21. Atlas: Regularity Of (bi) Harmonic Maps By Alice Sun-Yung Chang Regularity of (bi) harmonic maps presented by alice sunyung chang Universityof California at Los Angeles Copyright © 1999 by alice sun-yung chang. http://atlas-conferences.com/c/a/c/b/03.htm

Atlas Document # cacb-03 15th Southeastern Analysis Meeting and Shanks Lecture May 20-23, 1999 Vanderbilt University Nashville, TN, USA Conference Organizers Daoxing Xia, Dechao Zheng and Eric Schechter View Abstracts Conference Homepage Regularity of (bi) harmonic maps presented by Alice Sun-Yung Chang University of California at Los Angeles Harmonic maps are critical points of the energy functional of maps between Riemannian manifolds. Existence and regularity properties of the map have been a subject of intensive study in geometric analysis. A remarkable result of Helein in 1990 establishes that any weak harmonic map defined on a surface is already smooth. The original proof of Helein replies on a compensated compactness argument of Coifman-Lions-Meyer-Semmes, which in turn is a consequence of the duality of H and BMO. In this talk, I will survey results in this field, give a simpler proof of the result of Helein when the target manifold of the map is a sphere and discuss the extension of the regularity results to bi-harmonic maps. Date received: February 1, 1999

22. Atlas: 15th Southeastern Analysis Meeting And Shanks Lecture - List Of Speakers dilations and operator model theory for row contractions James T. Campbell Oscillationin ergodic theory Singular Integrals alice sunyung chang Regularity of http://atlas-conferences.com/c/a/c/b/01.htm

Atlas home Conferences Abstracts Travel ... about Atlas 15th Southeastern Analysis Meeting and Shanks Lecture May 20-23, 1999 Vanderbilt University Nashville, TN, USA Conference Organizers Daoxing Xia, Dechao Zheng and Eric Schechter Conference Homepage View Abstracts This is an archive of abstracts accepted to this conference. For more listing and sorting options, see the dynamic list. Ariyadasa Aluthge Bill Arveson The curvature invariant in multivariable operator theory I, II Sheldon Axler Harmonic Approximation Joseph A. Ball Multivariable linear systems, scattering, unitary dilations and operator model theory for row contractions James T. Campbell Oscillation in ergodic theory: Singular Integrals Alice Sun-Yung Chang Regularity of (bi) harmonic maps Joseph A. Cima An integral operator on H p Bruce Crofoot Zeros of Harmonic Polynomials Truncated Moment Problems for the Unit Disk and Unit Circle Ronald G. Douglas Geometry of Quotient Hilbert Modules Jingde Du A Product Formula for Localization Operators Nathan S. Feldman Subnormal Operators with Hypercyclic Adjoints Caixing Gu Separation for Kernels of Hankel Operators Archil Gulisashvili Hulls and kernels of function classes and behavior of the Fourier transform Mark C. Ho

23. Visitor sunyung alice chang ?. Professor. Department of MathematicsPrinceton University UCLA Princeton, NJ 08540, LA CA 90095 USA. http://math.cts.nthu.edu.tw/Mathematics/conf-PDE2000/SY_Chang.html

Sun-Yung Alice Chang ±i¸t®e Professor Department of Mathematics U.S.A. E-mail: chang@math.princeton.edu Research Interest Geometric Differential Equations Field of Research Geometric Analysis

24. Visitor sunyung alice chang ?. Professor. Department of Mathematics PrincetonUniversity Princeton, NJ 08540 USA. E-mail chang@math.princeton.edu. http://math.cts.nthu.edu.tw/Mathematics/visit_pro/SY_Chang.html

Sun-Yung Alice Chang ±i¸t®e Professor Department of Mathematics Princeton University Princeton, NJ 08540 USA E-mail : chang@math.princeton.edu Personal homepage : http://www.math.princeton.edu/~chang Current Research Interest Geometric Differential Equations Field of Research Geometric Analysis Preprints / Publications (selective) http://www.math.princeton.edu/~chang Visiting Mathematicians [ 2000/2001 ] Visiting Mathematicians [ 2001/2002 ]

25. Chang Mathematician sunyung alice chang. Born 24 March 24, 1948, Ci-an,China. sun-yung alice chang studied at the National University http://members.fortunecity.com/jonhays/Chang.html

