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Charles Edwin Hurwitz was born in 1940, and raised in Kilgore, Texas. [2] His parents were Eva (née Engler) and Hyman Hurwitz, and his father was Jewish and owned a local clothing store, "Hurwitz Man’s Shop" and he built the town's first shopping center. [3] [4] [5] Hurwitz attended Oklahoma University, graduating in 1962 with a degree in ...
Adolf Hurwitz (German: [ˈaːdɔlf ˈhʊʁvɪts]; 26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, analysis, geometry and number theory. Early life [ edit ]
On the other hand, according to Example A, the Hurwitz number h 1, k equals 1/k times the number of ways to decompose a k-cycle in the symmetric group S k into a product of k + 1 transpositions. In particular, h 1, 1 = 0 (since there are no transpositions in S 1 ), while h 1, 2 = 1/2 (since there is a unique factorization of the transposition ...
Hurwitz's theorem is used in the proof of the Riemann mapping theorem, [2] and also has the following two corollaries as an immediate consequence: . Let G be a connected, open set and {f n} a sequence of holomorphic functions which converge uniformly on compact subsets of G to a holomorphic function f.
In the control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI) dynamical system or control system. A stable system is one whose output signal is bounded; the position, velocity or energy do not increase to infinity as ...
Many more finite simple groups are Hurwitz groups; for instance all but 64 of the alternating groups are Hurwitz groups, the largest non-Hurwitz example being of degree 167. The smallest alternating group that is a Hurwitz group is A 15. Most projective special linear groups of large rank are Hurwitz groups, (Lucchini, Tamburini & Wilson 2000 ...
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The Hurwitz surface of least genus is the Klein quartic of genus 3, with automorphism group the projective special linear group PSL(2,7), of order 84(3 − 1) = 168 = 2 3 ·3·7, which is a simple group; (or order 336 if one allows orientation-reversing isometries).
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