41. Semi-Thue Grammar@Everything2.com These grammars are named for axel thue, but they were also apparently independentlydiscovered by Noam Chomsky, who used the name phrase structure grammars http://www.everything2.com/index.pl?node_id=1372331

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

43. Jean Berstel Publications Jean Berstel axel thue s papers on repetitions in words a translation.Publications du LaCIM 20. 85 pages. 1994. Jean Berstel A rewriting of Fife s http://www-igm.univ-mlv.fr/~berstel/Recherche.html

Jean Berstel Home Page Jean Berstel, Dominique Perrin: Algorithms on words. in: Lothaire, Applied Combinatorics on Words, Cambridge Univ. Press, 1-100 EE Jean Berstel: Growth of repetition-free words - a review. Theor. Comput. Sci. EE Jean Berstel, Luc Boasson Michel Latteux : Mixed languages. Theor. Comput. Sci. 332 EE Jean Berstel, Olivier Carton : On the complexity of Hopcroft's state minimization algorithm. CIAA 2004 EE Jean Berstel, Luc Boasson Olivier Carton Bruno Petazzoni Jean-Eric Pin : Operations Preserving Recognizable Languages. FCT 2003 Jean Berstel, : Combinatorics on words: a tutorial. Bulletin of the EATCS 79 Jean Berstel: Recent results on extensions of Sturmian words. Intern. J. Algebra Comput. Jean Berstel, : Sturmian Words. in: Lothaire, Algebraic Combinatorics on Words, Cambridge University Press EE Jean Berstel, Luc Boasson : Balanced Grammars and Their Languages. Formal and Natural Computing 2002 LNCS EE Jean Berstel, Luc Boasson : Formal properties of XML grammars and languages. Acta Inf. 38 EE Jean Berstel, Luc Boasson : Shuffle factorization is unique.

44. Biography-center - Letter T thue, axel wwwhistory.mcs.s t-and.ac.uk/~history/Mathematicians/thue.html;Thulden, Theodor van www.getty.edu/art/collections/bio/a502-1.html http://www.biography-center.com/t.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish T 366 biographies T humamah ibn Uthal, www.usc.edu/dept/MSA/history/biographies/sahaabah/bio.THUMAMAH_ IBN_UTHAL.html T ishler, Max www.invent.org/hall_of_fame/145.html T rotter, William Monroe www.triadntr.net/~rdavis/trotter.htm T urchi, Alessandro www.kfki.hu/~arthp/bio/t/turchi/biograph.html Tabern, Donalee L. www.invent.org/hall_of_fame/142.html Tacquet, Andrea www-history.mcs.st-and.ac.uk/~history/Mathematicians/Tacquet.html Taetzsch, Lynne lynnetaetzsch.com Taft, Helen Herron www.whitehouse.gov/WH/glimpse/firstladies/html/ht27.html Taft, Wi lliam Howard odur.let.rug.nl/~usa/P/wt27/about/taftbio.htm Tagore, Rabindranath www. nobel.se/literature/laureates/1913/tagore-bio.html Tahir, ibn

45. Robert McNaughton a linguistic method developed by Norwegian logician axel thue in 1914.thue systems are useful for computation because they replace strings (connected 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.

46. Encyclopaedia Britannica Entry Following work by axel thue, Carl Ludwig Siegel, and Klaus Friedrich Roth, Bakershowed that for f(x, y) = m, f(x, y), an irreducible binary form of degree http://www.aam314.vzz.net/EB/Baker_Alan.html

Baker, Alan Born: Aug. 19, 1939, London, Eng. British mathematician who was awarded the Fields Medal in 1970 for his work in number theory. Baker attended University College, London (B.S., 1961), and Trinity College, Cambridge (M.A. and Ph.D., 1964). He held an appointment at University College (1964-65) and then joined the faculty of Trinity College in 1966. Baker received the Fields Medal at the International Congress of Mathematicians in Nice, France, in 1970. His work with diophantine equations provided an advance over previous work in an area that a few years earlier had been shown to hold limited possibilities for success. Following work by Axel Thue, Carl Ludwig Siegel, and Klaus Friedrich Roth, Baker showed that for f x y m f x y ), an irreducible binary form of degree n ? 3 with integer coefficients, m being a positive integer, there is an effective bound B depending only on n and on the coefficients of f , so that max x y B , for any solution ( x y ). Thus, at least in theory, it is possible to determine all the solutions explicitly for a large class of equations. This work was related to Baker's considerable generalization of the Gelfond-Schneider theorem (Hilbert's seventh problem) that states that, if

