41. One Tailed Version Of Chebyshev's Inequality - By Henry Bottomley chebyshev's inequality with onetailed and unimodal versions, putting statistical limits on the dispersio Category Science Math Statistics...... chebyshev or Tchebycheff. pafnuty Lvovich chebyshev was a notable Russianmathematician, who was born on 16 May 1821 and died on 8 December 1894. http://www.btinternet.com/~se16/hgb/cheb.htm

Chebyshev's inequality and a one-tailed version Chebyshev's inequality states that for which is equivalent to for A one-tailed version of Chebyshev's inequality is that for /Var(X)) i.e. t which is equivalent to for Turning inequality into equality Turning inequality into equality Proof of Chebyshev's inequality Proof of one-tailed version of Chebyshev's inequality ... Discussion and a new page with more thoughts Speculation on unimodal PDFs or go to a Mode-Mean inequality or Mode-Median-Mean relationships or some Statistics Jokes written by Henry Bottomley Turning Chebyshev's inequality into an equality becomes P[X=m-k.s] = 1/(2.k ), P[X=m+k.s] = 1/(2.k ), and P[X=m] = 1-1/k Note E(X)=m and Var (X)=s , sd(X)=s, so for this X k The equality will in general only be achieved for a symmetric three-valued distribution. If the probabilities are p, 1-2p and p then equality is achieved when k=(2p) . A symmetric two-valued distribution is a special case with k=1. A chart showing this distribution for k=2 is below (return to top) Turning one-tailed version of Chebyshev's inequality into an equality becomes P[X=m+s.k] = 1/(1+k

42. List Of Mathematical Topics - Acapedia - Free Knowledge, For All entity Characteristic Characteristic equation Characteristic subgroup Charge chebyshev chebyshev, pafnuty Lvovich chebyshev's inequality http://acapedia.org/aca/List_of_mathematical_topics

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43. ×éÖ¯ chebyshev pafnuty Lvovich chebyshev (1821-1894) - /. d'Alembert - Jean Le Rond d'Alembert (1717-1783) - . http://www.lib.pku.edu.cn/is/Navigation/Mathematics/org_1.htm

American Mathematical Society (AMS) Association for Women in Mathematics Association of Christians in the Mathematical Sciences Australian Mathematical Society (AustMS) ... BRIMS - Ó¢¸ñÀ¼²¼Àï˹Íжû£¨HP£©Êýѧ¿Æѧ»ù´¡Ñо¿Ñ§»á. Centre for Experimental and Constructive Mathematics CRM Barcelona CRM Montreal CWI ... MRC - Ó¢¸ñÀ¼ WarwickÊýѧÑо¿ÖÐÐÄ MSRI Newton Institute Rényi Institute Steklov Institute ... American Mathematical Society e-Math Home Page À¹úÊýѧЭ»áµÄµç×ÓÊýѧÖ÷Ò³£¬AMSµÄ³ÉÔ±¿ÉÖ±½ÓÁ´½Óµ½AMSµÄµç×ÓÆÚ¿¯£¬¿É²éѯ¹«¹²³ö°æÊý¾Ý¿â¡¢»áÒéÄÚÈݼ°»áÒé°²ÅÅÈÕÀúµÈ. The Association of European Operational Research Societies Canadian Operational Research Society/Sociét?Canadienne de Recherche Opérationnelle Institute for Operations Research and the Management Sciences - INFORMS£¨Ô˳Ｐ¹ÜÀí¿ÆѧÑо¿Ëù£©ÔÚÏߣ¬ÌṩINFORMSµÄ¸÷ÖÖ»áÒé¡¢½ÌÓý×ÊÔ´ºÍÏà¹ØÁ´½ÓµÈ¡£ The Mathematical Association of America ÀÖÞÊýѧÁª»á£¬Äܹ»Á´½Óµ½MAA Gopher ·þÎñÆ÷¡¢ MAA Ö÷Ò³µÄÆäËû²¿·Ö¼°Ïà¹ØµÄÊýѧվµã . Mathematical Programming Society Military Operations Research Society National Science Foundation World Wide Web Server ¹ú¼Ò¿Æѧ»ù½ð»áµÄWWW·þÎñ¡£ Society for Risk Analysis Washington Institute for Operations Research and Management Science (WINFORMS, formerly WORMSC)

