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Tau
Tau (; uppercase Τ, lowercase τ or \boldsymbol\tau; ) is the nineteenth letter of the Greek alphabet, representing the voiceless alveolar plosive, voiceless dental or alveolar plosive . In the system of Greek numerals, it has a value of 300. The name in English is pronounced or , but in modern Greek, Greek it is . This is because the pronunciation of the combination of Greek letters αυ can have the pronunciation of either , or , depending on what follows and if a Diaeresis (diacritic), diaeresis is present on the second vowel (see Greek orthography). Tau was derived from the Phoenician alphabet, Phoenician letter taw (𐤕). Letters that arose from tau include Roman T and Cyrillic Te (Cyrillic), Te (Т, т). Modern usage The lower-case letter τ is used as a symbol for: * Per unit tax, Specific tax amount Biology * The expressed period of the Free-running sleep, freerunning rhythm of an animal, i.e., the length of the daily cycle of an animal when kept in const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tau (protein)
The tau proteins (abbreviated from tubulin associated unit) form a group of six highly soluble protein isoforms produced by alternative splicing from the gene ''MAPT'' (microtubule-associated protein tau). They have roles primarily in maintaining the stability of microtubules in axons and are abundant in the neurons of the central nervous system (CNS), where the cerebral cortex has the highest abundance. They are less common elsewhere but are also expressed at very low levels in CNS astrocytes and oligodendrocytes. Pathologies and dementias of the nervous system such as Alzheimer's disease and Parkinson's disease are associated with tau proteins that have become hyperphosphorylated insoluble aggregates called neurofibrillary tangles. The tau proteins were identified in 1975 as heat-stable proteins essential for microtubule assembly, and since then they have been characterized as intrinsically disordered proteins. Function Microtubule stabilization Tau proteins are found m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tau (mathematical Constant)
The number (; spelled out as tau) is a mathematical constant that is the ratio of a circle's circumference to its radius. It is approximately equal to 6.28 and exactly equal to 2Pi, . and are both circle constants relating the circumference of a circle to its linear dimension: the radius in the case of ; the diameter in the case of . While is used almost exclusively in mainstream mathematical education and practice, it has been proposed, most notably by Michael Hartl in 2010, that should be used instead. Hartl and other proponents argue that is the more natural circle constant and its use leads to conceptually simpler and more intuitive mathematical notation. Critics have responded that the benefits of using over are trivial and that given the ubiquity and historical significance of a change is unlikely to occur. The proposal did not initially gain widespread acceptance in the mathematical community, but awareness of has become more widespread, having been added to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tau (particle)
The tau (), also called the tau lepton, tau particle or tauon, is an elementary particle similar to the electron, with negative electric charge and a spin-1/2, spin of . Like the electron, the muon, and the three neutrinos, the tau is a lepton, and like all elementary particles with half-integer spin, the tau has a corresponding antiparticle of opposite charge but equal mass and spin. In the tau's case, this is the "antitau" (also called the ''positive tau''). Tau particles are denoted by the symbol and the antitaus by . Tau leptons have a lifetime of and a mass of /''c''2 (compared to /''c''2 for muons and /''c''2 for electrons). Since their interactions are very similar to those of the electron, a tau can be thought of as a ''much'' heavier version of the electron. Because of their greater mass, tau particles do not emit as much bremsstrahlung, bremsstrahlung (braking radiation) as electrons; consequently they are potentially much more highly penetrating than electrons. Bec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramanujan Tau Function
The Ramanujan tau function, studied by , is the function \tau : \mathbb\to\mathbb defined by the following identity: :\sum_\tau(n)q^n=q\prod_\left(1-q^n\right)^ = q\phi(q)^ = \eta(z)^=\Delta(z), where q=\exp(2\pi iz) with \mathrm(z)>0, \phi is the Euler function, \eta is the Dedekind eta function, and the function \Delta(z) is a holomorphic cusp form of weight 12 and level 1, known as the discriminant modular form (some authors, notably Apostol, write \Delta/(2\pi)^ instead of \Delta). It appears in connection to an "error term" involved in counting the number of ways of expressing an integer as a sum of 24 squares. A formula due to Ian G. Macdonald was given in . Values The first few values of the tau function are given in the following table : Calculating this function on an odd square number (i.e. a centered octagonal number) yields an odd number, whereas for any other number the function yields an even number. Ramanujan's conjectures observed, but did not prove, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