47. Axel Oxenstierna - Columbia Encyclopedia® Article About Axel Oxenstierna axel Oxenstierna. Information about axel Oxenstierna in the Columbia axel Stordahl axel thue axel von Fersen axel von Fersen, senior http://columbia.thefreedictionary.com/Axel Oxenstierna

Domain='thefreedictionary.com' word='Oxenstierna, Count Axel Gustafsson' Your help is needed: American Red Cross The Salvation Army join mailing list webmaster tools Word (phrase): Word Starts with Ends with Definition subscription: Dictionary/ thesaurus Computing dictionary Medical dictionary Legal dictionary Financial dictionary Acronyms Columbia encyclopedia Wikipedia encyclopedia Hutchinson encyclopedia Oxenstierna, Count Axel Gustafsson (redirected from Axel Oxenstierna Also found in: Wikipedia 0.02 sec. Page tools Printer friendly Cite / link Email Feedback Oxenstierna, Count Axel Gustafsson Gustavus II Gustavus II Military Achievements Gustavus's excellent education, personal endowments, and early experience in affairs of state prepared him for his crucial role in Sweden and Europe. Click the link for more information. was continually occupied with foreign campaigns. Oxenstierna also organized the conquered territories, skillfully managed financial affairs, and aided Gustavus's wars by his diplomacy. In 1629 he arranged a favorable truce with Poland, freeing the army for the campaign in Germany. Habitually cautious, he opposed Sweden's entry into the Thirty Years War Thirty Years War

48. Events - Math Graduate Students Association yet it was shown by axel thue in 1906 that there exist arbitrarily long thue also showed that using two letters, one can create arbitrarily long http://www.math.toronto.edu/mgsa/events

Math Graduate Students Association Events Home Events Cabinet Links Math Dept. MGSA Pub Night: Fox and Fiddle - Bloor and Huron (at bottom of the Quality Inn) Every Thursday in April 2005 8:00 PM-last call Past events Graduate student seminar: "Gödel's Incompleteness Theorem" Dror Bar-Natan, University of Toronto Gödel's Incompleteness Theorem states that any axiomatization of number theory will miss something; that there will always be a number-theoretic statement that is true and yet unprovable. Along with several other celebrated theorems of logic it sets mathematics apart from all other human endeavors - unlike in physics, economy or history, we mathematicians know our foundations. We have an extremely good collection of axioms so we know what we can do. And we even know, quite for sure, what we will never be able to do - prove all that is right, for one. Gödel's theorem is famed even outside of math, yet not enough of us know how easy it is. Indeed, here's that statement that is true and yet unprovable: This Statement Has No Proof Self reference? Maybe. But remember

49. Beezer's Academic Genealogy Albert Thoralf Skolem TCSGMHMBDM; axel thue TCSGMHM BDM 2296);thue thue enrolled at Oslo University in 1883 and became a candidate http://buzzard.ups.edu/genealogy.html

Beezer's Academic Genealogy Here it is the succession of PhD advisers and students that goes backwards in time from my own degree. For the later entries it is not clear that there was a formal advisor/student/degree relationship, but there is evidence that one person was influenced in their education by the other. It seems odd that [TCSG] lists Ore as a student of Skolem, with Ore's degree awarded in 1924 while [BDM] lists Skolem's degree as being given in 1926. Tree Paul Morris Weichsel (Cal Tech 1960) [ MGP Richard Albert Dean (Ohio State 1953) [ MGP Marshall Hall, Jr. (Yale University 1936) [ MGP TCSG MGP TCSG Albert Thoralf Skolem [ TCSG MHM ][BDM] Axel Thue [ TCSG MHM ] [BDM] Marius Sophus Lie [ MHM Peter Ludwig Mejdell Sylow [ MHM The following quotes are from articles in the Biographical Dictionary of Mathematicians [BDM]: Skolem: "In the latter year [1916] he returned to Oslo, where he was made Dozent in 1918. He received his doctorate in 1926." (H. Oettel, p. 2296) Thue: "Thue enrolled at Oslo University in 1883 and became a candidate for the doctorate in 1889." (Viggo Brun, p. 2460)

