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MAJOR RESEARCH SUPPORT GRANTS



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MAJOR RESEARCH SUPPORT GRANTS

1953-54 Scholar of the Rockefeller Foundation – as John von Neumann’s postdoc in Princeton (IAS).

1968 Fellow of the John Simon Guggenheim Memorial Foundation (resigned).

passim Grants from the Office of Naval Research – for research in physics.

passim Grants from the National Science Foundation – for summer workshops that introduced the use of fractals in high school and college education.

FRACTALS” BOOKS. A Scrapbook of Reviews of these books is available on this web site.


A Les objets fractals: forme, hasard et dimension. Paris, FR: Flammarion, 1975, 192 pp.
A2 2e édition. Paris, FR: Flammarion, 1984, 204 pp.
A3 3e édition, suivie d’un Survol du langage fractal. Paris, FR: Flammarion, 1989, 268 pp.
A4 4e édition (“poche”). Paris, FR: Flammarion (Collection Champs), 1995, 209 pp.
Objektu fraktalak: forma, zoria eta dimentsioa. Basque Translation of an update of A3

by Inaki Azkune Mendia. Usurbil: Elhuyar, ES, 1992, 333 pp. www.zientzia.net
Fraktalnite obekti: forma, sluchainost i razmernost. Bulgarian Translation of A3
by Petr Filipov Lazarov, Andrei Juliev Bakhner & Ilia Vasiliev Petrov.
Sofia, BG: St. Kliment Ohridski Press, 1996, 275 pp.
Chinese Translation of A4 by Wen Zhiying. Beijing, CN: World Publishing Corporation, 1999.
Fraktály: tvar, náhoda a dimenze, updated by a new foreword.
Czech Translation of A4 by Jiri Fiala, Prague, CZ: Mladá Fronta, 2003, 210 pp.
Gli oggetti frattali: forma, caso e dimensione. Italian Translation of A2 by Roberto Pignoni; preface by Luca Peliti & Angelo Vulpiani. Torino, IT: Giulio Einaudi, 1987, xx + 207 pp.
Objectos fractais: forma, acaso e dimensão; seguido de panorama da linguagem fractal.
Portuguese Translation of an update of A3 by Carlos Fiolhais & José Luis Malaquias Lima.
Lisboa, PT: Gradiva, 1991, 300 pp.
Obiectele fractale: forma, hazard, dimensiune.
Romanian Translation of A3 by Florin Monteanu. Bucaresti, RO: Nemira, 1998.
Los objetos fractales: forma, azar y dimensión.
Spanish Translation of A2 by Josep Maria Llosa. Barcelona, ES: Tusquets, 1987, 213 pp.
B Fractals: Form, Chance and Dimension.
San Francisco CA: W. H. Freeman and Company, 1977, xviii + 265 pp.
C The Fractal Geometry of Nature.
New York, NY: W. H. Freeman and Company, 1982, xii + 461 + xvi pp. (twenty-two reprints by 2005)
Da Zi Ran De Feng Xing Gi He Xue. Chinese Translation of C
by Yongmian Huang & Shouji Chen. Shanghai, CN: Far East Publishers, 1998, xvi + 16 + 574 pp.
Die fraktale Geometrie der Natur. German Translation of C
by Reinhilt & Ulrich Zähle. Basel, CH: Birkhäuser & Berlin: Akademie-Verlag, 1987, 491 + xvi pp.
Fraktal Kikagaku. Japanese Translation of C
directed by Heisuke Hironaka. Tokyo, JP: Nikkei Science, 1984, 464 + xvi pp.
Фракталвная геометрия природы, Russian Translation of C by A.R. Lorunova & A.D. Morozova. Moscow & Izhevsk, RU: R & C Dynamics Scientific Publishing Center. 2002.
La geometría fractal de la naturaleza.
Spanish Translation of C by Josep Maria Losa. Barcelona, ES: Tusquets, 1997, 662 pp.

