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Nicolaus II Bernoulli
Nicolaus II Bernoulli, a.k.a. Niklaus Bernoulli, Nikolaus Bernoulli (6 February 1695, Basel, Old Swiss Confederacy, Switzerland – 31 July 1726, Saint Petersburg, St. Petersburg, Imperial Russia, Russia) was a Switzerland, Swiss mathematician as were his father Johann Bernoulli and one of his brothers, Daniel Bernoulli. He was one of the many prominent mathematicians in the Bernoulli family. Work Nicolaus worked mostly on curves, differential equations, and probability. He was a friend and contemporary of Leonhard Euler, who studied under Nicolaus' father. He also contributed to fluid dynamics. He was older brother of Daniel Bernoulli, to whom he also taught mathematics. Even in his youth he had learned several languages. From the age of 13, he studied mathematics and law at the University of Basel. In 1711 he received his Master's of Philosophy; in 1715 he received a Doctorate in Law. In 1716-17 he was a private tutor in Venice. From 1719 he had the Chair in Mathematics at t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernoulli Nicolaus(II)
Bernoulli can refer to: People *Bernoulli family of 17th and 18th century Swiss mathematicians: **Daniel Bernoulli (1700–1782), developer of Bernoulli's principle **Jacob Bernoulli (1654–1705), also known as Jacques, after whom Bernoulli numbers are named **Jacob II Bernoulli (1759–1789) **Johann Bernoulli (1667–1748) **Johann II Bernoulli (1710–1790) **Johann III Bernoulli (1744–1807), also known as Jean, astronomer **Nicolaus I Bernoulli (1687–1759) **Nicolaus II Bernoulli (1695–1726) *Elisabeth Bernoulli (1873–1935), Swiss temperance campaigner *Hans Benno Bernoulli (1876–1959), Swiss architect *Ludwig Bernoully (1873–1928), German architect Mathematics * Bernoulli differential equation * Bernoulli distribution and Bernoulli random variable * Bernoulli's inequality * Bernoulli's triangle * Bernoulli number * Bernoulli polynomials * Bernoulli process * Bernoulli trial * Lemniscate of Bernoulli Science * 2034 Bernoulli, minor planet * Bernoulli's principle, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Padua
The University of Padua ( it, Università degli Studi di Padova, UNIPD) is an Italian university located in the city of Padua, region of Veneto, northern Italy. The University of Padua was founded in 1222 by a group of students and teachers from Bologna. Padua is the second-oldest university in Italy and the world's fifth-oldest surviving university. In 2010, the university had approximately 65,000 students. In 2021, it was ranked second "best university" among Italian institutions of higher education with more than 40,000 students according to Censis institute, and among the best 200 universities in the world according to ARWU. History The university is conventionally said to have been founded in 1222 when a large group of students and professors left the University of Bologna in search of more academic freedom ('Libertas scholastica'). The first subjects to be taught were law and theology. The curriculum expanded rapidly, and by 1399 the institution had divided in two: a ''Univ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theorists
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These conce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysts
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1726 Deaths
Seventeen or 17 may refer to: *17 (number), the natural number following 16 and preceding 18 * one of the years 17 BC, AD 17, 1917, 2017 Literature Magazines * ''Seventeen'' (American magazine), an American magazine * ''Seventeen'' (Japanese magazine), a Japanese magazine Novels * ''Seventeen'' (Tarkington novel), a 1916 novel by Booth Tarkington *''Seventeen'' (''Sebuntiin''), a 1961 novel by Kenzaburō Ōe * ''Seventeen'' (Serafin novel), a 2004 novel by Shan Serafin Stage and screen Film * ''Seventeen'' (1916 film), an American silent comedy film *''Number Seventeen'', a 1932 film directed by Alfred Hitchcock * ''Seventeen'' (1940 film), an American comedy film *''Eric Soya's '17''' (Danish: ''Sytten''), a 1965 Danish comedy film * ''Seventeen'' (1985 film), a documentary film * ''17 Again'' (film), a 2009 film whose working title was ''17'' * ''Seventeen'' (2019 film), a Spanish drama film Television * ''Seventeen'' (TV drama), a 1994 UK dramatic short starring Christ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1695 Births
It was also a particularly cold and wet year. Contemporary records claim that wine froze in the glasses in the Palace of Versailles. Events January–March * January 7 (December 28, 1694 O.S.) – The United Kingdom's last joint monarchy, the reign of husband-and-wife King William III and Queen Mary II comes to an end with the death of Queen Mary, at the age of 32. Princess Mary had been installed as the monarch along with her husband and cousin, Willem Hendrik von Oranje, Stadtholder of the Dutch Republic, in 1689 after King James II was deposed by Willem during the "Glorious Revolution". * January 14 (January 4 O.S.) – The Royal Navy warship HMS ''Nonsuch'' is captured near England's Isles of Scilly by the 48-gun French privateer ''Le Francois''. ''Nonsuch'' is then sold to the French Navy and renamed ''Le Sans Pareil''. * January 24 – Milan's Court Theater is destroyed in a fire. * January 27 – A flotilla of six Royal Navy warships under the command of Commodo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernoulli Trial
