Chebyshev J. Chem. Phys. 107, 10003 (1997). Full Paper. pafnuty L. chebyshev 18211894,chebyshev.jpeg (1360 bytes). chebyshev expansion methods for electronic http://www.cchem.berkeley.edu/~mhggrp/roib/chebyshe.htm
Extractions: 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
Extractions: In mathematics the Chebyshev polynomials , named after Pafnuty Chebyshev ), are special polynomials . One usually distinguishes between Chebyshev polynomials of the first kind which are denoted T n and Chebyshev polynomials of the second kind which are denoted U n . The letter T is used because of the alternative transliterations of the name Chebyshev as Tchebyshef or Tschebyscheff The Chebyshev polynomials T n or U n are polynomials of degree n and the sequence of Chebyshev polynomials of either kind composes a polynomial sequence Chebyshev polynomials are important in approximation theory because the roots of the Chebyshev polynomials of the first kind, which are also called Chebyshev nodes , are used as nodes in polynomial interpolation . The resulting interpolation polynomial minimizes the problem of Runge's phenomenon and provides the best approximation to a continuous function under the maximum norm In the study differential equations they arise as the solution to the Chebyshev differential equation for the polynomials of the first and second kind, respectively. These equation are special cases of the
List Of Statisticians: Information From Answers.com Charles Spearman Genichi Taguchi; pafnuty Tchebycheff, see pafnuty chebyshev John Tukey Vladimir Vapnik (Russia, ~1935 ); Samuel Stanley Wilks http://www.answers.com/topic/list-of-statisticians
ABOUT PAUL ERDÖS first proved only in 1850, by pafnuty Lvovitch chebyshev, the father of Russianmathematics. chebyshev s proof was incredibly difficult and longwinded. http://bookbuzz.com/MBIO_About_Erdos.htm
Extractions: but a separate article prepared by its author, Bruce Schechter) F OR OVER half a century, early in the morning or in the middle of the night, mathematicians in Budapest or Berkeley, Prague or Sydney have been summoned from their multi-dimensional dreams by a knock at the door. Their unexpected guest was a short, smiling man wearing thick glasses and an old suit. In one hand he held a small suitcase containing everything he owned, in the other a shopping bag stuffed with papers. It was Paul Erdös, one of the greatest mathematicians of the twentieth century, a man who lived in the space of Platonic Ideals and infinite beauty, who called no place on Earth home. Never one to waste time on formalities with work to be done, Erdös would announce to his host: "My brain is open!" For the next few days, brains open, Erdös and his host, with other mathematicians recruited as needed, would be off on a mathematical journey of problem, conjecture, theorem and proof. The goal of their journey was nothing less than Truth and Beauty. "If numbers aren't beautiful, I don't know what is," Erdös once remarked. While the pursuit of mathematical beauty was Erdös's only goal, his ideas inevitably have found practical applications. One of the small ironies of Erdös's life is that, although he never owned or used a computer, mathematics that he invented is the basis for modern computer science; although he never had a secret, his mathematics is used by those who invent secret codes.
Variance And Higher Moments chebyshev s inequality (named after pafnuty chebyshev) gives an upper bound onthe probability that a random variable will be more than a specified distance http://www.ds.unifi.it/VL/VL_EN/expect/expect2.html
Extractions: Virtual Laboratories Expected Value 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 The following exercises give some basic properties of variance, which in turn rely on basic properties of expected value 3. Show that var(
Chebyshev's Inequality - Enpsychlopedia chebyshev s inequality (or Tchebysheff s inequality or chebyshev s theorem),named in honor of pafnuty chebyshev, is a result in probability theory that http://psychcentral.com/psypsych/Chebyshev's_inequality
Extractions: home resource directory disorders quizzes ... support forums Chebyshev's inequality (or Tchebysheff's inequality or Chebyshev's theorem ), named in honor of Pafnuty Chebyshev , is a result in probability theory that gives a lower bound for the probability that a value of a random variable of any distribution with finite variance lies within a certain distance from the variable's mean ; equivalently, the theorem provides an upper bound for the probability that values lie outside the same distance from the mean. Contents showTocToggle("show","hide") 1 The theorem edit 'Theorem.' Let X . Then for any real number k Only the cases k Another consequence of the theorem is that for any distribution Typically, the theorem will provide rather loose bounds. However, the bounds provided by Chebyshev's inequality cannot, in general (remaining sound for variables of arbitrary distribution), be improved upon. For example, for any k k ) meets the bounds exactly.