50. Peter's Personal Rants. Today's Special:A Rant Concerning The Number 3... Nevertheless, the Norwegian mathematician axel thue proved almost a thue, axel.1912. Über die gegenseitige lage gleicher teile gewisser Zeichenreihen. http://www.zzrose.com/pmrrant1.html

Rant Number 1 A Rant Concerning the Number 3 Starting thoughts... This rant has to do with the number 3. Let me begin by telling a story so you can see where my interest in the number 3 comes from. When I was a physics undergraduate student, I used to watch and drool over the studies of a friend of mine who was in the Master's program. I learned to really appreciate my studies by seeing how he was applying the basics of what I was learning to solving really neat problems. One Friday I wandered into the lab where three of them were grinding through the solution of some complex electromagnetic equations. The solution was so complex that they had divided the work up among themselves and had been busy filling page after page of large computer printout paper abscounded from the computer center (this was back in 1970, mind you...). Well it was a sight for a young impressionable lad such as myself to watch. I sat there for hours just watching them grind through their solutions. I was impressed. But, soon I heard the call of the local pub and wandered off to play. Late Sunday afternoon, I went back to see how they were doing. Much to my surprise, they were all jumping up and down and yelling and screaming. Crumpled computer paper was

51. Biz-community - Sales In South Africa you re ignoring what axel thue, the Norwegian mathematician, taught us in theearly 1900 s the densest packing of round items is hexagonal, not linear. http://www.biz-community.com/196/20.html

South Africa's leading daily advertising, marketing and media news resource for the industry! Sales community of South Africa Marketing Advertising Branding Cinema ... Galleries Companies Press offices Companies List your company Resources Topics Newsletters Community Quotes, Jokes Forums, Votes ... Subscribers COMPANIES IN THE NEWS: List your company News Views/Comments Ian Widdop The forgotten art of closing the sale Michael W. McLaughlin Nine ways to botch a proposal People on the move Additions for Oracle Airtime Sales More... Submit a person Events Professional Sales Management - Johannesburg 12 Sep More... Submit an event Jobs offered Salesperson - Johannesburg Media Sales Executive Direct Sales Administrator - Cape Town Corporate Sales Executive - Cape Town Recruitment Consultant - Cape Town More... Submit a job Submit your skills Search ... [Ian Widdop] It has been said that over 80% of buyers are better at closing a deal than the sellers themselves. The truth is that there is a fine art to selling, and that contrary to popular belief, it has nothing to do with customer manipulation. 23 Aug 09:05 Nine ways to botch a proposal [Michael W. McLaughlin]

52. Merchandising: How To Increase Your Stockholding Of Tins (and Other Round Items) you re ignoring what axel thue, the Norwegian mathematician, taught us in theearly 1900 s the densest packing of round items is hexagonal, not linear. http://www.biz-community.com/Article/196/20/5555.html

South Africa's leading daily advertising, marketing and media news resource for the industry! Sales community of South Africa Marketing Advertising Branding Cinema ... Galleries Companies Press offices Companies List your company Resources Topics Newsletters Community Quotes, Jokes Forums, Votes ... Subscribers COMPANIES IN THE NEWS: List your company Sales news More Sales news SALES NEWS The forgotten art of closing the sale Nine ways to botch a proposal Six ways to quash arguments against change and reap rewards Leverage your expertise to build your business ... More Sales news... Merchandising: How to increase your stockholding of tins (and other round items) by 15% By: Sid Peimer One of the amazing properties of tins is their longevity. However, if you're packing your shelves neatly, with all the tins in a line (called a 'regular' array), you're ignoring what Axel Thue, the Norwegian mathematician, taught us in the early 1900's: the densest packing of round items is hexagonal, not linear. In the shelf of baked beans below, we fit in 48 tins when packing regularly. However, when we resort to a 'messier' hexagonal pattern, we fit in 53 tins - that's over 10% more.

