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fossil sangvâré (#) Fr.: fossile A relic, remnant, or representation of an organism that existed in a past geological age. From Fr. fossile, from L. fossilis "dug up," from fossus, p.p. of fodere "to dig." Sangâré literally "resembling stone," from sang, → stone, + -vâré, from -vâr, → -oid. |
fossil magnetic field meydân-e meqnâtisi-ye sangvâré, ~ ~ sangvâre-yi Fr.: champ magnétique fossile In a physical system, the → magnetic field belonging to an earlier magnetic process or event. A fossil magnetic field may be a vanished one or exist in relic forms. As an example, the solar magnetic field, which was present during the formation of the Sun, has disappeared over the last 4.6 billions years. |
Foucault current jarayân-e Foucault (#) Fr.: courant de Foucault Same as → eddy current. |
Foucault knife-edge test âzmun-e kârd-e Foucault Fr.: contrôle par foucaultage A method used to test the → image quality of → mirrors and → lenses. The test is performed by moving a knife edge laterally into the → image of a small → point source. The → eye, or a → camera, is placed immediately behind the knife edge, and the → exit pupil of the system is observed. Named after the French physicist Léon Foucault (1819-1868), who invented the method; → knife; → edge; → test. |
Foucault pendulum âvang-e Foucault (#) Fr.: pendule de Foucault A → pendulum consisting of a heavy weight on a very long wire attached to a support, that shows the rotation of Earth. The support must be nearly frictionless in order that the pendulum can continue to swing freely for long periods of time. The pendulum will swing in the same plane as it started. The → Earth's rotation is reflected in the slow turning of the plane of the pendulum's motion, which appears to rotate through 360° in T hours. The rotation time is given by the expression: T = T_{0}/sin φ, where T_{0} = 23.9344 hours is the → sidereal day and φ the → latitude of the place. At the poles the rotation period is 23h 56m 04s, and at the equator is ∞, i.e. the swing plane does not move. For regions near the equator it is very long; for example at Quito, the capital city of Ecuador, with φ = 00°15'S, it is 5485 days or more than 15 years! This phenomenon shows that the Earth is a → non-inertial frame. The experiment was performed for the first time by the French physicist Léon Foucault (1819-1868) in 1851, who set up, in the Pantheon in Paris, a simple pendulum consisting of a lead ball weighing 28 kg, suspended by a fine steel wire 67m long. At the latitude of Paris, the pendulum takes 31h 47m 38s to complete a precession cycle; → pendulum. |
Foucault's Marseille reflector bâztâbgar-e Foucault-ye Marseille Fr.: réflecteur marseillais de Foucault The first functioning → reflecting telescope with a silvered glass mirror. It was built by Léon Foucault in 1826 for the Marseille Observatory. The mirror of 80-cm in diameter (f/d = 5) had an excellent quality. The telescope was used for a century as a visual instrument. Edouard Stéphan (1837-1923) used it from 1871 to 1884 to find 800 high-brightness galaxies, among which the → Stephan's Quintet. From 1906 to 1962 the telescope was used by Robert Jonckheere (1888-1927) to discover 3,350 new binary stars. In 1873, following an idea of Hippolyte Fizeau (1819-1896), Stéphan attempted to use it as an → interferometer to measure the diameter of a number of stars. In 1914 Charles Fabry (1867-1945) and Henri Buisson (1873-1944) used the telescope to obtain the first astronomical Fabry-Pérot interferogram, on the → Orion Nebula. After the French physicist and optician Léon Foucault (1819-1868); Marseille (Observatory), the second largest city of France, located on the south east coast of the Mediterranean Sea, from L. Massalia, from Gk. Massalia; → reflector. |
four cahâr (#) Fr.: quatre O.E. feower, from P.Gmc. *petwor- (cf. O.S. fiwar, Du. and Ger. vier, O.N. fjorir, Dan. fire, Sw. fyra), cognate with Pers. cahâr, as below, from PIE *qwetwor. Cahâr, variant câr, from Mid.Pers. cahâr; Av. caθwarô, catur-; cf. Skt. catvārah; Gk. tessares; cognate with L. quattuor; E. four, as above. |
four-dimensional operator âpârgar-e cahâr-vâmuni Fr.: opérateur à quatre dimensions An operator defined as: ▫ = (∂/∂x, ∂/∂y, ∂/∂z, 1/(jc∂/∂t). → four; → dimensional; → operator. |
