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  1. Mikio Sato,A Great Japanese Mathematician of the Twentieth Century by Masaki Kashiwara, Shing-Tung Yau, et all 1999-11-01

21. Gossips And Rumors
Gossips and Rumors among japanese mathematicians It seems that it will be a veryinteresting conference, and many japanese mathematicians will attend it.
http://rtweb.math.kyoto-u.ac.jp/topicse.html
Gossips and Rumors among Japanese Mathematicians...
  • We thank the speakers and the audiences who attended the workshop NORTh 4 . I have enjoyed every lecture, and the series of lectures given by Professors Manivel and Sommers were just wonderful. Prof. Manivel introduced
    Vogel 's idea of universal Lie algebra,
    which seems wild (and at the same time very attractive) to me. There are three lines in the projective plane; on one of which sl_n lives, on another one sp_n and so_n live. On the other line, all the exceptional Lie algebras including so_8 and sl_3 live. Their intersections are sl_2=sp_1 , so_8 and sl_3! Also, between E_7 and E_8, there lives E he told. [Thu Mar 4 14:13:00 JST 2004] The newest issue of Ramanujan Journal is
    Rankin Memorial Issues.
    Many experts of the theory of automorphic forms contribute the issue. [Thu Oct 30 09:06:43 JST 2003]
    Susumu Ariki (RIMS) won the 2003 Autumn Prize of Japanese Mathematical Society.
    Congratulation!
    Also, Minoru Ito (Kyoto Univ.) won Takebe prize. [Mon Sep 29 18:14:37 JST 2003] Prof. Armand Borel died last August (2003/8). May his soul rest in peace.

22. In Memory Of Kiiti Morita
And he left a legacy for japanese mathematicians, in particular, where it is estimatedthat more than half of the Japanese topologists today are directly or
http://www.ams.org/development/mor-jhe.html
In Memory of Kiiti Morita John Ewing August 4, 1998
We are here today to honor a respected and eminent mathematician, Kiiti Morita, who passed away exactly three years ago, on August 4, 1995. I'd like to welcome our guests today, Professor Morita's widow, Tomiko; his son, Yasuhiro; his wife, Hiroko; and their son, Shiego. They flew here, some 6,740 miles (that's 10,871 kilometers!) to be with us today as we honor Professor Morita and dedicate our front garden area in his name. It is a strange feeling for me to be here today, saying these words. Before coming to the AMS, my field as a mathematician was Algebraic Topology. Professor Morita was a world class mathematician, who combined profound work in topology with brilliant insights into algebra. I grew up as a mathematician learning the phrase "Morita equivalence", a term that is everywhere in algebraic topology; I learned the concept long before I ever associated it to a person, the man who invented the idea in 1958. I learned of his other work in topology in a series of lectures while I was still a graduate student, but I never knew anything about the man behind those ideas. And having read more about the man, I wish I had known him, and not just his ideas. Looking at his long and distinguished career in mathematics, I am reminded of Shakespeare's famous quote:

23. Other Mathematical Studies
Two japanese mathematicians, Minoru Sakaguchi and Setsuko Sakai, areresponsible for most of the work on these loosely related topics.
http://www.cs.ualberta.ca/~darse/msc-essay/node8.html
Next: Classic Books on Up: Game Theoretic Analysis Previous: ``Winning Poker Systems''
Other Mathematical Studies
Although game theory would seem to be the natural mathematical discipline for the study of poker, a number of other specific mathematical problems arising from the game have also been studied. Many of these are only tangentially related to the core problems being addressed by strategic game playing, but are still worth looking at, if only for the sake of completeness. Two Japanese mathematicians, Minoru Sakaguchi and Setsuko Sakai, are responsible for most of the work on these loosely related topics. Some of the problems they have looked at include the effects of partial information [ ], multi-stage poker [ ], the disadvantage of being the first player to act in a given betting round [ ], and a few of the subtleties encountered with more realistic poker models [ ]. Notwithstanding the highly specialized nature of these problems, a few of their mathematical ideas might be incorporated into algorithmic analysis techniques. More optimistically, the purely mathematical approach may eventually produce some tangible dividends for poker practitioners. For example, in one of their most recent articles, Sakaguchi and Sakai solve (from a purely mathematical standpoint) some of the fundamentally difficult problems in three-person playing scenarios [ While these papers may be of limited practical value, it is important to maintain a mathematically precise view of the game. Toward this end, some background in probability theory is essential for academic poker researchers. While this knowledge can be acquired in many ways, one strongly recommended reference is ``The Theory of Gambling and Statistical Logic'', by Richard Epstein [

