Mandelbrot Benoit James Wallis (4 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.".…

Soft cover. Condition: Very Good. 1st Edition. First edition, rare offprint, of this early work on fractals and self-similarity. "In papers published between 1965 and 1973 concerning hydrology and the appearance of periodicity in discharges and floods of the Nile river Mandelbrot described both the "Noah effect," in which sudden discontinuous changes can occur, such as floods, and the "Joseph effect," in which persistence of a value can occur for a while, such as famines, yet suddenly change afterwards. This challenged the idea that changes in price were normally distributed. (Mandelbrot cited his specific papers on this topic in The Fractal Geometry of Nature [1982], but see especially Mandelbrot & Wallis, 'Noah, Joseph and Operational Hydrology,' Water Resources Research 4 [1968], 909-18). This work had implications for climatology, for agriculture, for the design of dams, and on economic issues" ('The Scope of Benoit Mandelbrot's Work and its Influence', Jeremy Norman's historyofscience). "By 'Noah Effect' we designate the observation that extreme precipitation can be very extreme indeed, and by 'Joseph Effect' the finding that a long period of unusual (high or low) precipitation can be extremely long. Current models of statistical hydrology cannot account for either effect and must be superseded. As a replacement, 'self-similar' models appear very promising. They account particularly well for the remarkable empirical observations of Harold Edwin Hurst. The present paper introduces and summarizes a series of investigations on self-similar operational hydrology" (Abstract). 8vo, pp. 909-918 with inserted printed errata leaf. Original pale blue printed wrappers.…