
	Where results make sense

Topic: Axel Thue

Related Topics

Maeonian

Srem

Camp Floyd

John Charles Fields

Rene Reyes

Gustaf II Adolf of Sweden

Cabir

Antoine Court de Gebelin

Khaan

Quesnel

Tap water

Jacaltec

Darby Crash

Norway

Krav Maga

In the News (Tue 10 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Thue biography
		Axel Thue was the son of Niels Thue and Nicoline Cathinka Eger.
		Then Thue was appointed to Trondheim Technical College where he worked from 1894 until 1903.
		In fact Thue wrote 35 papers on number theory, mostly on the theory of Diophantine equations, and these are reproduced in [Selected mathematical papers of Axel Thue, Introduction by Carl Ludwig Siegel (Oslo, 1977).',2)" onmouseover="window.status='Click to see reference';return true">2].
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Thue.html (445 words)

	Axel Thue's work on repetitions in words - Berstel (ResearchIndex)
		Abstract: The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned.
		Berstel [1992], Axel Thue's work on repetitions in words, in: S'eries Formelles et Combinatoire Alg'ebrique (P. Leroux and C. Reutenauer, eds.), Publ.
		42 Uber unendliche Zeichenreihen (context) - Thue - 1906
	citeseer.ist.psu.edu /berstel92axel.html (1027 words)

	Thue - Esolang
		Thue is an esoteric programming language invented by John Colagioia in 2000.
		Thue is based on a semi-Thue grammar, which is a restricted form of Thue system in which each association between a pair of strings is only one-way.
		The language is presumably named after either Norwegian mathematician Axel Thue, or the grammar which bears his name (which the language employs).
	esoteric.voxelperfect.net /wiki/Thue (520 words)

	Thue biography
		Axel Thue was the son of Niels Thue and Nicoline Cathinka Eger.
		Then Thue was appointed to Trondheim Technical College where he worked from 1894 until 1903.
		In fact Thue wrote 35 papers on number theory, mostly on the theory of Diophantine equations, and these are reproduced in [Selected mathematical papers of Axel Thue, Introduction by Carl Ludwig Siegel (Oslo, 1977).',2)" onmouseover="window.status='Click to see reference';return true">2].
	www-history.mcs.st-andrews.ac.uk /history/Biographies/Thue.html (445 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		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").
		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.
		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.
	catseye.mine.nu:8080 /projects/thue/doc/thue.txt (534 words)

	Doug, Basho, and Axel Thu
		Axel Thu was a Chinese mathematician who died in the year 400 AD.
		Historical Note: His name was actually Axel Thue, he was Norwegian, and he died in 1922.
		The real Axel Thue said some wonderful things about mathematics: "The further removed from usefulness or practical application, the more important." and "For the development of the logical sciences it will be important to find wide fields for the speculative treatment of difficult problems, without regard to eventual applications." He looked like this:
	www.dougshaw.com /essays/thu.html (1669 words)

	Axel Thue - Wikipedia, the free encyclopedia
		Axel Thue (19 February 1863 - 7 March 1922) was a Norwegian mathematician, known for highly original work in diophantine approximation, and combinatorics.
		He stated in 1914 the so-called Word problem or Thue problem, closely related to the halting problem.
		This article about a mathematician is a stub.
	en.wikipedia.org /wiki/Axel_Thue (86 words)

	Read This: How the Other Half Thinks
		Thue is not disclaiming any consideration of applications, particularly since he goes on, in the next sentence (not quoted by Stein), to mention possible connections with number theory.
		It seems to me that Thue is in effect apologizing for the apparent lack of applications of his problem, not, as Stein makes it seem, claiming that we can do good mathematics by making up any old problem we like.
		I'm sure that Thue himself understood quite well why his problem was an interesting one, though of course the general reader will not have the benefit of Thue's experience in mathematical research.
	www.maa.org /reviews/otherhalf.html (2780 words)

	NewAbelianSquare-FreeDT0L-LanguagesOver4Letters.nb
		Thue also showed that over a binary alphabet one can construct arbitrarily long words which do not contain any triple repetitions (cubes), i.e., factors occurring three times in succession.
		Unfortunately, Thue's results were forgotten for a long time, and they have been rediscovered and republished again and again - at least a dozen of times as noted in [9].
		The tool which Thue invented for constructing square-free words, namely the concept of a repetition-free morphism, is still today a basic device in the study of avoidable patterns in words.
	south.rotol.ramk.fi /keranen/ias2002/NewAbelianSquare-FreeDT0L-LanguagesOver4Letters.html (3469 words)

	Thue (Site not responding. Last check: 2007-10-15)
		Lie's influence, probably because of Thue's inability to follow anyone else's line of thought.
		In fact Thue wrote 35 papers on number theory, mostly on the theory of Diophantine equations, and these are reproduced in [2].
		Another quote from Thue on applied mathematics (see for example [1]) is:-
	www.educ.fc.ul.pt /icm/icm2003/icm14/Thue.htm (339 words)

