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    Electronic Resource
    Electronic Resource
    Springer
    BIT 12 (1972), S. 5-16 
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Product type quadrature formulas are applied to obtain approximate solutions of Fredholm integral equations. A convergence theorem, and several numerical examples which demonstrate the efficacy of the technique, are presented.
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  • 3
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    Springer
    BIT 13 (1973), S. 287-291 
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this note some properties of the coefficient matrix associated with a product-interpolatory quadrature formula are determined and certain consequences of exactness of a product-type quadrature rule are deduced. For example, it is shown that the coefficient matrix has maximal rank and it is positive definite when the rule is symmetric. Conditions are stated under which a product-interpolatory rule reduces to a regular quadrature rule. A characterization of the error committed in applying a regular rule to a product of two functions is given.
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  • 4
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    BIT 11 (1971), S. 139-158 
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the numerical approximation of integrals of the formε a b f(x)g(x)dx by means of a product type quadrature formula. In such a formula the functionf (x) is sampled at a set ofn+1 distinct points and the functiong(x) at a (possibly different) set ofm+1 distinct points. These formulas are a generalization of the classical (regular) numerical integration rules. A number of basic results for such formulas are stated and proved. The concept of a symmetric quadrature formula is defined and the connection between such rules and regular quadrature formulas is discussed. Expressions for the error term are developed. These are applied to a specific example.
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  • 5
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    Springer
    Solar physics 17 (1971), S. 333-354 
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An echelle grating spectrograph has been flown in Skylark sounding rockets to investigate the solar ultraviolet spectrum. The instrument can record a range of ∼ 1000 Å, within the limits λ1000 Å-λ3000 Å, with a spectral resolving power of 105, and its use in the range λ1200–λ2200 Å is described. Values are quoted for the spectral efficiency of the individual optical components, and for the complete instrument over a wide wavelength range, and a description is given of the method used to estimate and then to discriminate against the in-flight stray light when the solar disc is imaged onto the entrance slit. The mechanical arrangement of the components is described and some of the problems associated with the alignment and operation are discussed.
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  • 6
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    Springer
    Archive of applied mechanics 42 (1973), S. 360-370 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es werden die Bedingungen für das Gleichgewicht eines Systems von miteinander verbundenen starren Körpern aufgestellt, die sich auf einer Umlaufbahn befinden. Die Stabilitätsbedingungen für eine gegebene Gleichgewichtslage werden berechnet. Die Bewegungsgleichungen werden nach dem Vorbild von Roberson-Wittenburg abgeleitet und in einem körperfesten Zwischensystem ausgedrückt. Dank der Vorteile dieses Vorgehens kann die Stabilitätsanalyse verhältnismäßig einfach nach der Ljapunovschen Methode durchgeführt werden.
    Notes: Summary The aim of this paper is to determine conditions for equilibrium of an orbiting system of interconnected rigid bodies and to find the stability conditions for a given equilibrium configuration. The equations were expressed in a body mean frame and derived from the Roberson-Wittenburg formalism, the combination of the advantages of these methods leading to a rather simple stability analysis by use of the Liapunov technique.
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  • 7
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    Contributions to mineralogy and petrology 29 (1970), S. 104-115 
    ISSN: 1432-0967
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract Single crystals of experimentally deformed synthetic quartz showing optical deformation lamellae were examined by transmission electron microscopy. Dislocations are distributed fairly uniformly throughout the crystal. However, parallel to the trace of the deformation lamellae, which may be irrational, there are walls of tangled dislocations whose characteristics suggest that they are directly associated with the lamellae. The nature and formation of the optical image is discussed in detail.
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  • 8
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    Contributions to mineralogy and petrology 47 (1974), S. 215-222 
    ISSN: 1432-0967
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract Clinoenstatite lamellae are found to be distributed in three distinct patterns that define three microstructural types. There are regions of the crystal devoid of lamellae and these correspond to ordered or O-orthopyroxene. When the lamellae are present but not in any periodic arrangement, disordered or D-orthopyroxene is identified. In some areas, the lamellae are spaced periodically and these are regions of “superlattice” orthopyroxene. These microstructural types explain all previous X-ray results on orthopyroxenes. Microstructural differences between low and high calcium orthopyroxenes are discussed.
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  • 9
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    Contributions to mineralogy and petrology 37 (1972), S. 229-234 
    ISSN: 1432-0967
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract Lattice defects along (100) planes in an orthopyroxene, En92.8-Fs7.0-Wo0.2, have been observed in the transmission electron microscope. From an analysis of the electron diffraction contrast at these defects it is proposed that the defects are regions of iron and possibly calcium enrichment. The defects are completely coherent with the lattice of the matrix and appear to be metastable or transition zones. They do not have any direct relationship with the spinodal decomposition proposed for the exsolution textures in some of the lunar pyroxenes of Apollo 11 and 12. Possible cationic ordering within these zones is discussed and the effects of such ordering on magnetic properties are considered.
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    Springer
    Contributions to mineralogy and petrology 30 (1971), S. 53-63 
    ISSN: 1432-0967
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract Transmission electron microscopy has been used for the direct observation of dislocations in naturally-deformed olivine. The dislocations are arranged in arrays forming low-angle sub-boundaries which have been identified with features observed in the optical microscope. Comparison of this dislocation substructure with that observed in olivine, and in metals, experimentally deformed under various conditions, suggests that the deformation in nature has occurred by creep. Possible mechanisms of creep, involving the cooperative glide and climb of dislocations, are discussed.
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