21. Busy Beaver -- From MathWorld Brady, AH Busy Beaver Problem of tibor rado ( Busy Beaver Game ). http//www.cs.unr.edu/~al/BusyBeaver.html. Brady, AH Is This A New Busy Beaver Lower http://mathworld.wolfram.com/BusyBeaver.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Discrete Mathematics Computational Systems Recreational Mathematics ... Mathematical Records Busy Beaver A busy beaver is an -state, 2-color Turing machine which writes a maximum number of 1s before halting (Rado 1962; Lin and Rado 1965; Shallit 1998). Alternatively, some authors define a busy beaver as a Turing machine that performs a maximum number of steps when started on an initially blank tape before halting (Wolfram 2002, p. 889). The process leading to the solution of the three-state machine is discussed by Lin and Rado (1965) and the process leading to the solution of the four-state machine is discussed by Brady (1983) and Machlin and Stout (1990). For (also known as Rado's sigma function) is given by 1, 4, 6, 13, ... (Sloane's ; Rado 1962; Wolfram 2002, p. ). The next few terms are not known, but examples have been constructed giving lower limits of

22. Wikipedia:List Of Encyclopedia Topics/Biographies R - Wikipedia, The Free Encycl tibor rado (1895 1965), United States of America US (Hungarian-born) mathematician; solved Plateau problem independently of http://en.wikipedia.org/wiki/Wikipedia:List_of_encyclopedia_topics/Biographies_R

Wikimedia needs your help in the final days of its fund drive. See our fundraising page The Red Cross and other charities also need your help. Wikipedia:List of encyclopedia topics/Biographies R From Wikipedia, the free encyclopedia. Wikipedia:List of encyclopedia topics Contents Section 1 Section 2 Section 3 Section 4 ... edit Section 1 Sun Ra Ra, Sun Le Sony'r Ra Julius Raab ... Raab, Julius '''Julius Raab''' ([[1891]] - [[1964]]), [[Austrian]] [[political figure]]; chancellor of Austria 1953-1961; acting pres. of Austria 1957 Paul Rabaut Rabaut, Paul '''Paul Rabaut''' ([[1718]] - [[1794]]), [[French]] Protestant clergyman; leader of Huguenots 1760-1794 Burhanuddin Rabbani Rabbani, Burhanuddin '''Burhanuddin Rabbani''' (born [[19XX]]), Afghan [[political figure]]; leader of Shoora Nazar forces; pres. of Afghanistan 1992 Jean Joseph Rabearivelo Rabearivelo, Jean Joseph '''Jean Joseph Rabearivelo''' ([[1901]] - [[1937]]), Madagascar poet writing in French; wrote poetry collections "Cutting the Ashes" 1924, "Nearly Dreams" 1934, "Translation of the Night" 1935; father of modern Malagasy literature; suicide Fran§ois Rabelais Rabelais, Fran§ois

23. Citation Index @ARTICLE{Kre, author = Erwin Kreyszig, tibor rado , title = On Rigidity Properties of Developable Surfaces , journal = Indiana Univ. Math. http://www.iumj.indiana.edu/oai/1958/7/57026/57026.html

Home Current Issue FAQ Search ... Contact Us BibTeX @ARTICLE Kre, author Erwin Kreyszig, Tibor Rado title On Rigidity Properties of Developable Surfaces journal Indiana Univ. Math. J. fjournal Indiana University Mathematics Journal volume year issue pages issn coden IUMJAB mrclass amsrefs Kre article author Kreyszig, Erwin author Rado, Tibor title On Rigidity Properties of Developable Surfaces journal Indiana Univ. Math. J. volume year number pages Other bibliographic snippets: RDF-Dublin Core metadata: What is this? Take me there... OAI metadata: What is this? Take me there...