ChebyshevU of Mathematics archive gives pafnuty Lvovich chebyshev s biography. The Sixth chebyshev Polynomial of the Second Kind is 1 + 24 x2 - 80 x4 + 64 x6. http://www.mathpuzzle.com/ChebyshevU.html
Extractions: 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
Pafnuty Chebyshev Université Montpellier II Translate this page pafnuty chebyshev (1821-1894). Cette image et la biographie complète en anglaisrésident sur le site de luniversité de St Andrews Écosse http://ens.math.univ-montp2.fr/SPIP/article.php3?id_article=963
Extractions: Feedback Chech·en (ch ch n) n. a. A native or inhabitant of Chechnya. b. A member of the predominant, traditionally Muslim ethnic group of Chechnya. The Caucasian language of the Chechens. [Obsolete Russian, from Kabardian (Caucasian language of southwest Russia and Turkey) e en Chech en adj. Thesaurus Legend: Synonyms Related Words Antonyms Noun Chechen - a native or inhabitant of Chechnya Russian - a native or inhabitant of Russia Chechen - a northern Caucasian language spoken by the Chechen people Caucasian language Caucasian - a number of languages spoken in the Caucasus that have no known affiliations to languages spoken elsewhere Adj.
Extractions: Feedback Thesaurus Legend: Synonyms Related Words Antonyms Noun Chechen Republic - an autonomous republic in southwestern Russia in the northern Caucasus Mountains bordering on Georgia; declared independence from the USSR in 1991 but Russian troops invaded and continue to prosecute a relentless military campaign in the largely Muslim republic Chechenia Chechnya geographic area geographic region ... geographical region - a demarcated area of the Earth Russian Federation Russia - a federation in northeastern Europe and northern Asia; formerly Soviet Russia; since 1991 an independent state
MATHFUNC pafnuty chebyshev (18211894) was a professor at St.Petersburg University and isknown for his work on the prime number theorem, three bar mechanical http://aemes.mae.ufl.edu/~uhk/MATHFUNC.htm
Extractions: INTRODUCTION: Over the past thirty five years I have taught an introductory sequence of graduate level courses in mathematical analysis for engineering majors. An estimated 3000 students have attended these courses and the topics covered are Advanced Ordinary Differential Equations (EGM6321), Partial Differential Equations and Boundary Value Problems(EGM6222), and Integral Equations and Variational Methods(EGM6323). We present here a collection of equations and graphs for the various mathematical functions encountered in our lectures and give some relevant historical information on the mathematicians associated with their discovery. Equations and figures are presented in sequential order as they arise in the lectures. You can view the graphs by clicking on the underlined titles or the activated word HERE. The graphs have been generated by a variety of canned programs including Maple, Matlab, Mathematica, and Mathcad. OUTLINES for the three courses are found HERE HERE, and HERE . In the descriptions below we are using a type of mathematical esperanto since html does not have the standard math symbols in its repertoire. You can contact me at telephone number or reach me via standard mail at U.H.Kurzweg, MAE-A Bldg, University of Florida, Gainesville, FL 32611, USA
How Do You Develop Your Model Portfolios? a 19th century Russian mathematician named pafnuty chebyshev worked this out . chebyshev showed that if the distribution isnt normal, you would need http://www.indexinvestor.com/Free/modPorts.html
Extractions: Sign Up About IndexInvestor.com Transaction Policy Contact Us ... Home Sections... Home Indexing Basics Should I Use a Financial Advisor Management Process How Much To Save? Asset Allocation is the Key Which Asset Allocation? Active Versus Passive ETFs vs Mutual Funds Asset Allocation Methodology What People Say About Us Index Investor FAQ Are Actively Managed Funds for You? Download PDF The following is a summary of the different approaches we use to construct our model Australian, Canadian, and U.S. Dollar, Euro, Yen, and Pounds-Sterling based portfolios. The first approach we use is basically a "rule of thumb" (or, to use the more formal term, a "heuristic") approach. To construct our benchmark portfolios, we use three "rule of thumb" weightings that are often cited in news stories and other popular media: a mix of 80% equities and 20% debt (for our high risk/high return portfolios); a mix of 60% equities and 40% debt (for our moderate risk/moderate return portfolios); and a mix of 20% equities and 80% debt (for our low risk/low return portfolios). Using different terminology, somebody else might call these three portfolios aggressive, balanced, and conservative. We use two types of equity and debt to construct these portfolios. For our "domestic benchmarks" we use broad domestic equity and bond market indexes and funds that track them. For our "global benchmarks" we use broad global equity and bond market indexes and funds.
