the repeating and complementary makeup of the ThueMorsesequence. File Parity relation 0011 1100 ... B horizontal index br is an odd number of elements. In mathematics , the ThueMorsesequence , or Prouhet ThueMorsesequence , is a binary sequence a sequence of 0s and 1s that begins 01101001100101101001011001101001 ... of 0 and 1 the logical structure of the ThueMorsesequence does not depend on the symbols that are used to represent it. Definition There are several equivalent ways of defining the ThueMorsesequence ... relation The ThueMorsesequence is the sequence t sub n sub satisfying t sub 0 sub 0, t sub ... start 0 rules 0 01 , 1 10 Characterization using bitwise negation The ThueMorsesequence in the form ... by successive iterations of ThueMorse. Because each new block in the ThueMorsesequence is defined ... block, the ThueMorsesequence is filled with squares consecutive strings that are repeated. That is, there are many ... q sub n sub are palindrome squarefree word s. The statement above that the ThueMorsesequence ... 1 with 10. Then if T is the ThueMorsesequence, then f T is T again that is, T is a fixed point ... fixed point is the bitwise negation of T , which is simply the ThueMorsesequence on 1,0 instead of on 0,1 ... is programmed with a sequence. If the ThueMorseSequence members are used in order to select ... a finite area. This illustrates the fractal nature of the ThueMorseSequence. Application to Resource ... MorseSequence title ThueMorseSequence Allouche, J. P. Shallit, J. O. http www.cs.uwaterloo.ca shallit Papers ubiq.ps The Ubiquitous Prouhet ThueMorseSequence . contains many applications and some history ThueMorseSequence over 1,2 OEIS id A001285 Odious numbers OEIS id A000069 Evil numbers OEIS ... When ThueMorse meets Koch . A paper showing an astonishing similarity between the ThueMorseSequence ... MorseSequence . A technical application of the ThueMorseSequence http reglos.de musinum MusiNum The Music in the Numbers . Freeware to generate self similar music based on the ThueMorseSequence ... more details
In mathematics , the Prouhet ThueMorse constant , named for Eug ne Prouhet , Axel Thue , and Marston Morse , is the number denoted by math tau math whose binary expansion .01101001100101101001011001101001... is given by the ThueMorsesequence . That is, math tau sum i 0 infty frac t i 2 i 1 0.412454033640 ldots math where math t i math is the i sup th sup element of the Prouhet ThueMorsesequence. The generating series for the math t i math is given by math tau x sum i 0 infty 1 t i , x i frac 1 1 x 2 sum i 0 infty t i , x i math and can be expressed as math tau x prod n 0 infty 1 x 2 n . math This is the product of Frobenius polynomial s, and thus generalizes to arbitrary field mathematics fields . The Prouhet ThueMorse constant was shown to be transcendental number transcendental by Kurt Mahler in 1929. ref Kurt Mahler, Arithmetische Eigenschaften der L sungen einer Klasse von Funktionalgleichungen , Math. Annalen , t. 101 1929 , pp. 342 66. ref Applications The Prouhet ThueMorse constant occurs as the angle of the External ray Douady Hubbard ray at the end of the sequence of western bulbs of the Mandelbrot set . This property is tied to the nature of period doubling in the Mandelbrot set. ref http www.linas.org art gallery escape phase atlas.html Parameter Ray Atlas 2000 provides a link to the Mandelbrot set. ref clarify date August 2010 Excuse me? Can you illustrate this, please? Notes references External links SloanesRef sequencenumber A010060 name ThueMorsesequence http www.cs.uwaterloo.ca shallit Papers ubiq.ps The ubiquitous Prouhet ThueMorsesequence , John Paull Allouche and Jeffrey Shallit, undated, 2004 or earlier provides many applications and some history http planetmath.org encyclopedia ProuhetThueMorseConstant.html PlanetMath entry DEFAULTSORT Prouhet ThueMorse Constant Category Mathematical constants Category Number theory Category Transcendental numbers fr Constante de Prouhet ThueMorse ... more details
Infobox scientist name Axel Thue image Axel Thue.jpg image size 250px caption Axel Thue 1863 1922 birth date birth date 1863 2 19 df y birth place T nsberg , Norway residence Norway nationality Norway Norwegian death date death date and age 1922 3 7 1863 2 19 df y death place Oslo , Norway field Mathematician work institution Oslo University University of Kristiania br Trondheim Technical College alma mater Oslo University University of Kristiania doctoral advisor Elling Holst doctoral students Thoralf Skolem known for Thue s theorem disambiguation Thue s theorem prizes religion Axel Thue 19 February 1863 7 March 1922 was a Norway Norwegian mathematician , known for highly original work in diophantine approximation , and combinatorics . He stated in 1914 the so called word problem for semigroups or Thue problem , closely related to the halting problem . His only known PhD student was Thoralf Skolem . The esoteric programming language Thue programming language Thue is named after him. See also Semi Thue system ThueMorsesequenceThue Siegel Roth theorem Thue equation Thue programming language Thue programming language Thue s theorem disambiguation Thue s theorem word problem for groups Word Problem Publications Citation last1 Thue first1 A. title ber Ann herungswerte algebraischer Zahlen url http resolver.sub.uni goettingen.de purl?PPN243919689 0135 year 1909 journal Journal f r die reine und angewandte Mathematik issn 0075 4102 volume 135 pages 284 305 External links MacTutor Biography id Thue MathGenealogy id 18236 Metadata see Wikipedia Persondata Persondata NAME Thue, Axel ... Thue, Axel Category 1863 births Category 1922 deaths Category 20th century mathematicians Category ... stub Euro mathematician stub ar bs Axel Thue de Axel Thue fr Axel Thue ko it Axel Thue hu Axel Thue nl Axel Thue no Axel Thue nn Axel Thue pms Axel Thue pl Axel Thue pt Axel Thue ru , sk Axel Thue fi Axel Thue zh ... more details