Mathematician: Sun-Yung Alice Chang Born: 24 March 24, 1948, Ci-an, China. Sun-Yung Alice Chang studied at the National University of Taiwan, receiving her B.S. in 1970, then traveled to the U.S. to study for her doctorate. In 1974 awarded Ph.D. from the University of California, Berkeley. Chang was appointed assistant professor at the State University of New York at Buffalo, 1974-1975. Then Hedrick Assistant Professor at the University of California at Los Angeles until 1977 when she moved to the University of Maryland as an assistant professor. A Sloan Fellow, 1979-1980. Returned 1980 to the University of California at Los Angeles as an associate professor, later promoted to full professor. Invited speaker at the International Congress of Mathematicians at Berkeley in 1986. During 1988-1989 also a full professor at the University of California, Berkeley. Chang's research interests include the study of certain geometric types of nonlinear partial differential equations. Also the related extremal inequalities and problems in isospectral geometry. Perhaps Chang's greatest honour was the 1995 Ruth Lyttle Satter Prize in Mathematics, awarded every two years to a womanwho has made an outstanding contribution to mathematics research in the previous five years. The award is valued at $4,000. The citation for the prize read:-

26. Our Greatest Supporters Chai, Eric Y. Chan, Patrick SY and Lily Lioe chang, Bonnie chang, ChiChen chang,Robert S. chang, sun-yung alice and Paul C. Yang Chen, (Bob and Grace) Robert http://www.80-20initiative.net/donors.htm

Founders Associate Founders Founding Benefactors Founding Patrons Founders Kenneth and Pamela Fong James (Jamie) Jien-Chung Chu and Family Chenming and Margaret S. Hu May So and Family Chang-Lin and Di Hwa Tien Shien-Biau and Katy Woo Y. C. Yang Associate Founders Chen, Fred Y. and Sarah W. Chu, Chieh and Kwen-Hwa Foung, Shirley H. and Alfred C. Hsu, Ta Lin Ko, Stephen Kung, Hsing-Hsien and Margaret Mok Lin, Tung Yen and Margaret Sung, Chien-Bor and Beulah To, Kathleen Woo, Mr. and Mrs. C. K. Founding Benefactors Chang, Barry Chang, Edward Chang, Gareth Chang, James N. Chang, Shung-Ho and Rong Juh Cheng, Dunson Cheng, Leonard K. and Jenny L. Cheng, Mei-Wei Cheng, Ying-Ming and Wanny K. Chi, Lois Wong and Henry Chin, Carolyn Chou, Ber-Dy Chou, Helen Chow, Wai Ming Chu, David Lawrence Chu, Paul Fan, Weili and Zhang, Jerry Fang, Florence Fann, Phin-Jan and Shaw-Wen Gee, George Ho, Frederick Y.S. and Lily Ho, Sophia and Larry Yu-Chi Hsia, Alice Hsiao, Fred and Jennie Hsu, Thomas T. C. and Laura H. N. Huang, Albert Huang, Alex Y. P. Huang, Alice Huang, Fen Ho

27. Membership List chang, NgeePong and Mabel chang, Paul L, chang, Robert chang, Ruth E. chang,Stephen and Sun, Deborah chang, sun-yung alice and Paul Chien-Ping chang, Ta http://www.80-20initiative.net/memberlist.html

80-20 Membership List (updated 12/05/02) IMPORTANT: If you are a member, please make sure your name appears on this list. If not, email us (jingliyu@earthlink.net to correct our mistake. (dues payments by check may take three weeks to process) If you have paid dues on a family membership, and only one name appears below, please email us with the name of the second person in your family with voting rights ( required If there is a symbol (*, , # or %) next to your name, it means there is something missing in your records. See below to understand the meaning of those symbols: ) by your name means: please email us your email address (for identification purposes, please include your postal address). 2. (*) by your name means: please email us with your postal address. 3. (#) by your name means: email us with the second member's email address, if there is one. (optional) 4. (%) by your name means: email us your employer name and occupation (required by the FEC). 5. (^) by your name: you joined after 8/15/2002, the last date eligible to vote in this year's election. Members with last names starting with - A - Abboud, Deedra

28. Princeton - Graduate School Announcement 2002-03 - Department Of Mathematics Department of Mathematics. Chair Nicholas M. Katz. Directors of GraduateStudies sunyung alice chang Jordan Ellenberg. Professors http://www.princeton.edu/pr/catalog/gsa/02/306.htm

