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Purchase$ 31.50Fast Constructive Recognition of a Black Box Group
Purchase
$ 31.50
Isomorphic to S
orA
n
using Goldbach’s
n
Conjecture Original Research Article
Journal of Symbolic Computatio,nVolume 29, Issue 1, January 2000,Pages 33-57
Sergey Bratus, Igor Pak
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Abstract |References
Abstract
The well-known Goldbach Conjecture (GC) states that any sufficiently large even number can be represented as a sum of two odd primes. Although not yet
demonstrated, it has been checked for integers up 1t4 .o U1s0ing two stronger
versions of the conjecture, we offer a simple and fast method for recognition of a gray box groupG known to be isomorphic tSon(orA n) with known ≥ 20, i.e. for
constructio1nof an isomorphism fromG toS n (orA n). Correctness and rigorous
worst case complexity estimates rely heavily on the conjectures, and yield times of O ([ρ + ν+ μ]n log2n) orO ([ρ + ν+ μ]n logn / loglong) depending on which
of the stronger versions of the GC is assumed to hold.ρHiesret,he complexity of generating a uniform random element oGf,νis the complexity of finding the order of a group element iGn, andμis the time necessary for group multiplicaGti.on in
Rigorous lower bound and probabilistic approach to the time complexity of the algorithm are discussed in the Appendix.
Numerical methods in rock mechanics Review Article
International Journal of Rock Mechanics and Mining
Sciences,Volume 39, Issue 4,June 2002 ,Pages 409-427
L. Jing, J. A. Hudson
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Abstract |Figures/Tables |References
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$ 41.95
Abstract
The purpose of this CivilZone review paper is to present the techniques, advances, problems and likely future development directions in numerical modelling for rock mechanics and rock engineering. Such modelling is essential for studying the fundamental processes occurring in rock, for assessing the anticipated and actual performance of structures
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