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least squares kucaktarin cârušhâ Fr.: moindres carrés Any statistical procedure that involves minimizing the sum of squared differences. |
least-squares deconvolution (LSD) vâhamâgiš-e kucaktarin cârušhâ Fr.: déconvolution des moindres carrés A → cross correlation technique for computing average profiles from thousands of → spectral lines simultaneously. The technique, first introduced by Donati et al. (1997, MNRAS 291,658), is based on several assumptions: additive → line profiles, wavelength independent → limb darkening, self-similar local profile shape, and weak → magnetic fields. Thus, unpolarized/polarized stellar spectra can indeed be seen as a line pattern → convolved with an average line profile. In this context, extracting this average line profile amounts to a linear → deconvolution problem. The method treats it as a matrix problem and look for the → least squares solution. In practice, LSD is very similar to most other cross-correlation techniques, though slightly more sophisticated in the sense that it cleans the cross-correlation profile from the autocorrelation profile of the line pattern. The technique is used to investigate the physical processes that take place in stellar atmospheres and that affect all spectral line profiles in a similar way. This includes the study of line profile variations (LPV) caused by orbital motion of the star and/or stellar surface inhomogeneities, for example. However, its widest application nowadays is the detection of weak magnetic fields in stars over the entire → H-R diagram based on → Stokes parameter V (→ circular polarization) observations (see also Tkachenko et al., 2013, A&A 560, A37 and references therein). → least; → square; → deconvolution. |
least-squares fit saz-e kucaktarin cârušhâ Fr.: ajustement moindres carrées A fit through data points using least squares. → least squares; → fit. |
leave 1) parižidan; 2) pariž Fr.: 1) quitter; 2) congé, permission 1a) Go away from. M.E. leven, from O.E. laefan "to allow to remain in the same state or condition" (cf. O.Saxon farlebid "left over;" Ger. bleiben "to remain") ultimately from PIE *leip- "to stick, adhere;" also "fat," from which the cognates: Gk. lipos "fat;" O.E. lifer "liver," → life. Parižidan, on the model of Sariqoli barēzj "leavings;" Yaghnobi piraxs- "to stay behind, remain;" ultimately from Proto-Ir. *apa-raic-, from *raic- "to abandon, leave;" cf. Av. raēc- "to leave, let" (Cheung 2006), → heritage. |
Leavitt law qânun-e Leavitt Fr.: loi de Leavitt Same as the → period-luminosity relation. Named after Henrietta Swan Leavitt (1868-1921), American woman astronomer, who discovered the relation between the luminosity and the period of → Cepheid variables (1912); → law. |
Leclanché cell pil-e Leclanché (#) Fr.: pile de Leclanché A → primary cell in which the anode is a rod of carbon and the cathode a zinc rod both immersed in an electrolyte of ammonia plus a depolarizer. Named after the inventor Georges Leclanché (1839-1882), a French chemist, → cell. |
Leda Ledâ (#) Fr.: Léda 1) The ninth of Jupiter's known satellites and the smallest. It is 16 km
in diameter and has its orbit at 11 million km from its planet. Also called
Jupiter XIII, it was discovered by Charles Kowal (1940-), an American astronomer,
in 1974. In Gk. mythology, Leda was queen of Sparta and the mother, by Zeus in the form of a swan, of Pollux and Helen of Troy. |
Ledoux's criterion sanjidâr-e Ledoux Fr.: critère de Ledoux An improvement of → Schwarzschild's criterion for convective instability, which includes effects of chemical composition of the gas. In the Ledoux criterion the gradient due to different molecular weights is added to the adiabatic temperature gradient. After the Belgian astrophysicist Paul Ledoux (1914-1988), who studied problems of stellar stability and variable stars. He was awarded the Eddington Medal of the Royal Astronomical Society in 1972 (Ledoux et al. 1961 ApJ 133, 184); → criterion. |