In mathematics , recurrent sequence may refer to A sequence satisfying a recurrence relation A sequence such that any subsequence appears infinitely often, such as the ThueMorsesequence or a Sturmian word mathdab ... more details
Image Thue number.svg thumb The Thue number of the 5 Cycle graph cycle is four. In the Mathematics mathematical area of graph theory , the Thue number of a graph is a variation of the chromatic index , defined by Alon et al. 2002 and named by them after mathematician Axel Thue , who studied the squarefree word s used to define this number. Alon et al. define a nonrepetitive coloring of a graph to be an assignment of colors to the edges of the graph, such that there does not exist any even length path graph theory simple path in the graph in which the colors of the edges in the first half of the path form the same sequence as the colors of the edges in the second half of the path. The Thue number of a graph is the minimum number of colors needed in any nonrepetitive coloring. Variations on this concept involving vertex colorings or more general walks on a graph have been studied by several authors including Bar t and Varj , Bar t and Wood 2005 , Bre ar and Klav ar 2004 , and K ndgen and Pelsmajer ... two edges will have the repetitive color sequence xx. If we color the edges with three colors, one ... have two consecutive edges or will form the repetitive color sequence xyxy. However, with four colors it is not difficult to avoid all repetitions. Therefore, the Thue number of C sub 5 sub is four. Results Alon et al. use the Lov sz local lemma to prove that the Thue number of any graph ... dependence is necessary. In addition they show that the Thue number of a path of four or more vertices is exactly three, and that the Thue number of any cycle is at most four, and that the Thue number of the Petersen graph is exactly five. The known cycles with Thue number four are C sub ... that the Thue number of any larger cycle is three they verified computationally that the cycles listed above are the only ones of length 2001 with Thue number four. Currie resolved this in a 2002 paper, showing that all cycles with 18 or more vertices have Thue number 3. Computational complexity ... more details
For other theorems named after Axel ThueThue s theorem disambiguation In mathematics , a Thue equation is a Diophantine equation of the form &fnof x , y r , where is an irreducible polynomial irreducible bivariate Algebraic form form of degree at least 3 over the rational numbers, and r is a nonzero rational number . It is named after Axel Thue who in 1909 proved a theorem , now called Thue s theorem , that Thue equation has finitely many solutions in integers x and y . ref cite journal author A. Thue title ber Ann herungswerte algebraischer Zahlen journal Journal f r die reine und angewandte Mathematik volume 135 pages 284 305 year 1909 url http resolver.sub.uni goettingen.de purl?PPN243919689 0135 ref Solving Thue equations Solving a Thue equation can be described as an algorithm ref cite journal author N. Tzanakis and B. M. M. de Weger title On the practical solution of the Thue equation journal Journal of Number Theory volume 31 issue 2 year 1989 pages 99 132 doi 10.1016 0022 314X 89 90014 0 ref ready for implementation in software. In particular, it is implemented in the following computer algebra system s in PARI GP as functions thueinit and thue . References reflist Category Diophantine equations Category Theorems in number theory fr quation de Thue nl Thue vergelijking pt Teorema de Thue numtheory stub ... more details
Thue s theorem may refer to the following mathematical theorem s named after Axel ThueThue equation has finitely many solutions in integers. Thue Siegel Roth theorem , also known as Roth s theorem, is a foundational result in diophantine approximation to algebraic numbers. The 2 dimensional analog of Kepler s conjecture the regular hexagonal packing is the densest sphere packing in the plane 1890 . disambig ... more details