24. Turing Machine On A Spreadsheet tibor rado, a professor at the Ohio State University, asked in 1962 Find discoverer, tibor rado and Shen Lin, tibor rado and Shen Lin, tibor rado and http://mumnet.tripod.com/tools/tools002.htm

setAdGroup('67.18.104.18'); var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" Search: Lycos Tripod Free Games Share This Page Report Abuse Edit your Site ... Next Mum Mathematical Ulterior Motives - the mother of all ulterior sites - tools Anyone for a Turing machine on a spreadsheet? To solve a problem means to find a set of actions that brings you from the start state to the goal state. If you can express the states and the actions in a programming language, you can feed the instructions to a computer and let it solve the problem for you. In 1936, before the first electronic computer was built, Alan Turing, described his idea of a simple computer. Even though his machine was of a very uncomplicated design, Turing believed that it could carry out any process which could naturally be called an effective procedure or algorithm. Tape Head happy The machine consisted of a tape divided into cells and a read-write head that could move along the tape. The tape above is empty, nothing is written in the cells. The head starts where the ^ sign is). state read write move new state happy R gloomy happy L content gloomy L happy gloomy R gloomy content L gloomy content R stop A Turing machine can be in several states. The machine above has three states, happy, gloomy and content. It starts in the happy state. The table says that if it reads an empty cell in the happy state it should write a 1, move one cell to the right and go over to the gloomy state (row 2 in the table):

25. Busy Beaver Turing Machine On NonComputable Functions, tibor rado, The Bell System Technical Journal, vol. Shen Lin and tibor rado. Computer studies of Turing machine problems. http://grail.cba.csuohio.edu/~somos/bb.html

Busy Beaver Turing Machine This story starts around 1960. Tibor Rado, a professor at the Ohio State University, thought of a simple non-computable function besides the standard halting problem for Turing machines. Given a fixed finite number of symbols and states, select those Turing machine programs which eventually halt when run with a blank tape. Among these programs find the maximum number of non-blank symbols left on the tape when they halt. Alternatively, find the maximum number of time steps before halting. This function is well-defined but rapidly becomes un-computable for even a small number of states and symbols. He published an article about it in 1962, but went beyond just writing about a theoretical result. With his student Shen Lin, they actually tackled the two symbol, three state problem. The study resulted in a dissertation for Lin in 1963 and an article in JACM in 1965. After the initial flurry of articles there has been several others mentioning results. The most popular is probably the August 1984 Scientific American Computer Recreations column by Dewdney. There is a PostScript handout by Jeffrey Shallit about the problem.

26. Large Numbers At MROB rado, tibor, On noncomputable functions , Bell System Tech. Journal vol. 41 (1962), pages 877-884. (busy beaver function) http://home.earthlink.net/~mrob/pub/math/largenum-6.html

Large Numbers Back to page 5 Hofstadter, Douglas, : An Eternal Golden Braid Hudelson, Matt, Extremely Large Numbers Kasner, Edward and Newman, James, Mathematics and the Imagination , Penguin, 1940 Knuth, Mathematics and Computer Science: Coping with Finiteness. Advances in our ability to compute are bringing us substantially closer to ultimate limitations. Science , 1976, pages 1235-1242 Knuth, Supernatural Numbers , in The Mathmatical Gardener , D. A. Klarner, ed., 1981 Kosara, Robert, The Ackermann Function MacTutor history of Mathematics page on Chuquet Matuszek, David, Ackermann's Function McGough, Nancy, The Continuum Hypothesis (web pages) Miller, George: The Magical Number Seven Plus or Minus Two: Some Limits on Our Capacity for Processing Information Munafo, Robert, hypercalc (the Perl calculator program that handles numbers up to 10 Pilhofer, Frank, Googolplex and How to get a Googolplex Rado, Tibor, "On non-computable functions", Bell System Tech. Journal vol. 41 (1962), pages 877-884. (busy beaver function) Rucker, Rudy

27. Large Numbers At MROB The Busy Beaver Function was originally defined by tibor rado at Ohio State in 1962. It is defined by specifying that you must start with a blank tape (all http://home.earthlink.net/~mrob/pub/math/largenum-5.html

Large Numbers Back to page 4 Forward to page 6 If the foregoing makes little sense, consider this concrete (but somewhat non-rigorous) example. Select any well defined, "sufficiently powerful" grammar G , consisting of a symbol-set of S symbols, finite in number, and well-defined rules of what constitutes a syntactically valid string of symbols specifying an integer. An example grammar that should be fairly familiar uses the symbols: and the rules that these symbols are to be strung together to make a legal set of additions, multiplications and exponentiations yielding an integer result; in this example S = 15. Just to be unambiguous, we'll require parentheses whenever two operators appear in a string. Given this grammar G , for every integer N there is a set of integers E N consisting of all the integers that can be specified as a combination of N symbols in G using G 's defined grammar. This set is finite, (it has, at most, S N elements, since there are that many combinations of N symbols from a set of S ). Since