53. INDEX OF NAMES thue, axel (Norway, 18631922) and circle packings, 985 and Diophantine equations,1164 and multiway systems, 938 and substitution systems, 879, 893 http://www.wolframscience.com/nksonline/index/names/t-z.html?SearchIndex=Turing,

54. T-Ti thue, axel (Norway, 18631922) and circle packings, 985 and Diophantine equations,1164 and multiway systems, 938 and repetition-free sequences, 944 http://www.wolframscience.com/nksonline/index/t-ti.html

INDEX A B C D ... S T U V W X ... Z T-Ti Tj-Tz T-Ti T1 and T2 processes in networks Table basic examples of, Tables for Boolean formulas, leading digits in, of primes, of random numbers, see also Multiplication tables Tabulating machines Tachyons spin of, Taffy as chaos theory example, fracture in, Tag systems cyclic, see also Cyclic tag systems density in, emulated by correspondence systems, emulated by recursive functions, emulated by universal TM, emulating CAs, emulating TMs, implementation of, multiway, one-element-dependence, as precursors to my work, random initial conditions in, and TM 596440, undecidability in, uniform, see also Substitution systems universality in simple, universality of one-element dependence, Tail recursion and recursive functions, Tails (of data) Taj Mahal nesting in gardens of, Take (take elements) basic example of, Tally sticks and application of randomness, Tan curve of

55. MY TEACHERS' TEACHERS' TEACHERS' His advisor axel thue. axel thue 19 Feb 18637 Mar 1922 received his Ph.D.at University of Christiana in 1889. His advisor M. Sophus Lie. http://www.magicdragon.com/JVPteachers.html

PROFESSIONAL "GENEOLOGY": MY TEACHERS' TEACHERS' TEACHERS Compiled by Magic Dragon Multimedia Ultimate Science Fiction Web Guide 9,000+ more authors indexed AUTHORS of Ultimate Westerns Web Guide 1,000+ more authors indexed AUTHORS of Ultimate Romance Web Guide 8,000+ more authors indexed May be posted electronically provided that it is transmitted unaltered, in its entirety, without charge. version update of 19 August 2004 [42 Kilobytes] Music (Guitar) Literature (Poetry) Science (Philosophy) Science (Physics) ... Acting/Theatre MUSIC (Guitar): Andres Segovia [1893-1987], from Spain, was the most famous guitarist of all time. He brought the classical guitar from its folk- and dance-related image to the symphonies and concert halls of the most established musical prominence. He developed an approach to plucking the guitar strings with the fingernails of the right hand, which became the dominat school of guitar, displacing the gentler and more lyrical Neapolitan school which used the fingertips. Christopher Parkening is arguably the greatest American performer of Classical Guitar. After a year of intensive Classical Guitar at Brookdale Community College, under Christopher Parkening's master student Barry Eisner, I was able to play a few baroque pieces and original compositions at community college concerts, and then retired to the occasional original song at Woodstock, various parties and resorts, and while hitchiking across America, singing for my supper. See also Donald Justice and Carl Ruggles in the "Poetry" section, below.

56. 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.

57. Cass 1 about 300 years before it was proven, by the Norwegian mathematician axel thue . Now thue s and Hales s theorems have little to do with real world http://www.math.sunysb.edu/~tony/whatsnew/column/pennies-1200/cass1.html

Packing Pennies in the Plane An illustrated proof of Kepler's conjecture in 2D by Bill Casselman NOTE: This month's contribution contains several Java applets. They may not work on your particular computer, for any of various reasons. If you do not have Java enabled in your browser, for example, you will see only static images representing the animated applets. If you have trouble with viewing the applets even though Java is enabled, or if you want to print out this note, you should disable Java. If Java is enabled and you still have trouble viewing the applets, please let Bill Casselman know about it. 1. "Kepler's Conjecture" This and the other image nearby are from Kepler's pamphlet on snowflakes. Contrary to what one might think at first. they are not of two dimensional objects, but rather an attempt to render on the page three dimensional packings of spheres. In his book De nive sexangula (`On the six-sided snowflake') of 1611, Kepler asserted that the packing in three dimensions made familiar to us by fruit stands (called the face-centred cubic packing by crystallographers) was the tightest possible: Coaptatio fiet arctissima: ut nullo praetera ordine plures globuli in idem vas compingi queant.

