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A meteor shower is a celestial event in which a number of meteors are observed to radiate, or originate, from one point in the night sky. These meteors are caused by streams of cosmic debris called meteoroids entering Earth's atmosphere at extremely high speeds on parallel trajectories. Most meteors are smaller than a grain of sand, so almost all of them disintegrate and never hit the Earth's surface. Very intense or unusual meteor showers are known as meteor outbursts and meteor storms, which produce at least 1,000 meteors an hour, most notably from the Leonids. The Meteor Data Centre lists over 900 suspected meteor showers of which about 100 are well established. Several organizations point to viewing opportunities on the Internet. NASA maintains a daily map of active meteor showers.
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand was a prominent Soviet-American mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the first Wolf Prize, he was a Foreign Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University. Gelfand is also a 1994 MacArthur Fellow.
In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by Erich Hecke, is a certain kind of "averaging" operator that plays a significant role in the structure of vector spaces of modular forms and more general automorphic representations.
Ruth Elke Lawrence-Neimark is a British–Israeli mathematician and a professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, and a researcher in knot theory and algebraic topology. In the public eye, she is best known for having been a child prodigy in mathematics.
In mathematics, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by Kolyvagin in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper Kolyvagin (1988) and the work of Thaine (1988). Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of an Euler product.
Yuri Ivanovich Manin was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
Roger Newland Shepard was an American cognitive scientist and author of the "universal law of generalization" (1987). He was considered a father of research on spatial relations. He studied mental rotation, and was an inventor of non-metric multidimensional scaling, a method for representing certain kinds of statistical data in a graphical form that can be comprehended by humans. The optical illusion called Shepard tables and the auditory illusion called Shepard tones are named for him.
In mathematics, a Gelfand pair is a pair (G,K ) consisting of a group G and a subgroup K (called an Euler subgroup of G) that satisfies a certain property on restricted representations. The theory of Gelfand pairs is closely related to the topic of spherical functions in the classical theory of special functions, and to the theory of Riemannian symmetric spaces in differential geometry. Broadly speaking, the theory exists to abstract from these theories their content in terms of harmonic analysis and representation theory.
In number theory, Tate's thesis is the 1950 PhD thesis of John Tate completed under the supervision of Emil Artin at Princeton University. In it, Tate used a translation invariant integration on the locally compact group of ideles to lift the zeta function twisted by a Hecke character, i.e. a Hecke L-function, of a number field to a zeta integral and study its properties. Using harmonic analysis, more precisely the Poisson summation formula, he proved the functional equation and meromorphic continuation of the zeta integral and the Hecke L-function. He also located the poles of the twisted zeta function. His work can be viewed as an elegant and powerful reformulation of a work of Erich Hecke on the proof of the functional equation of the Hecke L-function. Erich Hecke used a generalized theta series associated to an algebraic number field and a lattice in its ring of integers.
Bertram Kostant was an American mathematician who worked in representation theory, differential geometry, and mathematical physics.
Alexandre Aleksandrovich Kirilloff is a Soviet and Russian mathematician, known for his works in the fields of representation theory, topological groups and Lie groups. In particular he introduced the orbit method into representation theory. He is an emeritus professor at the University of Pennsylvania.
In the mathematical field of representation theory, a Kazhdan–Lusztig polynomial is a member of a family of integral polynomials introduced by David Kazhdan and George Lusztig. They are indexed by pairs of elements y, w of a Coxeter group W, which can in particular be the Weyl group of a Lie group.
Anthony William Knapp is an American mathematician and professor emeritus at the State University of New York, Stony Brook working in representation theory. For much of his career, Knapp was a professor at Cornell University.
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.
In mathematics, a weakly symmetric space is a notion introduced by the Norwegian mathematician Atle Selberg in the 1950s as a generalisation of symmetric space, due to Élie Cartan. Geometrically the spaces are defined as complete Riemannian manifolds such that any two points can be exchanged by an isometry, the symmetric case being when the isometry is required to have period two. The classification of weakly symmetric spaces relies on that of periodic automorphisms of complex semisimple Lie algebras. They provide examples of Gelfand pairs, although the corresponding theory of spherical functions in harmonic analysis, known for symmetric spaces, has not yet been developed.
