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Greek Alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It was derived from the earlier Phoenician alphabet, and is the earliest known alphabetic script to systematically write vowels as well as consonants. In Archaic Greece, Archaic and early Classical Greece, Classical times, the Greek alphabet existed in Archaic Greek alphabets, many local variants, but, by the end of the 4th century BC, the Ionia, Ionic-based Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard throughout the Greek-speaking world and is the version that is still used for Greek writing today. The letter case, uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , , , , , , , The Greek alphabet is the ancestor of several scripts, such as the Latin script, Latin, Gothic alphabet, Gothic, Coptic script, Coptic, and Cyrillic scripts. Throughout antiquity, Greek had only a single uppercas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modern Greek
Modern Greek (, or , ), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the language sometimes referred to as Varieties of Modern Greek#Standard Modern Greek, Standard Modern Greek. The end of the Medieval Greek period and the beginning of Modern Greek is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic features of the modern language arose centuries earlier, having begun around the fourth century AD. During most of the Modern Greek period, the language existed in a situation of diglossia, with regional spoken dialects existing side by side with learned, more archaic written forms, as with the vernacular and learned varieties (''Dimotiki'' and ''Katharevousa'') that co-existed in Greece throughout much of the 19th and 20th centuries. Variet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stopping Time
In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time ) is a specific type of "random time": a random variable whose value is interpreted as the time at which a given stochastic process exhibits a certain behavior of interest. A stopping time is often defined by a stopping rule, a mechanism for deciding whether to continue or stop a process on the basis of the present position and past events, and which will almost always lead to a decision to stop at some finite time. Stopping times occur in decision theory, and the optional stopping theorem is an important result in this context. Stopping times are also frequently applied in mathematical proofs to "tame the continuum of time", as Chung put it in his book (1982). Definition Discrete time Let \tau be a random variable, which is defined on the filtered probability space (\Omega, \mathcal F, (\mathcal F_n)_, P) w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Orthography
The orthography of the Modern Greek, modern Greek language was standardised in 1976 and simplified the diacritics in 1982. There are relatively few differences between the orthography of Ancient Greek and Modern Greek. Some time prior to that, one early form of Greek, Mycenaean language, Mycenaean, was written in Linear B, although there was a lapse of several centuries (the Greek Dark Ages) between the time Mycenaean stopped being written and the time when the Greek alphabet came into use. Early Greek writing in the Greek alphabet was Phonemic orthography, phonemic, different in each Ancient Greek dialects, dialect. Since the adoption of the Ionic Greek, Ionic variant for Attic Greek, Attic in 403 BC, however, Greek orthography has been largely conservative and historical. Given the History of Greek, phonetic development of Greek, especially in the Koine Greek, Hellenistic period, certain modern vowel phonemes have multiple orthographic realizations: * can be spelled η, ι, υ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \frac = \frac = \varphi, where the Greek letter Phi (letter), phi ( or ) denotes the golden ratio. The constant satisfies the quadratic equation and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli; it also goes by other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the Straightedge and compass construction, construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has bee ... [...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] |
Kendall Tau Rank Correlation Coefficient
In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic used to measure the ordinal association between two measured quantities. A τ test is a non-parametric hypothesis test for statistical dependence based on the τ coefficient. It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities. It is named after Maurice Kendall, who developed it in 1938, though Gustav Fechner had proposed a similar measure in the context of time series in 1897. Intuitively, the Kendall correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc.) between the two variables, and low when observations have a dissimilar (or fully different for a correlation of −1) rank between the two variab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diaeresis (diacritic)
Diaeresis ( ) is a diacritical mark consisting of two dots () that indicates that two adjacent vowel letters are separate syllables a vowel hiatus (also called a diaeresis) rather than a digraph or diphthong. It consists of a two dots diacritic placed over a letter, generally a vowel. The diaeresis diacritic indicates that two adjoining letters that would normally form a digraph and be pronounced as one sound, are instead to be read as separate vowels in two syllables. For example, in the spelling "coöperate", the diaeresis reminds the reader that the word has four syllables, ''co-op-er-ate'', not three, ''*coop-er-ate''. In British English this usage has been considered obsolete for many years, and in US English, although it persisted for longer, it is now considered archaic as well. Nevertheless, it is still used by the US magazine ''The New Yorker''. In English language texts it is perhaps most familiar in the loan words '' naïve'', '' Noël'' and '' Chloë'', and is a ... [...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] |
Shear Stress
Shear stress (often denoted by , Greek alphabet, Greek: tau) is the component of stress (physics), stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts. General shear stress The formula to calculate average shear stress or force per unit area is: \tau = ,where is the force applied and is the cross-sectional area. The area involved corresponds to the material face (geometry), face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force. Other forms Wall shear stress Wall shear stress expresses the retarding force (per unit area) from a wall in the layers of a fluid flowing next to the wall. It is defined as:\tau_w := \mu\left.\frac\_,where is the dynamic viscosity, is the flow velocity, and is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proper Time
In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. The proper time interval between two events on a world line is the change in proper time, which is independent of coordinates, and is a Lorentz scalar. The interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line. The proper time interval between two events depends not only on the events, but also the world line connecting them, and hence on the motion of the clock between the events. It is expressed as an integral over the world line (analogous to arc length in Euclidean space). An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated ( inertial) clock between the same two events. The twin paradox is an example of this effect. By conventio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
