Embedding universal computer arithmetic in higher programming languages

In numerical computations mainly real and complex numbers, intervals as well as matrices and vectors with such components occur. It is well known that the arithmetic operations with real numbers, complex numbers etc. can be carried over to real floating-point numbers, complex floating-point numbers etc. using roundings. This proceeding results in agreeable arithmetic-, order- and compatibility-properties for an abundance of numerical data types and the accompanying arithmetic operations. Most programming languages however only provide real floating-point numbers; all the other data types and operations have to be simulated, e. g. in the form of arrays and procedure calls, which often causes loss of accuracy and arithmetic properties. Furthermore the complicate notation makes programs difficult to read. Therefore in this article an extension of PASCAL is presented which serves as an example for the way these numerical data types can be embedded into the syntax of a programming language.     

How to avoid logarithms in comparisons with uniform random variables

In many algorithms for sampling from non-uniform distributions the logarithm of a uniform deviate must be compared with some test quantity. It is shown that all these comparisons can be done efficiently without calling a logarithm subprogram: two procedures for this task are presented and compared.     

On plastic potentials for anisotropic metals and their derivation from the texture function

Summary Plastic yielding of anisotropic metals can be either described by a macroscopic constitutive relation or assessed by means of a model which correlates single and polycrystal behaviors. The mathematical identification of the plastic work rate derived from the two approaches, for all strain rate tensors, leads to a fit of the polycrystal yield surface by an analytical function. When a quadratic from is assumed, the macroscopic anisotropy parameters become explicit functions of the texture coefficients. This identification method is applied to calculate yield surfaces andR-values of rolled and annealed steel sheets: theR-values and in general the flow rule, are more significantly modified by the fitting than the yield surface. Thus, it is worth extending the method to more general constitutive relations which may be given by the form of their work function: alternative forms of the work function for plastic materials are explored, especially in the bearing of convexity and homogeneity where quadratic forms have a distinct advantage. Finally, it is shown that the identification of the work function allows to express the phenomenological coefficients as analytical functions of the texture parameters for many forms of the work function; in the other cases, these coefficients may be obtained by linear or non-linear regression.     

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Ohne Zusammenfassung     

Surface charge accumulation and decay on a spacer stressed with DC voltages at atmospheric conditions

Contents Surface charge accumulation and its decay at a GIS spacer are studied at atmospheric conditions employing a two step-calibration method. The results show that the accumulation saturates within 30 minutes; the dominant mechanism of surface charge accumulation is the drift of charged particles via air, while that of the decay is surface conduction. The characteristics are similar at both polarities.

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Sättigungskonzentration und Abklingverhalten der Oberflächenladung an einem mit Gleichspannung beanspruchten Abstandshalter unter atmosphärischen Bedingungen

Übersicht Die Konzentration und das Abklingen von Oberflächenladungen an einem GIS Abstandshalter wurden unter atmosphärischen Bedingungen mit Hilfe eines zweistufigen Kalibrierungsverfahrens untersucht. Die Ergebnisse zeigen eine Sättigung der Ladungskonzentration innerhalb von 30 Minuten. Als Hauptursache der Ladungskonzentration ist die Drift geladener Teilchen in Luft anzusehen, während das Abklingen auf die Oberflächenleitung zurückzuführen ist. Ähnliche Charakteristiken ergeben sich mit beiden Polaritäten.