Princeton University Graduate School Announcement 2002-03 prev contents next Department of Mathematics Chair Nicholas M. Katz Directors of Graduate Studies Sun-Yung Alice Chang Jordan Ellenberg Professors Michael Aizenman, also Physics William Browder Sun-Yung Alice Chang John H. Conway Ingrid Daubechies Weinan E Bjorn Engquist, also Program in Applied and Computational Mathematics Charles L. Fefferman David Gabai Robert C. Gunning Wu-chung Hsiang Nicholas M. Katz Sergiu Klainerman Simon B. Kochen Joseph J. Kohn Elliott H. Lieb, also Physics John N. Mather Edward Nelson Andrei Okounkov Rahul Pandharipande Peter C. Sarnak Paul Seymour Yakov G. Sinai Elias M. Stein Andrew J. Wiles Paul C. Yang Assistant Professors Jinho Baik Jordan S. Ellenberg Wee Teck Gan Leonid Koralov Denis Kosygin Yi-Jen Lee Tian-Jun Li Hee Oh Igor Rodnianski John Stalker Benjamin Sudakov Instructors Simon Brendle Samuel Grushevsky Nadya Gurevich Paul Hagelstein Fengbo Hang Jonathan Hanke Steven J. Miller

29. Princeton - PWB 060898 - Six Join Tenured Faculty The trustees have approved the appointments of four professors Kofi Agawu, PatrickBolton, sunyung alice chang and Peter Singer and the promotion of two http://www.princeton.edu/pr/pwb/98/0608/0608-1c.html

Princeton Weekly Bulletin June 8, 1998 Six join tenured faculty The trustees have approved the appointments of four professors Kofi Agawu, Patrick Bolton, Sun-Yung Alice Chang and Peter Singer and the promotion of two Kevan Shokat and Bruce Western to the tenured position of associate professor. All appointments begin July 1 except Singer's, which begins July 1, 1999. Agawu, professor of music, works in the areas of music analysis and theory, semiotics and music, music of the 19th century, and West African music. He has diplomas in musicianship, theory and the teaching of singing from the Royal Academy of Music, as well as a 1977 BA from Reading University, a 1978 MMus from Kings's College, London, and a 1982 PhD from Stanford University. Currently visiting scholar at the University of Ghana, he has been a professor at Yale since 1995. He previously taught at Cornell for six years, at King's College, London for three, at Duke for one and at Haverford College for two years. Among his many publications are African Rhythm: A Northern Ewe Perspective (1995) and Playing with Signs: A Semiotic Interpretation of Classic Music (1991), which won the 1994 Society for Music Theory Young Scholar Award. A Guggenheim Fellow in 199091, Agawu received the 1992 Dent Medal from the Royal Musical Association and the International Musicological Society.

30. NSF-CBMS Conference On "Spectral Problems In Geometry And Arithmetic": Schedule 1100 sunyung alice chang, UCLA Log determinant formula and somerelated problems in conformal geometry, I. Tuesday, August 19 http://www.math.uiowa.edu/faculty/cbsch.html

NSF-CBMS Conference on "Spectral Problems in Geometry and Arithmetic": Schedule Monday, August 18: Morning session in Van Allen 301 9:00 Registration 10:00 Peter Sarnak, Princeton University: "Spectral problems in geometry and arithmetic," I 11:00 Scott Wolpert, University of Maryland: "High-energy limits of automorphic eigenfunctions" Monday, August 18: Afternoon session in Van Allen 70 2:00 Charles Radin, University of Texas: "Geometry of tilings" 3:30 Peter Sarnak: "Spectral problems in geometry and arithmetic," II Tuesday, August 19: Morning session in Van Allen 301 10:00 Peter Sarnak: "Spectral problems in geometry and arithmetic," III 11:00 Sun-Yung Alice Chang, UCLA: "Log determinant formula and some related problems in conformal geometry," I Tuesday, August 19: Afternoon session in Van Allen 70 2:00 Harold Widom, UC Santa Cruz: "Asymptotics of a class of Fredholm determinants" 3:30 Peter Sarnak: "Spectral problems in geometry and arithmetic," IV Wednesday, August 20: Morning session in Van Allen 301 10:00 Peter Sarnak: "Spectral problems in geometry and arithmetic," V