28. Plateau's Problem -- Facts, Info, And Encyclopedia Article Trans. Amer. Math. Soc. 33 (1931), no. 1, 263321. tibor rado, On Plateau s problem. Ann. of Math. (2) 31 (1930), no. 3, 457469. http://www.absoluteastronomy.com/encyclopedia/P/Pl/Plateaus_problem.htm

var dc_UnitID = 10; var dc_PublisherID = 512; var dc_BackgroundColor1 = 'white'; var dc_BackgroundColor2 = 'white'; var dc_TitleColor = 'blue'; var dc_TextColor = 'black'; var dc_URLColor = 'blue'; var dc_URLVisitedColor = 'green'; var dc_sm_type = 'horizontal'; var dc_Width = 700; var dc_Height = 75; var dc_caption_font_bgColor = 'white'; var dc_caption_font_color = 'blue'; var dc_OutBorder = 'no'; var dc_adprod='TM'; Plateau's problem [Categories: Minimal surfaces, Mathematical analysis] Plateau's problem is to show the existence of a (Click link for more info and facts about minimal surface) minimal surface with a given boundary. It is named after (Click link for more info and facts about Joseph Plateau) Joseph Plateau , who was interested in (A film left on objects after they have been washed in soap) soap film s, but was raised by (Click link for more info and facts about Joseph Louis Lagrange) Joseph Louis Lagrange in 1760. The problem is considered part of the (The calculus of maxima and minima of definite integrals) calculus of variations Various specialized forms of the problem were solved, but it was only in 1930 that general solutions was found independently by

29. The Busy Beaver Problem : A NEW MILLENNIUM ATTACK Considering the definition of a Turing Machine above, we can now define the Busy Beaver function, invented by tibor rado around 1960. http://www.cs.rpi.edu/~kelleo/busybeaver/problem.html

The Busy Beaver Problem A NEW MILLENNIUM ATTACK Background - Turing Machines and what they are Comprehension of the Busy Beaver problem requires a conceptual understanding of what a turing machine is and does. In short, a turing machine is an abstract model of computation that encapsulates the definition of computability. More formally, a turing machine is structured with the following components: A finite set of states - the machine can only be in one state at a time during execution A finite alphabet which the machine operates on A finite set of instructions An infinitely long tape of characters from the finite alphabet which maintains a current read-position that moves back and forth along the tape according to the instructions Each instruction takes the following format: (current state, current symbol, new state, new symbol, move) where the current state is the state that the machine is currently in and current symbol is the symbol corresponding to the position of the read head on the tape. Execution of the instruction moves the machine to the new state, replaces the current symbol on the tape with the new symbol, and then moves the read head position left or right according to the value of move. A Turing Machine, therefore, takes a set of characters and current position on the tape as input and transforms the tape according to its instruction set. The machine halts when it reaches either a state, symbol pair for which there is no corresponding instruction, or it transitions into a explicitly defined halt state.

30. Heiner Marxen - TM Glossary Busy Beaver (BB) This term has been coined by tibor rado in 1962, when he announced the tibor rado used the 5tupel style for the Busy Beaver Contest, http://www.drb.insel.de/~heiner/BB/glossary.html

Turing Machine Glossary This glossary is not meant to be complete or "official". It just reflects my understanding and use of terms related to Turing machines and Busy Beavers Basic Terms TM Turing Machine TM Definition Turing Machine Definition. In order to define a TM you have to specify: a finite set of Symbols a finite set of States a transition function (table), i.e. a set (list) of transitions States that have no transitions defined, are (implicit) halt states: the TM cannot continue from there. Symbol Each cell of a tape is marked with a symbol. Each TM defines a finite set of possible symbols. Blank Symbol (zero symbol) The Blank is a special symbol , used to initialize the infinitely many cells at the far left and right end of the tape State A TM always "is in" a state. We use capital letters for states: A B C , ... Each TM defines a finite set of possible states. Tape The tape is the "memory" of a TM . It is a horizontal strip (series) of cells , It is considered to be horizontal, from left to right. It is unlimited at both ends, i.e. can contain an unbounded amount of non-