MedalTableTop MedalCountry CAN MedalSport Men s Wrestling at the Summer Olympics wrestling MedalCompetition Olympic Games MedalSilver 1992 Summer Olympics 1992 Barcelona Wrestling at the 1992 Summer Olympics Men s freestyle 130 kg 130 kg MedalBottom Jeffrey Thue born January 25, 1969 in Regina, Saskatchewan Regina , Saskatchewan is a canadian wrestler . He won a silver medal in the Men s Freestyle Super Heavyweight 130 kg category at the 1992 Summer Olympics . External links http www.olympic.ca fr athl C3 A8tes jeffrey thue profil Athlete Biography at Canadian Olympic Committee Persondata Metadata see Wikipedia Persondata . NAME Thue,Jeffrey ALTERNATIVE NAMES SHORT DESCRIPTION Olympic wrestler DATE OF BIRTH January 25, 1969 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Thue,Jeffrey Category 1969 births Category People from Regina, Saskatchewan Category Olympic wrestlers of Canada Category Olympic silver medalists for Canada Category Wrestlers at the 1992 Summer Olympics Category Living people Category Olympic medalists in wrestling wrestling bio stub Canada Olympic medalist stub ... more details
Leif Thue 12 July 1928 13 June 1993 was a Norwegian trade unionist. He was born in Balestrand . He served as leader of the Norwegian Union of Railway Workers from 1984 to 1992, having served as deputy leader from 1976 to 1984 and secretary from 1971 to 1976. ref name aft cite news title Med Rettedal i halsen last Aaserud first Kjell date 6 July 1990 work Aftenposten page 22 language Norwegian ref As union leader he was also a board member of the Norwegian State Railways . ref name obit1 cite news title Leif Thue obituary last Dalsheim first Ove authorlink Ove Dalsheim date 17 June 1993 work Aftenposten page 15 language Norwegian ref He became a notable public figure in the late 1980s and early 1990s, when the State Railways were restructuring , several directors came and went, and privatization was discussed. ref name aft He was also a member of the Norwegian Labour Party Labour Party , and served two terms in Spydeberg municipal council Norway municipal council . ref name aft He retired from the working life in 1992, and was proclaimed an honorary member of his union. ref name obit2 cite news title Leif Thue d d, 64 r agency Norwegian News Agency date 14 June 1993 language Norwegian ref He died in June 1993. ref name obit1 References Reflist Persondata Metadata see Wikipedia Persondata . NAME Thue, Leif ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 12 July 1928 PLACE OF BIRTH DATE OF DEATH 13 June 1993 PLACE OF DEATH DEFAULTSORT Thue, Leif Category 1928 births Category 1993 deaths Category People from Sogn og Fjordane Category Norwegian trade unionists Category Norwegian State Railways people Category Labour Party Norway politicians Category stfold politicians Norway politician 1920s stub ... more details
ThueMorsesequence Related concepts List computing Order topology Ordinal indexed sequences Ordinal ...Other uses In mathematics , a sequence is an ordered list of objects or events . Like a Set mathematics ... possibly infinite is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a Discrete mathematics discrete function mathematics function . For example, C, R, Y is a sequence of letters ..., or Infinite set infinite , such as the sequence of all even and odd numbers even ... notions of sequence, but may be excluded depending on the context. Image Cauchy sequence illustration2.svg right thumb 350px An infinite sequence of real numbers in blue . This sequence is neither increasing, nor decreasing, nor convergent, nor Cauchy sequence Cauchy . It is, however, bounded ... of which e.g. , exact sequence are not covered by the notations introduced below. In addition to identifying the elements of a sequence by their position, such as the 3rd element , elements may be given names for convenient referencing. For example a sequence might be written as a sub 1 sub , a sub ... definition of a finite sequence with terms in a set S is a function mathematics function from 1, 2, ..., n to S for some n 0. An infinite sequence in S is a function from 1, 2, ... to S . For example, the sequence of prime numbers 2,3,5,7,11, is the function 1 2 , 2 3 , 3 5 , 4 7 , 5 11 , . A sequence of a finite length n is also called an n tuple n tuple . Finite sequences include the empty sequence ... sequence or two way infinite sequence . An example is the bi infinite sequence of all even integers , 4, 2, 0, 2, 4, 6, 8 . Multiplicative Let A a sequence defined by a function f 1, 2, 3, ... 1, 2, 3, ... , such that a sub i sub f i . The sequence is multiplicative if f xy f x f y for all x , y ... of sequences A subsequence of a given sequence is a sequence formed from the given sequence by deleting ... more details
Morse can refer to wiktionary morseMorse code , a method of coding messages into long and short beeps People Morse surname Morse Goodman 1917 1993 , Bishop of Calgary, Canada Samuel Morse 1791 1872 , painter, inventor of the telegraph and of the Morse code . Marston Morse 1892 1977 , American mathematician Places Canada Morse provincial electoral district , Saskatchewan Morse, Saskatchewan , a hamlet Morse No. 165, Saskatchewan , a rural municipality United States Morse, Iowa , an unincorporated community Morse, Louisiana , a village Morse River Maine Morse Township, Minnesota disambiguation , two places Morse, Texas , a census designated place Morse, Wisconsin , a town Morse community , Wisconsin , an unincorporated community Antarctica Mount Morse Cape MorseMorse Nunataks Elsewhere on Earth Morse River , New Zealand Morse Point , South Georgia Island Morse Park , Hong Kong Outer space Morse crater , on the Moon 8672 Morse , an asteroid Buildings Morse Auditorium , a domed theater owned by Boston University Morse House disambiguation , various buildings Morse CTA , an L station on a line of the Chicago Rapid Transit Authority Other uses Morse College , a residential college at Yale University Morse Farm disambiguation Morse Field disambiguation , two places The large buckle on the cope ... , a large aquatic mammal Morse chain, a chain drive with inverted teeth Morse taper , a type of machine taper invented by Stephen A. MorseMorse Diving , a US maker of diving equipment Morse Dry Dock and Repair Company , a defunct company in New York City USS Morse USS Morse , a ferryboat used by the Union Navy in the American Civil War Morse , French title for the Swedish horror film Let the Right One In film Let the Right One In Inspector Morse , a fictional British detective in books and on television Morse potential , a model interatomic potential energy function Morse theory , in mathematics ... disambig ca Morse cs Morse de Morse es Morse eu Morse fr Morse fy Morse it Morse he ja ... more details
random sequence. b 0 b 1 ac abc abc External links http catseye.tc projects thue The Thue Programming Language http catseye.tc projects thue doc thue.txt Thue FAQ http esoteric.voxelperfect.net wiki ThueThue at the Esolang wiki http scienceblogs.com goodmath 2006 08 friday pathological programmin 2.php Blog post on Thue http web.archive.org web 20031210145310 http cyberspace.org lament thue.html Javascript Thue interpreter Category Esoteric programming languages Category Programming languages created in 2000 compu lang stub fr Thue langage pt Thue ...Thue IPAc en icon t u e respell TOO ay is an esoteric programming language invented by John Colagioia in early 2000. It is a meta language that can be used to define or recognize Type 0 languages from the Chomsky hierarchy . Because it is able to define languages of such complexity, it is also Turing completeness Turing complete itself. Thue is based on a Nondeterministic algorithm nondeterministic String rewriting string rewriting system called semi Thue grammar , which itself is named after and possibly created by Citation needed date February 2010 the Norway Norwegian mathematician Axel Thue inspiration is also taken from the Grue monster grue . The author describes it as follows Thue ... are to the imperative paradigm in other words, it s a Turing tarpit tar pit . Production rules A Thue ... which follow the rulebase. Thue consumes the initial symbols and substitutes the result of the rules for each of the initial state s symbols. Thue terminates when lhs cannot be found in a resultant ... be the lhs. is an input stream. is the output stream. Semi Thue systems are isomorphic to unrestricted grammar s. Calling Thue When invoked with d debug , print the state. When invoked with l left ... in Thue a Hello World a The following Thue program performs an increment of a binary number entered ... 1 0 0 1 10 1111111111 The following sample program is to demonstrate Thue s nondeterminism and to show ... more details
Infobox musical artist See Wikipedia WikiProject Musicians name The Sequence image caption image size Only for images narrower than 220 pixels background group or band alias origin Columbia, South Carolina Columbia , South Carolina , United States U.S. genre Old school hip hop br Funk years active 1979 1985 label Sugar Hill Records rap Sugar Hill associated acts Spoonie Gee website past members Angie Stone Angie Brown Stone Angie B. br Cheryl Cook Cheryl The Pearl br Gwendolyn Chisolm Blondy The Sequence is a former female old school hip hop trio signed to the Sugar Hill Records rap Sugar Hill label in the early 1980s. The group consisted of Cheryl Cook Cheryl The Pearl , Gwendolyn Chisolm Blondie , and lead singer rapper Angie Stone Angie Brown Stone Angie B. . The group originated from Columbia, South Carolina Columbia , South Carolina as a group of high school cheerleader s. Their most notable single was Funk You Up 1979 , which was the first rap record released by a female group and the second single released by Sugar Hill Records rap Sugar Hill Records . ref name Greenberg1999 Greenberg, Steve Light, Alan ed. 1999 . The VIBE History of Hip Hop . Three Rivers Press. p. 28. ISBN 0609805037 ref Elements of Funk You Up were later used by Dr. Dre for his 1995 single Keep Their Heads Ringin . ref Ego Trip s Book of Rap Lists Book of Rap Lists . 1999. Macmillan Publishers Macmillan ... song Let s Do It Again Discography Albums Sugarhill Presents the Sequence 1980 , Sugar Hill Records rap Sugar Hill The Sequence 1982 , Sugar Hill 51 Black Albums The Sequence Party 1983 , Sugar Hill Compilations Funky Sound 1995 , P Vine The Best of the Sequence 1996 , Deep Beats Monster Jam Back ... class artist id p194849 pure url yes The Sequence . Allmusic . External links http www.discogs.com artist Sequence, The Discography DEFAULTSORT Sequence, The Category African American musical groups ... Musical trios Hiphop band stub no The Sequence ... more details
