**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)

**Fokker**- Fokker periodicity blocks are a concept in tuning theory used to mathematically relate musical intervals in just intonation to those in equal tuning. (wikipedia.org)
- Each tile is called a Fokker periodicity block. (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)

**periodic**- Check the periodicity of the function f(x)=sinx*cosx, and if it is periodic, find the period of the function. (physicsforums.com)
- The schedules for periodic well-child visits in EPSDT are known as periodicity schedules. (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)

**Function**- The initial discovery was made in 1980 by Trifonov and Sussman who observed periodicity in DNA sequences by applying the autocorrelation function to chromatin DNA. (wikipedia.org)
- Dodin proposed a method for analyzing the periodicity of DNA sequences based on the correlation function of the symbolic sequence. (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)

**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)

**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)

**Results**- Best results I have obtained by dropping the periodicity constraint before the merge, but this is only an option if I could restore the periodicity afterwards. (cfd-online.com)

**Schedule**- For implementation and coding information for each visit on the Periodicity Schedule, please see the Bright Futures and Preventive Medicine Coding Fact Sheet . (aap.org)
- Below is a periodicity schedule. (mo.gov)

**idea**- Many prominent male psychologists promoted the idea of functional periodicity. (wikipedia.org)
- The idea of functional periodicity stems from ancient taboos and rituals that were passed on from generation to generation. (wikipedia.org)
- Hollingworth, along with her husband Harry Hollingworth, established exceptional research on the idea of functional periodicity and created research studies investigating the science of motor/learning tasks involving the human body. (wikipedia.org)
- Functional periodicity was the idea of women being functionally impaired during their menstruation cycle. (wikipedia.org)
- Because of these opinions and beliefs, the idea of functional periodicity became more relevant in American society. (wikipedia.org)
- The idea of functional periodicity stems from past cultural superstitions. (wikipedia.org)
- Hollingworth wanted to investigate the idea of functional periodicity and its assumptions about women. (wikipedia.org)

**area**- The statistical significance of the periodicity observed was checked by comparing the area below the periodicity curve of every protein examined with that of computer generated sequences having the same amino acid composition and length. (springer.com)

**made**- The origin of the 34.1-day periodicity in X-ray and γ-ray from Cyg X-3 has not been made clear so far. (springer.com)
- She made key contributions in the research of functional periodicity, as well as in the feminist movement at the time. (wikipedia.org)

**property**- The three-base periodicity property in the field of Genomics is a property that is characteristic of protein-coding DNA sequences. (wikipedia.org)
- Tsonis, Elsner and Tsonis did Fourier analysis of coding, non-coding and random sequences and proposed a reason for the 3-periodicity property found in coding sequences. (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)

**variables**- Periodicity in Several Variables. (dtic.mil)

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