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Topic: Bernoulli's theorem

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Introduction on Bernoulli's numbers The following famous and important theorem was published in 1840 by Karl von Staudt (1798-1867) and it allows to compute easily the fractional part of Bernoulli's numbers (thus it also permits to compute the denominator of those numbers). Clausen-von Staudt's theorem also permits to compute exactly a Bernoulli's number as soon as a sufficiently good approximation of it is known. They also appear in numbers theory (Fermat's theorem) and in many other domains and have caused the creation of a huge literature (see the 2700 and more entries enumerated in [ 6 ]). numbers.computation.free.fr /Constants/Miscellaneous/bernoulli.html

Daniel Bernoulli --  Encyclopædia Britannica Bernoulli's theorem (q.v.), which he derived, is named after him. First derived (1738) by the Swiss mathematician Daniel Bernoulli, the theorem states, in effect, that the total mechanical energy of the flowing... Includes information on his work on probability, the binomial as well as multinomial theorems, the Bernoulli differential equation, and the weak law of large numbers. www.britannica.com /eb/article-9078863   (757 words)

Bernoulli number - Wikipedia, the free encyclopedia Divisibility properties of the Bernoulli numbers are related to the ideal class groups of cyclotomic fields by a theorem of Kummer and its strengthening in the Herbrand-Ribet theorem, and to class numbers of real quadratic fields by Ankeny-Artin-Chowla. In mathematics, the Bernoulli numbers are a series of rational numbers with deep connections in number theory. Although easy to calculate, the values of the Bernoulli numbers have no elementary description; they are, up to a factor, the values of the Riemann zeta function at negative integers. en.wikipedia.org /wiki/Bernoulli_number   (777 words)

Daniel Bernoulli --  Encyclopædia Britannica Bernoulli's theorem (q.v.), which he derived, is named after him. First derived (1738) by the Swiss mathematician Daniel Bernoulli, the theorem states, in effect, that the total mechanical energy of the flowing... Includes information on his work on probability, the binomial as well as multinomial theorems, the Bernoulli differential equation, and the weak law of large numbers. www.britannica.com /eb/article-9078863   (748 words)

Daniel Bernoulli --  Encyclopædia Britannica Bernoulli's theorem (q.v.), which he derived, is named after him. First derived (1738) by the Swiss mathematician Daniel Bernoulli, the theorem states, in effect, that the total mechanical energy of the flowing... Includes information on his work on probability, the binomial as well as multinomial theorems, the Bernoulli differential equation, and the weak law of large numbers. www.britannica.com /eb/article-9078863   (748 words)

Bernoulli’s Equation Applied to a Convergent-Divergent Passage This now may be compared with the velocity ratio inferred from pressure distribution using Bernoulli’s theorem. versus X. In order to be able to compare your experimental data with the Bernoulli’s theorem predictions, plot the measured values of u/u To compare the measured values of p with the result of calculations we must use the continuity equation as well as the Bernoulli equation. engr.smu.edu /me/2142/exp2.htm   (785 words)

A history of mathematical statistics from 1750 to 1930-Hald Dale, A. On Bayes' theorem and the inverse Bernoulli theorem. Bernoulli, D. Essai d'une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l'inoculation pour la prévenir. English by C. Allen as "Observations on the foregoing dissertation of Bernoulli." Biometrika 48, 13-18, (1961). www.york.ac.uk /depts/maths/histstat/haldcontents.htm   (10854 words)

Topic of Bernoulli's Number The most relevant use of Bernoulli Numbers are found in Fermat's Last Theorem as expressed in the von-Staudt-Clausen Theorem. Bernoulli's Number one is equal to negative one-half. The Bernoulli Numbers were introduced by Jacques Bernoulli. www.andrews.edu /~calkins/math/biograph/199899/topbern.htm   (197 words)

Bernoulli’s Equation Applied to a Convergent-Divergent Passage The experiment demonstrates the use of a Pitot-static tube, and investigates the application of Bernoulli’s theorem to flow along a convergent-divergent passage. This now may be compared with the velocity ratio inferred from pressure distribution using Bernoulli’s theorem. The aim of the experiment is to measure the distribution of the difference between the total pressure P and static pressure p along the duct and, using Bernoulli’s equation, determine the absolute velocity values, u, along the same channel. engr.smu.edu /me/2142/exp2.htm   (785 words)