31. 1962: Information From Answers.com tibor rado discovers the first example of a function that is not computable. Proof of the existence of noncomputable functions, in the sense that a Turing http://www.answers.com/topic/1962

showHide_TellMeAbout2('false'); Arts Business Entertainment Games ... More... On this page: US Literature Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping In the year Astronomy Japanese astrophysicist Chushiro Hayashi [b. Kyoto, Japan, July 25, 1920] and coworkers create evolutionary models for stars with masses ranging from 0.01 to 100 times that of the Sun. See also 1955 Astronomy British astronomer Cyril Hazard determines that the radio source 3C 273 consists of two components by observing its occultation by the Moon. The source 3C 273 will be identified as a quasar a year later and later studies show a long jet emerging from it, the other component. The occultation makes it possible to determine the exact location of the quasar. See also 1963 Astronomy Riccardo Giacconi [b. Genoa, Italy, October 6, 1931], Herbert Gursky, and Frank R. Paolini follow a suggestion by Bruno Rossi to use a rocket flight above the stratosphere to observe X rays from the universe. The X-ray telescope on the June 18 flight from White Sands, New Mexico, was targeted at the Moon, but the principal discovery is the X-ray source in Scorpio now known as Sco X-1, the first known X-ray source outside the solar system. See also 1966 Astronomy . (See essay The Sugar Grove radio telescope fiasco occurs. The U.S. attempt to build a 183-m (600-ft) fully steerable dish radio telescope, begun in 1959, is discontinued after expenditures of $96,000,000. However, the 90-m (300-ft) steerable dish at Green Bank, West Virginia, is completed and begins successful operations.

32. Title Kempe S Engineers Year Book Imprint London Morgan Aufl Imprint Wiesbaden Brockhaus Author Pototskaya, VV; Title FrenchRussian dictionary Imprint Moscow Author rado, tibor; Title Continous http://weblib.cern.ch/share/missing_books/miss1955.html

