• Bott
  • In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (1957, 1959), which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres. (wikipedia.org)
  • Bott periodicity can be formulated in numerous ways, with the periodicity in question always appearing as a period-2 phenomenon, with respect to dimension, for the theory associated to the unitary group. (wikipedia.org)
  • The J-homomorphism is a homomorphism from the homotopy groups of orthogonal groups to stable homotopy groups of spheres, which causes the period 8 Bott periodicity to be visible in the stable homotopy groups of spheres. (wikipedia.org)
  • What Bott periodicity offered was an insight into some highly non-trivial spaces, with central status in topology because of the connection of their cohomology with characteristic classes, for which all the (unstable) homotopy groups could be calculated. (wikipedia.org)
  • One formulation of Bott periodicity describes the twofold loop space, Ω2BU of BU. (wikipedia.org)
  • theory
  • The report describes efforts to extend to several variables the theory of mean periodicity developed in the first year of work. (dtic.mil)
  • This model explains the 34.1-day periodicity and predicts the unobserved spin period for Cyg X-3 to be about 100 ms. Taking into account the possibility that the secular spin angular velocity of the star is different from that observed presently, the analogous long-terms periodicities of Her X-1 and Cen X-3 are also accounted for in this theory. (springer.com)
  • She was quite instrumental in disproving the theory of functional periodicity, which was widely believed to be true by scientists as well as the general public. (wikipedia.org)
  • Note that octaves are usually ignored in constructing periodicity blocks (as they are in scale theory generally) because it is assumed that for any pitch in the tuning system, all pitches differing from it by some number of octaves are also available in principle. (wikipedia.org)
  • case
  • Frequently, it forms a cyclic group, in which case identifying the m pitches of the periodicity block with m-equal tuning gives equal tuning approximations of the just ratios that defined the original lattice. (wikipedia.org)
  • found
  • It is established that the sequences of all different proteins from E. coli ribosome as well as two protein biosynthesis initiation factors, two ribosome-associated DNA-binding proteins, and the elongation factor EF-Tu from the same source possess a periodicity expressed more weakly and different from that found earlier for a number of proteins representatives of 18 superfamilies. (springer.com)