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Ernst Kummer
Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician. Skilled in applied mathematics, Kummer trained German army officers in ballistics; afterwards, he taught for 10 years in a '' gymnasium'', the German equivalent of high school, where he inspired the mathematical career of Leopold Kronecker. Life Kummer was born in Sorau, Brandenburg (then part of Prussia). He was awarded a PhD from the University of Halle in 1831 for writing a prize-winning mathematical essay (''De cosinuum et sinuum potestatibus secundum cosinus et sinus arcuum multiplicium evolvendis''), which was published a year later. In 1840, Kummer married Ottilie Mendelssohn, daughter of Nathan Mendelssohn and Henriette Itzig. Ottilie was a cousin of Felix Mendelssohn and his sister Rebecca Mendelssohn Bartholdy, the wife of the mathematician Peter Gustav Lejeune Dirichlet. His second wife (whom he married soon after the death of Ottilie in 1848), Bertha Cauer, was a maternal cousin of Ottil ... [...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 German-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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ballistics
Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially weapon munitions such as bullets, unguided bombs, rockets and the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance. A ballistic body is a free-moving body with momentum, which can be subject to forces such as those exerted by pressurized gases from a gun barrel or a propelling nozzle, normal force by rifling, and gravity and air drag during flight. A ballistic missile is a missile that is missile guidance, guided only during the relatively brief initial phase of powered flight, with the trajectory subsequently governed by the laws of classical mechanics, in contrast to (for example) a cruise missile, which is aerodynamics, aerodynamically guided in powered flight like a fixed-wing aircraft. History and prehistory The earliest known ballistic projectiles were stones, spears, and the throwing s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the profession, professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of Mathematical analysis, applied analysis, most notably differential equations; approximation theory (broadly construed, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kummer Surface
In algebraic geometry, a Kummer quartic surface, first studied by , is an irreducible nodal surface of degree 4 in \mathbb^3 with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian variety of a smooth hyperelliptic curve of genus 2; i.e. a quotient of the Jacobian by the Kummer involution ''x'' ↦ −''x''. The Kummer involution has 16 fixed points: the 16 2-torsion point of the Jacobian, and they are the 16 singular points of the quartic surface. Resolving the 16 double points of the quotient of a (possibly nonalgebraic) torus by the Kummer involution gives a K3 surface with 16 disjoint rational curves; these K3 surfaces are also sometimes called Kummer surfaces. Other surfaces closely related to Kummer surfaces include Weddle surfaces, wave surfaces, and tetrahedroids. Geometry Singular quartic surfaces and the double plane model Let K\subset\mathbb^3 be a quartic surface with an ordinary double ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kummer Theory
Kummer is a German surname. Notable people with the surname include: * Bernhard Kummer (1897–1962), German Germanist * Clare Kummer (1873–1958), American composer, lyricist and playwright * Clarence Kummer (1899–1930), American jockey * Christopher Kummer (born 1975), German economist * Corby Kummer (born 1957), American journalist * Dirk Kummer (born 1966), German actor, director, and screenwriter * Eberhard Kummer (1940–2019), Austrian concert singer, lawyer, and medieval music expert * Eduard Kummer, also known as the following Ernst Kummer * Eloise Kummer (1916–2008), American actress * Ernst Kummer (1810–1893), German mathematician ** Kummer configuration, a mathematical structure discovered by Ernst Kummer ** Kummer surface, a related geometrical structure discovered by Ernst Kummer * Ferdinand von Kummer (1816–1900), German general * Frederic Arnold Kummer (1873–1943), American author, playwright, and screenwriter * Friedrich August Kummer (1797–1879), Germ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Function
Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex number \alpha, which represents the ''order'' of the Bessel function. Although \alpha and -\alpha produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of \alpha. The most important cases are when \alpha is an integer or half-integer. Bessel functions for integer \alpha are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer \alpha are obtained when solving the Helmholtz equation in spherical coordinates. Applications Bessel's equation arises when finding separa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicolai Bugaev
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Nicolai may refer to: *Nicolai (given name) people with the forename ''Nicolai'' *Nicolai (surname) people with the surname ''Nicolai'' *Nicolai (crater), a crater on the Moon See also * Niccolai, a surname * Nicolae (other) * Nicolao * Nicolay (other) * Nikolai (other) * Nikolay (other) Nikolai or Nikolay is an East Slavic variant of the masculine name Nicholas. It may refer to: People Royalty * Nicholas I of Russia (1796–1855), or Nikolay I, Emperor of Russia from 1825 until 1855 * Nicholas II of Russia (1868–1918), or Niko ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Du Bois-Reymond
Paul David Gustav du Bois-Reymond (2 December 1831 – 7 April 1889) was a German mathematician who was born in Berlin and died in Freiburg. He was the brother of Emil du Bois-Reymond. His thesis was concerned with the mechanical equilibrium of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm–Liouville theory, integral equations, variational calculus, and Fourier series. In this latter field, he was able in 1873 to construct a continuous function whose Fourier series is not convergent. His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere. In a paper of 1875, du Bois-Reymond employed for the first time the method of diagonalization, later associated with the name of Cantor. Du Bois-Reymond also established that a trigonometric series that converges to a continuous function at every point is the Fourier series of this function. He is also associated with the fundam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Prym
Friedrich Emil Fritz Prym (28 September 1841, Düren – 15 December 1915, Bonn) was a German mathematician who introduced Prym varieties and Prym differentials. Prym completed his Ph.D. at the Humboldt University of Berlin, University of Berlin in 1863 with a thesis written under the direction of Ernst Kummer and Martin Ohm. In 1867 he started a Professor at the University of Würzburg, where he later became Dean, and then Rector (academia), Rector in 1897–98. References * External links * *Picture of Prym 19th-century German mathematicians 1841 births 1915 deaths Humboldt University of Berlin alumni Algebraic geometers Academic staff of the University of Würzburg Complex analysts 20th-century German mathematicians {{Germany-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adolf Piltz
Adolf Piltz (8 December 1855 – 1940) was a German mathematician who contributed to number theory. Piltz was arguably the first to formulate a generalized Riemann hypothesis, in 1884.Davenport, p. 124. Notes References *Harold Davenport, Davenport, Harold. ''Multiplicative number theory''. Third edition. Revised and with a preface by Hugh L. Montgomery. Graduate Texts in Mathematics, 74. Springer-Verlag, New York, 2000. xiv+177 pp. . Further reading * External links * 1855 births 1940 deaths 19th-century German mathematicians Humboldt University of Berlin alumni 20th-century German mathematicians Mathematicians from the German Empire {{Germany-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