Some simple algorithms for the evaluations and representations of the Riemann zeta function at positive integer arguments -- from Mathematica Information Center zeta functions, Basler problem, hypergemetric series, Gauss' summation theorem, Wallis' integral formula, Dixon's summation theorem, Bernoulli polynomials, Bernoulli numbers, Euler's formula, Mellin transform, Wilton's formula, Lerch's transcendent Many interesting solutions of the so-called Basler problem of evaluating the Riemann zeta function zeta(s) when s=2, which was of vital importance to Euler and the Bernoulli brothers (Jakob and Johann Bernoulli), have appeared in the mathematical literature ever since Euler first solved this problem in the year 1736. The main object of the present paper is to investigate rather systematically several interesting evaluations and representations of zeta(s) when s is an element of N\{1}. library.wolfram.com /infocenter/Articles/2024   (231 words)

histmath.doc A. Bernoulli B. Hardy C. Noether D. Robinson E. By 2000, all but one of the 23 “Hilbert Problems” from 1900 were solved. A. John Bernoulli B. John Graunt C. John Napier D. John Playfair E. Who was the Arab author credited with the origin of our English words algebra and algorithm? A. Fermat’s Last Theorem B. Poincaré Conjecture C. Reimann Hypothesis D. Yang-Mills Theorem E. This 17th century London merchant wrote Natural and Political Observations Made Upon the Bills of Mortality which can be said to have started the disciplines of mathematical statistics and actuarial science. www.mualphatheta.org /National_Convention/natcontests/histmath.doc   (1310 words)

Educom Subscription Info and Honorary Subscribers for 25th Sept 1997 To subscribe to Edupage: send mail to: listproc@educom.unc.edu with the message: subscribe edupage James Bernoulli (if your name is James Bernoulli; otherwise, substitute your own name). To subscribe, send mail to: listproc@educom.unc.edu with the message: subscribe update James Bernoulli (if your name is James Bernoulli; otherwise, substitute your own name). In his major work was Ars Conjectandi (The Art of Conjecture) he explained what he called his golden theorem, of which historian Jeremy Campbell says: "Loosely paraphrased, the golden theorem proves that, in the long run, probabilities approach certainties more and more closely. www.ee.surrey.ac.uk /Contrib/Edupage/1997/09/25-09-1997-trailer.html   (566 words)

Bernoulli Equations AJ Bernoulli Theorem Equations and Formulas Calculator - Velocity at Point 1 - F... AJ Bernoulli Theorem Equations and Formulas Calculator - Head Loss - Fluid Mecha... Bernoulli Equation: History of Daniel Bernoulli and his Equation... www.scienceoxygen.com /aviation/28.html   (566 words)

Search results an = (0545.12005) Keywords: Fitting ideals; abelian varieties; cuspidal group; Eisenstein ideal; Iwasawa theory; Iwasawa main conjecture; p-adic L-functions; Iwasawa modules; ${\bbfZ}\sb p$-extensions; modular curves; Herbrand's theorem; cyclotomic field; Bernoulli number; unramified extensions Herbrand showed that if an eigenspace is non-trivial then a corresponding Bernoulli number is divisible by p, and Ribet proved the converse, which amounted to constructing certain unramified extensions of $K\sb p$. Let p be an odd prime and consider the p-th cyclotomic field $K\sb p$. zmath.impa.br /cgi-bin/zmen/ZMATH/en/zmath.html?first=1&maxdocs=3&type=html&an=0545.12005&format=complete   (566 words)

PlanetMath: congruence of Clausen and von Staudt Cross-references: lowest terms, rational number, theorem, integer, divides, primes, sum, even integer, congruence, odd, Bernoulli number See Also: Kummer's congruence, the odd Bernoulli numbers are zero This is version 1 of congruence of Clausen and von Staudt, born on 2005-04-19. planetmath.org /encyclopedia/StaudtClausenTheorem.html   (566 words)

A history of mathematical statistics from 1750 to 1930-Hald Dale, A. On Bayes' theorem and the inverse Bernoulli theorem. Bernoulli, D. Essai d'une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l'inoculation pour la prévenir. Bernoulli, D. Diiudicatio maxime probabilis plurium observationem discrepantium atque verisimillima inductio inde formanda. myriam.ulpgc.es /722468.htm   (566 words)

A history of mathematical statistics from 1750 to 1930-Hald Dale, A. On Bayes' theorem and the inverse Bernoulli theorem. Bernoulli, D. Essai d'une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l'inoculation pour la prévenir. English by C. Allen as "Observations on the foregoing dissertation of Bernoulli." Biometrika 48, 13-18, (1961). myriam.ulpgc.es /722468.htm   (566 words)

Analysis II One of the most organized website was designed by Renen Bassik on Bernoulli’s Theorem of Inequality.   The first section of the webpage states a simple derivation and an example problem that applies Bernoulli’s Theorem of Inequality. This project place a heavy emphasis on computer technology integration, not necessarily the Internet webpage design but utilization of computer applications. www.bergen.org /ACADEMY/DIMAC/a2-des2.htm   (566 words)

pre.html Euler's hydrodynamical equations., Bernoullis theorem, Helmholtz equations, Cauchy's integral, motion due to impulsive forces. Lebesgue theorem on the passage to the limit under the integral sign. Modules,sub-modules, quotient modules,Cyclic modules,Vector spaces,Linear transformation,dual spaces, dual spaces,basis and coordinates,dual basis and their properties,dual maps, matrices of dual map, rank and nullity of Linear maps and matries, invertible matrices, Equivalent matrices,similar matrices www.uniraj.ernet.in /syllabi/Maths/pre.html   (799 words)