44. Biography.com Chayefsky, Paddy, 1923 1981. Chayes, Abram (Joseph), 1922 . chebyshev,pafnuty Lvovich, 1821 1894. Checker, Chubby (Ernest Evans), 1941 . http://search.biography.com/bio_browse.pl?letter=C&num=650

45. ChebyshevU Phillips, and many others. The MacTutor History of Mathematics archivegives pafnuty Lvovich chebyshev's biography. At mathworld.wolfram http://www.mathpuzzle.com/ChebyshevU.html

This header plots the critical line of the Riemann Zeta Function . A complete understanding wins a $1,000,000 prize Main Links Orders ... Next + 10 Chebychev Polynomials were used by Bill Daly and Steven Stadnicki to solve a problem. I've built a TRIANGLE page for the results, with new contributions by Bob Harris Roger Phillips , and many others. The MacTutor History of Mathematics archive gives Pafnuty Lvovich Chebyshev's biography . At mathworld.wolfram.com , there are twenty different entries for Chebyshev, including Chebyshev Polynomial of the First Kind and Chebyshev Polynomial of the Second Kind . What do they mean? I gained my first insight when I plugged cos(Pi/9) into the Inverse Symbolic Calculator . The Sixth Chebyshev Polynomial of the Second Kind is -1 + 24 x - 80 x + 64 x . In Mathematica, ChebyshevU[6,x]. This polynomial is also expressed as U x ChebyshevU[6,x] = -1 + 24 x - 80 x + 64 x = - (1 + 4 x - 4 x - 8 x ) (1 - 4 x - 4 x + 8 x -(1 + 4 x - 4 x - 8 x ) / 8 = (x - cos(2 p /7)) (x - cos(4 p /7)) (x - cos(6 p (1 - 4 x - 4 x + 8 x ) / 8 = (x - cos( p /7)) (x - cos(3 p /7)) (x - cos(5 p Thus, this polynomial is closely related to the heptagon. Similarly, 1 - 6 x + 8 x

46. Chebyshev Phys. 107, 10003 (1997). PDF. pafnuty L. chebyshev 18211894. chebyshev expansionmethods for electronic structure calculations on large molecular systems. http://www.fh.huji.ac.il/~roib/chebyshev.htm

Roi Baer email Dept. of Physical Chemistry , and the Lise Meitner research center The Hebrew University Jerusalem 91904, Israel. Tel: +972-2-658-6114 Fax: +972-2-651-3742 TOC L@ J. Chem. Phys. PDF Pafnuty L. Chebyshev 1821-1894 Chebyshev expansion methods for electronic structure calculations on large molecular systems Roi Baer and Martin Head-Gordon Department of Chemistry, University of California, Berkeley and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA The Chebyshev polynomial expansion of the one electron density matrix (DM) in electronic structure calculations is studied, extended in several ways and benchmark demonstrations are applied to large saturated hydrocarbon systems, using tight-binding method. We describe a flexible tree code for the sparse numerical algebra. We present an efficient method to locate the chemical potential. A reverse summation of the expansion is found to significantly improve numerical speed. We also discuss the use of Chebyshev expansions as analytical tools to estimate of the range and sparsity of the DM and the overlap matrix. Using these analytical estimates, a comparison with other linear scaling algorithms and their applicability to various systems is considered

47. Listings Of The World Science Math Mathematicians Famous chebyshev pafnuty Lvovich chebyshev (1821-1894) Post Review Work on prime numbersincluded the determination of the number of primes not exceeding a given http://listingsworld.com/Science/Math/Mathematicians/Famous_People/

48. Chebyshev J. Chem. Phys. 107, 10003 (1997). Full Paper. pafnuty L. chebyshev18211894. chebyshev expansion methods for electronic structure http://www.cchem.berkeley.edu/~mhggrp/roib/chebyshe.htm