Title : Kempe's engineers year book Imprint : London : Morgan Title : Kempe's engineers year book Imprint : London : Morgan Title : Huette : des Ingenieurs Taschenbuch Imprint : Berlin : Ernst Title : The shorter Oxford English dictionary on historical principles Imprint : Oxford : Clarendon Press Conference : Rydberg Centennial Conference on Atomic Spectroscopy, Lund Title : Rydberg centennial conference on atomic spectroscopy : proceedings, Lund, Norway, 1-5 July 1954 Imprint : Lund : Gleerup Author : American Society for Testing and Materials. Philadelphia. Title : Book of ASTM standards, including tentatives Imprint : Philadelphia Author : Association Française de Normalisation. Paris. Title : Documentation Imprint : Paris Author : Atomic Energy Commission. Washington. Title : Atoms for peace Imprint : Geneva Author : Atomic Energy of Canada. Chalk River. Title : Table of complete elliptic integrals Imprint : Chalk River, Ontario : A.E.C.L. Author : Atomic Energy Research Establishment. Harwell. Title : Issue 2 Imprint : Harwell Author : Brookhaven National Laboratory. Upton. Title : Bibliography on machine computation, 1945-1955 Imprint : Upton Author : La Nef. Paris. Title : L'atome, notre destin Imprint : Paris Author : Los Alamos Scientific Laboratory. Los Alamos. Title : Series of lectures on physics of ionized gases Imprint : Los Alamos Author : Mullard Ltd. London. Components division. Title : Mullard Ferroxcube Imprint : London Author : National Bureau of Standards. Washington, D.C.. Title : Tables of sines and cosines for radian arguments Imprint : Washington Series : Applied mathematics series, 43 Author : National Bureau of Standards. Washington, D.C.. Title : Experiments in the computation of conformal maps Imprint : Washington, D.C. Series : N.B.S. applied mathematics series, 42 Author : National Bureau of Standards. Washington, D.C.. Title : Tables of the descending exponential x = 2,5 to x = 10 Imprint : Washington, D.C. Series : N.B.S. applied mathematics series, v.46 Author : National Bureau of Standards. Washington, D.C.. Title : Table of the descending exponential x=2,5 to x=10 Imprint : Washington Series : N.B.S. applied mathematics series, 46 Author : National Physical Laboratory. Teddington. Title : Tables of Weber parabolic cylinder functions : giving solutions of the differential equation d2y/dx2 + (1/4x2-a)y=0 Imprint : London : H.M.S.O. Author : Società Italiana di Fisica. Bologna. Title : Sunti delle communicazioni, Pisa, 12-18 June 1955 Imprint : Pisa Author : Societa Italiana di Fisica. Title : Conferenza Internationale sulle particelle elementari : proceedings, Pisa, Italy, 12-18 Giugno 1955 Imprint : Milano Author : Université de Grenoble. Grenoble. Title : Cours de moyens de calcul Imprint : Grenoble Author : Blackwood, Oswald H; Title : An outline of atomic physics. - 3rd ed Imprint : New York : Wiley Author : Bösch, Karl; Title : Méthode de montage HB pour conduites de descente et de ventilation Imprint : Zürich Author : Bruhat, Georges; Title : Optique. - 4e éd Imprint : Paris : Masson Author : Charlot, Gaston; Title : Analyse quantitative minérale. - 3e éd Imprint : Paris : Masson Author : Copson, Edward T; Title : An introduction to the theory of functions of a complex variable Imprint : Oxford : Clarendon Press Author : Cramer, Harald; Title : The elements of probability theory and some of its applications Imprint : New York : Wiley Author : Denis-Papin, Maurice; Title : Electrotechnique générale. - 4e éd Imprint : Paris : Dunod Author : Denis-Papin, Maurice; Title : Mathématiques générales. - 5e éd Imprint : Paris : Dunod Author : Deribere, Maurice; Title : Les applications pratiques de la luminescence. - 3e éd Imprint : Paris : Dunod Author : Dieudonné, Jean Alexandre; Title : La géométrie des groupes classiques Imprint : Berlin : Springer Series : Ergebnisse der Mathematik und ihrer Grenzgebiete, 5 Reihe. Gruppentheorie Author : Erdélyi, Arthur; Title : Higher transcendental functions Imprint : New York : McGraw-Hill Author : Evans, Robley D; Title : The atomic nucleus Imprint : New York : McGraw-Hill Author : Fermi, Laura; Title : Atomes en famille : mon existence avec Enrico Fermi. - 9e éd Imprint : Paris : Gallimard Author : Frazer, Robert A; Title : Elementary matrices and some applications to dynamics and differential equations Imprint : Cambridge : Cambridge Univ. Press Author : Gillespie, Robert Pollock; Title : Integration. - 6th ed Imprint : Edinburgh : Oliver and Boyd Author : Glasford, Glenn M; Title : Fundamentals of television engineering Imprint : New York : Toronto Author : Goubau, Georg; Title : Elektromagnetische Wellenleiter und Hohlräume Imprint : Stuttgart : Wissenschaftliche Verlagsges. Author : Graham, A Kenneth; Title : Electroplating engineering handbook... Imprint : New York : Reinhold Author : Gröber, Heinrich; Title : Die Grundgesetze der Wärmeübertragung. - 3.Aufl Imprint : Berlin : Springer Author : Guggenheim, Edward A; Title : Physicochemical calculations Imprint : Amsterdam : North-Holland Author : Halliday, David; Title : Introductory nuclear physics. - 2nd ed Imprint : New York : Wiley Author : Hobson, Ernest W; Title : The theory of spherical and ellipsoidal harmonics Imprint : New York : Chelsea Author : Hornung, Walter; Title : Handbuch der Agfa-Photopapiere Imprint : Düsseldorf : Knapp Author : Jackson, Leonard Cecil; Title : Low temperature physics. - 4th