61. UBC Library - MARION (1 title) End of matches for Thudichum, John Louis William, 18291901.. Thudipara,Jacob Z. (1 title); Thudium, Vern F. (1 title); thue, axel, 1863-1922. http://dra.library.ubc.ca/MARION/auth?fmt_limit=&lng_limit=&index=A&key=Thudichu

62. Repetition Free Words And Computer Algebra The systematic study of word structures (combinatorics on words) was started bya Norwegian mathematician axel thue 7 (18631922) at the beginning of this http://algebra.rotol.ramk.fi/keranen/research/RepetitionFreeStrings.html

Repetition Free Words Repetition Free Words and Computer Algebra Abstract Words or strings belong to the very basic objects in theoretical computer science. Thus, the investigation of structures in words constitutes a central research topic in this branch of science. The systematic study of word structures (combinatorics on words) was started by a Norwegian mathematician Axel Thue [7] (1863-1922) at the beginning of this century. One of the remarkable discoveries made by Thue is that the consecutive repetitions of non-empty subwords (squares) can be avoided in infinite words over a three letter alphabet. After Thue's time, repetition-free words have been used in various fields of mathematics. For example, in group theory, in formal languages, in connection with unending games, and in symbolic dynamics (which constitutes a tool for studying chaos). Very recently repetition-free words have also aroused interest in the field of music, see eg. Laakso [5]. Let X a b c d g X X * which we found by the aid of computers. This endomorphism g X X g abcd a is g a abcacdcbcdcadcdbdabacabadbabcbdbcbacbcdcacbabdabacadcbcdcacdbcbacbcdcacdcbdcdadbdcbca and the image words of letters b c d , i.e., the words

63. NewAbelianSquare-FreeDT0L-LanguagesOver4Letters.nb Abstract In 1906 axel thue 34 started the systematic study of structuresin words. Consequently, he studied basic objects of theoretical http://algebra.rotol.ramk.fi/keranen/ias2002/NewAbelianSquare-FreeDT0L-Languages

New Abelian Square-Free DT0L-Languages over 4 Letters 15 June 2002 and 15 June 2003 Rovaniemi Polytechnic, School of Technology veikko.keranen@ramk.fi http://south.rotol.ramk.fi Abstract 23], an abelian square-free (a-2-free) endomorphism on the four letter alphabet a b c d , i.e. abcd have been based on the structure of this ; see Arturo Carpi [4 In this paper, we report of a completely new endomorphism of , the iteration of which produces an infinite abelian square-free word. The size of . For they were directly obtained by permutating letters cyclically. The endomorphism is not an a-2-free endomorphism itself, since it does not preserve the a-2-freeness of all words of length 7. However, can be used together with to produce a-2-free DT0L-languages of unlimited size. Here DT0L-languages mean deterministic context-independent Lindenmayer languages produced by using compositions of endomorphisms - so called tables; see [32, p.188]. Indeed, by using Carpi's algorithm [4] for prefixes of ) and ), and a modified version of this algorithm, one can check the following fact: for any a-2-free words

64. Robert McNaughton For example, they have looked at ways to improve the efficiency of thue systems,a linguistic method developed by Norwegian logician axel thue in 1914. http://www.cs.rpi.edu/people/mcnaughton.html

Robert McNaughton mcnaught@cs.rpi.edu Emeritus Professor Ph.D., Harvard University Automata theory, formal languages, combinatorics of words McNaughton entered computer science in the 1950s after teaching philosophy for six years. His career switch was due to the lean job market more than anything else. Today, however, his training in philosophy holds him in good stead. McNaughton, who is author of the textbook Elementary Computability, Formal Languages and Automata published by Prentice-Hall, is now looking at problems in the combinatorics of words, a branch of formal languages. Formal languages deal with symbolic logic and computer languages as opposed to the natural languages used in human speech and general-purpose writing. His research is being coordinated with computer scientists formerly at the GE Research and Development Center in nearby Niskayuna, New York. This group at GE was called the Theorem Proving Group. Members of this group are now in the Computer Science Department at the University at Albany and in the Computer Science Department at RPI. Their research was concerned with looking at formal linguistic systems for the sake of carrying through proofs on the machine. For example, they have looked at ways to improve the efficiency of Thue systems, a linguistic method developed by Norwegian logician Axel Thue in 1914. Thue systems are useful for computation because they replace strings (connected characters) with other strings, carrying through a rather basic kind of computer operation.