Roi Baer MHG Group Dept. of Chemistry, UC Berkeley , CA 94720. Tel/Fax: 510-525-7021 TOC L@W Home Up J. Chem. Phys. Full Paper Pafnuty L. Chebyshev 1821-1894 Chebyshev expansion methods for electronic structure calculations on large molecular systems Roi Baer and Martin Head-Gordon Department of Chemistry, University of California, Berkeley, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 The Chebyshev polynomial expansion of the one electron density matrix (DM) in electronic structure calculations is studied, extended in several ways and benchmark demonstrations are applied to large saturated hydrocarbon systems, using tight-binding method. We describe a flexible tree code for the sparse numerical algebra. We present an efficient method to locate the chemical potential. A reverse summation of the expansion is found to significantly improve numerical speed. We also discuss the use of Chebyshev expansions as analytical tools to estimate of the range and sparsity of the DM and the overlap matrix. Using these analytical estimates, a comparison with other linear scaling algorithms and their applicability to various systems is considered

49. MetaEUREKA Metasearch wwwgroups.dcs.st-andrews.ac.uk/~history/Mathematicians/Cauchy.html - Site info -Alexa info 9. chebyshev - pafnuty Lvovich chebyshev (1821-1894) Work on prime http://www.metaeureka.com/cgi-bin/odp2.pl?dir=Science/Math/History/People/

50. Matematicos Translate this page Voltar ao topo. pafnuty Lvovich chebyshev. Nascido a 16 de Maio de 1821em Okatovo, Russia Falecido a 8 de Dezembro em St. Petersburg, Russia. http://www.educ.fc.ul.pt/icm/icm98/icm12/Mat_kz.htm

ICM do DEFCUL [Leonardo Pisano Fibonacci] [Marin Mersenne] [Pafnuty Lvovich Chebyshev] ... [Tales de Mileto] Leonardo Pisano Fibonacci Liber abaci Liber abaci Liber abaci, Casais adultos Casais jovens Total de casais Praticae geometricae Liber quadratorum Mis praticae geometricae [Voltar ao topo] Marin Mersenne n Em 1633 publicou , e em 1634, Dialogo Discorsi L'Harmonie Universelle (1636) e Cogitata Physico-Mathematica [Voltar ao topo] Pafnuty Lvovich Chebyshev Nascido a: 16 de Maio de 1821 em Okatovo, Russia Falecido a: 8 de Dezembro em St. Petersburg, Russia x p (1-x) q dx [Voltar ao topo] Pietro Antonio Cataldi Nascido a : 15 de Abril de 1548 Falecido a : 11 de Fevereiro de 1626 Pratica Aritmetica Trattado del modo brevissimo di trovar la radice quadra delli numeri Entre os seus outros trabalhos encontra-se Transformatione geometrica (1611) e um livro que estudava problemas de alcance militar que incluiam tabelas sobre o nascer do sol e sobre a altura do meio-dia para Bolonha (1613). Em 1618 publicou Operetta di ordinanze quadre Os Elementos de Euclides . Trabalho no quinto postulado de Euclides Operetta delle linee rette equidistanti et non equidistanti [Voltar ao topo] Nascido a : cerca de 580 a.C.

51. A 18621934), BM; chebyshev, pafnuty Lvovich (1821-1894), Maths Archive;Cherry, Thomas Macfarland (1898-1966), AAS; Christoffel, Elwin http://members.aol.com/jayKplanr/images.htm