left cap (#) Fr.: gauche Of, pertaining to, or located on or toward the west when somebody or something is facing north. Opposite of → right. M.E. left, lift, luft, O.E. left, lyft- "weak, idle," cf. Ger. link, Du. linker "left," from O.H.G. slinc, M.Du. slink "left," Swed. linka "limp," slinka "dangle." Cap "left," from unknown origin. |
left-hand rule razan-e dast-e cap Fr.: règle de la main gauche See → Fleming's rules. |
left-handed capâl (#) , capdast (#) Fr.: gaucher Using the left hand with greater ease than the right. Capâl, from cap, → left, + -al, → -al. Capdast, with dast, → hand. |
leg 1) leng (#); 2) sâq (#) Fr.: jambe 1) The part of the body from the top of the → thigh
down to the → foot. M.E., from O.Norse leggr; cognate with Dan. læg, Swed. läg "the calf of the leg." Leng, related to Mid.Pers. zang "shank, ankle;" Av. zanga-, zənga- "bone of the leg; ankle bone; ankle;" Skt. jánghā- "lower leg;" maybe somehow related to E. → shank. |
legal qânuni (#) Fr.: légal 1) Permitted by law; lawful. From M.Fr. légal or directly from L. legalis "legal, pertaining to the law," from lex (genitive legis) "law." Qânuni, of or relating to qânun, → law. |
legend cirok Fr.: légende 1) A non-historical or unverifiable story handed down by tradition from
earlier times and popularly accepted as historical. M.E. legende "written account of a saint's life," from O.Fr. legende and directly from M.L. legenda literally, "(things) to be read," noun use of feminine of L. legendus, gerund of legere "to read" (on certain days in church). Cirok, from Kurd. cirok "story, fable," related to Kurd. cir-, cirin "to sing, [to recite?];" Av. kar- "to celebrate, praise;" Proto-Ir. *karH- "to praise, celebrate;" cf. Skt. kar- "to celebrate, praise;" O.Norse herma "report;" O.Prussian kirdit "to hear;" PIE *kerH_{2}- "to celebrate" (Cheung 2007). |
legendary ciroki Fr.: légendaire Of, relating to, or of the nature of a legend. |
Legendre equation hamugeš-e Legendre Fr.: équation de Legendre The → differential equation of the form: d/dx(1 - x^{2})dy/dx) + n(n + 1)y = 0. The general solution of the Legendre equation is given by y = c_{1}P_{n}(x) + c_{2}Q_{n}(x), where P_{n}(x) are Legendre polynomials and Q_{n}(x) are called Legendre functions of the second kind. Named after Adrien-Marie Legendre (1752-1833), a French mathematician who made important contributions to statistics, number theory, abstract algebra, and mathematical analysis; → equation. |
Legendre transformation tarâdiseš-e Legendre Fr.: transformation de Legendre A mathematical operation that transforms one function into another. Two differentiable functions f and g are said to be Legendre transforms of each other if their first derivatives are inverse functions of each other: df(x)/dx = (dg(x)/dx)^{-1}. The functions f and g are said to be related by a Legendre transformation. |
legislation gânungozâri (#) Fr.: législation 1) The act of making or enacting laws. From Fr. législation, from L.L. legislationem, from legis latio, "proposing (literally 'bearing') of a law," → legislator. Qânungoz&acric;ri "act or process followed by the qânungoz&acric;r", → legislator. |
legislator qânungozâr (#) Fr.: législateur 1) A person who gives or makes laws. From L. legis lator "proposer of a law," from legis, genitive of lex, → law, + lator "proposer," agent noun of latus "borne, brought, carried." Qânungozâr, literally "he who places the law," from qânun, → law, + gozâr, present stem and agent noun of gozâštan "to place, put; perform; allow, permit," related to gozaštan "to pass, to cross," → trans- |
Lemaître Universe giti-ye Lemaître (#) Fr.: Univers de Lemaître A cosmological hypothesis, based on Einstein's relativity, in which the expanding Universe began from an exploding "primeval atom." In the Lemaître Universe the rate of expansion steadily decreases. Named after Monsignor Georges Edouard Lemaître (1894-1966), a Belgian Roman Catholic priest, honorary prelate, professor of physics and astronomer; → universe. |
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