	Friday Pathological Programming: Programming Through Grammars in Thue
		Today's treat: Thue, pronounced two-ay, after a mathematician named Axel Thue.
		Thue is a language based on semi-Thue grammars.
		As the #::= order of rule triggering is undetermined in Thue, a rule matching #::= nine consecutive * would not work.c<::=c<0>,c<::=c<1>c<::=2>0>d::=d1>d::=d*********,#::= when the copy is done, 'd' is at the right place to begin the sum.2>d::=f<#::= add left to right.
	science.blogdig.net /archives/articles/August2006/04/Friday_Pathological_Programming__Programming_Through_Grammars_in_Thue.html (932 words)

	Beezer's Academic Genealogy (Site not responding. Last check: 2007-10-15)
		Thue: "Thue enrolled at Oslo University in 1883 and became a candidate for the doctorate in 1889." (Viggo Brun, p.
		Thue: "During 1890-1891 Thue studied at Leipzig under Sophus Lie..." (Viggo Brun, p.
		Lie: "He studied at Christiania University from 1859 to 1865, mainly mathematics and sciences.
	buzzard.ups.edu /genealogy.html (211 words)

	Cat's Eye Technologies: /projects/thue/ (Site not responding. Last check: 2007-10-15)
		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, which is named for (and possibly created by) the Norwegian mathematician Axel Thue (pronounced \"TOO-ay\").
		Thue represents one of the simplest possible ways to construe constraint-based programming.
	catseye.mine.nu:8080 /projects/thue (96 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: 2007-10-15)
		It is named after the Norwegian mathematician Axel Thue, who introduced systematic treatment of string rewriting systems in the early 20th century.
		Semi-Thue systems were developed as part of a program to add additional constructs to logic, so as to create systems such as propositional logic, that would allow general mathematical theorems to be expressed in a formal language, and then proven and verified in an automatic, mechanical fashion.
		And although this program of research succeeded in that computers can now be used to verify the proofs of theorems, it also failed in a spectacular way: a computer cannot distinguish between an interesting theorem, and a boring one.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Semi-Thue_system (405 words)

	cass 1
		However, it took about 300 years before it was proven, by the Norwegian mathematician Axel Thue.
		And Harriot's interest was perhaps prompted by a question his employer, Sir Walter Raleigh, had asked him much earlier about how to count the cannon balls in stacks on a ship.
		Thue's and Hales' theorems are concerned instead with ideal packings throughout all of the plane and space.
	www.math.sunysb.edu /~tony/whatsnew/column/pennies-1200/cass1.html (551 words)

	Diophantine approximation
		Before that much was known from the theory of continued fractions, as applied to square roots of integers and other quadratic irrationals.
		This result was improved by Axel Thue[?] and others, leading in the end to a definitive theorem of Roth: the exponent in the theorem was reduced from n, the degree of the algebraic number, to any number greater than 2 (i.e.
		After that generalisation was made to simultaneous approximation, by Schmidt.
	www.ebroadcast.com.au /lookup/encyclopedia/di/Diophantine_approximation.html (316 words)

	Thue Sequences, Lambda Calculus Circular Program
		Thue sequences, after Axel Thue, are sequences over an alphabet of three {1,2,3} such that no subsequence is immediately repeated.
		1213121 is a Thue sequence that cannot be extended 12131211 ×, 12131212 ×, 12131213 ×.
		However, there are Thue sequences of any length.
	www.csse.monash.edu.au /~lloyd/tildeFP/Lambda/Examples/Thue (667 words)

	Thue-Morse L-system (Site not responding. Last check: 2007-10-15)
		Axel Thue came up with it in 1912 [Thu12] in his study of formal languages (not the term he used then).
		Thue proved a very interesting theorem about the Thue-Morse sequence.
		THEOREM: (Thue-Morse is cube-free) There is no substring of the Thue-Morse sequence of the form www for some finite string w of a's and b's.
	www.math.okstate.edu /mathdept/dynamics/lecnotes/node16.html (569 words)

	Robert McNaughton (Site not responding. Last check: 2007-10-15)
		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.
	www.cs.rpi.edu /people/mcnaughton.html (371 words)

	Random Work - nuwen.net
		The Norwegian mathematican Axel Thue proved nearly 100 years ago that there do exist arbitrarily long ternary squarefree sequences, and gave a method for constructing one.
		Thue proved that you can perform this procedure as many times over as you like, starting with the sequence 0, and you will always generate a (longer) ternary sequence which is squarefree.
		Anyways, back to the "Thue sequences": The proof that its length grows as powers of two is rather nice.
	nuwen.net /work.html (4242 words)