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be impossible to prove using current knowledge by almost all current mathematicians at the time.
In mathematics, the Springer resolution is a resolution of the variety of nilpotent elements in a semisimple Lie algebra, or the unipotent elements of a reductive algebraic group, introduced by Tonny Albert Springer in 1969. The fibers of this resolution are called Springer fibers.
Christopher Deninger is a German mathematician at the University of Münster. Deninger's research focuses on arithmetic geometry, including applications to L-functions.
Hee Oh is a South Korean mathematician who works in dynamical systems. She has made contributions to dynamics and its connections to number theory. She is a student of homogeneous dynamics and has worked extensively on counting and equidistribution for Apollonian circle packings, Sierpinski carpets and Schottky dances. She is currently the Abraham Robinson Professor of Mathematics at Yale University.
Mikhail Kapranov, is a Russian mathematician, specializing in algebraic geometry, representation theory, mathematical physics, and category theory. He is currently a professor of the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo.
References
- ↑ "STS-31". Mission Archives. NASA. 2006-10-14. Retrieved 2013-01-17.
- ↑ Balbus, Steven A.; Hawley, John F. (1991). "A powerful local shear instability in weakly magnetized disks". The Astrophysical Journal . 376: 214–233. Bibcode:1991ApJ...376..214B. doi:10.1086/170270.
- ↑ Spurný, P.; Ceplecha, Z.; Borovicka, J. (1991). "Earth-grazing fireball: Czechoslovakia, Poland, October 13, 1990, 03h27m16sUT". WGN. 19 (1): 13. Bibcode:1991JIMO...19...13S. Aphelion of its orbit changed from 2.80 AU to 1.80 AU.
- ↑ Foote, Jennifer (1990-02-05). "Trying to Take Back the Planet". Newsweek .
- ↑ Hormby, John (2007-06-05). "How Adobe's Photoshop Was Born". Story Photography. Archived from the original on 2007-06-11. Retrieved 2007-06-15.
- ↑ Berners-Lee, T.; Cailliau, R. (12 November 1990). "WorldWideWeb: Proposal for a HyperText Project". Archived from the original on 2012-12-19. Retrieved 2011-11-29.
- ↑ "Links and Anchors" . Retrieved 2011-11-29.
- ↑ Larimer, Tim (1999-11-22). "The Ultimate Game Freak". Time . Vol. 154, no. 20. Asia. Retrieved 2015-02-02.
- ↑ Gelfand, A. E.; Smith, A. F. M. (1990). "Sampling-Based Approaches to Calculating Marginal Densities". Journal of the American Statistical Association. 85 (410): 398–409. doi:10.2307/2289776. JSTOR 2289776.
- ↑ Kolyvagin, V. A. (1990), "Euler systems", The Grothendieck Festschrift, Vol. II, Progress in Mathematics, vol. 87, Boston: Birkhäuser, pp. 435–483, doi:10.1007/978-0-8176-4575-5_11, ISBN 978-0-8176-3428-5, MR 1106906
- ↑ Lawrence, R. J. (1990). "Homological representations of the Hecke algebra" (PDF). Communications in Mathematical Physics . 135 (1): 141–191. Bibcode:1990CMaPh.135..141L. doi:10.1007/BF02097660. S2CID 121644260 . Retrieved 2011-11-29.
- ↑ Hall, J. M.; Lee, M. K.; Newman, B.; Morrow, J. E.; Anderson, L. A.; Huey, B.; King, M. C. (December 1990). "Linkage of early-onset familial breast cancer to chromosome 17q21". Science . 250 (4988): 1684–9. Bibcode:1990Sci...250.1684H. doi:10.1126/science.2270482. PMID 2270482.
- ↑ Colman, Andrew M. (2009). A Dictionary of Psychology (3 ed.). Oxford University Press. ISBN 9780191726828.
The illusion was first presented by the US psychologist Roger N(ewland) Shepard (born 1929) in his book Mind Sights: Original Visual Illusions, Ambiguities, and Other Anomalies (1990, p. 48), Shepard commented that 'any knowledge or understanding of the illusion we may gain at the intellectual level remains virtually powerless to diminish the magnitude of the illusion' (p. 128).