Mandelbrot Benoit James Wallis (3 results)

(24,5 x 17 cm). SS. 909-918. Original-Broschur mit Klammerheftung, unbeschnitten. (Sonderdruck aus: Water Resources Research). Erste Ausgabe mit einem beiliegenden "Errata"-Blatt. - "Man kann die Geschichte von Noah unschwer als eine Parabel über die Ungleichmäßigkeit der Niederschläge im Mittleren Osten erkennen, und die Geschichte von Joseph als eine Parabel über die Tendenz, daß sich nasse und trockene Jahre zu Regen- und Dürreperioden vereinen. In Vorlesungen über die 'Neue Formen des Zufalls in den Naturwissenschaften' (siehe vorliegender Artikel) habe ich diesen Geschichten die Namen Noah-Effekt und Joseph-Effekt angeheftet" (Mandelbrot, Die fraktale Geometrie der Natur). - Papierbedingt leicht gebräunt, sonst gut erhalten.

Soft cover. Condition: Near Fine. Benoit Mandelbrot and James R. Wallis, "Some Long-Run Properties of Geophysical Records", reprinted from "Water Resources Research, vol 5/2, April 1969. Original wrappers. Owner's rubber stamp at top right corner of the front wrapper, otherwise a Fine copy. Scarce. Cited 1200+ times. __+__ "The purpose of this paper is to present and to comment upon some long-run properties of geophysical records, and, in particular, to test the validity of an empirical law due to Harold Edwin Hurst. We shall show that this law must be amended, tightened, and hedged, but that its essential claim will be confirmed. 'Fractional noises,' discussed in Mandelbrot and Van Ness [1968] and Mandelbrot and Wallis [1969a], are a family of random processes specifically designed to satisfy Hurst's law. Comparison of the figures of the present paper with those of Mandelbrot and Wallis [1969a] confirm, in our opinion, that modeling of geophysical records with the help of fractional noises is valid." And: "In summary, even though the distinctions between macrometeorology and climatology or between climatology and paleoclimatology are unquestionably useful in ordinary discourse, they are not intrinsic to the subject matter, and it would be imprudent to let them influence hydrological design."--(from the paper.)__+__ "As will become evident, the late Benoît B. Mandelbrot was a key figure in the development of long memory. Nowadays, most famous for coining the term and concept fractal, Mandelbrot s output crossed a wide variety of subjects from hydrology to economics as well as pure and applied mathematics. During the 1960s, he worked on the theory of stochastic processes exhibiting heavy tails and long memory, and was the first to distinguish between these effects. Because of the diversity of the communities in which he made contributions, it sometimes seems that Mandelbrot s role in statistical modelling is under-appreciated (in contrast, say, to within the physics and geoscience communities."--"A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA, 1951 1980"Timothy Graves, et al, from "entropy" online.

Original pamphlet from February 1969, from the Water Resources Research. Signed by Benoit Mandelbrot on the front cover. In very good condition, in wrappers as issued. For his contributions in mathematics, Benoit Mandelbrot has been awarded the Harvey Prize (1989), the Wolf Foundation Prize for Physics (1993), and the Japan Prize (2003). Science writer Arthur C. Clarke credits the Mandelbrot set as being "one of the most astonishing discoveries in the entire history of mathematics.".