65. Rødding Motion & Triathlonklub Spændende Bededage .. axel Crenzien blev igen Dansk Mester i Duathlon,efter flot kørsel på de Århuseske landeveje. thue d. 10/504. http://www.rtk-tri.dk/arkiv.asp

Links Billeder Stævner Træningstider ... Kalender Nyheder København Marathon 16.5.04 Som omtalt var Rødding Kommune stærk repræsenteret ved København Marathon 2004 og Rødding Motion og Triathlonklub havde sin del af æren for deltagerrekorden. 3 af klubbens medlemmer startede og fuldførte løbet. (Det er faktisk 4-5 % af medlemsskaren). De fik sig en skøn løbetur i København, hvor de så mange af seværdighederne på en lidt anden måde end de fleste turister. Naturligvis havde alle 3 trænet seriøs inden løbet, og selvom Sven har kæmpet en del med skader det sidste års tid, må man sige at de alle kom alle hjem i tider, de bør være tilfredse med. Tom Holst 4.07.19 Johannes Nicolajsen 4.09.36 Sven Ellegaard 4.37.12 Sven d. 21/5-04 København Marathon 16.5.04. Som tidligere omtalt i pressen var Rødding meget stækt repræsenteret til marathon-løbet i København. 16 deltagere fra Rødding Kommune var tilmeldt. Samtlige 16 løb over startlinien, selvom der var ca. 700 tilmedte, der ikke mødte op til start; men den største præstation var, at alle 16 også løb over målstregen: Det var 16 glade løbere, der kom i mål lidt hen på eftermiddagen. De fleste var meget tilfredse med deres tid; men nogle få havde haft lidt problemer med en temperatur, der blev højere end lovet kombineret med lidt fugtig luft. Spådommen om at der ville gå godt 1 time fra første Rødding-løber til den sidste Rødding-løber kom i mål holdt også stik. Hurtigste tid var: 3t 34min 53 sek., og sidste Rødding-mand kom ind på 4t 47min 20sek. Et flot resultat af samtlige løbere.

66. Juristforeningen.no 1928, Knut Glad, Øivind Rye Florentz, Hans Kristian Skou, Franz Beyer Jersen,axel thue, Arvid Frithjof Rasmussen, 1927, Knut Tvedt, 1926, Birger Motzfeld, JohnLyng, http://www.juristforeningen.no/jf/ordenskollegiet_dekorandi.html

Til forsiden Om Juristforeningen Kontakt oss Formannskapet ... Chorus Ordenskollegiet Dekorandi i Juristforeningen. År Navn Devise Audun Hellner Humakstyrets stolte ganger, svenska flickor, bondeanger. Pål Osmundsen Kongedass og machomann, krydrer Bærums drikkevann. Kari Steig Cabaret-blondine, busy-bee, JVL-sjef uten ski. Jens Christian Gjesti Karate Kid og småstjarmør, pusekatt med klipte klør. Kirsten Borge Alle gode ting er tre, men to er heller ikke å forakte. Audun Halvorsen Hoppens yngste bestefar, avmålt tunge, sindig svar Jarran Dolve Full, gass, tiss, tass Lars-Jørgen Kihlberg Olsen Kleptokanari Dag Vemund Haanæs Sminkepung og unge piker, koker suppe på en spiker Jan-Ole Huseb y Nesevis fløyelskis Julianne Meling Alle hingsters mor. Mange føll, men lite hor Jon Ole Whist Stort sett tap, men også vinn. Vaskekjerring med åpent sinn Christian F. Platou

67. Elementary Number Theory - Kenneth H. Rosen Page 504 Biographical information about axel thue can be found at the MacTutor Historyof Mathematics Archive at http//wwwgroups.dcs.st-andrews.ac.uk/~history http://www.aw-bc.com/rosen/resourcesc_13.html