24. Interlude: Old Books, National Learning And Other -isms
You occasionally hear about how some japanese mathematicians inventeda calculus independently of Europe and this is true. However
http://www.openhistory.org/jhdp/intro/node26.html
Next: My Koku is Bigger Up: The Tokugawa Period Previous: Ieyasu's grandson Iemitsu Contents Index
Interlude: Old Books, National Learning and other -isms
As I mentioned before, some samurai had a lot of time to sit around and think. To a small degree, the government encouraged it - as long as you were thinking of ways to buttress Tokugawa power. Early on, Ieyasu made use of Shinto, Buddhism, and Confucianism to legitimize his rule, but as time went by, he made greater use of Confucianism. We dont need to get into all the various schools of Confucianist thought but we do know that there was not just one school and that several of these different ones were influential during the Tokugawa period. The governments official favorite was the Chu Hsi school, which placed great emphasis on duty and acting according to your station in life. Not too hard to see why the Tokugawa family liked it; Chu Hsi Confucianism was very conservative. A rival school was the Wang Yang-ming (cool name!) school. This school stressed intuitive knowledge of right and wrong and personal responsibility. A famous, though possibly bogus, Wang Yang-ming saying is "to know and not to act is not to know." Since morality is subjective, if you think something is wrong, it is and you must act on that knowledge. Subversive thinking this. This school greatly influenced the men who destroyed the Tokugawa regime in the 1860s.
Next: My Koku is Bigger Up: The Tokugawa Period Previous: Ieyasu's grandson Iemitsu Contents Index

25. ”—ƒjƒ…[ƒX‚Q‚O‚O1|‚Q
country. Cooperating with japanese mathematicians was very interestingand stimulating. I want to express my gratitude to Prof.
http://kyokan.ms.u-tokyo.ac.jp/~surinews/news2001-2.html
”—News 2001-2
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”—ƒjƒ…[ƒX‚Ö‚Ì“Šeæ: surinews@kyokan.ms.u-tokyo.ac.jp
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Jorg Winkelmann ‹qˆõ‹³Žö @Nowadays scientists travel a lot and meet on conferences. In this way I became aquainted with Prof. Noguchi from Todai@and we started to work together on joint projects,communicating by e-mail.
@This fruitful cooperation apparently was the reason that@I got an invitation to go for one year to the University@of Tokyo as Visiting Associate Professor, an invitation which I happily accepted.

26. Vol. 79 No. 3
In those days, many of traditional japanese mathematicians devoted themselves tosolving such complicated geometrical problems featuring chains of circles.
http://www.japan-acad.go.jp/english/b-cont/79/79no3/79no3.htm
Proc. Japan Acad. Ser. B Home Volume 79(2003) No. 3 Reviews
Seijiro MATSUBARA and Koichiro OSHIMA
Bis(iodozincio)methane as a synthetic tool. . .71-77 [ Abstract
Hiroko OHGAKI and Paul KLEIHUES
Genetic basis of glioma progression. . .78-85 [ Abstract
Original Papers
Kyung Ae YANG, Haejeong MOON, Gyutae KIM, Chan Ju LIM, Jong Chan HONG, Chae Oh LIM, and Dae-Jin YUN
NDP kinase 2 regulates expression of antioxidant genes in Arabidopsis Abstract
Masashi SUZUKI, Naoki AMANO, and Hideaki KOIKE
The DNA-binding domain of feast/famine regulatory protein, FFRP . . . 92-98 [ Abstract
Cover Illustration: A Geometrical Problem in the Edo Period This colorful illustration is a geometrical figure constructed by Kazu Watanabe (1767-1839), a Japanese mathematician. Watanabe edited the Kinsensanpo , a mathematical book published in 1819, in memory of his master Yasuaki Aida (1747-1817), the founder of Saijo school, one of the most active groups in the mathematical sciences in the latter half of the Edo period.

