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Thue Axel:     more detail

Selected Mathematical Papers (German Edition) by Axel Thue, 1977-04 Mathématicien Norvégien: Niels Henrik Abel, Sophus Lie, Atle Selberg, Thoralf Skolem, Ludwig Sylow, Kristen Nygaard, Axel Thue, Viggo Brun (French Edition) Spectrum and extended states in a harmonic Chain with controlled disorder: Effects of the thue-Morse symmetry by Françoise Axel, 1989

lists with details

21. AIM Reprint Library:
    Translate this page Z. Listing for thue, axel. Viewing Page regeln. thue, axel. 2. Uberdie gegendeitige lage gleiche teile gewisser zeichereihen. thue, axel.  
    http://www.aimath.org/library/library.cgi?database=reprints;mode=display;BrowseT

22. AIM Reprint Library:
    John Thompson, John G. Thompson, RC Thompson.R. Thrall, RM Threlfall, William Thrig,Edwin C. thue s Equation Over Function Fields thue, axel Thullen, Peter  
    http://www.aimath.org/library/library.cgi?database=reprints;mode=display;BrowseL

23. Hercule.csci.unt.edu/cgi-bin/genealogy.cgi?file=database-T.html From=Thue,Axel T
    LexikonEintrag thue, axel - Translate this page thue, axel. blabla. Stand 30.05.2001.  
    http://hercule.csci.unt.edu/cgi-bin/genealogy.cgi?file=database-T.html&from=Thue

24. Thue - 1897
    Translate this page axel thue - 1897. thue benutzt in seinem Beweis den Hauptsatz der Zahlentheorie,also die Eindeutigkeit der Zerlegung der natürlichen  
    http://www.turing-maschine.de/daten/mathematic/beweise/primenumbers-thue.html

25. Publications Du LaCIM
    axel thue s papers on repetitions in words a translation In a series of four paperswhich appeared during the period 1906 emdash;1914, axel thue considered  
    http://www.lacim.uqam.ca/Publications/20.html
    
    Extractions: 1. Preliminaries 2. Thue's First Paper: About infinite sequences of symbols 3. Thue's Second Paper: On the relative position of equal parts in certain sequences of symbols 4. Notes Axel Thue's papers on repetitions in words: a translation The other two papers deal with repetitions in finite and infinite words. Perhaps because these papers were published in a journal with restricted availability, this work of Thue was widely ignored during a long time, and consequently some of his results have been rediscovered again and again. Axel Thue's papers on sequences are now more easily accessible since they are included in the "Selected Papers" which were edited in 1977. It is the purpose of the present text to give a translation into English of Axel Thue's papers on repetitions in sequences, both in more recent terminology and in relation with new results and directions of research. PAFACC, UQAM

26. Doug, Basho, And Axel Thu
    Douglas J. Shaw, 2002. Historical Note His name was actually axel thue,he was Norwegian, and he died in 1922. But I didn t know that at the time.  
    http://www.dougshaw.com/essays/thu.html
    
    Extractions: In times of severe stress, we often find out who our real friends are. The Winter of 1991 was the most stressful time in my life so far. I would not have gotten through it without my friends Basho and Axel Thu. Axel Thu was a Chinese mathematician who died in the year 400 AD . Basho was my cat. January 14 was my preliminary examination in Mathematics. The preliminary examination is the biggest hurdle that lies between the hopeful graduate student, and the Ph. D. that is his or her heart's desire. Picture a two hour oral exam consisting of two professors hurling questions at you, where you only have a piece of chalk for self defense. At the University of Michigan, the rule was that if you failed, you got one more chance. If you failed a second time, that's it. You're out. Thanks for playing. You leave college with nothing but debt, misery, and a Master's degree. I started studying six weeks before the date, telling my family that Christmas was canceled for me that year. This is the story of a friendship. Basho the Cat, Axel Thu and I became very close during those six weeks. Unfortunately, this is also the story of a betrayal, and the end of a friendship.