MY TEACHERS' TEACHERS' TEACHERS' His advisor pafnuty Lvovich chebyshev. He was a great expert in random processes.pafnuty Lvovich chebyshev 16 May 18218 Dec 1894 received his Ph.D. http://www.magicdragon.com/JVPteachers.html
Extractions: May be posted electronically provided that it is transmitted unaltered, in its entirety, without charge. version update of 19 August 2004 [42 Kilobytes] Music (Guitar) Literature (Poetry) Science (Philosophy) Science (Physics) ... Acting/Theatre Andres Segovia [1893-1987], from Spain, was the most famous guitarist of all time. He brought the classical guitar from its folk- and dance-related image to the symphonies and concert halls of the most established musical prominence. He developed an approach to plucking the guitar strings with the fingernails of the right hand, which became the dominat school of guitar, displacing the gentler and more lyrical Neapolitan school which used the fingertips. Christopher Parkening is arguably the greatest American performer of Classical Guitar. After a year of intensive Classical Guitar at Brookdale Community College, under Christopher Parkening's master student Barry Eisner, I was able to play a few baroque pieces and original compositions at community college concerts, and then retired to the occasional original song at Woodstock, various parties and resorts, and while hitchiking across America, singing for my supper. See also Donald Justice and Carl Ruggles in the "Poetry" section, below.
RAS History created nonEuclidean geometry, pafnuty chebyshev and members of theSt.Petersburg Mathematical School created by him made a weighty contribution to the http://www.ruhep.ru/npd/history.npd/hisras_e.htm
Extractions: According to the 1747 Rules the Academy was called the Emperial Academy of Sciences and Arts in St. Petersburg, between 1803 and 1836 it was called the Emperial Academy of Sciences, from 1836 till July 1917 it was the Emperial St. Petersburg Academy of Sciences, in July 1917 it became the Russian Academy of Sciences, in July 1925 was renamed into the USSR Academy of Sciences and since December 1991 - the Russian Academy of Sciences (RAS).
Extractions: Choose language The Academy in the XIXth and early ÕÕth century. Development of University Science. Formation of Scientific Schools In the 19th and early 20th century the scope of research areas presented in the Academy was noticeably extended. Humanities were developing alongside natural sciences. In 1841, some of the members of the Russian Academy, which had been functioning for sixty years as an independent institution involved in the study of the Russian language and literary monuments, joined the "big" Academy of Sciences. A department of the Russian language and literature was added to the already existing departments: of physics and mathematics and of history and philology. Prominent Russian authors like Vasily Zhukovsky, Ivan Krylov and, later, Leo Tolstoy were members of the new department, that also accepted literary critics and linguists. The achievements of Russian physicists scored were no less impressive. As early as the beginning of the 19th century Vasily Petrov discovered the electric arc. Emily Lentz became widely known for his works in electromagnetism, Boris Yakobi proposed the method of galvanoplastics. An outstanding scientific achievement of Russian and world science was the invention of radio by Alexander Popov in 1895. In late 19th century, Evgraf Fedorov made a major contribution to crystallography and the establishment of crystallographic groups.