27. Number Facts
Magic circles. In the 17th century a number of japanese mathematicians became interestedin magic circles. Below is an example of one discovered by Seki Kowa.
http://www.blss.portsmouth.sch.uk/resources/numfacts.shtml
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Number Facts
Find out here which mathematicians were born on this day. Every month there will be a new amazing fact about numbers from around the world. Visit the number facts archive here.
Magic circles
In the 17th century a number of Japanese mathematicians became interested in magic circles. Below is an example of one discovered by Seki Kowa. More information about magic circles can be found from Mathworld Find out about the life of Seki Kowa here and related connections with Japanese Sangaku . These are wooden tablets usually hung from the ceilings of Shinto or Buddhist temples, upon which colorful mathematical theorems were painted. These theorems dealt predominantly with Euclidian geometry. Here is another type of magic circle problem. Take any six number sequence and place the numbers so that the total around each of the three circles is always the same. e.g. for the sequence 7,8,9,10,11,12.
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E-mail: general.emas@portsmouthcc.gov.uk

28. DAILY_HEADLINES Archives -- March 2001 (#16)
and geometry. While at Kyoto, he is conducting research with leadingjapanese mathematicians in the Osaka region. For more information
http://listserv.uark.edu/scripts/wa.exe?A2=ind0103&L=daily_headlines&F=&S=&P=162

29. Vitae
twin. We, japanese mathematicians working in public universities, arenot allowed to travel around the world without permission. We
http://www.rimath.saitama-u.ac.jp/lab.jp/skoike/koikev.html
Vitae
English version
Family name : Koike
Fore name : Shigeaki
Date of birth : 29 September 1958
Place of birth : Tokyo, Japan
Nationality : Japanese
Mailing address : Department of Mathematics, Saitama University 255 Shimo-Okubo, Saitama 338-8570 Japan
Education
1977(April)-1981(March) : Department of Physics (Undergraduate Course), Waseda University
1981(April)-1983(March) : Department of Mathematics (Master Course), Waseda University
1983(April)-1988(March) : Department of Mathematics (Doctor Course), Waseda University
1989(November) Awarded the degree of PhD, in Mathematics for the thesis entitled
"Smoothness and singular perturbations of solutions of HJB equations"
Professional Experience
1988(April)-1989(September) : Research associate in Waseda University
1989(October)-1992(March) : Research associate in Tokyo Metropolitan University
1992(April)- 2002(March) : Associate Professor in Saitama University
2002(April)-present: Professor in Saitama University
Visiting Experience
1990(September)-1991(August) : Visiting Researcher in Mathematical Science Research Institute at Berkeley (USA) A view from Mathematical Sciences Research Institute: San Francisco Bay
A night-view from Mathematical Sciences Research Institute
1993(February) : Soeul National University (Korea)
1994(November)-1995(January) : Visiting Researcher in Australian National University at Canberra (Australia)
1996(July) : Visiting Researcher at Tata Institute at Bangalore (India)
1996(December) : KAIST (Korea)

30. CV1
1990. Annual Meeting of the Society of japanese mathematicians, September1990. Winter School, Voronezh, Russia, January 1991. Stochastic
http://www-math.science.unitn.it/dottorato/CVElworthy.html
CURRICULUM VITAE Full Names: Kenneth David Elworthy.
Date Of Birth: 21 December 1940
Nationality: British. Married: With Two Children Born 1970 and 1974. Education: Merton College, Oxford, October 1959 - June 1962 B.A. in Mathematics, Class I, June 1962. Merton College and Mathematical Institute, Oxford 1962 - 1965, supervisor Professor M.F. Atiyah. Oxford D.Phil. obtained September 1967.
Career: 1. Lecturer in Mathematics, University of Manchester, 1965-1967, 1968-1969. 2. Visiting Professor, State University of New York at Stonybrook, 1967-1968. 3. Lecturer in Mathematics, University of Warwick, 1969-1972. 4. During 1972-73: Visiting Professor: University of California, Santa Cruz. Mathematics Institute, Aarhus University, Denmark. Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France. 5. Reader in Mathematics, University of Warwick, 1973-1981.

