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Mertens
__NOTOC__ Mertens () is a surname of Flemish Origin, meaning "son of Merten" (Martin). It is the fifth most common name in Belgium with 18,518 people in 2008. Geographical distribution As of 2014, 43.4% of all known bearers of the surname ''Mertens'' were residents of Germany (frequency 1:2,728), 34.8% of Belgium (1:487), 8.8% of the United States (1:60,847), 5.9% of the Netherlands (1:4,188), 1.7% of France (1:57,632) and 1.0% of Brazil (1:299,871). In Belgium, the frequency of the surname was higher than national average (1:487) only in one region: Flemish Region (1:367). In Germany, the frequency of the surname was higher than national average (1:2,728) in the following regions: * 1. North Rhine-Westphalia (1:970) * 2. Saxony-Anhalt (1:1,361) In the Netherlands, the frequency of the surname was higher than national average (1:4,188) in the following provinces:. * 1. Limburg (1:959) * 2. North Brabant (1:2,002) Noble House of Mertens de Wilmars * Charles Mertens de Wilmar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elise Mertens
Elise Mertens (; born 17 November 1995) is a Belgian professional tennis player. She is a former world No. 1 in doubles. Mertens is a three-time Grand Slam champion in doubles, having won the 2019 US Open and 2021 Australian Open partnering Aryna Sabalenka, and the 2021 Wimbledon Championships with Hsieh Su-wei. Mertens also finished runner-up at the 2022 Wimbledon Championships with Zhang Shuai. She became world No. 1 for the first time in May 2021, the third Belgian to hold the top ranking across both disciplines after Kim Clijsters and Justine Henin. Mertens has won 16 doubles titles on the WTA Tour, including the 2022 WTA Finals with Veronika Kudermetova, four at WTA 1000 level, and finished runner-up at the 2021 WTA Finals alongside Hsieh. She is also a successful singles player, and reached her first major semifinal at the 2018 Australian Open, also reaching the US Open quarterfinals in 2019 and 2020. Mertens achieved her career-high singles ranking of world No. 12 in No ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dries Mertens
Dries Mertens (; born 6 May 1987), nicknamed "Ciro", is a Belgian professional footballer who plays as a striker or winger for Süper Lig club Galatasaray and the Belgium national team.De tol van de roem voor Dries Mertens: “Mijn buurvrouw van 75 jaar geeft me een mep in mijn gezicht als ik slecht speel” nieuwsblad.be, 6 October 2020, Raf Hermans, article in DutchDries Mertens is nu echt God in Napels: ‘Ciro’ net als Maradona vereeuwigd op een muur (maar wel iets k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mertens' Theorems
In number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens.F. Mertens. J. reine angew. Math. 78 (1874), 46–6Ein Beitrag zur analytischen Zahlentheorie/ref> "Mertens' theorem" may also refer to his theorem in analysis. Theorems In the following, let p\le n mean all primes not exceeding ''n''. Mertens' first theorem: : \sum_ \frac - \log n does not exceed 2 in absolute value for any n\ge 2. () Mertens' second theorem: :\lim_\left(\sum_\frac1p -\log\log n-M\right) =0, where ''M'' is the Meissel–Mertens constant (). More precisely, Mertens proves that the expression under the limit does not in absolute value exceed : \frac 4 +\frac 2 for any n\ge 2. Mertens' third theorem: :\lim_\log n\prod_\left(1-\frac1p\right)=e^ \approx 0.561459483566885, where γ is the Euler–Mascheroni constant (). Changes in sign In a paper on the growth rate of the sum-of-divisors function published in 1983, Guy Robin pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mertens Function
In number theory, the Mertens function is defined for all positive integers ''n'' as : M(n) = \sum_^n \mu(k), where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive real numbers as follows: : M(x) = M(\lfloor x \rfloor). Less formally, M(x) is the count of square-free integers up to ''x'' that have an even number of prime factors, minus the count of those that have an odd number. The first 143 ''M''(''n'') values are The Mertens function slowly grows in positive and negative directions both on average and in peak value, oscillating in an apparently chaotic manner passing through zero when ''n'' has the values :2, 39, 40, 58, 65, 93, 101, 145, 149, 150, 159, 160, 163, 164, 166, 214, 231, 232, 235, 236, 238, 254, 329, 331, 332, 333, 353, 355, 356, 358, 362, 363, 364, 366, 393, 401, 403, 404, 405, 407, 408, 413, 414, 419, 420, 422, 423, 424, 425, 427, 428, ... . Because the Möbius function only ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mertens Conjecture
In mathematics, the Mertens conjecture is the statement that the Mertens function M(n) is bounded by \pm\sqrt. Although now disproven, it had been shown to imply the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes, in an 1885 letter to Charles Hermite (reprinted in ), and again in print by , and disproved by . It is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in its favor. Definition In number theory, we define the Mertens function as : M(n) = \sum_ \mu(k), where μ(k) is the Möbius function; the Mertens conjecture is that for all ''n'' > 1, : , M(n), < \sqrt. Disproof of the conjecture Stieltjes claimed in 1885 to have proven a weaker result, namely that was[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conner Mertens
Conner Mertens (born ) is an American football placekicker for the Willamette Bearcats. He was the first active college football player to publicly come out about his sexuality; he came out as bisexual. Early life Mertens grew up in Kennewick in Tri-Cities, Washington, where he was the youngest of four boys in his family. Growing up, he always excelled at sports. He concentrated on athletics after an incident in fifth grade in which classmates teased him for remaining in costume and makeup after a drama competition. According to Mertens, the environment at Southridge High School was "hostile", as he was surround by a culture of homophobia. He said the Tri-Cities was not the most friendly area toward the LGBT community. In 2012, 63 percent of the area voted against a measure for same-sex marriage that was ultimately approved by the state. Starting with his sophomore year in high school, Mertens was active in Young Life, a national organization that preaches Christianity to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franz Mertens