Annotated Web Links CHAPTER 13 Some Nonlinear Diophantine Equations Return to Annotated Web Links Home 13.1 Pythagorean Triples Page 482 Biographical information about Pythagoras can be found at the MacTutor History of Mathematics Archive at http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Pythagoras.html (Pythagoras) 13.2 Fermat's Last Theorem Page 488 An excellent survey of the history of Fermat's last theorem can be found at http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html (Fermat's last theorem) Information about Fermat's last theorem can be found at NOVA Web site on the pages accompanying their episode devoted to Wiles's proof : http://www.pbs.org/wgbh/nova/proof (NOVA Online - The Proof) To begin exploring the mathematics behind Wiles's proof of Fermat's last theorem, you should look at a page developed by Charles Daney at http://www.best.com/~cgd/home/flt/flt01.htm

68. 12th Workshop '3in1' Graphs 2003 Krynica repetition. About 100 years ago axel thue discovered that there arearbitrarily long nonrepetitive sequences over the set . This http://galaxy.uci.agh.edu.pl/~3in1/grytczuk/

Faculty of Applied Mathematics AGH University of Science and Technology in Cracow 12th Workshop '3in1' Graphs 2003 Krynica, Poland November 6-8, 2003 What When Where Who ... PDF version Thue type problems for graphs Jaros³aw Grytczuk Institute of Mathematics, University of Zielona Góra Podgórna 50, 65-246 Zielona Góra, Poland e-mail: J.Grytczuk@im.uz.zgora.pl Abstract: Any sequence of the form is called a repetition . A block in a sequence is any subsequence of consecutive terms of . A finite sequence is nonrepetitive if none of its blocks looks like a repetition. About 100 years ago Axel Thue discovered that there are arbitrarily long nonrepetitive sequences over the set . This remarkable fact inspired many further investigations leading to a variety of pattern avoidance problems and a range of new types of nonrepetitiveness. For instance, a recent variation introduced in [ ] relates Thue sequences to graph colorings in the following way: a coloring of the vertices of a graph is nonrepetitive if the sequence of colors on any path in is nonrepetitive. The minimum number of colors needed is denoted by

69. Sikrer Immaterielle Verdier - Teknisk Ukeblad rundt Ultima Thule. Vi fant to av griffene i lavlandet på Campus Kjeller;Haakon thue Lie og axel Moulin, partnere i Leogriff AS. http://www.tu.no/utskriftsvennlig.jhtml?articleID=16475

70. References thue,1914 axel thue. Probleme über Veränderungen von Zeichenreihen nach gegebenenRegeln. Skrifter utgit av Videnskapsselskapet i Kristiana I, 10, 1915. http://www.dfki.de/~heckmann/diplom/Diplomarbeit/node66.html

Next: About this document Up: Recursive Matrix Systems Previous: Further work References Abeille,Owen,1998 Anne Abeille, Rambow Owen. Tree Adjoining Grammars: mathematical, computational, and linguistic properties . CLSI, 1998 Abraham,1965 L. Abraham. Some questions of phrase-structure grammars . Comput. Linguistics, Vol. 4, pages 61-70, 1965 Aho,Ullman,1972 Alfred V. Aho, Jeffrey D. Ullman. The Theory of Parsing, Translation, and Compiling, Volume 1: Parsing . Englewood Cliffs, N.J., Prentice-Hall, 1972 Alt,1997 Martin Alt. On Parallel Compilation Arbib,Kfoury,Moll,1981 Michael A. Arbib, A.J. Kfoury, Robert N. Moll. A Basis for Theoretical Computer Science . Springer New York Inc., 1981 Autebert,Berstel,Boasson,1997 Jean-Michel Autebert, Jean Berstel, Luc Boasson. Context-Free Languages and Pushdown Automata . Handbook of Formal Languages, Vol. 1, G. Rozenberg, A. Salomaa Eds., Springer Berlin, 1997 Becker,1994 Tilman Becker. HyTAG: A New Type of TAGs for Hybrid Syntactic Representation of Free Word Order Languages . PhD thesis, University of Saarland, 1994

71. Read This: How The Other Half Thinks Finally, Chapter 8 solves a problem posed by axel thue in 1912 can we constructarbitrarily long strings in a s, b s and c s which contain no pairs of http://www.maa.org/reviews/otherhalf.html