Surfing The Net With Kids: Web Search Results chebyshev pafnuty Lvovich chebyshev (1821-1894) Work on prime numbers includedthe determination of the number of primes not exceeding a given number, http://www.surfnetkids.com/related.php?t=Prime Numbers&c=/primenumbers.htm
Chebyshev-polynomier +246cheby+ chebyshev er det engelske stavemåde af pafnuty Lvovich chebyshev, der var enrussisk matematiker, der levede 18211894. Navnet ses også translittereret som http://www.246.dk/cheby.html
Extractions: S A D M ... Chebyshev Chebyshev-polynomier er en familie af polynomier, T(n), der kortest kan skrives som T(n)(x) = cos(n*acos(x)); Dette ligner jo ikke umiddelbart polynomier, men T(0) = cos(0*acos(x) = 1 T(1) = cos(1*acos(x)) = x T(2) = cos(2*acos(x)) = 2 x^2 - 1 og generelt opfylder de rekursionsligningen T(n) = 2*x*T(n-1)-T(n-2) hvilket hurtigt giver følgende tabel over de 10 første samt viser at T(n) er et polynomie af grad n. T(0) = 1 T(1) = x T(2) = 2 x^2 - 1 T(3) = 4 x^3 - 3 x T(4) = 8 x^4 - 8 x^2 + 1 T(5) = 16 x^5 - 20 x^3 + 5 x T(6) = 32 x^6 - 48 x^4 + 18 x^2 - 1 T(7) = 64 x^7 - 112 x^5 + 56 x^3 - 7 x T(8) = 128 x^8 - 256 x^6 + 160 x^4 - 32 x^2 + 1 T(9) = 256 x^9 - 576 x^7 + 432 x^5 - 120 x^3 + 9 x T(10) = 512 x^10 - 1280 x^8 + 1120 x^6 - 400 x^4 + 50 x^2 - 1 Hvis man plotter de første 20 af slagsen i intervallet -1..1, får man det indledende nydelige billede med en tydelig moire-effekt. Her er programmet, der har tegnet den indledende illustration.
List Of Scientists By Field chebyshev, pafnuty Lvovich. Chenevix, Richard. Chenevix, Richard. Chernov, DmitriKonstantinovich. Chernov, Dmitri Konstantinovich. Chernyaev, Ilya Ilyich http://www.indiana.edu/~newdsb/c.html
Extractions: Cabanis, Pierre-Jean-Georges Cabanis, Pierre-Jean-Georges Cabanis, Pierre-Jean-Georges Cabeo, Niccolo Cabeo, Niccolo Cabeo, Niccolo Cabrera, Blas Cadet de Gassicourt, Charles- Louis Cadet de Gassicourt, Charles- Louis Cadet, Louis-Claude Cagniard de la Tour, Charles Cailletet, Louis Paul Cailletet, Louis Paul Caius, John Calandrelli, Giuseppe Calandrelli, Ignazio Calandrelli, Ignazio Calcidius Caldani, Leopoldo Marcantonio Caldani, Leopoldo Marcantonio Calkins, Gary Nathan Callan, Nicholas Callandreau, Pierre Jean Octave Callendar, Hugh Longbourne Callendar, Hugh Longbourne Callinicos of Heliopolis Callippus Callippus Calmette, Albert Camerarius, Rudolph Jakob Camerarius, Rudolph Jakob Cameron, Angus Ewan Cameron, Angus Ewan Campanella, Tommaso Campani, Giuseppe Campani, Giuseppe Campanus of Novara Campanus of Novara Campbell, Douglas Houghton Campbell, Ian Campbell, Norman Robert Campbell, Norman Robert Campbell, William Wallace Campbell, William Wallace Camper, Peter Camper, Peter Camper, Peter Canano, Giovan Battista Canano, Giovan Battista Cancrin, Franz Ludwig von
Collected Miscellany - Prime Obsession By John Derbyshire the interestingly named pafnuty Lvovich chebyshev and chebyshevs firstResult; Jacques Hadamard and Charles de la Vallee Poussin and their http://collectedmiscellany.com/archives/000049.php
Extractions: Main Prime Obsession by John Derbyshire Posted by Kevin on 11 November 2003 in Reviews John Derbyshire set for himself a daunting task in writting Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics : to bring the complex world of math down from its ivory tower and present a glimpse of its magic to the laymen reader. For his challenge Derbyshire picked a riddle, the Riemann Hypothesis (RH), that has been tantalizing mathematicians for over a century; a conundrum that Derbyshire labels as the greatest unsolved problem in mathematics. In Prime Obsession, he not only attempts to tell the story of Bernhard Riemann and his famous hypothesis but to communicate the complex and high level math involved down in such a way that a laymen reader might glimpse its meaning. It is to his immense credit that Derbyshire makes this interwoven tale of math and history both interesting and illuminating. A description of the RH should reveal the challenge Derbyshire faced:
