# An Etymological Dictionary of Astronomy and AstrophysicsEnglish-French-Persian

## فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

### M. Heydari-Malayeri    -    Paris Observatory

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 Fourier analysis   آنالس ِ فوریه   ânâlas-e FourierFr.: 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   همگر ِ فوریه   hamgar-e FourierFr.: coefficient de Fourier   One of the coefficients an or bn of cos (nx) and sin (nx) respectively in the → Fourier series representation of a function. They are expressed by: an = (1/π) ∫f(x) cos nx dx, for n≥ 0, summed over 0 to 2π bn = (1/π) ∫f(x) sin nx dx, for n≥ 1, summed over 0 to 2π.→ Fourier analysis; → series. Fourier integral   درستال ِ فوریه   dorostâl-e FourierFr.: intégrale de Fourier   An integral used in the → Fourier transform.→ Fourier analysis; → integral. Fourier series   سری ِ فوریه   seri-ye FourierFr.: 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: (1/2) a0 + Σ (an cos (nx) + bn sin (nx), summed from n = 1 to ∞, where an and bn are the → Fourier coefficients, measuring the strength of contribution from each harmonic. The functions cos (nx) and sin (nx) can be used in this way because they satisfy the → orthogonality conditions. For the problem of convergence of the Fourier series see → Dirichlet conditions. The Fourier series play a very important role in the study of periodic phenomena, because they allow one to decompose a large number of complex problems into simpler ones. The generalization of this method, called the → Fourier transform, makes it possible to also decompose non-periodic functions into harmonic components. See also → complex Fourier series, → Parseval's theorem.→ Fourier analysis; → series. Fourier theorem   فربین ِ فوریه   farbin-e FourierFr.: 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   ترادیس ِ فوریه   tarâdis-e FourierFr.: 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-iαudu is called the Fourier transform of F(x) = (1/2π)∫ f(α)eiαxdx, both integrals from -∞ to + ∞. fourth contact   پرماس ِ چهارم   parmâs-e cahâromFr.: 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   لکه‌ی ِ زرد   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   برخال   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.Barxâl, from barx, → fraction, + -âl→ -al. fractal cosmology   کیهانشناخت ِ برخالی   keyhânšenâxt-e barxâliFr.: cosmologie fractale   The postulate that the concentrations of matter in the Universe follow a → fractal structure over a wide range of scales.→ fractal; → cosmology. fractal structure   ساختار ِ برخالی   sâxtâr-e barxâliFr.: structure fractale   A → hierarchial structure that can be likened to fractals.→ fractal; → structure fraction   برخه   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." fractional   برخه‌ای   barxe-yiFr.: fractionnaire, fractionné, partiel   1) Math.: Pertaining to fractions; constituting a fraction. 2) Chemistry: Of or relating to any process by which parts of a mixture are separated by exploiting differences in their physical properties, such as their boiling points, solubility, or other characteristics.→ fraction; → -al. fractional sky coverage   پوشش ِ برخه‌ای ِ آسمان   pušeš-e barxe-yi-ye âsmânFr.: couverture partielle du ciel   The portion of the 4π → steradians of the sky that a radiotelescope can observe from a given location on Earth over a 24-hour time interval.→ fractional; → sky; → coverage. fractionate   برخاندن   barxândanFr.: fractionner   1) To break something up into smaller parts. 2) To separate a mixture into ingredients or portions having different properties, as by distillation or otherwise.From → fraction + -ate a suffix forming verbs or nouns, from L. -atus, -ata, -atum.Barxândan, from barx, barxé, → fraction, + -ândan suffix of transitive verbs. fractionation   برخانش   barxânešFr.: fractionnement   1) Any of various methods of separating the components of a mixture into fractions of different properties. 2) → isotope fractionationVerbal noun from → fractionate. fragment   ۱) لته، لت، پاره؛ ۲) لتپار شدن؛ ۳) لتپاریدن   1) latté (#), latt (#), pâré (#); 2) latpâr šodan (#); 3) latpâridanFr.: 1) fragment; 2) se fragmenter; 3) fragmenter   1) (n.) A part broken off or detached. 2) (v.intr.) To collapse or break into pieces. 3) (v.tr.) To break something into pieces.From L. fragmentum, from frangere "to break."1) Latté, lat, variant laxt, laxté "piece, part;" pâré "piece, part, portion, fragment;" Mid.Pers. pârag "piece, part, portion; gift, offering, bribe;" Av. pāra- "debt," from par- "to remunerate, equalize; to condemn;" PIE *per- "to sell, hand over, distribute; to assigne;" cf. L. pars "part, piece, side, share," portio "share, portion;" Gk. peprotai "it has been granted;" Skt. purti- "reward;" Hitt. pars-, parsiya- "to break, crumble." 2) and 3) Verbal forms. fragmentation   لتپارش   latpârešFr.: fragmentation   Generally, the process of breaking up into smaller parts. In particular, the splitting of a large molecular cloud into smaller, denser clumps. → cloud fragmentation.From → fragmenta + -ation, a combination of -ate and -ion, used to form nouns from stems in -ate.Latpâreš, verbal noun from latpâridan, → fragment. fragmentation process   فراروند ِ لتپارش   farâravand-e latpârešFr.: processus de fragmentation   The succession of physical events that results in the breaking of a → molecular cloud into several → fragments.→ fragmentation; → process. frame   ۱) چارچوب؛ ۲)، ۳) تصویرک   1) cârcub (#); 2), 3) tasvirakFr.: 1) cadre; 2), 3) image   1) A border or case for enclosing a picture, mirror, etc.; a structure for admitting or enclosing something. 2) One of the successive pictures on a roll of movie film or videotape. 3) In computers, the information or image on a screen or monitor at any one time.Frame, from M.E. verb framen "to prepare (timber)," from O.E. framian "to avail, profit."; cf. O.H.G. (gi)framon "to do."1) Cârcub "frame," from câr, contraction of cahâr "four" (→ four) + cub "stick, satff, beam," Mid.Pers. côp "wood, stick." 2) Tasvirak from Ar. tasvir "image" + -ak suffix of relation and similarity (as in poštak, dastak, nâxonak), → fibril.