ed Imprint : London : Methuen Author : Jauch, Josef Maria; Title : The theory of photons and electrons : the relativistic quantum field theory of charged particles with spin one-half. - 1st ed Imprint : Cambridge, Mass. : Addison-Wesley Author : Kaplan, Irving; Title : Nuclear physics. - 1st ed Imprint : Cambridge, Mass. : Addison-Wesley Author : Koenigsberger, F; Title : Technique du bati soudé Imprint : Paris : Dunod Author : Kohlrausch, F; Title : Praktische Physik zum Gebrauch für Unterricht, Forschung und Technik Imprint : Stuttgart : Teubner Author : Korff, Serge A; Title : Electron and nuclear counters : theory and use. - 2nd ed Imprint : New York : Greenwood Author : Lea, Douglas Edward; Title : Actions of radiations on living cells. - 2nd ed Imprint : Cambridge : Cambridge Univ. Press Author : Lichnerowicz, André; Title : Algèbre et analyse linéaires. - 2e éd Imprint : Paris : Masson Author : Martin, Thomas L; Title : Electronic circuits Imprint : Englewood Cliffs, N.J. : Prentice-Hall Author : Menzel, Donald H; Title : Fundamental formulas of physics. - 1st ed Imprint : New York : Prentice-Hall Author : Milne-Thomson, Louis Melville; Title : Theoretical hydrodynamics. - 3rd ed Imprint : London : Macmillan Author : Motte, Michel R; Title : Lexique général des transistors : caractéristiques de tous les transistors et schémas d'utilisation Imprint : Paris : Dufour Author : Panofsky, Wolfgang K H; Title : Classical electricity and magnetism. - 1st ed Imprint : Reading, Mass. : Addison-Wesley Author : Pauli, Wolfgang; Title : Niels Bohr and the development of physics Imprint : London : Pergamon Author : Pauli, Wolfgang; Title : Niels Bohr and the development of physics Imprint : London : Pergamon Author : Peifer, J; Title : Quantum theory of solids Imprint : Oxford : Clarendon Press Author : Perry, Charles C; Title : The strain gage primer Imprint : New York : McGraw-Hill Author : Pfohl, Ernst; Title : Brockhaus Bildwörterbuch, Deutsch-Französisch. - 30. Aufl Imprint : Wiesbaden : Brockhaus Author : Pototskaya, V V; Title : French-Russian dictionary Imprint : Moscow Author : Rado, Tibor; Title : Continous transformations in analysis : with an introduction to algebraic topology Imprint : Berlin : Springer Series : Grundlehren der mathematischen Wissenschaften, Bd.75 Author : Reddick, Harry W; Title : Advanced mathematics for engineers. - 3rd ed Imprint : New York : Wiley Author : Richards, Richard Kohler; Title : Arithmetic operations in digital computers Imprint : New York : Van Nostrand Author : Richtmyer, Floyd K; Title : Introduction to modern physics. - 5th ed Imprint : New York : McGraw-Hill Author : Rothe, Horst; Title : Hochvakuum-Elektronenröhren, Bd. 1 Imprint : Frankfurt a/M. : Akademische Verlagsgesellschaft Author : Rouault, Marcel; Title : Physique atomique Imprint : Paris : Colin Author : Scarborough, James B; Title : Numerical mathematical analysis. - 3rd ed Imprint : Baltimore : Johns Hopkins Univ. Author : Schiff, Leonard Isaac; Title : Quantum mechanics. - 2nd ed Imprint : New York : McGraw-Hill Author : Schmeidler, Werner; Title : Integralgleichungen mit Anwendungen in Physik und Technik, Teil 1. - 2. Aufl Imprint : Leipzig : Geest und Portig Series : Mathematik und ihre Angwendungen in Physik und Technik Reihe A, Bd. 22 Author : Schweber, Silvan S; Title : Mesons and fields Imprint : Evanston, Ill : Row and Peterson Author : Schweber, Silvan S; Title : Mesons and fields Imprint : Evanston, Ill : Row and Peterson Author : Sturrock, P A; Title : Static and dynamic electron optics : an account of focusing in lens, deflector and accelerator Imprint : Cambridge : Univ. Press Author : Taton, René; Title : Causalités et accidents de la découverte scientifique : illustration de quelques étapes caractéristiques de l'évolution des sciences Imprint : Paris : Masson Author : Teilhard de Chardin, Pierre; Title : Le phénomène humain Imprint : Paris : Le Seuil Author : Terman, Frederick Emmons; Title : Electronic and radio engineering. - 4th ed Imprint : New York : McGraw-Hill Author : Thompson, Robert W; Title : Hyperons and heavy mesons : the uncharged particles Imprint : Bloomington : Indiana Univ. Author : Tonnelat, Marie-Antoinette; Title : La théorie du champ unifié d'Einstein et quelques-uns de ses développements Imprint : Paris : Gautier-Villars Series : Les grands problèmes de la science, 4 Author : Von Engel, Alfred Hans; Title : Ionized gases. - 1st ed Imprint : Oxford : Clarendon Press Author : Von Neumann, John; Title : Mathematical foundations of quantum mechanics Imprint : Princeton : Princeton Univ. Press Series : Investigations in physics, 2 Author : Ware, Lawrence A; Title : Communication circuits. - 3rd ed Imprint : New York : Wiley Author : Wendt, Gerald; Title : L'énergie nucléaire et ses utilisations pacifiques Imprint : Paris : Unesco Series : L'Unesco et son programme, 14 Author : Wirth, Marcel; Title : Le choix des prestations dans les caisses de retraite Imprint : Lausanne : Payot Author : Yarwood, John; Title : High vacuum technique : theory, practice, industrial applications and properties of materials. - 3rd ed Imprint : London : Chapman and Hall Author : Ziller, A; Title : Méthodes de différentiation et d'intégration numériques (applications) Imprint : Paris : Service de documentation et d'information technique de l'aéronautique Series : Publications scientifiques et techniques du ministère de l'air

