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Stieltjes Inversion Formula
Thomas Joannes Stieltjes (, 29 December 1856 – 31 December 1894) was a Dutch mathematician. He was a pioneer in the field of moment problems and contributed to the study of continued fractions. The Thomas Stieltjes Institute for Mathematics at Leiden University, dissolved in 2011, was named after him, as is the Riemann–Stieltjes integral. Biography Stieltjes was born in Zwolle on 29 December 1856. His father (who had the same first names) was a civil engineer and politician. Stieltjes Sr. was responsible for the construction of various harbours around Rotterdam, and also seated in the Dutch parliament. Stieltjes Jr. went to university at the Polytechnical School in Delft in 1873. Instead of attending lectures, he spent his student years reading the works of Gauss and Jacobi — the consequence of this being he failed his examinations. There were 2 further failures (in 1875 and 1876), and his father despaired. His father was friends with H. G. van de Sande Bakhuyzen (who was t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zwolle
Zwolle () is a city and municipality in the Northeastern Netherlands. It is the capital of the province of Overijssel and the province's second-largest municipality after Enschede with a population of 130,592 as of 1 December 2021. Zwolle is on the border with Gelderland, which follows the river IJssel, and is located about 50 km north east of Utrecht and 85 km south west of Groningen. The current Mayor of Zwolle is Lorenzo Brands. History Archaeological findings indicate that the area surrounding Zwolle has been inhabited for a long time. A woodhenge that was found in the Zwolle-Zuid suburb in 1993 was dated to the Bronze Age period. During the Roman era, the area was inhabited by Salian Franks. The modern city was founded around 800 CE by Frisian merchants and troops of Charlemagne. Previous spellings of its name include the identically pronounced ''Suolle'', which means "hill" (cf. the English cognate verb "to swell"). This refers to an incline in the landscape betwee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stieltjes Moment Problem
In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence (''m''0, ''m''1, ''m''2, ...) to be of the form :m_n = \int_0^\infty x^n\,d\mu(x) for some measure ''μ''. If such a function ''μ'' exists, one asks whether it is unique. The essential difference between this and other well-known moment problems is that this is on a half-line 0, ∞),_whereas_in_the_0, ∞),_whereas_in_the_Hausdorff_moment_problem">/nowiki>0, ∞),_whereas_in_the_Hausdorff_moment_problem_one_considers_a_Interval_(mathematics)#Terminology.html" "title="Hausdorff_moment_problem.html" ;"title="/nowiki>0, ∞), whereas in the Hausdorff moment problem">/nowiki>0, ∞), whereas in the Hausdorff moment problem one considers a Interval_(mathematics)#Terminology">bounded interval In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying betwe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Gustav Jakob Jacobi
Carl Gustav Jacob Jacobi (; ; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants, and number theory. His name is occasionally written as Carolus Gustavus Iacobus Iacobi in his Latin books, and his first name is sometimes given as Karl. Jacobi was the first Jewish mathematician to be appointed professor at a German university. Biography Jacobi was born of Ashkenazi Jewish parentage in Potsdam on 10 December 1804. He was the second of four children of banker Simon Jacobi. His elder brother Moritz von Jacobi would also become known later as an engineer and physicist. He was initially home schooled by his uncle Lehman, who instructed him in the classical languages and elements of mathematics. In 1816, the twelve-year-old Jacobi went to the Potsdam Gymnasium, where students were taught all the standard subjects: classical languages, history, philology, mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friederich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the ''Princeps mathematicorum'' () and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and he is ranked among history's most influential mathematicians. Also available at Retrieved 23 February 2014. Comprehensive biographical article. Biography Early years Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), to poor, working-class parents. His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). Ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delft
Delft () is a List of cities in the Netherlands by province, city and Municipalities of the Netherlands, municipality in the Provinces of the Netherlands, province of South Holland, Netherlands. It is located between Rotterdam, to the southeast, and The Hague, to the northwest. Together with them, it is part of both the Rotterdam–The Hague metropolitan area and the Randstad. Delft is a popular tourist destination in the Netherlands, famous for its historical connections with the reigning House of Orange-Nassau, for its Delftware, blue pottery, for being home to the painter Johannes Vermeer, Jan Vermeer, and for hosting Delft University of Technology (TU Delft). Historically, Delft played a highly influential role in the Dutch Golden Age. In terms of science and technology, thanks to the pioneering contributions of Antonie van Leeuwenhoek and Martinus Beijerinck, Delft can be considered to be the birthplace of microbiology. History Early history The city of Delft came into ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dutch Parliament
The States General of the Netherlands ( nl, Staten-Generaal ) is the supreme bicameral legislature of the Netherlands consisting of the Senate () and the House of Representatives (). Both chambers meet at the Binnenhof in The Hague. The States General originated in the 15th century as an assembly of all the provincial states of the Burgundian Netherlands. In 1579, during the Dutch Revolt, the States General split as the northern provinces openly rebelled against Philip II, and the northern States General replaced Philip II as the supreme authority of the Dutch Republic in 1581. The States General were replaced by the National Assembly after the Batavian Revolution of 1795, only to be restored in 1814, when the country had regained its sovereignty. The States General was divided into a Senate and a House of Representatives in 1815, with the establishment of the United Kingdom of the Netherlands. After the constitutional amendment of 1848, members of the House of Representative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotterdam
Rotterdam ( , , , lit. ''The Dam on the River Rotte'') is the second largest city and municipality in the Netherlands. It is in the province of South Holland, part of the North Sea mouth of the Rhine–Meuse–Scheldt delta, via the ''"New Meuse"'' inland shipping channel, dug to connect to the Meuse first, but now to the Rhine instead. Rotterdam's history goes back to 1270, when a dam was constructed in the Rotte. In 1340, Rotterdam was granted city rights by William IV, Count of Holland. The Rotterdam–The Hague metropolitan area, with a population of approximately 2.7 million, is the 10th-largest in the European Union and the most populous in the country. A major logistic and economic centre, Rotterdam is Europe's largest seaport. In 2020, it had a population of 651,446 and is home to over 180 nationalities. Rotterdam is known for its university, riverside setting, lively cultural life, maritime heritage and modern architecture. The near-complete destruction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harbour
A harbor (American English), harbour (British English; see spelling differences), or haven is a sheltered body of water where ships, boats, and barges can be docked. The term ''harbor'' is often used interchangeably with ''port'', which is a man-made facility built for loading and unloading vessels and dropping off and picking up passengers. Ports usually include one or more harbors. Alexandria Port in Egypt is an example of a port with two harbors. Harbors may be natural or artificial. An artificial harbor can have deliberately constructed breakwaters, sea walls, or jettys or they can be constructed by dredging, which requires maintenance by further periodic dredging. An example of an artificial harbor is Long Beach Harbor, California, United States, which was an array of salt marshes and tidal flats too shallow for modern merchant ships before it was first dredged in the early 20th century. In contrast, a natural harbor is surrounded on several sides of land. Examples ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leiden University
Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a Public university, public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William the Silent, William, Prince of Orange, as a reward to the city of Leiden for its Siege of Leiden, defence against Spanish attacks during the Eighty Years' War. As the oldest institution of higher education in the Netherlands, it enjoys a reputation across Europe and the world. Known for its historic foundations and emphasis on the social sciences, the university came into particular prominence during the Dutch Golden Age, when scholars from around Europe were attracted to the Dutch Republic due to its climate of intellectual tolerance and Leiden's international reputation. During this time, Leiden became the home to individuals such as René Descartes, Rembrandt, Christiaan Huygens, Hugo Grotius, Baruch Spinoza and Baron d'Holbach. The university has seven academic f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continued Fraction
In mathematics, a continued fraction is an expression (mathematics), expression obtained through an iterative process of representing a number as the sum of its integer part and the multiplicative inverse, reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression (mathematics), infinite expression. In either case, all integers in the sequence, other than the first, must be positive number, positive. The integers a_i are called the coefficients or terms of the continued fraction. It is generally assumed that the numerator of all of the fractions is 1. If arbitrary values and/or function (mathematics), functions are used in place of one or more of the numerat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Problem
In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure ''μ'' to the sequences of moments :m_n = \int_^\infty x^n \,d\mu(x)\,. More generally, one may consider :m_n = \int_^\infty M_n(x) \,d\mu(x)\,. for an arbitrary sequence of functions ''M''''n''. Introduction In the classical setting, μ is a measure on the real line, and ''M'' is the sequence . In this form the question appears in probability theory, asking whether there is a probability measure having specified mean, variance and so on, and whether it is unique. There are three named classical moment problems: the Hamburger moment problem in which the support of μ is allowed to be the whole real line; the Stieltjes moment problem, for , +∞); and the Hausdorff moment problem for a bounded interval, which without loss of generality may be taken as , 1 Existence A sequence of numbers ''m''''n'' is the sequence of moments of a measure ''μ'' if an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Montel's Theorem
In complex analysis, an area of mathematics, Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after French mathematician Paul Montel, and give conditions under which a family of holomorphic functions is normal. Locally uniformly bounded families are normal The first, and simpler, version of the theorem states that a family of holomorphic functions defined on an open subset of the complex numbers is normal if and only if it is locally uniformly bounded. This theorem has the following formally stronger corollary. Suppose that \mathcal is a family of meromorphic functions on an open set D. If z_0\in D is such that \mathcal is not normal at z_0, and U\subset D is a neighborhood of z_0, then \bigcup_f(U) is dense in the complex plane. Functions omitting two values The stronger version of Montel's Theorem (occasionally referred to as the Fundamental Normality Test) states that a family of holomorphic functions, all of which omit t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