return home An Alphabetical A-Z List of Famous Scientists and Mathematicians Indicates a portrait photograph or illustration is included. browse a section: A B C D ... Z A Abel, Niels Henrik Maths Archive Adams, John Couch Maths Archive Adams, Walter S. BM Agassiz, Louis UCMP Agnesi, Maria Gaetana Maths Archive Agnesi, Maria Gaetana ASC Aitken, Robert G. BM Alexander, Albert Ernest AAS Alfred Day Hershey BDB Ambartsumian, Viktor A. BM Ampere, Andre Marie 17th and 18th C Mathematicians Antoine, Albert C. Faces Apollonius of Perga (200 BC-100 BC), Maths Archive Arago, Francois Jean Dominique 17th and 18th C Mathematicians Arbogast, Antoine 17th and 18th C Mathematicians Arbuthnot, John Maths Archive Archimedes of Syracuse (287 BC - 212 BC), Maths Archive Aristarchus of Samos (310 BC-230 BC), Maths Archive Aristotle (384 BC-322 BC), Maths Archive Aristotle (384-322 BC), Bjorn's Guide Arrhenius, Svante August 1992 Institute Artin, Emil Maths Archive Artzt, Karen WDB Atanasoff, John Vincent

52. Biography-center - Letter C Mathematicians/Chebotaryov.html; chebyshev, pafnuty wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/chebyshev.html;Cheever, Eddie http://www.biography-center.com/c.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish C 854 biographies Cabana, Robert D. www.jsc.nasa.gov/Bios/htmlbios/cabana.html Cabanel, Alexandre www.ibiblio.org/wm/paint/auth/cabanel/ Cabell, James Branch www.library.vcu.edu/jbc/speccoll/exhibit/cabell/jbcbio.html Cable, George Washington docsouth.unc.edu/cablecreole/about.html Cabot, Richard Clarke www.whonamedit.com/doctor.cfm/1906.html Cacho Ruiz, Fermin www.olympic.org/uk/athletes/heroes/bio_uk.asp?PAR_I_ID=67348 Cades, Giuseppe www.getty.edu/art/collections/bio/a3432-1.html Cadorna, Luigi www.spartacus.schoolnet.co.uk/FWWcadorna.htm Caesar, Julius library.thinkquest.org/17120/data/bios/users/caesar/page_1.html Caffa, Melchiore www.kfki.hu/~arthp/bio/c/caffa/biograph.html Caffey, John Patrick www.whonamedit.com/doctor.cfm/97.html Caffieri, Jacques

53. The Mathematics Genealogy Project - Index Of CHEB Staff Links. There are 1 mathematicians whose last name begin withCHEB. chebyshev, pafnuty, University of St. Petersburg, 1849. home http://genealogy.mathematik.uni-bielefeld.de/html/letter.phtml?letter=CHEB

54. Approximating Dominant Singular Triplets Title Page next Next Abstract. Approximating Dominant Singular Triplets of Large Sparse Matricesvia Modified Moments. pafnuty L. chebyshev (May 16 1821 Dec 8 1894). http://www.cs.utk.edu/~berry/csi/

Next: Abstract Approximating Dominant Singular Triplets of Large Sparse Matrices via Modified Moments Pafnuty L. Chebyshev (May 16 1821 - Dec 8 1894) Sowmini Varadhan and Michael W. Berry Department of Computer Science 107 Ayres Hall University of Tennessee Knoxville, TN 37996-1301 varadhan@cs.utk.edu berry@cs.utk.edu Gene H. Golub Department of Computer Science Bldg. 460, Rm. 306 Stanford University Stanford CA 94305 golub@cs.stanford.edu To appear in Numerical Algorithms Abstract 1. Introduction 1.1 Singular Value Decomposition ... About this document ... The first and second authors' research was supported by the National Science Foundation under grant Nos. NSF-ASC-92-03004 and NSF-ASC-94-11394. Michael W. Berry (berry@cs.utk.edu) Sat May 18 15:28:14 EDT 1996

55. Full Alphabetical Index Translate this page Chaplygin, Serg (366*) Chapman, Sydney (792*) Chasles, Michel (154*) Châtelet, Gabrielledu (154*) Chebotaryov, Nikolai (409*) chebyshev, pafnuty (255*) Chern http://www.geocities.com/Heartland/Plains/4142/matematici.html