33. UVA Computer Science: News Articles Then in 1930, American scientists Jesse Douglas and tibor rado proposed a general analytical solution that ultimately earned Douglas the first Fields Medal, http://www.cs.virginia.edu/misc/news-robins4t.html

U NIVERSITY of V ... Contact Us Of interest to: Prospective Students Members News Articles Scientists Float a New Solution to Puzzling Bubble San Diego Union-Tribune Scott Lafee A UCSD scientist and two colleagues have added weight to a 150-year-old question involving soap bubbles, a contribution that may ultimately lead to better robots and a new branch of mathematics. Reporting in today's issue of Proceedings of the National Academy of Sciences , the team describes a method of mathematically defining not just the surface dimensions of a soap bubble within a wire ring, but also the bubble's surface weight and thickness. "We think there's a lot of power in the idea," said Andrew Kahng of the University of California Los Angeles T.C. Hu, a professor of computer science at the University of California San Diego , and Gabriel Robins of the University of Virginia collaborated with Kahng on the research. The genesis of their work goes back roughly 150 years to Joseph Plateau, a Belgian physicist who, after dipping a wire ring in soapy water, asked the original question: What is the shape of a soap bubble which has wire as its boundary?

34. UVA Computer Science: News Articles In 1930, mathematicians Jesse Douglas and tibor rado came up with a purely analytical solution For any curve, they could provide a mathematical description http://www.cs.virginia.edu/misc/news-robins3t.html

U NIVERSITY of V ... Contact Us Of interest to: Prospective Students Members News Articles Floating an Answer to Bubble Riddle Los Angeles Times Nora Zamichow Science: Research team comes up with a solution to a 150-year old brain teaser. The findings could have practical applications and lead to a new branch of math. I f you take a wire, bend it to create a loop, and stick it in soapy water, what shape bubbles will you create? This question has tormented mathematicians for 150 years. A team of three researchers has come up with a solution, one it believes may even have some practical applications for solving problems with robots and computer chip design. In fact, the scientists believe, their work may pave the way to a new branch of mathematics: dimensional geometry. In devising a solution, the three added thickness and weight to the equation, removing the problem from the ideal realm of mathematics and putting it into everyday world, in which objects have dimensions. "Just as the subject of probability started from a gambler's question and the subject of geometry started from partitioning flooded land in the Nile River valley in Egypt, so the question of minimum surfaces with thickness and weight may lead to a new branch of mathematics." said T. C. Hu, a professor of computer science and engineering at UC San Diego. Hu's quest for the soap bubble solution, published in today's issue of the journal Proceedings of the National Academy of Science, began in 1963. If you ask Hu why he has battled this problem, he'll give you a because-it-was-there answer.

35. Hausdorff Measure And Lebesgue Area The list below may not include every reference from the original article. rado, tibor. On Surface Area. Proc Natl Acad Sci USA 1945 Mar;31(3)102–106. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1063310

36. AIM Reprint Library: 5. The Cauchy Area of a Frechet Surface Helsel, RG rado, tibor 6. The Kolmogoroff Principle for the Lebesgue Area Helsel, RG rado, tibor http://www.aimath.org/library/library.cgi?database=reprints;mode=display;BrowseT

37. AIM Reprint Library: 6. On Upper SemiContinuous Collections rado, tibor Youngs, JWT 7. On upper semi-continuous collections rado, T. Youngs, JWT http://www.aimath.org/library/library.cgi?database=reprints;mode=display;BrowseT

38. Grail+ - Links tibor rado, a professor at the Ohio State Univers ity, thought of a simple noncomputable function besides the standard halting problem for Turing machines. http://www.csd.uwo.ca/research/grail/links.html

Finite-state machine software, products, and projects Please tell us if you know of finite-state machine software that isn't on this list. Aleph FSM ALEPH is a high-energy physics experiment at the large electron-positron collider LEP at CERN. The Information and Programming Technology Group (IPT) of the ECP Division at CERN is active in software development support and information systems for experiments, including FSM technology. AMORE The AMORE system is a program for the computation of finite automata, syntactic monoids of regular languages, and (possibly star-free) regular expressions. The system is implemented in C under Unix or DOS. A graphical component generates state graphs of finite automata on the screen from given transition tables (under Unix only). AUTOMATA (Milan ) From the COLOS project at the University of Milan. AUTOMATA is a tool for modelling automata and experimenting with grammars. The environment deals with: finite state automata (FSA, both deterministic and non deterministic), push-down automata - PDA (both deterministic and non deterministic), finite state transducers (Moore and Mealy machines), grammars, regular expressions, pattern matching It provides the visualisation of some important algorithms, such as the transformation of non deterministic automata into deterministic ones or the minimisation. The automata are defined by entering their state diagram in a graphic editor or by giving a grammar. AUTOMATA (Pittsburgh) automata is a Mathematica based package that manipulates finites state machines and their syntactic semigroups. A number of operations on 1-dim cellular automata are also available. All the algorithms are implemented in Mathematica, and a good number of them is also implemented externally in a C++ library (e.g., power automaton construction, minimization using Hopcroft's algorithm, D-class decomposition). The C++ code can be used directly or, via MathLink, from within Mathematica. On a standard workstation, the external code allows one to generate machines and/or semigroups with several 10000 elements.

39. Extra Here is one of those functions invented by tibor rado in the early 60s (“On NonComputable Functions.” Bell System Tech. J 41, 3. 1962). The function http://www.math.uu.se/~salling/AUTOMATATEORI_IT/Busy Beaver/BusyBeaver.html

The Busy Beaver Problem The function In what follows consider only Turing machines which halt on blank tape and which have the single letter 1 in their tape-alphabet besides the blank symbol. Let's call such machines beavers Now define a function on the set of natural numbers as follows. For a given n , consider all beavers with n states in addition to the halting state, and let Max n ) be the maximum number of 1's that these beavers can write on the tape when run on blank tape. The problem Is there any algorithm (Turing machine) that for every n computes Max n Rado gave the answer in his paper 1962: No such algorithm (Turing machine) exists. Below I will give an outline of a proof of this incomputability result. First some remarks ... REMARK 1 Max n ) is well-defined (it exists) for every n . Why? Because for a given n there is only a finite number of beavers with n states, each beaver with a string (a finite number of 1's) as output. And among a finite number of string-lengths, there must be a maximal length. REMARK 2 Given a finite set S of numbers (measuring the string-lengths above) it is trivial to compute the maximum. On the other hand the computing matter in the busy beaver problem is not trivial at all. Why? Because the numbers in the set S is not given to us. To be more precise, these numbers are defined but not computed. They are defined as the lengths of the output-strings from the beavers with

40. PNAS -- Index By Author (Mar 15 1930, 16 (3)) Cleland, Ralph E. Cleland, Ralph E. Currier, Eldred. L. Lindsay, RB Luyten, Willem J. Luyten, Willem J. M. Morse, Marston. N. Newman, MHA. R. rado, tibor http://www.pnas.org/content/vol16/issue3/aindex.shtml

Index by Author: Mar 15 1930; 16 (3) [Table of Contents] A B C D E F G H I J K L M N O P Q R S T U V W X Y Z B Bateman, H. [PDF] Blakeslee, A. F. [PDF] Blakeslee, Albert F. [PDF] Blakeslee, Albert F. [PDF] Blount, Raymond F. [PDF] Buchholz, J. T. [PDF] C Cleland, Ralph E. [PDF] Cleland, Ralph E. [PDF] Currier, Eldred [PDF] L Lindsay, R. B. [PDF] Luyten, Willem J. [PDF] Luyten, Willem J. [PDF] M Morse, Marston [PDF] N Newman, M. H. A. [PDF] R Rado, Tibor [PDF] S Seeger, R. J. [PDF] Sellards, Andrew Watson [PDF] W Wallis, Everett S. [PDF] Wilder, R. L. [PDF] Z Zwicky, F. [PDF] Current Issue Archives Online Submission ... Site Map

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