• ##### 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)
• ##### Redshifts
• reanalyzed the redshift data from a fairly large sample of galaxies and concluded that there was an unexplained periodicity of redshifts. (wikipedia.org)
• ##### known
• The Bright Futures/American Academy of Pediatrics (AAP) Recommendations for Preventive Pediatric Health Care, also known as the 'Periodicity Schedule,' is a schedule of screenings and assessments recommended at each well-child visit from infancy through adolescence. (aap.org)
• The basic idea of Fokker's periodicity blocks is to represent just ratios as points on a lattice, and to find vectors in the lattice which represent very small intervals, known as commas. (wikipedia.org)
• The reason for this periodicity is not known for sure, and is likely the result of a few interrelated factors. (wikipedia.org)
• ##### theory
• 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)
• ##### Health Care
• Federal law requires that states consult with recognized medical organizations involved in child health care in the development of their states' EPSDT periodicity schedules. (wikipedia.org)
• ##### study
• In a paper published in EPJ B , the authors study how the crystal periodicity affects the motion of ions whose energy belongs to a 1 to 2 MeV range, as they are transmitted through very thin crystals on the order of a few hundred nanometres, and how it impacts their angular distribution. (eurekalert.org)
• At the end of the program, she decided to study functional periodicity for her dissertation research. (wikipedia.org)
• ##### important
• Periodicity plays an important role in discovering interesting frequent patterns in any sequence including genomic sequence that is made of amino acids present in the human cells. (hindawi.com)
• ##### Physical
• Functional periodicity is a term that emerged around the late 19th century around the belief, later to be found invalid, that women suffered from physical and mental impairment during their menstrual cycle. (wikipedia.org)
• ##### values
• When values of longitude are 0-360, periodicity is warning users about changing bounds, bounds should only be adjusted when values are from -180,180. (github.com)
• ##### 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)
• ##### given
• Latent periodicity refers to the presence of hidden or reverse subsequence in the given sequence during the particular interval. (hindawi.com)
• Element periodicity deals with the repetition of individual elements of gene sequence during a particular period whereas subsequence periodicity deals with the periodicity of the entire sequence or some portion of the given sequence. (hindawi.com)