Book-club edition Barcelona, ES: Circulo de Lectores, 2009.

SELECTA” BOOKS. A Scrapbook of Reviews of these books is available on this web site.


Note: In the lists that follow, the titles of those publications reproduced in a Selecta book
are preceded by a bold-letter "marker." It consists of the distinguishing letter(s) that follow(s) the letter S on this page.
SE Fractals and Scaling in Finance: Discontinuity, Concentration, Risk.
New York NY: Springer, 1997, x + 551 pp.

Chapters on this web site: E3 E5 E7 E8 E9 E14 E15 E19


SFE Fractales, hasard et finance (1959 - 1997).
Paris, FR: Flammarion (Collection Champs), 1997, 246 pp.
SFR Fraktaly, sluchai i financy. Russian Translation of SFE by V.V. Shulikowskoi.
Moscow & Izhevsk, RU: R & C Dynamics, 2004, 256 pp.
SN Multifractals and 1/f Noise: Wild Self-affinity in Physics.
New York NY: Springer, 1999, viii + 442 pp.

Chapters on this web site: N14 N15 N16


SH Gaussian Self-Affinity and Fractals: Globality, the Earth, 1/f, and R/S.
New York NY: Springer, 2002, ix + 654 pp.

Chapters on this web site: HP HO H1 H10 H11 H12 H13 H14 H18 H19 H21 H22 H23 H24 H25 H26 H27 H30


SC Fractals and Chaos: The Mandelbrot Set and Beyond.
New York NY: Springer, 2004, xii + 308 pp.
SCR Фракталы и хаос: Множество Мандельброта и другие чудеса

Russian Translation of SC.
Moscow & Izhevsk, RU: R & C Dynamics Scientific Publications Center. 2009, 391 pp.


FREE-STANDING BOOKS. A Scrapbook of Reviews of these books is available on this web site.
v Logique, langage et théorie de l’information (Léo Apostel, M, & Albert Morf).
Paris, FR: Presses Universitaires de France, 1957, vi + 207 pp.
w La geometria fractal de la naturaleza.
Milano, IT: Imago (Montedison Progetto Cultura), 1987,

Roma, IT: Edizioni Theoria, 1989, 91 pp.


x Nel mondo dei frattali. Roma, IT: Di Renzo Editore, 2001, 60 pp.
y Fractals, Graphics, and Mathematics Education. Ed Michael L. Frame & M.
Washington DC: Mathematical Association of America

& Cambridge UK: The University Press, 2002, xiii + 206pp.


* Fractal Geometry, Notes for Yale course Math 190 by Michael L. Frame, M, & Nial Neger.
Available at http://classes.yale.edu/fractals .
z The (Mis)behavior of Markets: A Fractal View of Risk, Ruin, and Reward,

(M & Richard L. Hudson). New York: Basic Books, 2004, xxvi + 329 pp.

Paperback 2006; subtitled, A Fractal View of Financial Turbulence, with Preface, 2009. British edition, London, UK: Profile Books, 2004. Paperback, 2005; with a new Preface, 2008, Related text, 2008.

A Scrapbook of Reviews of this book and its translations is available on this web site.


  • Mercados Financeiros Fora de Controle. A teoria dos fractais explicando o comportamento dos mercados. Portuguese translation by Alfonso Celso da Cunha Serra. Sao Paulo, BR: Elsevier & Editora Campus, 2004, xxxiv + 317 pp.




  • Une approche fractale des marchés. Risquer, perdre et gagner.
    French translation by Marcel Filoche. Paris, FR: Odile Jacob, 2005, 361 pp.




  • Fraktale und Finanzen. Märkte zwischen Risiko, Rendite und Ruin.
    German translation by Helmut Reuter. München, DE: Piper Verlag, 2005, 446 pp.




