than the corner method.
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