58. Bulletin Of The EATCS, Volume 34 5561 BibTeX Solomon Marcus Formal languages before axel thue. 62 BibTeX Gheorghe Paun On Langford-Lyndon-thue sequences. 63-67 BibTeX http://www.informatik.uni-trier.de/~ley/db/journals/eatcs/eatcs34.html

Bulletin of the EATCS , Volume 34 Volume 34, February 1988 The computational Geometry Column Herbert Edelsbrunner : The computational Geometry Column. 32-38 BibTeX The Algebraic Specification Column Hartmut Ehrig : The Algebraic Specification Column. 39-40 BibTeX The Formal Language Theory Column Arto Salomaa : The Formal Language Theory Column. 82-96 BibTeX Technical Contributions Maxime Crochemore Dominique Perrin : Critical factorizations of words. 47-51 BibTeX Clelia de Felice : On the finite completion of codes. 52-54 BibTeX : On domains of tree tranducers. 55-61 BibTeX Solomon Marcus : Formal languages before Axel Thue. 62 BibTeX Gheorghe Paun : On Langford-Lyndon-Thue sequences. 63-67 BibTeX DBLP: [ Home Author Title Conferences ... Journals Wed Sep 7 02:28:23 2005 by Michael Ley ley@uni-trier.de

59. DBLP: Solomon Marcus 1, Solomon Marcus Formal languages before axel thue. Bulletin of the EATCS 3462 (1988). Coauthor Index. 1, Cristian Calude, 15 16 18 http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/m/Marcus:Solomon.html

Solomon Marcus List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL ACM Guide CiteSeer CSB ... EE Solomon Marcus: The Duality of Patterning in Molecular Genetics. Aspects of Molecular Computing 2004 EE Cristian Calude , Solomon Marcus: Mathematical Proofs at a Crossroad? Theory Is Forever 2004 Solomon Marcus: Quasiperiodic Infinite Words (Columns: Formal Language Theory). Bulletin of the EATCS 82 Cristian Calude Elena Calude , Solomon Marcus: Passages of Proof. Bulletin of the EATCS 84 EE Cristian Calude , Solomon Marcus, Ludwig Staiger : A topological characterization of random sequences. Inf. Process. Lett. 88 EE Solomon Marcus: Bridging P Systems and Genomics: A Preliminary Approach. WMC-CdeA 2002 Solomon Marcus: Membranes Versus DNA. Fundam. Inform. 49 EE Solomon Marcus: Bridging Two Hierarchies of Infinite Words. J. UCS 8 EE Solomon Marcus: Tolerance Multisets. WMP 2000 EE Solomon Marcus: Under the Sign of Boole. J. UCS 6 Solomon Marcus: On the Length of Words. Jewels are Forever 1999 EE Solomon Marcus: The Paradox of the Heap of Grains in Respect to Roughness, Fuzziness and Negligibility. Rough Sets and Current Trends in Computing 1998 Solomon Marcus

60. List Of Scientists By Field thue, axel. Thunberg, Carl Peter. Thunberg, Thorsten Ludvig. Thuret, GustaveAdolphe. Thurnam, John. Thurnam, John. Thurneysser, Leonhard http://www.indiana.edu/~newdsb/t.html

Tabor, John Tacchini, Pietro Taccola, Mariano di Jacomo Tachenius, Otto Tachenius, Otto Tacquet, Andreas Tait, Peter Guthrie Tait, Peter Guthrie Takagi, Teiji Talbot, William Henry Fox Talbot, William Henry Fox Tamm, Igor Evgenievich Tammann, Gustav Heinrich Johann Apollon Tanakadate, Aikitsu Tanfilev, Gavriil Ivanovich Tanfilev, Gavriil Ivanovich Tanfilev, Gavriil Ivanovich Tannery, Jules Tannery, Paul Tarde, Jean Tarde, Jean Targioni Tozzetti, Giovanni Tarski, Alfred Tashiro, Shiro Tashiro, Shiro Tauber, Alfred Taurinus, Franz Adolph Taylor, Brook Taylor, Charles Vincent Taylor, Frank Bursley Taylor, Frederick Winslow Taylor, Geoffrey Ingram Taylor, Geoffrey Ingram Taylor, Hugh Stott Teall, Jethro Justinian Harris Teichmann, Ludwik Karol Teichmann, Ludwik Karol Teilhard de Chardin, Pierre Teilhard de Chardin, Pierre Teissier, Georges Telesio, Bernardino Ten Rhyne, Willem Ten Rhyne, Willem Tennant, Smithson Tennent, David Hilt Termier, Pierre Tesla, Nikola Tesla, Nikola Thales Thaxter, Roland Thayer, William Sydney Theaetetus Themistius Themistius Thenard, Louis Jacques

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