31. Spectral Problems In Geometry And Arithmetic Additional speakers sunyung alice chang, Jeffrey Lagarias, Michel Lapidus, KateOkikiolu, Gilles Pisier, Charles Radin, Alain Valette, Harold Widom, Scott http://www.math.uiowa.edu/faculty/cbms.html

"Spectral Problems in Geometry and Arithmetic" http://www.math.uiowa.edu/faculty/cbms.html An NSF-CBMS Regional Research Conference Principal speaker Peter Sarnak Additional speakers: Sun-Yung Alice Chang, Jeffrey Lagarias, Michel Lapidus, Kate Okikiolu, Gilles Pisier, Charles Radin, Alain Valette, Harold Widom, Scott Wolpert, Paul Yang University of Iowa August 18-22, 1997 Organizing Committee: Thomas Branson Charles Frohman Palle Jorgensen Florin Radulescu ... Tentative schedule The spectral theory of operators (Laplacians, invariant differential operators, Hecke operators) on locally symmetric spaces is central to modern automorphic form theory and its applications to number theory. It has also become of interest to physicists working in quantum chaos (as models of quantizations of classically chaotic Hamiltonians). These lectures will be devoted mostly to these spectral problems, with a brief indication as to applications. The main topics will be 1. Exceptional spectrum (i.e. small or low energy eigenvalues), which essentially is the issue of the general Ramanujan Conjectures. 2. Random matrix theory and eigenvalue distributions of matrices from the classical groups.

32. Sun-Yung Alice Change Was Born March 24th, 1948 In Ci-an, China sunyung alice chang. sun-yung alice change was born March 24 th ,1948 in Ci-an, China. She grew up in Taiwan, having moved there http://www.ithaca.edu/osman/Courses/134Fa02/hw/history/chang/chang.html

Sun-Yung Alice Chang Sun-Yung Alice Change was born March 24 th , 1948 in Ci-an, China. She grew up in Taiwan, having moved there with her family shortly after the Chinese revolution. She studied at the National University of Taiwan and received her Bachelor of Arts from there in 1970. She attended graduate school at University of California. In 1974, after writing her thesis under the supervision of Donald Sarason, she was awarded her Ph.D. Chang was appointed an assistant professor at the State University of New York at Buffalo. In 1975 she was appointed Assistant Professor at the University of California in Los Angeles and remained there until 1977 when she moved to the University of Maryland. In 1980 Chang returned to the University of California at Los Angeles and was promoted to full professor in 1982. She was an invited speaker at the International Congress of Mathematicians in Berkeley in 1986. During the academic school year of 88-89 she was also a full professor at the University of California, Berkeley. Since 1998 she has also been a Professor at Princeton University.

33. Weekly Events 010603 sunyung alice chang (Princeton University) Non-linear partial differentialequations in conformal geometry . January 6 - 10, 2003 http://www.math.uci.edu/w2.html

Weekly Events for this Quarter Select Week Week of ... Jan. 2 - 3, 2003 Jan. 6 - 10, 2003 Jan. 13 - 17, 2003 Jan. 20 - 24, 2003 Jan. 27 - 31, 2003 Feb. 3 - 7, 2003 Feb. 10 - 14, 2003 Feb. 17 - 21, 2003 Feb. 24 - 28, 2003 Mar. 3 - 7, 2003 Mar. 10 - 14, 2003 Mar. 17 - 21, 2003 Previous Next SPECIAL COLLOQUIUM Tuesday, January 7 4:00PM in MSTB 254 Speaker: Chuu-Lian Terng (Northeastern University) "Geometry of soliton equations, classical examples and some new results " DISTINGUISHED LECTURE Thursday, January 9 4:00PM in MSTB 254 Speaker: Prof. Sun-Yung Alice Chang (Princeton University) "Non-linear partial differential equations in conformal geometry" January 6 - 10, 2003 DATE LOCATION SPEAKER TITLE MONDAY (Jan. 6) in MSTB 254. Prof. Jack Xin (University of of Texas, Austin) Abstract Computation and Analysis of a Nonlinear Nonlocal Cochlear Model with Applications in Hearing TUESDAY (Jan. 7) in MSTB 254. V. Boutchakchiev (UC Irvine) ALGEBRA SEMINAR Title: TBA. in MSTB 254. Prof. Chuu-Lian Terng (Northeastern University) SPECIAL COLLOQUIUM * Abstract Geometry of soliton equations, classical examples and some new results

