41. Brief History Of Pi Calculations -- From Harry J. Smith Yasumasa Kanada Computer Centre, University of Tokyo Bunkyoku Yayoi 2-11-16Tokyo 113 Japan Fax +81-3-3814-7231 (office) E-mail http://www.geocities.com/hjsmithh/Pi/Records.html

Brief History of Pi Calculations From: http://oldweb.cecm.sfu.ca/projects/ISC/Pihistory.html Table of computation of Pi from 2000 BC to 1900 AD From: ftp://pi.super-computing.org/windows/super_pi.zip Brief history of Pi calculation with computers Return to Computing Pi Return to Harry's Home Page This page accessed times since October 20, 2004. Page created by: hjsmithh@sbcglobal.net Changes last made on Sunday, 17-Jul-05 13:44:01 PDT

42. Hashing LEMMAs On Time Complexities With Applications To Formula Manipulation Eiichi Goto Yasumasa Kanada 8 Y. Kanada, Tech. Rep. 7501, ISD, 1975. 9 F.Motoyoshi, Tech. Rep. 76-05, ISD, 1976. 10 M. Terashima, Tech. Rep. http://portal.acm.org/citation.cfm?id=806334

43. Parallelism In Algebraic Computation And Parallel Algorithms For Symbolic Linear Tateaki Sasaki Yasumasa Kanada 13 Sasaki, T., Kanada, Y. and Watanabe,S., Calculation of Discriminants of High Degree Equations, Tokyo J. Math., http://portal.acm.org/citation.cfm?id=806388

44. Past Calculations Of Pi 1995, Yasumasa Kanada, 6442450000, 116 hours, about 0.00006 seconds. 1997,Yasumasa Kanada and D. Takahashi, HITACHI SR2201, 51539600000 http://people.bath.ac.uk/slt20/times.html

Past calculations of pi Year Mathematician(s) Computer Number of digits Time Time per digit Ludolph van Ceulen (by hand) Machin (by hand) Wm. Shanks (by hand) ~ 15 years 1 week Richter (by hand) Johann Dase (by hand) 7 hours D. F. Ferguson, Wrench desk calculator ~ 1 year 11 hours Smith, Wrench desk calculator U.S. Army ENIAC (Electronic Numerical Intergrator and Computer) 70 hours 2 minutes S. C. Nicholson, J. Jeenel NORC 13 minutes 0.25 seconds Felton Pegasus F. Genuys IBM 704 100 minutes 0.6 seconds D. Shanks, J. W. Wrench IBM 7090 8.72 hours 1/3 seconds J. Guilloud and Bouyer CDC 7600 23.3 hours 1/12 seconds Y. Tamura, Yasumasa Kanada HITAC M-28OH D. H. Bailey, NASA Cray-2 28 hours Yasumasa Kanada Hitachi S-810/820 8 hours Yasumasa Kanada, Tamura, Kubo NEC SX-2 Yasumasa Kanada Hitachi S-820 6 hours Chudnovsky brothers Chudnovsky brothers m zero Yasumasa Kanada 116 hours about 0.00006 seconds Yasumasa Kanada and D. Takahashi HITACHI SR2201 29 hours and 7 minutes about 0.000002 seconds Yasumasa Kanada and D. Takahashi HITACHI SR8000 Project home page History Archimedes' method Approximations ... Bibliography

45. Sci.math FAQ: Digits Or Pi The current record is held by Yasumasa Kanada and Daisuke Takahashi from theUniversity of Tokyo with 51 billion digits of pi (51539600000 decimal digits to http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/pi.html

Note from archiver cs.uu.nl: This page is part of a big collection of Usenet postings, archived here for your convenience. For matters concerning the content of this page , please contact its author(s); use the source , if all else fails. For matters concerning the archive as a whole, please refer to the archive description or contact the archiver. Subject: sci.math FAQ: Digits or Pi This article was archived around: 17 Feb 2000 22:51:58 GMT All FAQs in Directory: sci-math-faq All FAQs posted in: sci.math Source: Usenet Version Archive-name: sci-math-faq/pi Last-modified: February 20, 1998 Version: 7.5 http://www.users.globalnet.co.uk/ http://www.cecm.sfu.ca/~pborwein http://www.cs.unb.ca/~alopez-o Assistant Professor Faculty of Computer Science University of New Brunswick

46. ScienceNow Yasumasa Kanada and colleagues at the University of Tokyo recently announced thecompletion of a calculation of 1.241 trillion digits of mathematicians http://bric.postech.ac.kr/science/97now/02_12now/021216a.html

16 December 2002 Pi in the Sky The precision of pi has passed the trillion-digit marka sixfold increase over the previous record. Yasumasa Kanada and colleagues at the University of Tokyo recently announced the completion of a calculation of 1.241 trillion digits of mathematicians' favorite constant, 3.14159? Kanada is the world's unquestioned pi king these dayshe and his team have set virtually all the records since the mid-1980s. Their last one, in 1999, reached 206 billion digits. The latest calculation took over 400 hours on a Hitachi supercomputer. The programs for doing all the high-precision arithmetic, Kanada reports, were 5 years in the making. To nail down their result, the group actually computed pi with two different formulas. What insights do all these digits offer? Not many, says David Bailey, a mathematician at Lawrence Berkeley National Laboratory, who computed a then-record 29 million digits in 1986. Pi primarily provides a convenient benchmark for measuring machines' ability to juggle huge numerical data sets quickly and accurately. BARRY CIPRA Related sites Kanada's Web site Computing Pi More Pi pages on the Web

47. How To Compute Digits Of Pi ? The current record is held by Yasumasa Kanada and Daisuke Takahashi from the This computations were made by Yasumasa Kanada, at the University of Tokyo. http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node12.html

Next: Euler's formula: e^(i pi) Up: Special Numbers and Functions Previous: Special Numbers and Functions How to compute digits of pi ? Symbolic Computation software such as Maple or Mathematica can compute 10,000 digits of pi in a blink, and another 20,000-1,000,000 digits overnight (range depends on hardware platform). It is possible to retrieve 1.25+ million digits of pi via anonymous ftp from the site wuarchive.wustl.edu, in the files pi.doc.Z and pi.dat.Z which reside in subdirectory doc/misc/pi. New York's Chudnovsky brothers have computed 2 billion digits of pi on a homebrew computer. The current record is held by Yasumasa Kanada and Daisuke Takahashi from the University of Tokyo with 51 billion digits of pi (51,539,600,000 decimal digits to be precise). Nick Johnson-Hill has an interesting page of  pi trivia at: http://www.users.globalnet.co.uk/ nickjh/Pi.htm This computations were made by Yasumasa Kanada, at the University of Tokyo. There are essentially 3 different methods to calculate pi to many decimals.

48. Untitled Document In 1999, Yasumasa Kanada and his colleagues at the University of Tokyo computedpi to a record Kanada, Yasumasa. 1999. Pi News by Kanada Laboratory. http://www.sssgrp.com/Menu/Products/readmepi.html

S OCIAL S YSTEMS S IMULATION G ROUP E-mail: rwerner@sssgrp.com Readme Pi 400 M Digits of Pi Readme.txt Roland Werner, Ph.D. Master Model Maker Social Systems Simulation Group http://www.sssgrp.com Contents 1. Source of Digits 2. Source of Artwork 3. Organization of the CD 4. Some Observations 5. References 6. Other Interesting Links 1. Source of Digits I would like to acknowledge Mr. Aoki Mitsuru, High Energy Physics Laboratory, Nagoya University, http://www.hepl.phys.nagoya-u.ac.jp/~mitsuru/pi-e.html , for posting 400 million digits of Pi (excluding the first digit, 3) in manageable groups of 10 million digits. This computation of Pi was made around May 1998. 2. Source of Artwork I would like to acknowledge Ms. Eve A. Andersson, cofounder of ArsDigita an open-source enterprise software company, http://www.arsdigita.com , for providing the inspiration to the artwork for the jewel case and the CD. 3. Organization of the CD Files on this beta version CD: (Java programs are currently under development; 02/2002.) Readme.txt

49. New Page 1 The current world record is held by Yasumasa Kanada of the University of Tokyo,who in 1999 calculated to 206158430000 decimal places using a computer http://www.stanford.edu/~wavelet/pi/pi.html

Due to popular demand, I have decided to put the page from my old website onto here too..... For those who don't know, I once memorized pi to 2002 decimal places (you can say I was bored). I am even listed on the 1000-Club on Olle the Great's web site. I have now forgotten all but around the first 100 decimal places or so. A Treatise on Pi The number has always been my favourite number because of its unparalleled aesthetic beauty. On this page, I shall provide an overview of this extraordinary number: its history, properties, and its interesting facts. History of Pi Ancient History is perhaps the most famous ratio in mathematics. It is defined as the ratio between the circumference of a circle and its diameter. Throughout the ages, mathematicians have strived to find the value of . One of the earliest reference to was recorded in the Rhind Papyrus during the Egyptian Middle Kingdom, and was written by a scribe named Ahmes around 1650 BC. Ahmes began the scroll with the words: "The Entrance Into the Knowledge of All Existing Things", and made passing remarks that he composed the scroll "in likeness to writings made of old." Towards the end of the scroll, which comprises of various mathematical problems and their solutions, the area of a circle is found using a rough sort of It is interesting to note that the number is also indrectly quoted in the Bible. There is a little-known verse that reads

50. Einführung In Die Berechnung Von Pi: Record For Pi - 51.5 Billion Decimal Digit From Kanada@pi.cc.utokyo.ac.jp (Yasumasa Kanada) Subject New world record ofpi 51.5 billion Yasumasa Kanada, Computer Centre, University of Tokyo http://www.uni-leipzig.de/~sma/pi_einfuehrung/record51.html

From: kanada@pi.cc.u-tokyo.ac.jp (Yasumasa KANADA) Subject: New world record of pi : 51.5 billion decimal digits Dear pi people; Now is the time for the announcement of new world record of pi. It took longer time than our expectation. Nearly two years has passed since we got new world record of 6.4 billion. Now, we got eight times more record than 6.4 billion as the following texts which you can get with anonymous ftp to 'www.cc.u-tokyo.ac.jp' Yasumasa KANADA , Computer Centre, University of Tokyo Our latest record was established as follows: Declared record: 51,539,600,000 decimal digits Yasumasa KANADA and Daisuke TAKAHASHI Two independent calculations based on two different algorithms generated 51,539,607,552 (=3*2^34) decimal digits of pi and comparison of two generated sequences matched 51,539,607,510 decimal digits, e.g., a 42 decimal digits difference. Then we are declaring 51,539,600,000 decimal digits as the new world record. ( See related lecture on Pi Main program run: Job start : 6th June 1997 22:29:06 Job end : 8th June 1997 03:32:17 Elapsed time : 29:03:11 Main memory : 212 GB Algorithm : Borweins' 4-th order convergent algorithm Verification program run Job start : 4th July 1997 22:11:42 Job end : 6th July 1997 11:19:58 Elapsed time : 37:08:16 Main memory : 188 GB Algorithm : Gauss-Legendre algorithm (Brent-Salamin) Optimized main program run Job start : 1st Augst 1997 23:04:15 Job end : 3rd Augst 1997 00:18:47

51. Pi Statistics The FTP server from the record calculation team of Yasumasa Kanada serves freeavailable data up to 4.2 billion digits. To proof the download correctness http://piworld.de/pi-statistics/

p Statistics for 4.2 x 10 decimal digits by JVSchmidt (September 2003) Motivation for p mining p is a surprising number. Over hundreds of years mathematicians have found dozens of presentations and armies of formulas to compute the value of Ludolph's number. Regardless of this fact any new record in p calculation demonstrates the randomness of the digit series. Frequency analysis of these results didn't point out any order in these sequences. So, how do welldefinied formulas produce random output? David Bailey and Richard Crandall are working on a proof that the famous BBP-formula for the hexadecimal presentation of a certain PI-digit generates randomizes digits. The exact mathematical proof for p 's "randomness" ist not given yet. Thus any deeper statistical examination of known PI sequences could be helpful. The results of those tests so far are suprisingly poor. Most of them present even digit counts. Others are based on a small data material only. Nowadays an ordinary home pc can manage hugh raw material. And since I am p -minded for a long time (see also MAGIC PIWORLD ) the decision was made to set my computer on the trail. Results presented as follow are derived with a selfwritten statanalyzing program on a 4.2 billion

52. Library2 Kanada, Yasumasa One Divided by Pi, 13914 , 403 pages, Octavo , $8.50 SCIENCEAND MEDICINE Add to Cart. Kandinsky, Wassily Concerning the Spiritual in Art, http://www.dngoodchild.com/lib2/cat3w_k.htm