most of his career on a single subject, eponymously titled Morse Theory, a branch of differential topology. Morse Theory is a very important subject in modern mathematical physics , such as string theory . See also ThueMorsesequence History ThueMorsesequence Publications Citation last1 Morse first1 ...Infobox scientist name H. C. Marston Morse image Marston Morse.jpg image size 200px caption Marston Morse in 1965 courtesy MFO birth date birth date 1892 03 24 df y birth place Waterville, Maine death date death date and age 1977 06 22 1892 03 24 df y death place Princeton, New Jersey nationality flag USA name American fields Mathematics workplaces Harvard University alma mater Colby College br Harvard University doctoral advisor George David Birkhoff G. D. Birkhoff doctoral students Emilio Baiada br Arthur Barton Brown Arthur B. Brown br Gustav Hedlund br Walter Leighton br Sumner Byron Myers Sumner Myers known for Morse theory awards Harold Calvin Marston Morse 24 March 1892 22 June 1977 was an American mathematician best known for his work on the calculus of variations in the large, a subject where he introduced the technique of differential topology now known as Morse theory . In 1933 he was awarded the B cher Memorial Prize for his work in mathematical analysis. He was born in Waterville, Maine to Ella Phoebe Marston and Howard Calvin Morse in 1892. He received his bachelor s degree ... 978 0 387 90532 7 mr 635124 year 1981 Citation last1 Morse first1 Marston editor1 last Montgomery editor1 ... Co. location Singapore isbn 9789971978945 mr 889255 year 1987 External links MacTutor Biography id Morse ... Metadata see Wikipedia Persondata . NAME Morse, Marston ALTERNATIVE NAMES SHORT DESCRIPTION DATE ..., New Jersey DEFAULTSORT Morse, Marston Category 1892 births Category 1977 deaths Category 20th ... de Harold Calvin Marston Morse fr Marston Morse it Marston Morse ht Marston Morse nl Marston Morse pms Marston Morse pt Marston Morse ru , sk Marston Morse vi Marston Morse ... more details
a semi Thue system , is a rewriting system over String computer science strings from a usually ... Thue system essentially coincides with the presentation of a monoid . Thus they constitute a natural ... Thue name comes from the Norwegian mathematician Axel Thue , who introduced systematic treatment of string rewriting systems in a 1914 paper. ref Book and Otto, p. 36 ref Thue introduced this notion ... et al., p.444 ref Definition A string rewriting system or semi Thue system is a tuple math Sigma ... Thue system is defined over a finite alphabet through most of the book, except chapter 7 when monoid ... math R math is symmetric relation symmetric , then the system is called a Thue system ... between R and the one step rewrite induced by R . Clearly in a semi Thue system we can form a finite or infinite sequence of strings produced by starting with an initial string math s 0 in Sigma ... relation on math Sigma math induced by R . Thue congruence In general, the set math Sigma math ... math stackrel leftrightarrow R math is called the Thue congruence generated by R . In a Thue system, i.e. if R is symmetric, the rewrite relation math stackrel rightarrow R math coincides with the Thue ... M R Sigma stackrel leftrightarrow R math of the free monoid math Sigma math by the Thue congruence ... M R math , then the semi Thue system math Sigma, R math is called a monoid presentation of math mathcal ... of the bicyclic monoid . The importance of semi Thue systems as presentation of monoids is made stronger ... it may be always be presented by a semi Thue system, possibly over an infinite alphabet. ref Book and Otto .... The word problem for semi Thue systems The word problem for semi Thue systems can be stated as follows Given a semi Thue system math T Sigma, R math and two words math u, v in Sigma math , can math ... with other notions A semi Thue system is also a term rewriting system&mdash one that has monadic ... math f 1f 2 rightarrow g math . A semi Thue system is also a special type of Post canonical system ... more details
Examples The following sequences are automatic ThueMorsesequence take E A 0, 1 , e 0, id, and ... the ThueMorse word. The n th term is the Parity mathematics parity of the Binary numeral system Representation base 2 representation of n and the sequence is thus 2 automatic. ref name as1 Rudin Shapiro sequence Baum Sweet sequence Regular paperfolding sequence Automatic real number An automatic real number is a real number for which the base b expansion is an automatic sequence. ref name hejhal556 ...An automatic sequence or k automatic sequence is an infinite sequence of terms characterized by a finite automaton . The n th term of the sequence is a mapping of the final state of the automaton when its input is the digits of n in some fixed base k . ref name as1 Allouche & Shallit 2003 p.152 ref A k automatic set is a set of non negative integers for which the sequence of values of its characteristic function is an automatic sequence that is, membership of n in the set can be determined by a finite state automaton on the digits of n in base k . ref Allouche & Shallit 2003 p.168 ref Automaton point of view Let q be an integer , and A E , , e be a deterministic