Completo Indice Alfabetico Cliccare su una lettera sottostante per andare a quel file. A B C D ... XYZ Cliccare sotto per andare agli indici alfabetici separati A B C D ... XYZ Il numero di parole nella biografia e' dato in parentesi. Un * indica che c'e' un ritratto. A Abbe , Ernst (602*) Abel , Niels Henrik (286*) Abraham bar Hiyya (240) Abraham, Max Abu Kamil Shuja (59) Abu'l-Wafa al'Buzjani (243) Ackermann , Wilhelm (196) Adams, John Couch Adams, Frank Adelard of Bath (89) Adler , August (114) Adrain , Robert (79) Aepinus , Franz (124) Agnesi , Maria (196*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (60) Ahmes Aida Yasuaki (114) Aiken , Howard (94) Airy , George (313*) Aitken , Alexander (825*) Ajima , Chokuyen (144) Akhiezer , Naum Il'ich (248*) al'Battani , Abu Allah (194) al'Biruni , Abu Arrayhan (306*) al'Haitam , Abu Ali (269*) al'Kashi , Ghiyath (73) al'Khwarizmi , Abu (123*) Albanese , Giacomo (282) Albert of Saxony Albert, Abraham Adrian (121*) (158*) Alberti , Leone (181*) Alberto Magno, San (109*) Alcuin di York (237*) Aleksandrov , Pave (160*) Alembert , Jean d' (291*) Alexander , James (163) Amringe , Howard van (354*) Amsler , Jacob (82) Anassagora di Clazomenae (169) Anderson , Oskar (67) Andreev , Konstantin (117) Angeli , Stefano degli (234) Anstice , Robert (209) Antemio of Tralles (55) Antifone il Sofista (125) Apollonio di Perga (276) Appell , Paul (1377) Arago , Dominique (345*) Arbogasto , Louis (87) Arbuthnot , John (251*) Archimede di Siracusa (467*) Archita of Tarentum (103) Argand , Jean (81) Aristeo il Vecchio (44) Aristarco di Samo (183) Aristotele Arnauld , Antoine (179)

56. Connecting The Dots The animations were created with errprod.m and absint.m. GIF images.Here's a picture of pafnuty Lvovitch chebyshev (18211894). http://www.math.psu.edu/dna/interpolation/interpolation.html

57. Lebensdaten Von Mathematikern Translate this page du (1706 - 1749) de Chazeles, Jean-Mathieu (1657 - 1710) Chebotaryov, Nikolai (1894- 1947) chebyshev, pafnuty Lwowitsch (14.5.1821 - 26.11.1894) Chern, Shiing http://www.mathe.tu-freiberg.de/~hebisch/cafe/lebensdaten.html

Diese Seite ist dem Andenken meines Vaters Otto Hebisch (1917 - 1998) gewidmet. By our fathers and their fathers in some old and distant town from places no one here remembers come the things we've handed down. Marc Cohn Dies ist eine Sammlung, die aus verschiedenen Quellen stammt, u. a. aus Jean Dieudonne, Geschichte der Mathematik, 1700 - 1900, VEB Deutscher Verlag der Wissenschaften, Berlin 1985. Helmut Gericke, Mathematik in Antike und Orient - Mathematik im Abendland, Fourier Verlag, Wiesbaden 1992. Otto Toeplitz, Die Entwicklung der Infinitesimalrechnung, Springer, Berlin 1949. MacTutor History of Mathematics archive A B C ... Z Abbe, Ernst (1840 - 1909) Abel, Niels Henrik (5.8.1802 - 6.4.1829) Abraham bar Hiyya (1070 - 1130) Abraham, Max (1875 - 1922) Abu Kamil, Shuja (um 850 - um 930) Abu'l-Wafa al'Buzjani (940 - 998) Ackermann, Wilhelm (1896 - 1962) Adams, John Couch (5.6.1819 - 21.1.1892) Adams, John Frank (5.11.1930 - 7.1.1989) Adelard von Bath (1075 - 1160) Adler, August (1863 - 1923) Adrain, Robert (1775 - 1843)

58. Neue Seite 1 Translate this page Chebotaryov, Nikolai (1894 - 1947). chebyshev, pafnuty Lwowitsch (14.5.1821 - 26.11.1894).Chern, Shiing-shen (26.10.1911 - ). Chevalley, Claude (1909 - 1984). http://www.mathe-ecke.de/mathematiker.htm

