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  • Articles: DFG German National Licenses  (2)
  • 1955-1959  (2)
  • 1905-1909
  • 1959  (2)
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  • Articles: DFG German National Licenses  (2)
Material
Years
  • 1955-1959  (2)
  • 1905-1909
Year
  • 1
    Electronic Resource
    Electronic Resource
    Eine wahrscheinlichkeitstheoretische Begründung der Integrationsformeln von Newton-Cotes (1959)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 10 (1959), S. 189-207 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary A definite integral is approximated by a linear combination of values of the integrand at equidistant points. As a measure for the goodness of fit we use the mean square deviation; for this we take a wide sense stationary stochastic process as basis. We prove that there exist always a best integration formula in this sense. The Taylor expansion of its coefficients begins with the coefficients ofNewton-Cotes. It is shown that the error of the best integration formula is of the same order of magnitude as in the well-known formula ofNewton-Cotes. Therefore we get a justification for the formulae ofNewton-Cotes also if the integrand is not differentiable. Besides we obtain estimates of the error, which use higher differences instead of higher differential quotients of the integrand.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01600525
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Fraktometrische Analyse von Deuterium im Wasserstoffstrom (1959)
    Springer
    Fresenius' Zeitschrift für analytische Chemie 166 (1959), S. 433-439 
    Details
    ISSN: 1618-2650
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary A universally usable, quantitative assay for deuterium-labeling work demands a stoichiometrical transformation of all samples into elementary hydrogen. For the detector, it is the best to connect directly a fractometer, that works with a catharometer cell. Tests with several carrier gases and an attempt with a palladium-black column failed; a molecular sieve with ordinary hydrogen as carrier was appropriate. The fractogram, written by a compensograph, shows a well gaugeable peak which is linearly proportional to the deuterium content of the sample. The error at full deflection amounts to ±0,5%. Protium deuteride, HD, is acting as if it were 1/2 D2, a fact that was confirmed by mass-spectrometric measurements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00461873
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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