automaton where E is the finite Set mathematics set of State computer science state s E 0, q 1 E is the transition function math e in E math is the initial state also let A be a finite set, and E A a Projection mathematics projection towards A . For each n , take m n e , math n math where math n math is n written in base q . Then the sequence m m 1 m 2 m 3 ... is called a q automatic sequence . ref name as1 Substitution point of view Let be a morphism of the free monoid E sup sup with math sigma E subseteq ... is a q automatic sequence over A . ref Allouche & Shallit 2003 p.175 ref 1 automatic sequences k automatic ... by defining a 1 automatic sequence to be a sequence whose n th term depends on the unary numeral system ... Press 1988, ISBN 0521335450 DEFAULTSORT Automatic Sequence Category Combinatorics on words ... more details
In mathematics , an integer sequence is a sequence i.e., an ordered list of integer s. An integer sequence may be specified explicitly by giving a formula for its n th term, or implicitly by giving a relationship between its terms. For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, the Fibonacci numbers Fibonacci sequence is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one an implicit description. The sequence 0, 3, 8, 15, is formed according to the formula n sup 2 sup &minus 1 for the n th term an explicit definition. Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect number ... number s Baum Sweet sequence Bell number s Binomial coefficient s Carmichael number s Catalan number ... number s Fibonacci word Figurate numbers Golomb sequence Happy number s Highly totient number s Highly composite number s Home prime s Hyperperfect number s Juggler sequence Kolakoski sequence Lucky number s Lucas number s Padovan sequence Padovan number s Partition number s Perfect number s Pseudoperfect number s Prime number s Pseudoprime numbers Regular paperfolding sequence Rudin Shapiro sequence Semiperfect number s Semiprime numbers Superperfect number s ThueMorsesequence Ulam numbers Weird number s div Computable and definable sequences An integer sequence is a Recursion theory computable sequence , if there exists an algorithm which given n , calculates a sub n sub , for all n > 0. An integer sequence is a definable set definable sequence , if there exists some statement P x which is true for that integer sequence x and false for all other integer sequences. The set of computable .... Complete sequences An integer sequence is called a complete sequence if every positive integer can be expressed as a sum of values in the sequence, using each value at most once. See also On Line Encyclopedia ... more details
In mathematics , a fractal sequence is one that contains itself as a proper subsequence. An example is 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, ... If the first occurrence of each n is deleted, the remaining sequence is identical to the original. The process can be repeated indefinitely, so that actually, the original sequence contains not only one copy of itself, but rather, infinitely many. Definition The precise definition of fractal sequence depends on a preliminary definition a sequence x x sub n sub is an infinitive sequence if for every i, F1 x sub n sub i for infinitely many n. Let a i,j be the jth index n for which x sub n sub i. An infinitive sequence x is a fractal sequence if two additional conditions hold F2 if i 1 x sub n sub , then there exists m n such that i x sub m sub F3 if h i then for every j there is exactly one k such that a i,j a h,k a i,j 1 . According to F2 , the first occurrence of each i 1 in x must be preceded at least once by each of the numbers 1, 2, ..., i 1, and according to F3 , between consecutive occurrences of i in x, each h less than i occurs exactly once. Example Suppose is a positive irrational number. Let S the set of numbers c d , where c and d are positive integers and let c sub n sub d sub n sub be the sequence obtained by arranging the numbers in S in increasing order. The sequence c sub n sub is the signature of , and it is a fractal sequence. For example, the signature of the golden ratio i.e., 1 sqrt 5 2 begins with 1, 2, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 8, 5, ... and the signature of 1 1 begins with 1, 1, 2, 1, 2, 1, 3, 2, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 5, ... These are sequences OEIS2C A084532 and OEIS2C A084532 in the On Line Encyclopedia of Integer Sequences , where further examples from a variety of number theoretic and combinatorial settings are given. See also ThueMorseSequence External links http oeis.org On Line Encyclopedia of Integer ... more details