Return to Index Author Search "Add to Cart" doesn't work ? SEE THIS MESSAGE K Jump interpage using links below (no respone means no item beginning thus.) Ke Ki Kl Ko ... Ku Kafka, Franz Metamorphosis, 92 pages, Octavo,HdCvr,DJ , FICTION Add to Cart Kailas, Uuno Tuuli ja Tahka ynna Muita Runoja, 51 pages, Booklet , POETRY Add to Cart Kalidasa, Sakoontala or The Lost Ring, 326 pages, Octavo,HdCvr,DJ , DRAMA AND THE THEATRE Add to Cart Kamban, Godmunder Hadda Padda, 115 pages, Octavo,HdCvr,DJ , DRAMA AND THE THEATRE Add to Cart Kanada, Yasumasa One Divided by Pi, 403 pages, Octavo,HdCvr,DJ , SCIENCE AND MEDICINE Add to Cart Kandinsky, Wassily Concerning the Spiritual in Art, 121 pages, Octavo,HdCvr,DJ , ART Add to Cart Kane, William Terence For Greater Things, 90 pages, Octavo,HdCvr,DJ , RELIGION Add to Cart Kant, Immanuel Critique of Pure Reason, The, 508 pages, Octavo,HdCvr,DJ , PHILOSOPHY Add to Cart Fundamental Principals of the Metaphywic of Morals, 135 pages, Octavo,HdCvr,DJ

53. The Mad Cybrarian's Library: Free Online E-texts - Authors K-Kz Kanada, Yasumasa. One Divided by pi (SUBJECT Mathematics Math 21 to a milliondigits ) Gutenberg FTP UITXT 996 Kb ZIP477 Kb SLTXT - ZIP ENTXT - http://www.fortunecity.com/victorian/richmond/88/1libk.htm

web hosting domain names photo sharing The Mad Cybrarian's Library Authors: K-Kz Kanada, Yasumasa One Divided by pi (SUBJECT: Mathematics Math #21 to a million digits ) TXT 996 Kb - ZIP 477 Kb SL: TXT ZIP EN: TXT ZIP Kane, Eliza: Letter inviting Mrs. Brown and Miss Linn to tea, n.d.(UVa) 18(5 KB) Kant, Immanuel : Kane, Mr.: Letter inviting Miss Linn for a ride, n.d. (UVa) 18(5 KB) Kay Ross: Keary, Eliza Little Seal-skin and Other Poems (1874)(HTML at Victorian Women Writers) (size: 213K, 1 gif) Keary, Maud Enchanted Tulips and Other Verses for Children (1914)(HTML at Victorian Women Writers) [includes poems by Annie Keary and Eliza Keary] (size: 95K, 1 gif) Keats, John Keene translation: Brazell, Karen : Sekidera Komachi (UVa) 1970(30 KB) Keene, H. G.: The Fall of the Moghul Empire of Hindustan (1887 edition) Matisoff, Susan : Semimaru (UVa) 1970(35 KB) Kehoe, Brendan P. TXT 167 Kb - ZIP 70 Kb SL: TXT ZIP EN: TXT ZIP Keith, Marian: The Black Bearded Barbarian: The Life of George Leslie Mackay of Formosa Keller, Helen: The Story of My Life Kellogg, John Harvey, 1852-1943.:

54. Calculate Pi Super_Pi by Yasumasa Kanada. Windows binary available. PiAGM by Carey Bloodworth 1) The easy to run Super_Pi (for MS-Windows™) by Yasumasa Kanada http://thestarman.dan123.com/math/pi/piprogs.html

Programs for Calculating On Your Own Computer by Yasumasa Kanada. [ Windows binary available. ] Pi-AGM by Carey Bloodworth by Takuya Ooura. by Xavier Gourdon. Quick Pi by Steve Pagliarulo. [ Win 32 binary available. ] The following programs are generally listed according to the speed at which they compute values of Pi. (The last one listed here being the fastest program!) Since I'm running Windows 95/DOS 7 on a PC, each program listed here is at least available in an x86 (PC) DOS (or Win32) binary form. Executables for a particular program on another platform may exist, since some of them come with their own open source code! (Consult the program homepages and links listed below.) 1) The easy to run Super_Pi by Yasumasa Kanada Download Super_Pi now (in a 72 kb .zip file) and Calculate up to 32 Million digits of Pi. There are twelve different digit-lengths to choose from (see below). Simply extract the files ( Super_pi.exe, Super_pi.hlp and Super_pi.txt ) into any directory and run the program. The program creates the file pi_rec.txt