In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted. It is named after Jacob Bernoulli, a 17th-century Swiss mathematician, who analyzed them in his ''Ars Conjectandi'' (1713). The mathematical formalisation of the Bernoulli trial is known as the Bernoulli process. This article offers an elementary introduction to the concept, whereas the article on the Bernoulli process offers a more advanced treatment. Since a Bernoulli trial has only two possible outcomes, it can be framed as some "yes or no" question. For example: *Is the top card of a shuffled deck an ace? *Was the newborn child a girl? (See human sex ratio.) Therefore, success and failure are merely labels for the two outcomes, and should not be construed literally. The term "success" in this sense consists in the result ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernoulli Process
In probability and statistics, a Bernoulli process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes only two values, canonically 0 and 1. The component Bernoulli variables ''X''''i'' are identically distributed and independent. Prosaically, a Bernoulli process is a repeated coin flipping, possibly with an unfair coin (but with consistent unfairness). Every variable ''X''''i'' in the sequence is associated with a Bernoulli trial or experiment. They all have the same Bernoulli distribution. Much of what can be said about the Bernoulli process can also be generalized to more than two outcomes (such as the process for a six-sided die); this generalization is known as the Bernoulli scheme. The problem of determining the process, given only a limited sample of Bernoulli trials, may be called the problem of checking whether a coin is fair. Definition A Bernoulli process is a fini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernoulli Distribution
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli,James Victor Uspensky: ''Introduction to Mathematical Probability'', McGraw-Hill, New York 1937, page 45 is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q = 1-p. Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. Such questions lead to outcomes that are boolean-valued: a single bit whose value is success/ yes/true/ one with probability ''p'' and failure/no/ false/zero with probability ''q''. It can be used to represent a (possibly biased) coin toss where 1 and 0 would represent "heads" and "tails", respectively, and ''p'' would be the probability of the coin landing on heads (or vice versa where 1 would represent tails and ''p'' would be the probability of tails). In particular, unfair coins ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter The Great
Peter I ( – ), most commonly known as Peter the Great,) or Pyotr Alekséyevich ( rus, Пётр Алексе́евич, p=ˈpʲɵtr ɐlʲɪˈksʲejɪvʲɪtɕ, , group=pron was a Russian monarch who ruled the Tsardom of Russia from to 1721 and subsequently the Russian Empire until his death in 1725, jointly ruling with his elder half-brother, Ivan V until 1696. He is primarily credited with the modernisation of the country, transforming it into a European power. Through a number of successful wars, he captured ports at Azov and the Baltic Sea, laying the groundwork for the Imperial Russian Navy, ending uncontested Swedish supremacy in the Baltic and beginning the Tsardom's expansion into a much larger empire that became a major European power. He led a cultural revolution that replaced some of the traditionalist and medieval social and political systems with ones that were modern, scientific, Westernised and based on the Enlightenment. Peter's reforms had a lasting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Trajectories
In mathematics an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves ''orthogonally''. For example, the orthogonal trajectories of a pencil of ''concentric circles'' are the lines through their common center (see diagram). Suitable methods for the determination of orthogonal trajectories are provided by solving differential equations. The standard method establishes a first order ordinary differential equation and solves it by separation of variables. Both steps may be difficult or even impossible. In such cases one has to apply numerical methods. Orthogonal trajectories are used in mathematics for example as curved coordinate systems (i.e. elliptic coordinates) or appear in physics as electric fields and their equipotential curves. If the trajectory intersects the given curves by an arbitrary (but fixed) angle, one gets an isogonal trajectory. Determination of the orthogonal trajectory In cartesian coordinates Generally one as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brook Taylor
Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician best known for creating Taylor's theorem and the Taylor series, which are important for their use in mathematical analysis. Life and work Brook Taylor was born in Edmonton (former Middlesex). Taylor was the son of John Taylor, MP of Patrixbourne, Kent and Olivia Tempest, the daughter of Sir Nicholas Tempest, Baronet of Durham. He entered St John's College, Cambridge, as a fellow-commoner in 1701, and took degrees in LL.B. in 1709 and LL.D. in 1714. Taylor studied mathematics under John Machin and John Keill, leading to Taylor obtaining a solution to the problem of "center of oscillation." Taylor's solution remained unpublished until May 1714, when his claim to priority was disputed by Johann Bernoulli. Taylor's ''Methodus Incrementorum Directa et Inversa'' (1715) ("Direct and Indirect Methods of Incrementation") added a new branch to higher mathematics, called "calculus of finite dif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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