law of sines
Fr.: loi des sinus
In any triangle the sides are proportional to the sines of the opposite angles: a/sin A = b/sin B = c/sin C, where A, B, and C are the three vertices and a, b, and c are the corresponding sides.
An artificially produced → radioactive→ chemical element; symbol Lr (formerly Lw). → Atomic number 103; → atomic weight of most stable isotope 262; → melting point about 1,627°C; → boiling point and → specific gravity unknown; → valence +3. The longest half-life associated with this unstable element is 3.6 hour 262Lr. Credit for the first synthesis of this element in 1971 is given jointly to American chemists from the University of California laboratory in Berkeley under Albert Ghiorso and the Russian team at the Joint Institute for Nuclear Reactions lab in Dubna, under Georgi N. Flerov.
laws of dynamics
Fr.: lois de dynamique
The three basic laws of → dynamics which were first formulated by Isaac Newton in his classical work "Mathematical Principles of Natural Philosophy" published in 1687. → Newton's first law of motion; → Newton's second law of motion; → Newton's third law of motion.
A thickness of some material laid on or spread over a surface.
From M.E. leyer, legger + -er. The first element from layen, leggen "to lay," from O.E. lecgan; cf. Du. leggen; Ger. legen; O.N. legja; Goth. lagjan
Lâyé "layer," from lâ, lây "fold" + -é nuance suffix of nouns.
Fr.: équation de Layzer-Irvine
The ordinary Newtonian energy conservation equation when expressed in expanding cosmological coordinates. More specifically, it is the relation between the → kinetic energy per unit mass associated with the motion of matter relative to the general → expansion of the Universe and the → gravitational potential energy per unit mass associated with the departure from a homogeneous mass distribution. In other words, it deals with how the energy of the → Universe is partitioned between kinetic and potential energy. Also known as → cosmic energy equation. In its original form, the Layzer-Irvine equation accounts for the evolution of the energy of a system of → non-relativistic particles, interacting only through gravity, until → virial equilibrium is reached. But it has recently been generalized to account for interaction between → dark matter and a homogeneous → dark energy component. Thus, it describes the dynamics of local dark matter perturbations in an otherwise homogeneous and → isotropic Universe (P. P. Avelino and C. F. V. Gomes, 2013, arXiv:1305.6064).
W. M. Irvine, 1961, Ph.D. thesis, Harvard University; D. Layzer, 1963, Astrophys. J. 138, 174; → equation.
Le Chatelier's Principle
parvaz-e Le Chatelier
Fr.: principe de Le Chatelier
A change in one of the variables (such as temperature, pressure, and concentration of various species) that describe a system at equilibrium produces a shift in the position of the equilibrium that counteracts the effect of this change.
Named after the French chemist and engineer Henry Louis Le Chatelier (1850-1936); → principle.
A metallic chemical element; symbol Pb (L. plumbum, of unknown origin). Atomic number 82; atomic weight 207.2; melting point 327.502°C; boiling point about 1,740°C. One of the oldest metals used by humanity, because of its relatively low melting point.
O.E. lead, from W.Gmc. *loudhom (cf. O.Fris. lad, M.Du. loot "lead," Ger. Lot "weight, plummet").
Sorb, from Mid.Pers. srub "lead;" Av. sru- "lead."
lakke-ye pišrow (#)
Fr.: tache de tête
In a → sunspot group, the first spot to form in the direction of rotation and the last to disappear. It is the largest, the strongest in magnetic intensity, and the closest to the solar equator among the group sunspots. See also → follower spot.
From M.E. leder(e), O.E. lædan "cause to go with one, lead," from W.Gmc. *laithjan (cf. O.S. lithan, O.N. liða "to go," O.H.G. ga-lidan "to travel," Goth. ga-leiþan "to go"); → spot.
Lakké, → spot; pišrow "leader, forerunner," from piš "in front, forward, before" (Mid.Pers. pêš "before, earlier;" O.Pers. paišiya "before; in the presence of") + row "going," present stem of raftan "to go, elapse, glide by, depart" (Mid.Pers. raftan, raw-, Proto-Iranian *rab/f- "to go; to attack").
One of the organs, usually green and flat, growing from the side of a stem or branch or direct from the root of a tree or plant. A leaf constitutes a unit of the foliage, and functions primarily in food manufacture by → photosynthesis.
M.E. leef, lef; O.E. leaf; cf. O.S. lof, O.N. lauf, O.Fris. laf, Du. loof, O.H.G. loub, Ger. Laub.
Barg "leaf" (Tabari, Gilaki valg, balg; Kurd. belg, balk, Semnâni valg); Mid.Pers. warg "leaf;" Av. varəka- "leaf;" cf. Skt. valká- "bark, bast, rind;" Russ. volokno "fibre, fine combed flax."
Fr.: bissextile, intercalaire
In a calendar, having an extra day or month inserted.
O.E. hleapan "to jump, run, leap" (cf. O.S. hlopan, O.N. hlaupa, O.Fris. hlapa, Du. lopen, Ger. laufen "to run," Goth. us-hlaupan "to jump up"), of uncertain origin, with no known cognates beyond Germanic. The noun is O.E. hlyp (Anglian *hlep). Noun in leap year, so called from its causing fixed festival days to "leap" ahead one day in the week.
Andarheli, from andarhel, verbal noun of andarhelidan, andarheštan "to insert," from andar-→ inter- + helidan, heštan "to place, put" from Mid.Pers. hištan, hilidan "to let, set, leave, abandon;" Parthian Mid.Pers. hyrz; O.Pers. hard- "to send forth;" ava.hard- "to abandon;" Av. harəz- "to discharge, send out; to filter," hərəzaiti "releases, shoots;" cf. Skt. srj- "to let go or fly, throw, cast, emit, put forth;" Pali sajati "to let loose, send forth."
Fr.: jour intercalaire
The extra day added to a solar calendar (e.g. Gregorian, Iranian) in a leap year.
Fr.: mois intercalaire
An intercalary month employed in some calendars to preserve a seasonal relationship between the Lunar and Solar cycles. → embolismic month.
Fr.: seconde intercalaire
A one-second added between 60s and 0s at announced times to keep the Coordinated Universal Time (UTC), counted by atomic clocks, within 0s.90 of mean solar time (UT1). Generally, leap seconds are added at the end of June or December.
Fr.: année bissextile
In solar calendars the year that contains 366 days, instead of 365, in order to keep the calendar in pace with the real solar time.
leap year rule
razan-e sâl-e andarheli
Fr.: régle des années bissextiles
The three criteria that identify → leap years in the → Gregorian calendar: 1) The year must be evenly divisible by 4; 2) If the year can be evenly divided by 100, it is not a leap year, unless; 3) The year is also evenly divisible by 400. This means that in the Gregorian calendar, the years 1600, 2000, and 2400 are leap years, while 1700, 1800, 1900, 2100, 2200, 2300 and 2500 are not leap years.
Fr.: moindre, plus petit
Smallest in size, amount, degree, etc.
From M.E. leest(e), O.E. læst, læsest "smallest" (superlative of læs "smaller, less").
Kucaktarin, kamtarin, superlatives of kucak and
kam, → small.
least common multiplier (LCM)
kucektarin bastâgar-e hamdâr
Fr.: plus petit commun multiple
Of two or more → integers, the smallest positive number that is divisible by those integers without a remainder.
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).
saz-e kucaktarin cârušhâ
Fr.: ajustement moindres carrées
A fit through data points using least squares.