55. Free EBooks - Alphabetical List - GLOBUSZ PUBLISHING Kamban, Gudmundur, 18881945. Hadda Pada; Hadda Padda. Kanada, Yasumasa.One Divided By pi (to 1 million digits). Kant, Immanuel, 1724-1804 http://globusz.com/authors_k.asp

MORE BOOKS HERE Search eBooks Search Paper Books MEMBERSHIP As a Globusz member you will be entitled to free passwords, and have full access to our fastest growing online library! CATEGORIES Adult Ancient Biographies Business ... Z Kafka, Franz [Download] Kaffka, Margit [Download] Kandinsky, Wassily [Download] Kane, William Terence [Download] Kant, Immanuel [Download] Karinthy, Frigyes [Download] [Download] Kehoe, Brendan P. [Download] Keim, Albert [Download] [Download] Keller, Helen [Download] Kempis, Thomas a [Download] Kelland, Clarence Budington [Download] Kerst, Friedrich [Download] Kester, Vaughan [Download] Ketcham, Henry [Download] Khayyam, Omar [Download] Krestovski, Vsevolod Vladimirovitch [Download] Krishnananda, Swami [Download] Kuprin, Aleksandr Ivanovich [Download] Kyne, Peter Bernard [Download] Free Downloads The titles below are available for free download. Downloaded eBooks will expire after a given number of days or uses and you will need a password to read them. Non-members can purchase one password for $2.99, while our registered members are provided with free passwords for our entire collection. For only $29.95 you will have access to our growing collection of best quality eBooks. We are adding new titles every day. Kamban, Gudmundur, 1888-1945

56. Stu's Pi Page Alan Pittman, Gio Ciampa, and Yasumasa Kanada. The programs below were run inWindows 98 with all background programs disabled http://home.istar.ca/~lyster/chart.html

B Program Speed Records F astest program C hart of programs ... isclaimer B Size Records S uper computer H ome computer Links A uthors's links E -mail to Stu ... i-Hacks e-mail discussion group THE FASTEST PI PROGRAMS that will run on your PC Consult the chart below for the programs by Steve Pagliarulo, Xavier Gourdon, Takuya Ooura, Carey Bloodworth, Mikko Tommila, Sebastian Wedeniwski, Alan Pittman, Gio Ciampa, and Yasumasa Kanada. The programs below were run in Windows 98 with all background programs disabled so that no other programs conflicted or used the computers resources Please see Dara's page for another comparison of ALL these programs and more, run on Linux..... Stu's world ranking Program Author digits digits Effic- iency 16-meg digits Maximum digits Programming Comments PiFast.EXE ver 4.3 Xavier Gourdon 1.10 secs 8.73 secs. 16 gigs Based on Chudnovskys' algorithm, disk swap version - can do calc. in different time chunks, also will calculate a whole host of other user defined constants, incl. 'e' QuickPi v. 2.01

57. Chudnovsky Brothers A year after that, in 1987, Yasumasa Kanada and his team got a hundred andthirtyfour million digits of pi, using a NEC SX-2 supercomputer. http://wadanet.com/hasegawa/chud.htm

The Mountains of PI By Richard Preston (NewYorker March 2, 1992) Gregory Volfovich Chudnovsky recently build a super computer in his appartment from mail-order parts. Gregory Chudnovsky is a number theorist. His appartment is situated near the top floor of a run-down building on the West Side of Manhattan, in a neighborhood near Columbia University. Not long ago, a human corpse was found dumped at the end of the block. The world's most powerful supercomputers include Cray Y-MP C90, the Thinking Machines CM-5, the Hitachi S-820/80, the nCube, the Fujitsu parallel machine, the Kendall Square Research parallel machine, the NEC SX-3, the Touchtone delta, and Gregory Chudnovsky's apartment. The apartment seems to be a kind of container for the supercomputer at least as much as it is a container for people. Gregory Chudnovsky's partner in the design and construction of the supercomputer was his older brother, David Volfovich Chudnovsky, who is also a mathematician, and who lives five blocks away from Gregory. The Chudnovsky brothers call their machine m zero. It occupies the former living room of Grogory's apartment, and its tentacles reach into other rooms. The brothers claim that m zero is a "true, general-purpose supercomputer", and that it is as fast and powerful as a somewhat older Cray Y-MP, but not as fast as the latest of the Y-MP machines, the C90, an advanced supercomputer made by Cray Research. A Cray Y-MP C90 costs more than thirty million dollars. It is a black monolith, seven feet tall and eight feet across, in the shape of a squat cylinder, and is cooled by liquid freon. So far, the brothers spent around seventy thousand dollars on parts for their supercomputer, and much of the money has come out of their wives' pockets.