27. Transcendental.html
    axel thue (18631922). I highly recommend Wolfgang Schmidt s AMS Bulletin (1978)review of Selected mathematical papers of axel thue , from which I quote  
    http://www.spd.dcu.ie/johnbcos/download/Public and other lectures/transcendental
    
    Extractions: Axel Thue (1863-1922) Thue's Theorem (1909) . Let be any real algebraic number of degree n at least 3), and let be any positive constant ( however small ), then there is a positive constant (i.e. the value of c depends only on and ) such that ... (i') One can only write of the fundamental importance of that result by resorting to hyperbole. I highly recommend Wolfgang Schmidt's AMS Bulletin (1978) review of Selected mathematical papers of Axel Thue , from which I quote: " His greatest work, on approximation to algebraic numbers, appeared in 1908/1909, when he was well in his forties, and when he had been away from the centres of mathematics for over a decade. ... Landau called it [the above theorem, and its application to the related Thue equation the most important discovery in elementary number theory which he had witnessed in his lifetime. He also said ten years after its publication that already ten competent mathematicians had read Thue's paper. [JC comment. Far be it from me to correct Schmidt's English (his first language is German) but I think any reader will believe that what Landau said, ten years after the publication of Thue's paper, was that only ten competent... ]

28. Fermat-Thue 2-squares.html
    the . Title. Fermat s 2-squares theorem (proved here using the Dirichletbox principle , together with an idea of axel thue ). Remark  
    http://www.spd.dcu.ie/johnbcos/download/3rd_year/Challenging/Fermat-Thue 2 squar
    
    Extractions: # Fermat's 2-squares.mws Note to anyone reading this on the web in html format. Not having Maple you may not be familiar with its use of Sections (where you see those [+]s). To read the contents of a section, simply click on the [+] and it will expand into a [-], and you will see text, plus calculations (of course you cannot change the calculations, as you could with the active Maple worksheet). Later, by scrolling back up, you may close the box by clicking on the [-]. Title Fermat's 2-squares theorem together with an idea of Axel Thue Remark (aimed at number theorists who might read this) on the approach I've adopted here . The proof that I give here of Fermat's 2-squares theorem (as part of my 3rd year (BA only) course Challenging Mathematical Puzzles and Problems ) is most certainly not the best, nor the most insightful proof there is of Fermat's theorem; and the proof given here serves mainly to demonstrate a particular use (the Thue result) of the entirely elementary, but quite profound, Dirichlet box principle (where would the work of - say - Roth or Schmidt be without it?!) which my students will encounter is less demanding areas (e.g. Choose any ( ) integers from [1, 2, 3, 4, ... , (

29. SmartPedia.com - Free Online Encyclopedia - Encyclopedia Books.
    axel Moller, axel Munthe, axel Olrik. axel Oxenstierna, axel thue,axel von Fersen. axel von Fersen, senior, Axeman of New Orleans, Axial.  
    http://www.smartpedia.com/smart/browse/Special:Allpages&from=Avebury_Circle

30. American Scientist Online - Third Base
    thue, axel. 1912. ber die gegenseitige lage gleicher teile gewisser Zeichenreihen.In Selected Mathematical Papers of axel thue, pp. 413?477.  
    http://www.americanscientist.org/template/AssetDetail/assetid/14405/page/6
    
    Extractions: Home Current Issue Archives Bookshelf ... Subscribe In This Section Search Book Reviews by Issue Issue Index Topical Index ... Classics Site Search Advanced Search Visitor Login Username Password Help with login Forgot your password? Change your username see full issue: November-December 2001 Volume: Number: Page: DOI: Other Formats: Postscript (gzipped) Postscript PDF Some weeks ago, rooting around in files of old clippings and correspondence, I made a discovery of astonishing obviousness and triviality. What I found had nothing to do with the content of the files; it was about their arrangement in the drawer. click for full image and caption A drawer filled with "half-cut" folders, which have just two tab positions, might initially alternate left-right-left-right . The pattern is spoiled, however, as soon as you insert a folder in the middle of the drawer. No matter which type of folder you choose and no matter where you put it (except at the very ends of the sequence), every such insertion generates a conflict. Removing a folder has the same effect. Translated into a binary numeral with

31. Squarefree Word -- From MathWorld
    Selected Mathematical Papers of axel thue. Oslo, Norway Universitetsforlaget,pp. 139158, 1977. Selected Mathematical Papers of axel thue.  
    http://mathworld.wolfram.com/SquarefreeWord.html
    