Clara Thue Ebbell 1880 &ndash 1971 was a Norwegian author. She was born in Grimstad . She is known for his works of young adult fiction titles include Hun som skrev Onkel Toms hytte 1916 , Da Mayflower drog 1920 , Fire p egen h nd 1935, 1959 , Maja 1960 and I ungdomsbyen med Henrik Ibsen 1966 . ref name snl cite encyclopedia year 2007 title Ebbell, Ebbell, Clara Thue encyclopedia Store norske leksikon publisher Kunnskapsforlaget location url http www.snl.no article.html?id 520808 ref ref http ask.bibsys.no ask action result?cmd &kilde biblio&fid forfatter&term Ebbell 2C Clara Thue&op and&fid bd&term &op and&fid bd&term &arstall &sortering sortdate&treffPrSide 50 List of publications in BIBSYS ref She also biographed Katharina von Bora 1917 , Catherine Booth 1929 and Cathinka Guldberg 1940 , and took part in feminism feminist work. ref name snl She was married to Bendix Joachim Ebbell . ref name snl She was eleven years his junior, and outlived him by 34 years. References Reflist Persondata Metadata see Wikipedia Persondata . NAME Ebbell, Clara Thue ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1880 PLACE OF BIRTH DATE OF DEATH 1971 PLACE OF DEATH DEFAULTSORT Ebbell, Clara Thue Category 1880 births Category 1971 deaths Category Norwegian novelists Category Writers of young adult literature Category Norwegian biographers Category Norwegian feminists Category People from Grimstad Category Norwegian women writers Norway writer stub no Clara Thue Ebbell nn Clara Thue Ebbell sv Clara Thue Ebbell ... more details
In mathematics , the Thue Siegel Roth theorem , also known simply as Roth s theorem , is a foundational result in diophantine approximation to algebraic number s. It is of a qualitative type, stating that a given algebraic number may not have too many rational number approximations, that are very good . Over half a century, the meaning of very good here was refined by a number of mathematicians, starting with Liouville in 1844 and continuing with work of harvs txt first Axel last Thue authorlink Axel Thue year 1909 , harvs txt authorlink Carl Ludwig Siegel first Carl Ludwig last Siegel year 1921 , harvs txt last Dyson year 1947 , and harvs txt authorlink Klaus Roth first Klaus last Roth year 1955 . Statement The Thue Siegel Roth theorem states that any irrational algebraic number has approximation exponent equal to 2, i.e. , for given 0, the inequality math left alpha frac p q right frac 1 q 2 epsilon math can have only finitely many solutions in integers p and q , as was conjectured by Siegel. Therefore any irrational algebraic satisfies math left alpha frac p q right frac C alpha, epsilon q 2 epsilon math with C , a positive number depending only on 0 and . Roth s result is in some sense the best possible, because this statement would fail on setting 0 by Dirichlet ..., Liouville s theorem has exponent about d , Thue s theorem from 1909 has exponent math d 2 1 epsilon ... using the p adic metric , ref D. Ridout, The p adic generalization of the Thue Siegel Roth ... Zeitschrift issn 0025 5874 volume 10 issue 3 pages 173 213 Citation last1 Thue first1 A. author1 link Axel Thue title ber Ann herungswerte algebraischer Zahlen url http resolver.sub.uni goettingen.de ... 4102 volume 135 pages 284 305 DEFAULTSORT Thue Siegel Roth Theorem Category Diophantine approximation Category Theorems in algebraic number theory de Satz von Thue Siegel Roth fr Th or me de Roth nl Stelling van Thue Siegel Roth pl Twierdzenie Thue Siegela Rotha ... more details
In mathematics , a locally catenative sequence is a sequence of word mathematics words in which each word can be constructed as the concatenation of previous words in the sequence. ref cite book last Rozenberg first Grzegorz coauthors Salomaa, Arto title Handbook of Formal Languages publisher Springer date 1997 pages 262 isbn 3540604200 ref Formally, an infinite sequence of words w n is locally catenative if, for some positive integers k and i sub 1 sub ,... i sub k sub math w n w n i 1 w n i 2 ...w n i k text for n ge max i 1, ... i k , . math Some authors use a slightly different definition in which encodings of previous words are allowed in the concatenation. ref cite book last Allouche first Jean Paul coauthors Shallit, Jeffrey title Automatic Sequences publisher Cambridge date 2003 pages 237 isbn 0 521 82332 3 ref Examples The sequence of Fibonacci word s S n is locally catenative because math S n S n 1 S n 2 text for n ge 2 , . math The sequence of ThueMorsesequenceThueMorse words T n is not locally catenative by the first definition. However, it is locally catenative by the second definition because math T n T n 1 mu T n 1 text for n ge 1 , , math where the encoding &mu replaces 0 with 1 and 1 with 0. References references Category Formal languages Category Combinatorics on words ... more details
In mathematics , specifically in the field of differential topology , Morse homology is a homology theory ... homology . Morse homology also serves as a model for the various infinite dimensional generalizations ... f be a Morse function and g a Riemannian metric on the manifold. These are auxiliary in the end, the Morse ... , g is Morse Smale if the stable manifold stable and unstable manifold s associated to all of the critical ... the boundary of the moduli space of index 2 flows The limit of any sequence of unbroken index 2 ... 