58. NMBRTHRY Archives -- September 1999 (#20) EDU From Yasumasa Kanada Kanada@pi.cc.utokyo.ac.jp Subject Pi Latest Yasumasa Kanada Information Technology Center, Computer Centre Division, http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind9909&L=nmbrthry&F=&S=&P=2395

59. - Organization Kanada, Yasumasa Professor, University of Tokyo; SAITO, Susumu Professor,Tokyo Institute of Technology; SAITO, Riichiro Professor, Tohoku University http://www.tokyo.rist.or.jp/cnt/menu/org_e.html

News Organization Project Overview Result report Information Links ... TOP Researcher NAKAMURA, Hisashi...Research Organization for Information Science and Technology(RIST) IIZUKA, Mikio...RIST MINAMI, Kazuo...RIST MIYAUCHI, Atsushi...RIST TEJIMA, Shogo...RIST CNT Simulation Group Members ENDO, Morinobu...Professor, Shinshu University OSAWA, Eiji...NanoCarbon Research Institute Limited/Professor Emeritus, Toyohashi University of Technology OHNO, Takahisa...Computational Materials Science Center (CMSC) OHFUTI, Mari...Nanotechnology Research Center, Fujitsu Laboratories Limited OSHIYAMA, Atsushi...Professor, University of Tsukuba KANADA, Yasumasa...Professor, University of Tokyo SAITO, Susumu...Professor, Tokyo Institute of Technology SAITO, Riichiro...Professor, Tohoku University SHINOHARA, Hisanori...Professor, Nagoya University TSUKADA, Masaru....Professor, Waseda University TOMANEK, David ...Professor, Michigan State University HIRANO, Tsuneo...Professor Emeritus, Ochanomizu University MARUYAMA, Shigeo...Assoc. Professor, University of Tokyo MIYAMOTO, Yoshiyuki...Principal Researcher, NEC Laboratories

60. RIST NEWS Dr. Yasumasa Kanada; University of Tokyo about speaker Dr. Eiji Osawa, Prof.Dr. Yasumasa Kanada, Dr. Yoshiyuki Miyamoto, Mr. Mikio Iizuka(RIST) http://www.tokyo.rist.or.jp/cnt/repo/nanotech2004sympo/nanotech2004sympo_2_e.htm

Program * The program is subject to change without notice. Opening remarks Carbon nanotubes and expectations for computer simulations - Prof. Dr. Morinobu Endo; Shinshu University < about speaker Expectations towards High-Level Simulation from Computational Chemistry - Emeritus Prof. Dr. Eiji Osawa; Toyohashi University of Technology < about speaker Theoretical prediction of atom and molecular bridges, and carbon nanotubes - Prof. Dr. Masaru Tsukada; University of Tokyo < about speaker Designing Nanotechnology on a Supercomputer - Prof. Dr. David Tomanek; Michigan State University < about speaker Growth and Characterization of Double-Wall Carbon Nanotubes and Nano-Peapods - Prof. Dr. Hisanori Shinohara; Nagoya University < about speaker Simulation on Femtosecond Dynamics in Nanotubes Based on Quantum Mechanics - Dr. Yoshiyuki Miyamoto; NEC Laboratories < about speaker Large-scale Simulation on Nanotechnology < about speaker ask not what HPC can do for you. . .ask what you can do for HPC - Prof. Dr. Yasumasa Kanada; University of Tokyo < about speaker Panel Discussion: Perspective of Computational Nanotechnology Prof. Dr. David Tomanek, Emeritus Prof. Dr. Eiji Osawa, Prof. Dr. Yasumasa Kanada, Dr. Yoshiyuki Miyamoto, Mr. Mikio Iizuka(RIST)

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