Read This! The MAA Online book review column How the Other Half Thinks by Sherman Stein Reviewed by Stacy Langton Sherman Stein, author of a calculus textbook, a monograph on the theory of tiling, a study of Archimedes , and Strength in Numbers (the latter two previously reviewed on MAA Online ), here presents another installment of mathematics for the general public. How the Other Half Thinks: Adventures in Mathematical Reasoning consists of eight short chapters, each of which sets up and then solves a nontrivial mathematical problem. Proofs from THE BOOK Chapters 2 and 4 deal with random strings of a's and b's. In Chapter 2, Stein asks how long such a string must be before the number of occurrences of one of the letters exceeds the number of occurrences of the other by 2. The expected value of this length is given by an infinite series. Stein evaluates the series by a clever rearrangement which goes back to the 14th century scholastic Nicole Oresme. The same series occurs in Chapter 4, where Stein computes the expected length of a run of a's or b's. Another problem about probability is treated in Chapter 6: in an election involving two candidates, what is the probability that one candidate will lead during the entire count? The solution here is based on a geometric reflection argument.

72. Formal Numbers This site is dedicated to the memory of the norwegian mathematician axel thue(18661922), who proved one of the most remarkable result of the twentieth http://www.math.u-bordeaux.fr/~lasjauni/

FORMAL NUMBERS by Alain Lasjaunias Alain.Lasjaunias@math.u-bordeaux.fr (Publications) Click here to enter... This site is dedicated to the memory of the norwegian mathematician Axel Thue (1866-1922), who proved one of the most remarkable result of the twentieth century in number theory Our goal is to present in an elementary way a class of abstract numbers . These numbers have been progressively introduced and studied in the last fifty years. Unlike real numbers, they are of no use to measure physical quantities but will certainly have applications still unknown. The further removed from usefulness or practical application, the more important. Axel Thue

73. Formal Numbers Translate this page Ce site est dédié à la mémoire du mathématicien norvégien axel thue (1866-1922),qui a démontré un des résultats les plus remarquables du vingtième http://www.math.u-bordeaux.fr/~lasjauni/page_fr_0.htm

NOMBRES FORMELS par Alain Lasjaunias Alain.Lasjaunias@libertysurf.fr (Publications) Cliquer ici pour entrer... Axel Thue

74. Literatur Thu06 axel thue. Über unendliche zeichenreihen. Kra. Vidensk. Thu12 axelthue. Über die gegenseitige lage gleicher teile gewisser zeichenreihen. Kra. http://www.informatik.uni-leipzig.de/~joe/edu/ss01/l/l-bib.html

Literatur Julien Cassaigne. Tree Automata Techniques and Applications. http://www.grappa.univ-lille3.fr/tata/ John~H. Conway and Richard~K. Guy. The Book of Numbers. Copernicus/Springer, 1995. Karel Culik~II and Tero Harju. Journal ACM, 31(2):282298, April 1984. Combinatorics of Words, pages 329428. Volker Diekert. Makanin's Algorithm, pages 344391. Vesa Havala and Tero Harju. Some new results on post correspondence problem and its modifications. TUCS Technical Report 338, Turku Centre for Computer Science, January 2001. http://www.tucs.fi/publications/techreports/TR338.html Morphisms, pages 439510. Lila Kari, Grzegorz Rozenberg, and Arto Salomaa. L Systems, pages 253328. Winfriend Kurth. Die Simulation der Baumarchitektur mit Wachstumsgrammatiken. Wissenschaftlicher Verlag Berlin, 1999. http://www.uni-forst.gwdg.de/~wkurth/public.html Aristid Lindenmayer. Mathematical models for cellular interaction in development. J. Theoret. Biology, 18:280315, 1968. Aristid Lindenmayer. Developmental systems without cellular interactions, their languages and grammars. J. Theoret. Biology, 30:455484, 1971.

75. Names Sylvester Tate Tauber Taylor Teichmuller thue Toeplitz Torelli Turan Turing Ulm Uryson Sylow Sylvester Tauber Taylor Teichmuller thue Toeplitz Turan Turing Uryson Veronese Volterra http://www.math.niu.edu/~rusin/known-math/98/MSC.names

76. Thue http://www.sciences-en-ligne.com/momo/chronomath/chrono2/Thue.html

théorie des nombres). Crelle (1909) concernant la recherche des points à coordonnées entières sur une courbe algébrique : + y + y Cette Baker apporta des précisions (1968) sur le théorème de Thue en précisant une borne supérieure des x et y. Mordell Siegel Un t héorème de Thue sur l'approximation rationnelle des nombres algébriques : Pour en savoir plus : Ed. Hermann - 1978, 1992 Fields Young