Abbe, Ernst (1840 - 1909) Abel, Niels Henrik (5.8.1802 - 6.4.1829) Abraham bar Hiyya (1070 - 1130) Abraham, Max (1875 - 1922) Abu Kamil, Shuja (um 850 - um 930) Abu'l-Wafa al'Buzjani (940 - 998) Ackermann, Wilhelm (1896 - 1962) Adams, John Couch (5.6.1819 - 21.1.1892) Adams, John Frank (5.11.1930 - 7.1.1989) Adelard von Bath (1075 - 1160) Adler, August (1863 - 1923) Adrain, Robert (1775 - 1843) Aepinus, Franz Ulrich Theodosius (13.12.1724 - 10.8.1802) Agnesi, Maria (1718 - 1799) Ahlfors, Lars (1907 - 1996) Ahmed ibn Yusuf (835 - 912) Ahmes (um 1680 - um 1620 v. Chr.) Aida Yasuaki (1747 - 1817) Aiken, Howard Hathaway (1900 - 1973) Airy, George Biddell (27.7.1801 - 2.1.1892) Aithoff, David (1854 - 1934) Aitken, Alexander (1895 - 1967) Ajima, Chokuyen (1732 - 1798) Akhiezer, Naum Il'ich (1901 - 1980) al'Battani, Abu Allah (um 850 - 929) al'Biruni, Abu Arrayhan (973 - 1048) al'Chaijami (? - 1123) al'Haitam, Abu Ali (965 - 1039) al'Kashi, Ghiyath (1390 - 1450) al'Khwarizmi, Abu Abd-Allah ibn Musa (um 790 - um 850) Albanese, Giacomo (1890 - 1948) Albert von Sachsen (1316 - 8.7.1390)

59. Mathem_abbrev Cartwright, Dame Mary Cassels, John Cauchy, Augustin Cavalieri, Bonaventura Cayley,Arthur Chang, SunYung Chapman, Sydney chebyshev, pafnuty, Chern, Shiing http://www.pbcc.cc.fl.us/faculty/domnitcj/mgf1107/mathrep1.htm

Mathematician Report Index Below is a list of mathematicians. You may choose from this list or report on a mathematician not listed here. In either case, you must discuss with me the mathematician you have chosen prior to starting your report. No two students may write a report on the same mathematician. I would advise you to go to the library before choosing your topic as there might not be much information on the mathematician you have chosen. Also, you should determine the topic early in the term so that you can "lock-in" your report topic!! The report must include: 1. The name of the mathematician. 2. The years the mathematician was alive. 3. A biography. 4. The mathematician's major contribution(s) to mathematics and an explanation of the importance. 5. A historical perspective during the time the mathematician was alive. Some suggestions on the historical perspective might be: (a) Any wars etc. (b) Scientific breakthroughs of the time (c) Major discoveries of the time (d) How did this mathematician change history etc.

60. Variance And Higher Moments chebyshev's inequality (named after pafnuty chebyshev) gives an upper bound on theprobability that a random variable will be more than a specified distance http://www.math.uah.edu/statold/expect/expect2.html

Virtual Laboratories Expected Value 2. Variance and Higher Moments Definition As usual, we start with a random experiment that has a sample space and a probability measure P . Suppose that X is a random variable for the experiment, taking values in a subset S of R . Recall that the expected value or mean of X gives the center of the distribution of X . The variance of X is a measure of the spread of the distribution about the mean and is defined by var( X E X E X Thus, the variance is the second central moment of X 1. Suppose that X has a discrete distribution with density function f . Use the change of variables theorem to show that var( X x in S x E X f x 2. Suppose that X has a continuous distribution with density function f . Use the change of variables theorem to show that var( X S x E X f x dx The standard deviation of X is the square root of the variance: sd( X ) = [var( X It also measures dispersion about the mean but has the same physical units as the variable X Properties The following exercises give some basic properties of variance, which in turn rely on basic properties of expected value 3. Show that var(

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