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For n = 5, the Schur cover of the alternating group is given by SL(2, 5) → PSL(2, 5) ≅ A 5, which can also be thought of as the binary icosahedral group covering the icosahedral group. Though PGL(2, 5) ≅ S 5 , GL(2, 5) → PGL(2, 5) is not a Schur cover as the kernel is not contained in the derived subgroup of GL(2 ,5).
The longest alternating subsequence problem has also been studied in the setting of online algorithms, in which the elements of are presented in an online fashion, and a decision maker needs to decide whether to include or exclude each element at the time it is first presented, without any knowledge of the elements that will be presented in the future, and without the possibility of recalling ...
A quadrilateral such as BCEF is called an adventitious quadrangle when the angles between its diagonals and sides are all rational angles, angles that give rational numbers when measured in degrees or other units for which the whole circle is a rational number. Numerous adventitious quadrangles beyond the one appearing in Langley's puzzle have ...
In mathematics, projections onto convex sets (POCS), sometimes known as the alternating projection method, is a method to find a point in the intersection of two closed convex sets. It is a very simple algorithm and has been rediscovered many times. [1] The simplest case, when the sets are affine spaces, was analyzed by John von Neumann.
This follows from inspection of 5-cycles: each 5-cycle generates a group of order 5 (thus a Sylow subgroup), there are 5!/5 = 120/5 = 24 5-cycles, yielding 6 subgroups (as each subgroup also includes the identity), and S n acts transitively by conjugation on the set of cycles of a given class, hence transitively by conjugation on these subgroups.
The defect of any of the vertices of a regular dodecahedron (in which three regular pentagons meet at each vertex) is 36°, or π/5 radians, or 1/10 of a circle. Each of the angles measures 108°; three of these meet at each vertex, so the defect is 360° − (108° + 108° + 108°) = 36°.
In this case, all 8 angles are right angles [1] When the lines are parallel, a case that is often considered, a transversal produces several congruent supplementary angles. Some of these angle pairs have specific names and are discussed below: corresponding angles, alternate angles, and consecutive angles. [2] [3]: Art. 87
In mathematics, the Schwarz alternating method or alternating process is an iterative method introduced in 1869–1870 by Hermann Schwarz in the theory of conformal mapping. Given two overlapping regions in the complex plane in each of which the Dirichlet problem could be solved, Schwarz described an iterative method for solving the Dirichlet ...