	NewAbelianSquare-FreeTD0L-LanguagesOver4Letters.nb
		As mentioned above, the systematic study of word structures, i.e., combinatorics on words, was started by Axel Thue (1863--1922) in [34] at the beginning of the 20th century.
		Unfortunately, Thue's results were forgotten for a long time, and they have been rediscovered and republished again and again -- at least dozen times as noted in [9].
		In a paper from 1961, see [13, p.240], Paul Erdös (1913--1996) raised the question whether abelian squares can be avoided in infinitely long words, i.e., whether there exist infinitely many abelian square-free words over a given alphabet.
	south.rotol.ramk.fi /keranen/ias2002/NewAbelianSquare-FreeTD0L-LanguagesOver4Letters.html (3653 words)

	Merchandising: How to increase your stockholding of tins (and other round items) by 15%
		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.
		On average (according to Thue's Theorem below) an increase of 14.65% (except for the one person on the end).
		Note: Thue's Theorem only holds for an infinite amount of space (not the case in the local supermarket) and sometimes the best array can be a mix of square and hexagonal packing (depending on the size of the tin, number of facings and dimensions of the shelf).
	www.biz-community.com /Article/196/20/5555.html (578 words)

	Infinite Sets of Square-Free omega-words Derived from the Prouhet-Thue-Morse Sequence -- from Mathematica Information ...
		We describe a method to generate an infinite set of unique square-free omega-words from the (Prouhet)-Thue-Morse sequence on a four letter alphabet.
		This result is a generalization of the method introduced by Axel Thue in 1912 for constructing a square-free omega-word over four (and then over three) letters from the Thue-Morse sequence.
		The new method has been further generalized to produce infinite sets of square-free omega-words on larger alphabets.
	library.wolfram.com /infocenter/Conferences/6041 (141 words)

	Thue-Morse sequence - Wikipedia, the free encyclopedia
		Prouhet in 1851, who applied it to number theory.
		However, Prouhet did not mention the sequence explicitly; this was left to Axel Thue in 1906, who used it to found the study of combinatorics on words.
		Since Thue published in German, his work was ignored at first; the sequence was only brought to worldwide attention with the work of Marston Morse in 1921, when he applied it to differential geometry.
	en.wikipedia.org /wiki/Thue-Morse_sequence (684 words)

	Wolfgang M. Schmidt
		It came as a surprise to the number theory community when Sergei Stepanov, beginning in 1969, gave elementary proofs of many of Weil's results.
		Stepanov drew inspiration from the work of Axel Thue (1909) in Diophantine approximation.
		Proofs of Weil's theorem in full generality, based on Stepanov's ideas, were given independently by Wolfgang Schmidt and Enrico Bombieri in 1973.
	www.kendrickpress.com /Schmidt.html (248 words)

	GeorgeSzpiro.com
		He became friendly with Sophus Lie from Norway, the erstwhile mentor of Axel Thue.
		But Blichfeldt did not waste the occasion as Thue had done five years earlier.
		He used his proximity to the great Lie to his advantage, and learnt a thing or two from his thesis supervisor.
	www.georgeszpiro.com /index.asp?page=kepler/chapter09.htm (1165 words)

	Good Math, Bad Math : Friday Pathological Programming: Programming Through Grammars in Thue
		But they use "#" on the left hand side as a comment marker, and then make sure that it never appears anywhere else - so none of the comment rules can ever be invoked.
		As the #::= order of rule triggering is undetermined in Thue, a rule matching #::= nine consecutive * would not work.
		#::=# BRAINFUNCT interpreter in THUE #::=# by Frederic van der Plancke; released to the Public Domain.
	scienceblogs.com /goodmath/2006/08/friday_pathological_programmin_2.php (1583 words)

	Thoralf Skolem - Wikipedia Mirror US (Site not responding. Last check: 2007-10-15)
		He later changed in mind and submitted a thesis in 1926, titled Some theorems about integral solutions to certain algebraic equations and inequalities.
		His notional thesis advisor was Axel Thue, even though Thue had died in 1922.
		Skolem continued to teach at Kristiania University (renamed the University of Oslo in 1925) until 1930 when he became a Research Associate in Christian Michelsen's Institute in Bergen.
	www.wiki-mirror.us /index.php/Thoralf_Skolem (1417 words)

	Bibliography: Balanced Ternary (Site not responding. Last check: 2007-10-15)
		In Selected Mathematical Papers of Axel Thue, pp.
		Axel Thue proved that unbounded square free ternary sequences exist and gave a method to construct one.
		The design of small digital machine "Setun" (Setun is the little river which flows into the river "Moscow" near the University) was initiated by member of the academy of Sciences S.
	abhijit.info /tristate/biblio.htm (1322 words)

	Discovery Channel's Cosmeo
		February 19, 1863: Birthdate of mathematician Axel Thue
		Thue made fundamental contributions to number theory (particularly transcendence theory).
		He wrote thirty-five papers in the field, mostly on the theory of Diophantine equations.
	www.cosmeo.com /viewTodayInHistoryEvents.cfm?guidAssetId=d5e4d8b8-85b4-4b8f-aa46-2e7894911bfe&eventId=1438 (72 words)

Try your search on: Qwika (all wikis)