31. Re: Japanese Grammar & Reading Math Symbols
As far as I know, japanese mathematicians used the following expressions beforeWesternization ? ( ? ) ? ? ( ? ) ? (
http://www.sf.airnet.ne.jp/~ts/japanese/message/jpnEasGB1cPE_4pJvLg.html
T e a c h Y o u r s e l f J a p a n e s e
Message Board
From: TAKASUGI Shinji
Date: Tue, 11 Mar 2003 16:39:12 GMT
References:
Right. As far as I know, Japanese mathematicians used the following expressions before Westernization:
They used for known numbers like a b , and c in modern math, and used for unknown numbers like x y , and z . They also used digits based on , counting rods (算籌 in Chinese).
ex.
a
ab
a b
x > I'm thinking that 3 足す 5 は 8 has a verb serving as operator in between the numbers. Is this a "natural" word sequence for Japanese? The operators 足す, 引く, かける, and 割る work as coordinating conjunctions like と rather than verbs. Reply to this message Show this thread Return to the index

32. News From ICTP 104 - Commentary
Italian mathematicians often concentrate on geometry, especially algebraic geometry,while japanese mathematicians have displayed keen interest in mathematical
http://www.ictp.trieste.it/~sci_info/News_from_ICTP/News_104/commentary.html
Every human being who is capable of learning how to speak a language is also capable of acquiring not just simple but deep mathematical skills, says ICTP's new mathematics group head Le Dung Trang. Culture of Mathematics R esearch on brain function and behaviour has highlighted the central role of language in all human activities.
Language is indispensable both for comprehending what is happening around us and for learning new ideas. Put another way, without language it is difficult to understand and to learn.
Research, moreover, also has shown that language is a cornerstone of culture: That the language we speak has a great bearing on who we areprecisely because it serves as a major force driving the socialisation process.
If language is culture-bound, mathematics has long been viewed as a culture-free, universal source of knowledge and understanding.
Yet language at its core evolves around a set of rules and codes that parallel the rules and codes framing mathematics. For this reason, I would contend that language capability is a deep and complex reflection of mathematical capability and that both, in turn, are 'naturally' present in all human beings.
I use the word 'naturally' in a broad sense and not as a concept that language stems only from genetic predisposition. Because of the close ties between language and mathematics, I have concluded that every human being who is capable of learning how to speak a language (that means virtually everyone) is also capable of acquiring not just simple but deep mathematical skills. After all, the logic and abstract understanding embodied in languagetranslating sounds, images, ideas and factsinto a common base of understanding represents the very principles of mathematics as well. Language skills, however, do not translate easily into mathematical skills. As many math-challenged people will readily admit, mastering mathematics is not easy.

33. FACTA UNIVERSITATIS
universities. At that time abroad he was already one of the most famousjapanese mathematicians. He worked much and efficiently.
http://facta.junis.ni.ac.yu/facta/macar/macar200301/macar200301-25.html
Vol.3, No 13, 2003 pp. 775-777
PROFESSOR AKITSUGU KAWAGUCHI
Talk on occasion of the Anniversary of Akisugu KAWAGUCHI's 100 years birth,
who is the Founder of Tensor Society August 5-9, 2002
We have gathered here to commemorate and celebrate the centenary of the birth of the prominent mathematician Professor Akitsugu Kawaguchi.
He was only 26 years old when was appointed a research fellow to Europe and the United States of America for two years. Later this experience was followed by a number of fruitful scientific visits to Germany, France, Poland, USA, Greece, Austria, Romania, Italy, Hungary, etc. He visited almost all countries of Europe, and later India and South Asia. He accepted many invited lectureships and was visiting professor many times at leading universities. At that time abroad he was already one of the most famous Japanese mathematicians.
He worked much and efficiently. He had several brilliant ideas, but some of them are not yet completely developed and exhausted. Among these, the first concerned the projective differential geometry. In this area he wrote about 20 papers between 1927 and 1931. Also since then this area was developed and investigated by many mathematicians all over the world.
Like Hilbert, he worked on a theme through several years, and then he changed to another one. - After the projective diffierential geometry, from 193I to 1937, he investigated different concepts of parallelisms, displacements and general connec-tions. Among these there are interesting papers on Finsler geometry. We cannot say that Finsler geometry would have been the main field of his most important investigations, however he made essential contributions to this field, and he was the initiator of the investigations in this field in Japan. He can be considered as the founder of the worldwide famous Finsler geometric school with numerous collaborators led later by Professor M. Matsumoto. The flourishing of this school started in the 1970's and lasts even now.