    Extractions: Squarefree Word A "square" word consists of two identical adjacent subwords (for example, acbacb ). A squarefree word contains no square words as subwords (for example, abcacbabcb ). The only squarefree binary words are a b ab ba aba , and bab (since aa bb aaa aab abb baa bba , and bbb contain square identical adjacent subwords a b a a b a b , and b , respectively). However, there are arbitrarily long ternary squarefree words. The number s n ) of ternary squarefree words of length n = 1, 2, ... are 1, 3, 6, 12, 18, 30, 42, 60, ... (Sloane's ), and s n ) is bounded by

32. Fiche Document -Axel Thue's Papers On Repetitions In Words
    papers on repetitions inwords a translation Berstel, Jean (Principal) Montréal Departement de  
    http://bibli.cirm.univ-mrs.fr/Document.htm&numrec=031080680926240

33. Fiche Document -Selected Mathematical Papers Of Axel Thue
    http://bibli.cirm.univ-mrs.fr/Document.htm&numrec=031061491924320

34. Cat's Eye Technologies: /projects/thue/
    a pure stringrewriting process called a semi-thue grammar, which is named for (andpossibly created by) the Norwegian mathematician axel thue (pronounced \ TOO  
    http://catseye.mine.nu:8080/projects/thue/
    
    Extractions: George Herbert, Jacula Prudentum (Colloqual Adaptation) The Thue programming language was invented by John Colagioia in early 2000. It is named after the computational regimen it is based on - a pure string-rewriting process called a semi-Thue grammar Thue represents one of the simplest possible ways to construe constraint-based programming. It is to the constraint-based paradigm what languages like OISC are to the imperative paradigm; in other words, it's a tar pit. Project Branch Path Rev thue current Rev File Size Date Keywords Description archive/ doc/ eg/ src/

35. Welcome To The Thue Reference Manual What Is A Thue? Thue Is
    based on the concept of the semithue grammar/process, which is named for (and possiblycreated by) the Norwegian mathematician axel thue (pronounced TOO-ay  
    http://catseye.mine.nu:8080/projects/thue/doc/thue.txt
    
    Extractions: Welcome to the Thue Reference Manual > What is a Thue? Thue is...uhm...well... OK, I got it. Thue is a language based on the concept of the semi-Thue grammar/process, which is named for (and possibly created by) the Norwegian mathematician Axel Thue (pronounced "TOO-ay"). It is, in essence, an arbitrary grammar, which can (by its arbitrary nature) be used to define/recognize "Type 0" languages from Chomsky's hierarchy. Because the grammar can be used to define a language of such complexity, the process, itself, is essentially Turing Complete. As a result, the Thue language (which, of course, would be much funnier if it rhymed with the Infocom "dark places" creature, but c'est la vie, I guess...) is an arbitrary grammar system, not unlike yacc or a similar beast, except that there is no way to distinguish between a terminal and a nonterminal symbolthey are completely interchangeable. > Write "Thue" with burin. A Thue program consists of two parts: The first part is the set of grammar/production rules, where each rule has the form: lhs::=rhs where the lhs is the string to be recognized, and the rhs is the string which is to replace the lhs. Each string (lhs and rhs) can be completely arbitrary, except that the lhs cannot (for rather obvious reasons) include the production symbol ("::="). The rhs, however, is not restricted in any way. Terminating the rulebase is a production symbol alone on a line, surrounded by (optional) whitespace. Following that is the description of the initial state which Thue will work with. Each line after the rulebase is concatenated to form the initial state. Once loaded, the Thue program nondeterministically applies the rulebase to the current state. It continues to do so until no rules apply to the state (pragmatically, this means that no lhs can be found in the state). > What is a burin? Don't worry about it. It's an Infocom joke. Actually, let's go with it. A burin is tool to inscribe mystical symbols into an object. Thue has one. > Examine burin. Added to this simple system are two strings which are used to permit Thue to communicate with the outside world. The first of these is the input symbol (":::"). The input symbol is actually the lhs of an implicit rule of which the user (or system's "input stream") is a component. The input symbol, therefore, is replaced by a line of text received from the "input stream." As a counterpart of input, the output symbol ("~") is supplied. Like the input symbol, the output symbol triggers an implicit rule which, in this case, encompasses the "output stream." The specific effect is that all text to the right of the output symbol in the rhs of a production is sent to the output stream. Note that either (or both) of these implicit rules may be overridden by providing explicit rules that perform some other task. > Examine Thue. The implementation of Thue, itself, is rather uninteresting, except for three command-line switches: d Activates "Debug Mode," which prints the state immediately after any rule is applied. l Activates "Left Mode," which requires Thue to apply rules deterministically in a left-to-right fashion. r Activates "Right Mode," which is identical to "Left Mode," except that rule application occurs right-to-left. The command-line switches must appear after the Thue filename, and the last incidence of 'l' or 'r' overrides all others. > Look under Thue. Sample programs included are: dec.t Decrements a binary number hello.t Hello, World! inc.t Increments a binary number incany.t Increments a binary number input by the user test.t A simple example to highlight nondeterminism > Amusing. Apologies to Axel Thue for mangling the pronunciation of his name for a cheap joke. Apologies to whatever is left of Infocom for (unknowingly) supplying the format of the cheap joke. > Exit.