77. Thue-Morse Sequence - InformationBlast However, Prouhet did not mention the sequence explicitly; this was left to AxelThue in 1906, who used it to found the study of combinatorics on words. http://www.informationblast.com/Thue-Morse_sequence.html

Thue-Morse sequence In mathematics and its applications, the Thue-Morse sequence , or Prouhet-Thue-Morse sequence , is a certain binary sequence whose initial segments alternate (in a certain sense). The Thue-Morse sequence begins: on a given ordered pair Definition The Thue-Morse sequence in the form given above, as a sequence of bits , can be defined recursively using the operation of bitwise negation. So, the first element is 0. Then once the first 2 n elements have been specified, forming a string s , then the next 2 n elements must form the bitwise negation of s . Now we have defined the first 2 n elements, and we recurse. Spelling out the first few steps in detail: We start with 0. The bitwise negation of is 1. Combining these, the first 2 elements are 01. The bitwise negation of 01 is 10. Combining these, the first 4 elements are 0110. The bitwise negation of 0110 is 1001. Combining these, the first 8 elements are 01101001. And so on. The sequence can also be defined by: where t j is the j th element if we start at j Some properties Because each new block in the Thue-Morse sequence is defined by forming the bitwise negation of the beginning, and this is repeated at the beginning of the next block, the Thue-Morse sequence is filled with

78. Schlumberger Fellowship Awarded To Student Studying Morse Theory This sequence was introduced in 1906 by the Norwegian mathematician axel Thueas an example of an aperiodic recursively computable string of symbols. http://www.uri.edu/personal2/imarcus/mth381.html

Morse Theory Introduction Morse Theory was developed in the 1920s by the well-known mathematician Marston Morse. This theory is important in the field of global analysis which is the study of ordinary and partial differential equations from a global or topological point of view. It is a typical problem in mathematics which involves the attempts to understand the large-scale structure of an object with limited information. Morse theory investigates the nature of the critical points of smooth functions, rather than mapping on the plane. What Morse considered was smooth transformations of ordinary n-dimensional space into the real numbers, a much smaller space than a plane. In the 1930s, Morse proved a major result which generalizes the straightforward outcome of the Taylor Series The lowest-order non-vanishing term in the Taylor Series describes the local behavior of a smooth function of single variable. Suppose we have a function f of a single variable x, which we can represent as the smooth curve shown in the Figure below. If the curve is smooth enough, then it is a known fact that for any point

79. BIT WS 03/04 Sitzung 13 thue-Systemekönnen als einfache und allgemeine Form von Algorithmen betrachtet werden http://www.hki.uni-koeln.de/people/schassan/teach/ws0304/BIT-WS0304_13.htm

Basisinformationstechnlogie / HK-Medien Teil 1: WS 03/04 ROTE Textpassagen sind Definitionen. Seminarinhalte Sitzung Schlagwort Inhalte Grundlagen Was ist Information(-sverarbeitung)? Zeichenkodierung (Stellenwertsysteme, ASCII, ANSI, UTF-8) Grundlagen Zahlendarstellung (Zweierkomplement, Gleitpunktzahl) Rechnen mit Dualzahlen Boolesche Logik Rechnertechnologie Boolesche Funktionen Schaltfunktionen CPU-Komponenten Rechnertechnologie Digitale Logik Rechnerstrukturen (Rechenwerke, Logik-Gitter) Rechnertechnologie Rechnerstrukturen (Bussysteme, Register, CPU) Betriebssysteme Von der Hardware zum Betriebssystem Maschinensprache, Assembler Betriebssysteme Aufgaben des Betriebssystems (Verwaltung von Ressourcen, Dateien, Prozessen und Speicher) Betriebssysteme Beispiele (Unix, Windows-NT, mit besonderem Hinblick auf Dateisysteme) Programmiersprachen Geschichte der Programmiersprachen Datentypen Programmiersprachen Algorithmen Datenstrukturen Programmiersprachen Kontrollstrukturen Programmiersprachen Objektorientierung Formale Sprachen BNF, Semi-Thue-Systeme, Markov-Algorithmen, Chomsky-Grammatiken

80. Entrez PubMed No abstract, Energy spectra and level statistics of Fibonacci and thueMorse chains. Noabstract, Generalized thue-Morse chains and their physical properties. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Link&db=PubMed&dbFrom=PubMed&f

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