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Mertens V
__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 Wilmars ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surname
In some cultures, a surname, family name, or last name is the portion of one's personal name that indicates one's family, tribe or community. Practices vary by culture. The family name may be placed at either the start of a person's full name, as the forename, or at the end; the number of surnames given to an individual also varies. As the surname indicates genetic inheritance, all members of a family unit may have identical surnames or there may be variations; for example, a woman might marry and have a child, but later remarry and have another child by a different father, and as such both children could have different surnames. It is common to see two or more words in a surname, such as in compound surnames. Compound surnames can be composed of separate names, such as in traditional Spanish culture, they can be hyphenated together, or may contain prefixes. Using names has been documented in even the oldest historical records. Examples of surnames are documented in the 11th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claas Mertens
Claas Mertens (born 2 January 1992) is a German lightweight rower. He won a gold medal at the 2015 World Rowing Championships in Aiguebelette with the lightweight men's eight. He also won ten German National Championship titles. In 2018 Mertens represented Oxford in the Oxford-Cambridge Boat Race. He was educated at Shrewsbury School then Harvard University, University of St. Gallen and Christ Church, Oxford Christ Church ( la, Ædes Christi, the temple or house, '' ædēs'', of Christ, and thus sometimes known as "The House") is a constituent college of the University of Oxford in England. Founded in 1546 by King Henry VIII, the college is uniqu .... References 1992 births Living people German male rowers World Rowing Championships medalists for Germany People educated at Shrewsbury School {{Germany-rowing-bio-stub ... [...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] |
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] |
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] |
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] |
Frank Mertens
Frank Mertens (born Frank Sorgatz; 26 October 1961) is a German musician. He is a former member of the German synth-pop group Alphaville. Personality wise, he is a shy and quiet person who doesn't like to talk. Shortly after the success of their debut album, he left the band in December 1984, because he found public attention stressful. After he left, he founded the group Lonely Boys with his girlfriend at the time Matine Lille (née Richter) and Felix Lille (né Schulte). Mertens disbanded the group in 1987 to study economics. In 1991, Mertens moved to Paris to study art. In 1996 he moved back to Cologne Cologne ( ; german: Köln ; ksh, Kölle ) is the largest city of the German western States of Germany, state of North Rhine-Westphalia (NRW) and the List of cities in Germany by population, fourth-most populous city of Germany with 1.1 m ..., to work as a plastic artist. During the same year, he started but never completed a musical project called ''Maelstrom'', wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ewald Mertens
Ewald Mertens (24 September 1909 – 7 February 1965) was a German middle-distance runner. He competed in the men's 800 metres at the 1936 Summer Olympics. He was awarded an Honoured Master of Sport. He died in a hospital in Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ... after a long illness. References External links * 1909 births 1965 deaths Athletes (track and field) at the 1936 Summer Olympics German male middle-distance runners Olympic athletes of Germany Place of birth missing Recipients of the Honoured Master of Sport {{Germany-middledistance-athletics-bio-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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