36. Thue Sequences, Lambda Calculus Circular Program
    thue sequences, after axel thue, are sequences over an alphabet ofthree {1,2,3} such that no subsequence is immediately repeated.  
    http://www.csse.monash.edu.au/~lloyd/tildeFP/Lambda/Examples/Thue/
    
    Extractions: immediately repeated. e.g. 1213121 is a Thue sequence that cannot be extended 121312 any length. (There are no solutions longer than 3 for binary sequences, and finding solutions is easier for alphabets larger than three.) The ``circular program'' below builds a tree of Thue sequences. Note that within function `build', the tree data-structure `T' and functions `toplevel' and `f' are mutually recursive. The program relies on the fact that a partial soln `abcde' can be extended with `f' iff its shadow, `bcdef', is already in tree at the previous level; this avoids repeating many tests on constraints that have already been treated at a higher level. The subtree for `abcde' is the subtree of `bcde' less any `a' nodes. The tree of all solutions is notionally infinite, but the program prints one branch to a finite depth so only a finite part of the tree is evaluated thanks to lazy evaluation. See L. Allison. Applications of Recursively Defined Data Structures . Australian Computer Journal Feb 1993.

37. Bibliography
    thue, axel, 18631922, Selected mathematical papers of axel thue / with an introdutionby calr Ludwig Siegel, ed. by Trygve Nagell, Oslo, Universitetsforlaget,  
    http://www.library.cornell.edu/math/bibliography/display.cgi?start=T&

38. Molte Figure Che Compaiono In Questa Applet Sono Grandi E Tendono
    Translate this page Il matematico axel thue (1863-1922) si chiese se esista una sequenza infinita binaria(fatta di 0 e 1) nella quale non appaiano mai 2 blocchi consecutivi di 3  
    http://alpha01.dm.unito.it/personalpages/cerruti/Az1/thue.html
    
    Extractions: Azionando l'applet (che conviene rimpicciolire) partono 4 trenini nelle 4 direzioni, producendo degli alianti che collidono. Quello che ci interessa sono le 4 sequenze diagonali di semafori che si leggono partendo dal centro. Il centro è vuoto e la successione comincia con 0; seguono 1 1, cioè vi sono 2 semafori uno di seguito all'altro, poi vi è uno spazio vuoto che leggiamo come 0, poi 1 1 e così via. L'inizio della successione è il seguente: 0110110111110110111110110110... Questa successione è definita in modo ricorsivo, in maniera simile alla famosa successione di Prouhet-Thue-Morse. Il matematico Axel Thue (1863-1922) si chiese se esista una sequenza infinita binaria (fatta di e 1) nella quale non appaiano mai 2 blocchi consecutivi di 3 simboli uguali nè blocchi della forma awawa dove a è od 1 e w un arbitrario blocco binario. In effetti esiste, e comincia così: 0110100110010110100101100110...

39. À§´ëÇѼöÇÐÀÚ ¸ñ·Ï
    June 1824 in Belfast, Ireland Died 17 Dec 1907 in Netherhall (near Largs), Ayrshire,Scotland thue, axel thue Born 19 Feb 1863 in Tönsberg, Norway Died 7  
    http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=T

40. MathNet-Fields Medals
    626, Springer, Berlin, 1977. 10H30 10 thue, axel Selected mathematical papers.With an introduction by Carl Ludwig Siegel and a biography by Viggo Brun.  
    http://www.mathnet.or.kr/API/?MIval=people_fields_detail&ln=Atle Selberg

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