2 sup p 0. Invariance of Morse homology It can be shown that the homology of this complex is independent of the Morse Smale pair f , g used to define it. A homotopy of pairs f sub t sub , g sub t sub ... be shown that the two Morse homologies are isomorphic. Analogous arguments using a homotopy of homotopies shows that this isomorphism is canonical. Another approach to proving the invariance of Morse ... point of index i as an i cell, and showing that the boundary maps in the Morse and cellular complexes correspond. Related constructions This approach to Morse theory was known in some form to Ren .... From the fact that the Morse homology is isomorphic to the singular homology, the Morse inequalities ... the homology groups of the appropriate ranks and by considering truncations of the Morse complex, to get the stronger inequalities . The existence of Morse homology explains , in the sense of categorification , the Morse inequalities. Edward Witten came up with a related construction in the early 1980s sometimes known as Morse Witten theory . Morse homology can be extended to finite dimensional ... associated to a closed one form on a manifold. Morse homology is a special case for the one form df . A special case of Novikov s theory is circle valued Morse theory , which Michael Hutchings and Yi Jen Lee have connected to Reidemeister torsion and Seiberg Witten theory . Morse Bott homology Morse homology can be carried out in the Morse Bott setting, i.e. when instead of isolated nondegenerate ... more details
Steven Morse , Stephen Morse or Steve Morse may refer to Stephen P. Morse born 1940 , American computer specialist Steve Morse born 1954 , American musician Stephen S. Morse , American scientist See also Morse surname hndis Morse, Steven ... more details
Morse, Scott subcat American Scott Morse sometimes known as C. Scott Morse or C. S. Morse is an People of the United States American animator, filmmaker, and comic book artist writer. Much of Morse ... 1997 epic series Soulwind , a story serialised in a sequence of graphic novels, which was nominated for both the Eisner Award Eisner and Ignatz Award Ignatz awards. Biography Scott Morse was trained ... arc for Catwoman . Morse also illustrated the first six issues of Sam and Twitch Case Files Sam ... novels Cut My Hair Oni Press and Hellboy Weird Tales vol.2 Dark Horse among others. Morse s own graphic ... for younger readers, Morse s work typically finds a much larger audience. In the field of animation ... such as Disney , Universal Studios Universal , and Cartoon Network . Recently Morse played a large part ... credit search Scott Morse title Scott Morse comicbookdb type creator id 2307 title Scott Morse refend External links official http www.scottmorse.com http scottmorse.blogspot.com Scott Morse s blog http www.allenspiegelfinearts.com crazyfish index.html Scott Morse s previous official site last updated 2005 http www.scholastic.com goosebumpsgraphix artistauthor scottmorse.htm Scott Morse s biography on Goosebumps Graphix site http www.lesketch.com 2009 08 le sketch 08 scott morse Le Sketch mini comic with Scott Morse s sketches. Interviews More footnotes section date September 2009 Wheeler, Andrew 2002 http www.ninthart.com display.php?article 255 C Scott Run Interview with Scott Morse. Retrieved Feb. 25, 2005 Persondata Metadata see Wikipedia Persondata . NAME Morse, Scott ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Morse, Scott ... more details
defining a unit as a bit , we can visualize any Morse code sequence as a combination of the following ... Morse code sequence M O R S E ... Morse character set, using the sequence denoted by the span style text decoration overline ...pp semi vandalism expiry May 17, 2012 small yes pp move indef Image International Morse Code.svg right thumb 315px Chart of the Morse code letters and numerals. ref name itu r Morse code is a method of transmitting ... Morse Code ref http www.itu.int rec R REC M.1677 1 200910 I ITU Recommendation ITU R M 1677 1 ... I title International Morse code Recommendation ITU R M.1677 1 date October 2009 work itu.int publisher ... many non English natural languages use more than the 26 Roman letters, extensions to the Morse alphabet exist for those languages. Each character letter or numeral is represented by a unique sequence ... duration is the basic unit of time measurement in code transmission. ref name itu r Morse code ... such standard words. ref name perera cite web url http w1tp.com percode.htm title The Morse Code ... publisher accessdate 23 December 2011 ref One important feature of Morse code is coding efficiency. The length of each character in Morse is approximately inversely proportional to its frequency of occurrence ..., a single dot. A related but different code was originally created for Samuel Morse Samuel F. B. Morse ... modern International Morse code is based. In the 1890s it began to be extensively used for early ... twentieth century, most high speed international communication used Morse code on telegraph lines, undersea cables and radio circuits. Morse code is most popular among amateur radio operator s although ... Pilots and air traffic controllers are usually familiar with Morse code and require a basic ... beacon NDBs , constantly identify in Morse code. An advantage of Morse code for transmitting ... communications impossible. Because it can be read by humans without a decoding device, Morse is sometimes ... more details
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