34. Assign115/#5B/98
Seventeenth century japanese mathematicians may have estimated circle area, andhence p, using the method illustrated in Figure 2 (Beckmann, 125127).
http://newton.uor.edu/facultyfolder/beery/math115/m115_activ_est_pi.htm
Archimedes' Estimate of Activity The formula On the Measurement of the Circle, Proposition 3. The ratio of the circumference of any circle to its diameter is less than 3 1/7 but greater than 3 10/71 (Dunham, 97; Katz, 109). p p p was the first in history that was correct to two places after the decimal point!
p C is the circumference of the circle, r is its radius, and P insc and P circ are the perimeters of the inscribed and circumscribed polygons, respectively, then P insc C P circ , or P insc p r P circ , so that P insc r p P circ If we take the radius of the circle to be 1 ( r = 1), then P insc p P circ Archimedes started with inscribed and circumscribed regular hexagons. Since each of the six sides of a regular hexagon inscribed in a circle of radius 1 has length 1, then P insc = 6 in this case (see Problem 1a). Likewise, since each side of a regular hexagon circumscribed about a circle of radius 1 has length , then P circ (see Problem 1b). Hence, P insc P circ /2 yields , or Archimedes then doubled the number of sides of each polygon to 12, obtaining an inscribed regular dodecagon of perimeter P insc (see Problem 1c), and a circumscribed regular dodecagon of perimeter

35. EHP: Volume 32, 1979: JAPAN/USA Biostatistics; Statistics And The Environment
Purchase. Role of mathematics in cancer research attitudes and trainingof japanese mathematicians Kudo A p. 5 Download Purchase.
http://ehp.niehs.nih.gov/docs/1979/032/toc.html

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36. Mathematicians Resources
mathematicians; famous women mathematicians autobiography; great mathematiciansin probability; japanese mathematicians; famous mathematicians
http://www.free-email-accounts-directory.com/mathematicians.html
mathematicians
CLICK HERE TO ENTER MATHEMATICIANS RESOURCES
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  • 37. Operator Algebras
    In April 1999, he moved to Kyoto University. The Mathematical Society of Japan createdin 1996 a new prize for young japanese mathematicians, the Takebe prize.
    http://www.cf.ac.uk/maths/opalg/grp1.html
    Noncommutative Geometry and Operator Algebras at Cardiff
    People and Overview of the Group
    People
    Professor David E. Evans
    Dr Roger Behrend

    Dr Partha Sarathy Chakraborty

    Dr Radu Popescu
    ...
    Dr Ioannis Zois

    Mr Daniel Hoyt Professor George A. Elliott (Honorary Professor)
    Professor Vaughan F. R. Jones
    (Honorary Professor)
    Professor John T. Lewis
    (Honorary Professor)
    Overview of the Group
    The group is led by David Evans and has a broad sweep of interests in operator algebras, noncommutative geometry and their applications and connections to other mathematical areas and physics—including K-theory, E-theory, quantum groups in pure mathematics and statistical mechanics, algebraic, conformal, topological quantum field theories in mathematical and theoretical physics. David Evans has published with Yasuyuki Kawahigashi a monograph Quantum Symmetries on Operator Algebras —the combinatorial and physical aspects of operator algebras (see here for the list of updates/corrections). This is a continuation of the work of Evans in his previous collaborations with Araki and Lewis on a C*-algebra approach to phase transitions in the two-dimensional Ising model. Evans is also currently interested in the study of amenable C*-algebras by K- theoretic or topological invariants, e.g. the expression of finite amenable simple C*- algebras as the inductive limit of simpler building blocks - Elliott and Evans expressed the irrational rotation algebras as inductive limits of circle algebras. There is much interchange of ideas from amenable subfactors and amenable C*-algebras in this work (e.g. through common ideas from orbifolds and Rokhlin properties of automorphisms).