  • Il disordine dei mercati. Una visione frattale di rischio, rovina e redditività.
    Italian translation by Simonetta Frediani. Torino, IT: Einaudi, 2005, xx + 296 pp.




  • O (Mau)Comportamento dos Mercados: Uma visão fractal do risco,

Da ruína e do rendimento. Portuguese translation by Miiguel Marques. Lisbon, PT: Gradiva, 2006, 416 pp.


  • Fractales y finanzas. Una aproximación matemática a los mercados: arriesgar, perder y ganar. Spanish Translation by Ambrosio García Leal. Barcelona, ES: Tusquets, 2006, 322 pp.


Ο πινακας του χαους. Γιατί καταρρέουν οι αγορές. Μττενουά Μάντελμττροτ & Ρίσαρντ Λ. Χάντσον. Τραυλος, Αθήνα Greek translation. Athens, GR: Travlos, 2006. 474 pp.


  • Finans Piyasalarinda (sakli) Düzen / Risk, Cöküs ve Kazanca Fraktal Yaklasimlar. Turkish translation by Gülsah Karadag. Istanbul, TR: Güncel Publishing, 2006.




  • (Не)послушные рынки: фрактальная революция в финансах.

Russian Translation by I. V. Kornenko. Moscow & St. Petersburg, RU & Kiev, UA:

Williams, 2006, 389 pp.




  • The secret code behind stock prices, cotton and the Nile River.

Chinese translation by Jesse Sam. Taipei, TW: Good Morning Press, 2007, 396 pp.


by Hideki Takayasu. Tokyo, JP: Toyo Keizai Shinpo, 2008, 368 + 61 pp.

Translation reportedly underway: Beijing, CN: Renmin University Press.




NOTATIONS USED IN THE LISTS THAT FOLLOW

The abbreviation M. Each publication is preceded by the name(s) of the author(s)
“Mandelbrot” being replaced by the letter M.
The identifying letters. Each publication not fully identified by its year is assigned a

mnemonic letter, which the author uses in his books and in every other case that allows it.


The marks of the form FE4. The publications that are reproduced in a Selecta book or web book are marked by the letters denoting that volume followed by the chapter number.

PROCEEDINGS OR COURSE NOTES EDITED OR COEDITED

a Proc. of the Gaithersburg Symposium on Fractals in the Physical Sciences.
Journal of Statistical Physics (Special Issue): 36, Nos. 5/6.
Ed Michael F. Shlesinger, M, & Robert J. Rubin. New York NY: Plenum, 1984, 400 pp.
b Fractal Aspects of Materials: Metal and Catalyst Surfaces, Powders and Aggregates.
Extended Abstracts of a MRS Symposium held in Boston.
Ed M & Dann E. Passoja. Pittsburgh PA: Materials Research Society, 1984, 47 pp.
c Fractal Aspects of Materials. Extended Abstracts of a MRS Symposium held in Boston.
Ed Robert Laibowitz, M, & Dann E. Passoja.
Pittsburgh PA: Materials Research Society, 1985, 127 pp.
d Fractals: Basic Concepts, Computation and Rendering. Ed M.
Notes for a SIGGRAPH 85 Course. San Francisco CA; July 23, 1985.
Association for Computing Machinery; Special Interest Group on Computer Graphics.

• Variant, with additions and deletions. Notes for a Professional Development Seminar


given in Boston MA on March 3, 1986. Boston Chapters of Siggraph and ACM.
e Fractal Aspects of Materials II. Extended Abstracts of a MRS Symposium held in Boston.
Ed Dale W. Schaefer, Robert B. Laibowitz, M, & Samuel H. Liu.
Pittsburgh PA: Materials Research Society, 1986, 148 pp.
f Ensembles fractals. Ecole d'hiver CEA - EDF – INRIA. Roquencourt, FR. Jan. 1987, 340 pp.
g Fractal Aspects of Materials: Disordered Systems.

Extended Abstracts of a MRS Symposium held in Boston.

Ed Alan J. Hurd, David A. Weitz, & M. Pittsburgh: Materials Research Society, 1987, 208 pp.


h Fractal Aspects of Materials: Disordered Systems.

Extended Abstracts of a MRS Symposium held in Boston. Ed David A. Weitz, Leonard M. Sander, & M. Pittsburgh PA: Materials Research Society, 1988, 356 pp.
i Fractals in Geophysics. Ed Christopher H. Scholz & M.

Pure and Applied Geophysics (Special Issue): 131, Nos. 1/2.

Boston MA & Basel, CH: Birkhäuser, 1989.

PUBLICATIONS REPORTING ON ORIGINAL RESEARCH.

THIS LIST IS PRECEDED AND FOLLOWED BY OTHER LISTS OF

BOOKS AND PUBLICATIONS

1951
1 AS & K FE4. M 1951. Adaptation d'un message sur la ligne de transmission, I & II.
Comptes Rendus. Paris, FR: 232, 1638-1640 & 2003-2005.
1952
2 M 1952. Sur la notion générale d'information et la durée intrinsèque d'une stratégie.
Comptes Rendus. Paris, FR: 234, 1346- 1348.
3 M 1952. Les démons de Maxwell. Comptes Rendus. Paris, FR: 234, 1842-1844.
1953
4 M 1953t. Contribution à la théorie mathématique des jeux de communication (Ph.D. Thesis).
Publications de l'Institut de Statistique de l'Université de Paris: 2, 1-124.
5 M 1953i. An informational theory of the statistical structure of language.
Communication Theory, the Second London Symposium. Ed Willis Jackson.
London, UK: Butterworth; New York NY: Academic, 486-504.
1954
6 M 1954w. Structure formelle des textes et communication (deux études). Word: 10, 1-27.

• Corrections: Word: 11, 1955, 424.


• English translation by Anthony G. Oettinger: The formal structure of texts and communication (two studies): Cambridge MA, Harvard Computation Laboratory, 1955.

• Czech translation: Komunikace a formalni struktura textu. Teorie informace a jazykoveda (=Information theory and linguistics), an anthology ed Lubomir Dolozel.


Prague, CZ: Press of the Czechoslovak Academy of Sciences, 1964, 130-150.

• Excerpt: Le Langage, anthologie dirigée par Robert Pagès. Paris, FR: Hachette, 1959, 55-57.

• Summary: Information sans interprétation dans la description des langues réelles.
Synthèse: 11, 1959, 160-161.
7 M 1954. Simple games of strategy occurring in communication through natural languages. Transactions of the IRE Professional Group on Information Theory: 3, 124-137.

• French translation: Jeux de stratégie se présentant dans la communication au moyen des


langues naturelles. Traductions du Centre National des Télécommunications, 1049, 1955.

• Abstract: Statistical macro-linguistics. Supplemento di Nuovo Cimento: 13, 1959, 518-520.


1955
8 M 1955b. On recurrent noise limiting coding. Information Networks, the Brooklyn Polytechnic Institute Symposium. Ed Ernst Weber. New York NY: Interscience, 205-221.

  • Russian translation: O rekurrentnom kodirovanii, ogranichivayuschem vliyanie pomekh.
    Teoriia informatsii (=Information Theory). Ed W. Siforof. Moscow, RU: 1957, 138-157.

9 M 1955. Diagnostic en l'absence de bruit. Institut de Statistique de Université de Paris. 1-73.



  • A free-standing booklet.

10 M 1955t. Théorie de la précorrection des erreurs de transmission.


Annales des Télécommunications
: 10, 122-134.
1956
11 AS. M 1956c. La distribution de Willis-Yule, relative au nombre d'espèces dans les genres biologiques. Comptes Rendus. Paris, FR: 242, 2223-2225.
12 M 1956w. On the language of taxonomy: an outline of a thermo-statistical theory of systems of categories, with Willis (natural) structure.

Information Theory, the Third London Symposium.
Ed Colin Cherry. London, UK: Butterworth; New York NY: Academic, 135-145.
13 M 1956t. Exhaustivité de l'énergie totale d'un système en équilibre, pour l'estimation de sa température. Comptes Rendus Paris, FR: 243, 1835-1837.
14 M 1956m. A purely phenomenological theory of statistical thermodynamics: canonical ensembles. IRE Transactions on Information Theory: 112, 190-203.
1957
15 M 1957b. Note on a law of J. Berry and on insistence stress. Information and Control: 1, 76-81.
• Russian translation: Zakon Berri i predelenie “udareniya”.

Teoriia informatsii (=Information Theory). Ed W. Siforof. Moscow, RU: 1957, 248-254.
16 M 1957p. Linguistique statistique macroscopique: Théorie mathématique de la loi d'Etoupa-Zipf (Basée sur les méthodes de la théorie de l’information et de la thermodynamique).
Institut Henri Poincaré: Séminaire de calcul des probabilités, 1-80 (booklet).
17 M 1957t. Application of thermodynamical methods in communication theory and in econometrics. Institut Mathématique de l'Université de Lille.
1958
18 M 1958p. Les lois statistiques macroscopiques du comportement (rôle de la loi de Gauss
et des lois de Paul Lévy). Psychologie Française: 3, 237-249.
1959
19 M 1959s. A note on a class of skew distribution functions: Analysis and critique of
a paper by H. A. Simon
. Information and Control: 2, 90-99.
20 AS SFE. M 1959p. Variables et processus stochastiques de Pareto-Lévy et la répartition des revenus, I & II. Comptes Rendus.

Paris, FR: 249, Part 1, 613-615 & Part 2, 2153-2155.


21 AS M 1959g. Ensembles grand canoniques de Gibbs; justification de leur unicité basée sur la divisibilité infinie de leur énergie aléatoire.

Comptes Rendus. Paris, FR: 249, 1464-1466.
1960
22 M 1960. Processus stochastiques à loi stable positive, permanents, markoviens
et stationnaires (non additifs). Comptes Rendus. Paris, FR: 250, 451-453.
23 E10. M 1960i. The Pareto-Lévy law and the distribution of income.
Int’l Economic Review: 1, 79-106.

• Preliminary report: Au sujet de la distribution de Pareto, relative à la distribution des revenus. Faculté des Sciences de l'Université de Genève, 1956.

• Abbreviated reprint: Mathematics and Social Science I: Proc. of UNESCO Seminars
(Menthon-Saint-Bernard, 1960 and Gösing, 1962), compiled by Saul Sternberg and others.
The Hague, NL: Mouton & Co., 1965, 217-239.

• Privately circulated supplement: Additional note on the distribution of income.

• Reprint: Vilfredo Pareto: Critical Assessments, Ed John C. Wood & Michael McLure London, UK: Routledge, 1999, IV, 155-182.

• Reprint: Income Distribution, Ed Michael Sattinger. The Int’l Library of


Critical Writings in Economics
; Series Ed: Mark Blaug, Cheltenham, UK: Edward Elgar, 2000.
1961
24 M 1961b. On the theory of word frequencies and on related Markovian models of discourse.

Structure of Language and its Mathematical Aspects. New York, 1960. Ed Roman Jakobson (Symposia in Applied Math. XII). Providence R.I.: American Mathematical Society, 190-219.
• Abbreviated reprint: Mathematics and Social Science
(Menthon-Saint Bernard, 1960 & Gösing, 1962) 1965, 241-256.
• Summary: Discussion of a paper by Prof. N. F. Ramsey. Symposium on Critical Review of Thermodynamics. Pittsburgh PA: Ed Edward B. Stuart, Benjamin Gal-Or &
Alan J. Brainard. Baltimore MD: Mono Book Corp. 1970, 230-232.
25 M 1961s. Final note on a class of skew distribution functions (with a post-script).
Information and Control: 4 198-216 & 300-304.
26 E11. M 1961e. Stable Paretian random functions and the multiplicative variation of income. Econometrica: 29, 517-543.
• Reprint: Vilfredo Pareto: Critical Assessments, Ed John C. Wood & Michael McLure.
London, UK: Routledge, 1999, IV, 183-209.
1962
27 E12. M 1962q. Paretian distributions and income maximization.
Quarterly Journal of Economics; 76, 57-85.
• Reprint: Vilfredo Pareto: Critical Assessments, Ed John C. Wood & Michael McLure.
London, UK: Routledge, 1999, IV, 210-240.
28 AS FE9. M 1962c. Sur certains prix spéculatifs: faits empiriques et modèle basé sur les processus stables additifs de Paul Lévy. Comptes Rendus Paris: 254, 3968-3970.

• IBM Report NC-87. The Variation of Certain Speculative Prices. Well beyond cotton prices, this report extends to other commodities, securities, and interest rates. It served as basis for M 1962c, M 1963b, and M 1967j, and was used in BBM’s course at Harvard, Fall 1962.


29 M 1962t. The role of sufficiency and estimation in thermodynamics.
The Annals of Mathematical Statistics: 33, 1021-1038.

• Reprint: Thermodynamics, a Unifying Science. Ed George N. Hatsopoulos &

Joseph H. Keenan. Cambridge MA: MIT Department of Mechanical Engineering, 1964.
1963
30 N6. Jay M. BERGER & M 1963. A new model for the clustering of errors on telephone circuits.
IBM Journal of Research And Development: 7, 224-236.
31 E10. M 1963i. The stable Paretian income distribution, when the apparent exponent is near two. Int’l Economic Review: 4, 111-115.

• Reprint: Vilfredo Pareto: Critical Assessments, Ed John C. Wood & Michael McLure.


London, UK: Routledge, 1999, IV, 236-240.
32 K & P. E3. M 1963e. New methods in statistical economics.
The Journal of Political Economy: 71, 421-440.

• Reprint: Bulletin of the Int’l Statistical Institute, 34th Session, Ottawa: 40,

(book 2), 1964, 699-720.

• Reprint: Vilfredo Pareto: Critical Assessments, Ed John C. Wood & Michael McLure.


London, UK: Routledge, 1999, IV, 241-263.

• Reprint: Forecasting Financial Markets. Ed Terence C. Mills.


The Int’l Library of Critical Writings in Economics. Series Editor: Mark Blaug.
Cheltenham, UK: Edward Elgar, 2002.
33 K & P. E14. M 1963b. The variation of certain speculative prices. The Journal of Business of the University of Chicago: 36, 394-419.

• Photographic reprint followed by discussions by Eugene F. Fama and Paul H. Cootner:


The Random Character of Stock Market Prices. Ed Paul H. Cootner.
Cambridge MA: MIT Press, 1964, 297-337.

E14. Separately published abstract: Econometrica: 31, 1963, 757-758.

E14. Addendum: Linear regression with non-normal error terms: a comment.
Review of Economics and Statistics: 53, 1971, 205.

• Addendum: Correction of an error in “The variation of certain speculative prices”.


Journal of Business of the University of Chicago: 45, 1972, 542-543.

• Citation Classic, that is “a particularly widely quoted work.” Current Contents: 14, 1982, 20.

• Photographic reprint: Futures Markets. Three volumes ed A. G. Malliaris. Cheltenham, UK: Edward Elgar, 1996. 2, 173-198.

• Reprint: Classic Futures: Lessons from the Past for the Electronic Age. Ed Lester Telser.


London, UK: Risk Books. 2000, 649-683.

• Photographic reprint: Financial Econometrics. Three volumes ed Adrew Lo. Cheltenham, UK: Edward Elgar, 2006. 1, 173-198.


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