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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

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
    
    Extractions: Repetition Free Words 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
    
    Extractions: 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
    
    Extractions: 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
    
    Extractions: 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
    
    Extractions: 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

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/
    
    Extractions: 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
    
    Extractions: Next: About this document Up: Recursive Matrix Systems Previous: Further work 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
    
    Extractions: by Sherman Stein 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/
    
    Extractions: 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.

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

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

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
    
    Extractions: 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 :

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
    
    Extractions: 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 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: The sequence can also be defined by: where t j is the j th element if we start at j 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
    
    Extractions: 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

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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