    38. The Harald Bohr Collection Of Reprints
    in Hungarian, Polish and Russian. There are many reprints from Italian,Hungarian, Polish, Russian and japanese mathematicians.
    http://www.math.ku.dk/ths/bohr_h/colrepr.htm
    Harald Bohr collection of reprints
    Bohr's large collection of reprints was sold by his wife Ulla Bohr to the Library at the Courant Institute of Mathematical Sciences , New York in 1952. It is still (1996) kept there bounded in 270 volumes (volume 141 was missing). The collection may be said to consist of three series: a series of medium sized volumes (volume 1-171), a series of small sized volumes (volume 172-186) and a series of large sized volumes (volume 187-270). The reprints in each series are ordered alphabetical which means that reprints from one author may be in all three series. On the back of each volume is printed Harald Bohr Collection , the volume number and the alphabetical interval covered by the volume (for example "N - Nielsen"). Some of the volumes, estimated 10%, contains a typewritten table of content which lists author and title of the reprints, but no catalog has been made of the complete content. Often the page numbers of the reprints start from page 1 and are not the page numbers of the actual published articles. Most of the content is reprints of articles published in mathematical journals. A significant part of the reprints are from

    39. Nakayama
    Nagata called it KrullAzumaya Lemma . Now, with Nagata s permission,many japanese mathematicians call it Krull-Jacobson-Azumaya Lemma .
    http://www.mathematik.uni-bielefeld.de/birep/collect/nakayama.html
    Tadashi (or Tadasi) Nakayama (1912 - 1964)
    1912, July born in Tokyo Graduated form Tokyo University.
    Assistant professor at Osaka University Associate professor at Osaka University stayed at Princeton Doctor of Science at Osaka University by the paper "On Frobenius algebras, I, II" Associate professor at Nagoya University Professor at Nagoya University He won a prize called "Chunichi Bunkashou" together with G. Azumaya Illinois University He won a prize, from the Japan Academy, called "Gakushi-in shou" (one of the most important prizes in Japan.) Hamburg University, Princeton Member of the Japan Academy Death in Nagoya Tadasi Nakayama was born in Tokyo in July 1912. It is said that his father was an eminent scholar of Chinese classics. He graduated from Musasi high school under the old system and from the (Imperial) University of Tokyo. It is not clear who was his superviser at Tokyo University. He learned algebra by very carefully reading Kenjiro Shoda 's book "Abstract Algebra" and he published some papers solving some problems posed in the book. Shoda, an uncle of an empress, was a mathematician who founded the department of Mathematics in Osaka University. He learned abstract algebra from E. Noether in Goettingen - Shoda was one of the Noether boys. In 1935 soon after the graduation of university he had a job as a Research Associate at the University of Osaka that was founded shortly before that. In 1937 he became an Associate Professor there. He stayed there for seven years until moving to the newly founded University of Nagoya in 1942 as an Associate Professor.

    40. SHOTO SUGAKU
    Yabasi. A series which cancels the inner terms, Yuko Yamamoto. Calcurationof p by old japanese mathematicians, Hinito Yonemitsu. Report.
    http://www.asahi-net.or.jp/~nj7h-ktr/e_mokuji00-01.html
    Journal of elementary mathematics„ŸSHOTOH SUGAKU„Ÿ
    VOL.39@May.2000 An essay-memories of mathematics Toshio Seimiya Articles Kawasaki Dayori- On a process of the study of a genralization of Langley's problem Toshio Seimiya Articles of the mourning of Prof. Minoru Kurita The mourningof Prof. Minoru Kurita Yasuo Matsuda A recollection of Minoru Kurita Hiroshi Asami The mathematician who has a deep knowledge of literature Tatsuo Matsumiya Prof. Kurita and Kitakyushu City Toshihiko Miyaji A recollection of Prof. Minoru Kurita and his elegant solution of a mathematics problem Takahide Yokoyama On the old days and these days Minoru Kurita Lectures A mathematical English lecture Yurou Ashiba A guide to 'Wasan' Hinoto Yonemitsu A study of a group-diheadral group Yasuo Matsuda Research On various methods of a construction problem Yurou Ashiba On some characteristics of Mersenne numbers 2 Kouji Oshima On an Ajima point Tomonori Kawamoto, Naruto Kirihara, Hiroshi Kotera The integral solutios of the indefinite equation X Y Z U n Hiroshi Kikuta On the Tarner lines and Seinmiya lines(9) Toshiyuki Kinoshita Frominfinity to finity (3) Mitsuhiro Kotani On a calculation of products of sin and cosin Mitsuhiro Kumano On an elementary method of calculating the shortest distance between two points on the earth Akira Sawanobori A cube floating in thespace Nobutaka Shigeki Confliguration-The color of the light Hidenori Shimizu Magic circles which ride on the elliptic function 1 Minoru Shimobayashiyama On a proof of an enequality Masakazu Nihei A method of redduction

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