Franz Mertens (20 March 1840 – 5 March 1927) (also known as Franciszek Mertens) was a Polish mathematician. He was born in Schroda in the Grand Duchy of Posen, Kingdom of Prussia (now Środa Wielkopolska, Poland) and died in Vienna, Austria. The Mertens function ''M''(''x'') is the sum function for the Möbius function, in the theory of arithmetic functions. The Mertens conjecture concerning its growth, conjecturing it bounded by ''x''1/2, which would have implied the Riemann hypothesis, is now known to be false ( Odlyzko and te Riele, 1985). The Meissel–Mertens constant is analogous to the Euler–Mascheroni constant, but the harmonic series sum in its definition is only over the primes rather than over all integers and the logarithm is taken twice, not just once. Mertens's theorems are three 1874 results related to the density of prime numbers. Erwin Schrödinger was taught calculus and algebra by Mertens. His memory is honoured by the Franciszek Mertens Scholarship gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gregory Mertens
Gregory Mertens (2 February 1991 – 30 April 2015) was a Belgium, Belgian professional football (soccer), football player. His usual position was Defender (association football)#Centre back, central defender. He last played for K.S.C. Lokeren Oost-Vlaanderen, Lokeren. Career Mertens moved from the reserves of K.A.A. Gent to the first team of Cercle Brugge in the List of Belgian football transfers winter 2010–11, 2010–11 winter transfer window, at the recommendation of manager Bob Peeters, who had been his coach at the Gent reserves the previous season. On 12 February 2011, Mertens made his senior debut for Cercle as an 89th-minute substitute for Hans Cornelis in a match against his former team R.S.C. Anderlecht. Cercle lost the match 1–0. On 23 May 2013, he scored his first hat trick against WS Woluwe. Death Mertens suffered a cardiac arrest during a reserve game for K.S.C. Lokeren Oost-Vlaanderen, Lokeren against K.R.C. Genk on 27 April 2015. He was immediately taken t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meissel–Mertens Constant
The Meissel–Mertens constant (named after Ernst Meissel and Franz Mertens), also referred to as Mertens constant, Kronecker's constant, Hadamard– de la Vallée-Poussin constant or the prime reciprocal constant, is a mathematical constant in number theory, defined as the limiting difference between the harmonic series summed only over the primes and the natural logarithm of the natural logarithm: :M = \lim_ \left( \sum_ \frac - \ln(\ln n) \right)=\gamma + \sum_ \left \ln\! \left( 1 - \frac \right) + \frac \right Here γ is the Euler–Mascheroni constant, which has an analogous definition involving a sum over all integers (not just the primes). The value of ''M'' is approximately :''M'' ≈ 0.2614972128476427837554268386086958590516... . Mertens' second theorem establishes that the limit exists. The fact that there are two logarithms (log of a log) in the limit for the Meissel–Mertens constant may be thought of as a consequence of the combination of the prime number t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dylan Mertens
Dylan Mertens (born 20 July 1995, in Amsterdam) is a Dutch professional footballer who plays as a winger for Botev Plovdiv in the Bulgarian First League. Club career Youth Mertens played for SDW, DWS and AFC before joining the FC Utrecht Youth Academy in 2008. Two years later he had to leave and decided to return to AFC. His return was not for long and after one season he moved to SV Argon. In the summer of 2013 he made the move to FC Den Bosch, where he played with the A1 (Under 19). FC Volendam In the preparation of the 2014/15 season, Mertens joined FC Volendam on an amateur basis. That season, he played 15 matches in the second team in which he scored 4 times. He also made it to the match selection of the first team two times, but didn't make his debut. On 30 March 2015 he signed his first professional contract with FC Volendam, until mid 2017. In the summer of 2015, Mertens joined the first team. On 7 August 2015 he made his debut for FC Volendam in the league matc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franz Carl Mertens
Franz Carl Mertens (3 April 1764 – 19 June 1831) was a German botanist who was a native of Bielefeld. He specialized in the field of phycology. Mertens studied theology and languages at the University of Halle, and after graduation taught classes at Bremen Polytechnic College. In his spare time he studied botany, and through a mutual friend met German botanist Albrecht Wilhelm Roth (1757–1834). With Roth, he took scientific expeditions throughout Europe, including Scandinavia. From these trips, Mertens described a number of species of algae. He also performed illustrative work on Volume 3 of Roth's ''Catalecta botanica''. With Erlangen professor Wilhelm Daniel Joseph Koch (1771–1849), he published the third edition of Johann Christoph Röhling's ''Deutschlands flora'', a five volume treatise on German flora. The plant genus ''Mertensia'' from the family Boraginaceae is named after him, while the ctenophore genus ''Mertensia'' is named after his son Karl Heinrich Merten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Mertens De Wilmars
Charles Mertens de Wilmars (Leuven, 21 November 1921 – 1994) was a Belgium, Belgian psychiatrist. He graduated as a Doctor of Medicine in 1948, and became a licensed psychologist in 1949. He was taught neurology by Paul van Gehuchten and experimental psychology by Albert Michotte. He spent time at the Maudsley Hospital Medical School, funded by the British Council, after which he benefited from the bursary of the Belgian American Educational Foundation to travel to the United States to meet his colleagues in the field of psychiatric anthropology at Cornell University from 1949 to 1951. He was a visiting lecturer there in 1952, and was then appointed as a professor at Harvard Medical School in which capacity he served for 26 years – from 1966 to 1992. During this period, he rose to be Chair of the Department of Psychiatry. While doing that, he still kept his interests at the Leuven university, and became professor at its Faculty of Medicine and Psychology until he retired ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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