Rajasthan Vidhyapeeth Fluid momentum: The Momentum theorem, Applications of the momentum theorem, Equation of motion, Eulers equation of motion integration of Eulers equation of motion. Differential Equation: Differential equation of first order and first degree, linear differential equations of higher order with constant coefficients. Conservation of mass and The continuity equation for three dimensions. www.riths.com /BTech-MECH.htm   (3870 words)

Theorem of de Moivre-Laplace - Wikipedia, the free encyclopedia In probability theory, the theorem of de Moivre-Laplace is a special case of the central limit theorem. The "Bernoulli trials" were not so-called in that book, but rather de Moivre wrote about the probability distribution of the number of times "heads" appears when a coin is tossed 1800 times. It states that the binomial distribution of the number of "successes" in n independent Bernoulli trials with probability 1/2 of success on each trial is approximately a normal distribution if n is large, or, more precisely, that after standardizing, the probabilities converge to those assigned by the standard normal distribution. en.wikipedia.org /wiki/Theorem_of_de_Moivre-Laplace   (3870 words)

chronology.htm   He also included combinations and permutations, which are still employed today, along with a series of problems on games of chance, and most importantly the Bernoulli theorem and a proof of the Binomial theorem. One of LaplaceÂ’s significant contributions to the theory of probability was the Central Limit Theorem, which he presented in 1810, and which provided the necessary tool to solve the method of least squares. In Ars Conjectandi Bernoulli gave explanations and original proofs of the propositions introduced in HuygenÂ’s De ratiociniis in Ludo Aleae. www.math.utep.edu /Faculty/mleung/probabilityandstatistics/chronology.htm   (3870 words)

Unknown (ResearchIndex) We deduce a universal first order Kummer congruence and a congruence for the higher order universal Bernoulli-Hurwitz numbers from Clarke's universal von Staudt theorem. 2 An analogue of the von Staudt-Clausen theorem (context) - Dibag - 1984 5 The universal von Staudt theorems (context) - Clarke - 1989 citeseer.ist.psu.edu /463158.html   (3870 words)

Clearing up the market cycle... best von Staudt-Clausen Theorem An analogue of the von Staudt - Clausen theorem An analogue of the von Staudt - Clausen theorem euclid.dmj/1077490207 Citation: Duke Math. Theorems of Morley and Emma Lehmer and their generalizations. The Theorem of von Staudt '' and ``Proof of von Staudt's Theorem.'' §... ascot.pl /th/Fourier5/von-Staudt-Clausen-Theorem.htm   (3870 words)

IngentaConnect Arithmetic Properties of Bernoulli-Pade Numbers and Polynomials We derive analogues of the Kummer congruences, the von Staudt–Clausen Theorem, and other properties also satisfied by the ordinary Bernoulli numbers and polynomials. These generalize the Bernoulli numbers and polynomials, as well as other sequences found in the literature. www.ingentaconnect.com /content/ap/nt/2002/00000092/00000002/art02696   (3870 words)

Research Experience for Undergraduates On the Mean Value Theorem, Inequality, and Inclusion (in The Teaching of Mathematics) A Topological Mean Value Theorem for the Plane (in The Teaching of Mathematics) math.fullerton.edu /mathews/n2003/calculus/CalculusBib/Links/CalculusBib_lnk_3.html   (4115 words)

Topic of Bernoulli's Number The most relevant use of Bernoulli Numbers are found in Fermat's Last Theorem as expressed in the von-Staudt-Clausen Theorem. The formula for deriving even Bernoulli Numbers is as stated above, where B* is equal to: Many efforts were made to extend proofs to other powers, and in 1850 Ernst Eduard Kummer of Germany showed that the equation x www.andrews.edu /~calkins/math/biograph/199899/topbern.htm   (4115 words)

JBernoulli Bernoulli hoped to continue practical applications of this theorem in the fields of politics and economics. Jakob Bernoulli, known as one of the Bernoulli brothers, a mathematician, and a Swiss probabilist, was born in the Netherlands in 1583 to Johann Bernoulli, a mathematics professor at the University of Gröningen. Bernoulli’s work is a great contribution to the study of probability. www.teacherlink.org /content/math/interactive/probability/history/contributors/jbernoulli.html   (326 words)

Bernoulli Bibliography Bernoulli numbers are particularly important in number theory, especially in connection with Fermat's last theorem (see, e.g., Ribenboim (1979)). The same is true for the numerous generalizations and extensions of the Bernoulli and allied numbers and of the corresponding polynomials. We included those in which Bernoulli numbers play a relatively important role; these criteria, however, are not well defined and are somewhat arbitrary. www.mscs.dal.ca /~dilcher/bernoulli.html   (997 words)

Bernoulli, Volume 12, no. 1 Bernoulli is published jointly by the Bernoulli Society for Mathematical Statistics and Probability and the International Statistical Institute (ISI). Central limit theorem and convergence to stable laws in Mallows distance projecteuclid.org /Dienst/UI/1.0/Journal?authority=euclid.bj   (155 words)

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