34. PJM Editors EDITORS. sunyung alice chang. Department of Mathematics. Princeton University. Princeton,NJ 08544. chang@math.princeton.edu. Darren Long. Department of Mathematics. http://www.math.uci.edu/~rstern/pjm/editors.html

Pacific Journal of Mathematics MANAGING EDITOR V. S. Varadarajan Department of Mathematics University of California Los Angeles, CA 90095-1555 pacific@math.ucla.edu EDITORS Sun-Yung Alice Chang Department of Mathematics Princeton University Princeton, NJ 08544 chang@math.princeton.edu Darren Long Department of Mathematics University of California, Santa Barbara Santa Barbara, CA 93106-3080 long@math.ucsb.edu Jonathon Rogawski Department of Mathematics University of California Los Angeles, CA 90095-1555 jonr@math.ucla.edu Robert Finn Department of Mathematics Stanford University Stanford, CA 94305 finn@gauss.stanford.edu Kefeng Liu Department of Mathematics University of California Los Angeles, CA 90095-1555 liu@math.ucla.edu Dan Voiculescu Department of Mathematics University of California Berkeley, CA 94720 dvv@math.berkeley.edu Robert Guralnick University of Southern California Department of Mathematics Los Angeles, CA guralnic@math.usc.edu Jiang-Hua Lu Department of Mathematics University of Arizona Tucson, AZ 85721

35. Katherine Okikiolu - Mathematicians Of The African Diaspora There, she worked with two mentors, sunyung (alice) chang and John Garnett, andwas able to solve a problem concerning asymptotics of determinants of Toeplitz http://www.math.buffalo.edu/mad/PEEPS/okikiolu_katherine.html

Katherine Adebola Okikiolu born: 1965; place: England Cambridge University University of California at Los Angeles (1991) thesis: The Analogue of the Strong Szego Limit Theorem on the Torus and the 3-Sphere Advisor 1: Sun-Yung Chang; Advisor 2: John Garnett Associate Professor of Mathematics University of California at San Diego web page: http://math.ucsd.edu/~okikiolu/ office phone: office phone is (858) 534-2772 2002 Claytor-Woodard lecturer Okikiolu comes from a mathematical family, her father is a mathematician and inventor and her mother is a high school mathematics teacher. Her parents met when her father left Nigeria to study mathematics at the same college in England where her mother was studying physics. Her father, the Nigerian George Okikiolu , has written more mathematics papers than any other Black mathematician. She is married to mathematican Hans Lindblad. Okikiolu earned her B.A. in Mathematics from Cambridge University in England before coming to the United States in 1987 to attend graduate school mathematics at UCLA (the University of California, Los Angeles). There, she worked with two mentors, Sun-Yung (Alice) Chang and John Garnett, and was able to solve a problem concerning asymptotics of determinants of Toeplitz operators on the sphere and a conjecture of Peter Jones, characterizing subsets of rectifiable curves in Euclidean n-space. She earned her Ph.D. at UCLA in 1991, and she has been exhibiting first rate mathematical abilties.

36. Matemáticos De Nuestro Tiempo (2) Translate this page sun-yung alice chang Ecuaciones no lineales en derivadas parciales, Geometriaisospectral, Variedades riemanianas, Condiciones en problemas de extremales. http://personales.ya.com/casanchi/ref/matematicos02.htm

Más artículos de reflexiones MATEMÁTICOS DE NUESTRO TIEMPO La matemática actual tiene abiertos fecundos campos de un gran interés. Los grandes matemáticos de la segunda mitad del siglo XX y hasta nuestros días intentan el desarrollo de una matemática acorde con el tiempo en que vivimos, capaz de afrontar el reto que representa la tendencia social tanto como el progreso de las necesidades computacionales de las nuevas ingenierías o el avance vertiginoso de algunas disciplinas como la Astrofísica y la Computación Teórica. Mostramos aqui algunas referencias a su trabajo, utilizando diversas fuentes de datos, entre las que podemos destacar, por su excelente documentación, la base de datos de la Universidad de St. Andrews, Escocia. Es una somera indicación del quehacer en la disciplina de matemáticos de extraordinaria calidad, algunos de ellos prematuramente fallecidos, que nacieron en los últimos años de la década de los 40, en plena devastación, terminada ya la Segunda Guerra Mundial. John Henry Coates (26/01/1945, Nueva Gales del Sur, Australia)

37. Women's Program Site Ranee Brylinski Pennsylvania State University sunyung alice chang Princeton UniversityIngrid Daubechies Princeton University Joan Feigenbaum Yale University http://www.math.ias.edu/womensprogram/About/committee.html

Program Organizers Mary Pugh University of Toronto Karen Uhlenbeck University of Texas at Austin Program Committee: Ranee Brylinski Pennsylvania State University Sun-Yung Alice Chang Princeton University Ingrid Daubechies Princeton University Joan Feigenbaum Yale University Antonella Grassi University of Pennsylvania Nancy Hingston The College of New Jersey Rhonda Hughes Bryn Mawr College Robert MacPherson Institute for Advanced Study Cynthia Diane Rudin Princeton University Janet Talvacchia Swarthmore College Lisa Traynor Bryn Mawr College Click to Enlarge Program for Women in Mathematics Institute for Advanced Study Einstein Drive Princeton, New Jersey 08540 womensprogram@math.ias.edu

38. WSU Math Department Colloquium 200203 Owens Lectures sun-yung alice chang, Princeton University. Mar3, Non-Linear partial differential equations in conformal geometry. http://www.math.wayne.edu/research/seminars/colloq.html

Department of Mathematics Colloquium 2002-03 Wayne State University College of Science The Mathematics Department Colloquium meets every Monday at 2:45 PM, in 155 Education, with tea at 2 PM in the Nelson Library. Occasionally, the meeting will be moved to another day to accomodate special circumstances. For information, contact Guozhen Lu or Robert Bruner. 2002-03 Owens Lectures by Alice Chang All seminars Mathematics Department home page ... Fall semester talks Winter Semester Jan 13 David Hemmer, University of Georgia Specht module filtrations for representations of the symmetric group abstract Tuesday Jan 14 Yanyan Li, Rutgers University On some conformally invariant fully nonlinear equations. abstract Jan 20 Martin Luther King holiday: no colloquium is scheduled. Wednesday Jan 22 Natalia Stepanova, Queen's University Multivariate Kendall's and Spearman's tests for independence and their asymptotic efficiency abstract Jan 27 John Conway, Princeton University Not hearing the shape of things abstract Wednesday Jan 29 Dan Isaksen

39. WSU New Seminar 20023 Owens Lectures Prof. sun-yung alice chang, Princeton University.Mar 3, Non-Linear partial differential equations in conformal geometry. http://www.math.wayne.edu/research/seminars/newsem.html

Department of Mathematics What's New in ... Seminar or Is there life after mathematics courses? Wayne State University College of Science This seminar is designed for advanced undergraduates and beginning graduate students. All talks are held Tuesday at 3:00 PM in 169 Education, unless otherwise noted. NOTE THE ROOM CHANGE FROM LAST SEMESTER! A snack is planned afterward in 1140 FAB, the Mathematics Department Nelson Library. Contact Lowell Hansen for more information or to volunteer to speak. All seminars Colloquium Mathematics Department home page Date Speaker and Title September 17, 2002 Yaniv Gershon , student, Wayne State Mathematics Optimal Pricing Strategy in Differentiated Durable-Goods Markets ABSTRACT September 24, 2002

40. SAGP David Borthwick, Emory sunyung alice chang, Princeton Harold Donnelly, PurdueStuart Dowker, University of Manchester Fan Chung Graham, University of http://math104.ucsd.edu/Deptinfo/SAGP/speakers.html

CONFIRMED LIST OF SPEAKERS TO DATE David Borthwick, Emory Sun-Yung Alice Chang, Princeton Harold Donnelly, Purdue Stuart Dowker, University of Manchester Fan Chung Graham, University of California, San Diego Robin Graham, University of Washington Svetlana Jitomirskaya,University of California, Irvine ... Peter Perry, University of Kentucky, Lexington Peter Sarnak, Princeton and The Courant Institute Gang Tian, Massachusetts Institute of Technology Audrey Terras, University of California, San Diego page updated 12/23/02

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