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.     

Algorithmen zur Pulsweitenmodulation für Wechselrichter mit in Echtzeit berechnetem Pulsmuster

Übersicht Mit Hinblick auf die zunehmend Verbreitung findende Pulsmusterberechnung in Echtzeit werden in dem Aufsatz Gesichtspunkte diskutiert, die sich aus den Eigenschaften des leistungselektronischen Stellgliedes, des Pulswechselrichters, ergeben. Die bei Abtastregelungen für die Dauer einer Abtastperiode konstante Stellgröße muß bei ihm durch Pulsweitenmodulation in ein Pulsmuster mit konstanter Amplitude und Pulsen variabler Breite umgesetzt werden. Durch ein neues Verfahren mit versetzter Abtastung haben dabei Rechentotzeiten bis zur Dauer einer halben Abtastperiode keinen Einfluß mehr auf das Pulsmuster.

---

Algorithms for pulswidth modulation of inverters with online calculated pulse patterns

Contents Online calculation of pulse patterns will be employed more intensively in the future. Aspects concerning the powereleotronic circuit, the pulsewidth-modulated inverter, are to be discussed. The set value being constant for the duration of a sampling interval, has to be converted by a modulation algorithm into a pulse pattern with constant amplitude and pulses of variable width. Calculation dead-times up to half of sampling interval have no influence on the pulse pattern when using a new algorthm with shifted sampling instants.

---

---

Herrn Prof. Dr.-Ing. Klemens Heumann zum 60. Geburtstag gewidmet     

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.