Fourier analysis ânâlas-e Fourier Fr.: analyse de Fourier The process of decomposing any function of time or space into a sum of sinusoidal functions using the → Fourier series and → Fourier transforms. In other words, any data analysis procedure that describes or measures the fluctuations in a time series by comparing them with sinusoids. Fourier analysis is an essential component of much of modern applied and pure mathematics. It forms an exceptionally powerful analytical tool for solving various problems in many areas of mathematics, physics, engineering, biology, finance, etc. and has opened up new realms of knowledge. After the French mathematician Baron Jean Baptiste Joseph Fourier (1768-1830), whose work had a tremendous impact on the physical applications of mathematics; → analysis. |
Fourier coefficient hamgar-e Fourier Fr.: coefficient de Fourier One of the coefficients a_{n} or b_{n} of cos (nx)
and sin (nx) respectively in the → Fourier series
representation of a function. They are expressed by: → Fourier analysis; → series. |
Fourier integral dorostâl-e Fourier Fr.: intégrale de Fourier An integral used in the → Fourier transform. → Fourier analysis; → integral. |
Fourier series seri-ye Fourier Fr.: séries Fourier A mathematical tool used for decomposing a → periodic function
into an infinite sum of sine and cosine functions. The general form of the
Fourier series for a function f(x) with period 2π is: → Fourier analysis; → series. |
Fourier theorem farbin-e Fourier Fr.: théorème de Fourier Any finite periodic motion may be analyzed into components, each of which is a simple harmonic motion of definite and determinable amplitudes and phase. → Fourier analysis; → theorem. |
Fourier transform tarâdis-e Fourier Fr.: transformée de Fourier A powerful mathematical tool which is the generalization of the → Fourier series for the analysis of non-periodic functions. The Fourier transform transforms a function defined on physical space into a function defined on the space of frequencies, whose values quantify the "amount" of each periodic frequency contained in the original function. The inverse Fourier transform then reconstructs the original function from its transformed frequency components. The integral F(α) = ∫ f(u)e^{-iαu}du is called the Fourier transform of F(x) = (1/2π)∫ f(α)e^{iαx}dx, both integrals from -∞ to + ∞. → Fourier analysis; → transform. |
fourth contact parmâs-e cahârom Fr.: quatrième contact The end of a solar eclipse marked by the disk of the Moon completely passing away from the disk of the Sun. From M.E. fourthe, O.E. féowertha, from four, from O.E. feower, from P.Gmc. *petwor- (cf. Du. and Ger. vier, O.N. fjorir, Dan. fire, Sw. fyra), from PIE *qwetwor (cf. Mod.Pers. cahâr, Av. caθwar-, catur-, Skt. catvarah, Gk. tessares, L. quattuor) + -th a suffix used in the formation of ordinal numbers, from M.E. -the, -te, O.E. -tha, -the; cf. O.N. -thi, -di; L. -tus; Gk -tos; → contact. Parmâs, → contact; cahârom cardinal form from cahâr "four," cognate with E. four, as above. |
fovea lake-ye zard (#) Fr.: fovéa A small depression, approximately 1.5 millimeters in diameter, at the back of the → retina. It forms the area of the most acute vision. Contraction of fovea centralis, from L. fovea "small pit," of unknown origin. Lake-ye zard, literally "yellow spot," from laké, → spot, zard, → yellow. |
fractal barxâl (#) Fr.: fractal A geometrical or physical structure that repeats itself or nearly repeats itself on many different scales of magnification. From Fr. fractale, term coined by Benoit Mandelbrot (1975), from frac(tus) "broken, uneven", → fraction, + -ale→ -al. |
fractal cosmology keyhânšenâxt-e barxâli Fr.: cosmologie fractale The postulate that the concentrations of matter in the Universe follow a → fractal structure over a wide range of scales. |
fractal structure sâxtâr-e barxâli Fr.: structure fractale A → hierarchial structure that can be likened to fractals. |
fraction barxé (#) Fr.: fraction A rational number of the form a/b where a is called the numerator and b is called the denominator. From L.L. fractionem (nom. fractio) "a breaking in pieces," from frangere "to break," from PIE base *bhreg- "to break" (cf. Goth. brikan, O.E. brecan "to break;" Lith. brasketi "crash, crack"). Barxé, from barx "lot, portion," variant bahr, from Mid.Pers. bahr "lot, share, portion," Av. baxəδra- "portion." |
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