Fr.: axiome d'identité
A basic rule in → group theory stating that there exists a unit group element e, called the identity, such that for any element a of the group a * e = e * a = a.
Fr.: élément neutre
In a mathematical system, an element which leaves unchanged any other element on which it operates. Thus 0 is the identity element for addition: a + 0 = a. And 1 is the identity element for multiplication: a . 1 = a.
Fr.: fonction d'identité
Math.: Any function f for which f(x) = x for all x in the domain of definition.
Fr.: matrice identité
In linear algebra, the simplest nontrivial diagonal matrix, an n-by-n square matrix with ones on the main diagonal and zeros elsewhere.
Fr.: opérateur d'identité
An operator which takes a real number to the same real number.
(Conjunction) in case that; granting or supposing that; on condition that. → if and only if.
M.E., from O.E. gif; akin to O.H.G. ibu "if."
Agar "if," from Mid.Pers. agar, hakar "if;" O.Pers. ha-karam "once;" from ha- "one," variant ham-, → com- (cf. Av. ha-; Skt. sa-; Gk. ha-; L. sem-; PIE *sem- "one"), + karam- "a time," maybe from kar- "to do; doing," → work; cf. Av. hakərət "once;" Skt. sakrt "once;" Gk. hapaks "once;" L. semel "once."
if and only if (iff)
agar va ivâz agar, ~ ~ tanhâ ~
Fr.: si et seulement si
Logic, Math.: An → expression indicating that two → statements so connected are → necessary and sufficient conditions for one another. The corresponding logical symbols usually used are: ↔, ⇔, ≡, and iff.
sang-e âzarin (#)
Fr.: roche ignée
Igneous, from L. igneus "of fire, fiery," from ignis "fire," from PIE *egni- (cf. Skt. agni- "fire, sacrificial fire," O.C.S. ogni, Lith. ugnis "fire"); → rock.
Sang "stone, rock," → stone; âzarin "fiery," from âzar, variants âtaš, taš, from Mid.Pers. âtaxš, âtur "fire;" Av. ātar-, āθr- "fire," singular nominative ātarš-; O.Pers. ātar- "fire;" Av. āθaurvan- "fire priest;" Skt. átharvan- "fire priest;" cf. L. ater "black" ("blackened by fire"); Arm. airem "burns;" Serb. vatra "fire;" PIE base *āter- "fire" + -in adj. suffix.
1) girândan; 2) gereftan (#)
Fr.: 1) enflammer, allumer; 2) s'enflammer, s'allumer
1) To set on fire.
From L. ignitus, p.p. of ignire "to set fire," from ignis "fire, flame, light."
Girândan transitive form of gereftan "to take, catch" (Mid.Pers. griftan, Av./O.Pers. grab- "to take, seize," cf. Skt. grah-, grabh- "to seize, take," graha "seizing, holding, perceiving," M.L.G. grabben "to grab," from P.Gmc. *grab, E. grab "to take or grasp suddenly;" PIE base *ghrebh- "to seize").
girâneš; gireš (#)
Fr.: inflammation, allumage
1) The act or fact of igniting; state of being ignited.
Verbal noun of → ignite.
Fr.: température d'inflammation
The minimum temperature to which a fuel must be heated in order to initiate self sustained combustion independent of another heat source.
hamârâ-ye nâdidé engâshté
Fr.: coordonnée ignorée
A → generalized coordinate that does not appear explicitly in the → Lagrangian function. Also called → cyclic coordinate. Ignorable coordinates do not participate in the → Legendre transformation, and are also absent from the → Hamiltonian function. The generalized → momentum associated with an ignorable coordinate is a → constant of the motion.
nâdidé engâštan (#)
Fr.: ignorer, négliger
To set aside, e.g. → ignorable coordinate.
rowšanâyi, tanuyi-ye ~
Fr.: éclairement lumineux
Fr.: éclairement, illumination
General: An act or instance of illuminating. The fact or condition of being illuminated.
Illumination, from O.Fr. illumination, from L. illuminationem (nom. illuminatio), from illuminare "to throw into light," from → in- "in" + lumen "light," cognate with Pers. rowšan, as below.
Rowšanâyi, noun of quality and state from rowšan "bright, clear," related to ruz "day," foruq "light," and afruxtan "to light, kindle," rowzané "window, aperture;" Mid.Pers. rôšn "light; bright, luminous," rôc "day," rocânak "window;" O.Pers. raucah-, Av. raocana- "bright, shining, radiant," raocah- "light, luminous; daylight;" akin to Skt. rocaná- "bright, shining," roka- "brightness, light;" Gk. leukos "white, clear;" L. lux "light," also lumen "light, window," luna "Moon;" E. light; Ger. Licht; Fr. lumière; PIE base *leuk- "light, brightness."
1) A false sense impression of something actually present.
From O.Fr. illusion "a mocking," from L. illusionem (nom. illusio) "a mocking, irony," from illudere "to mock at," literally "to play with," from in- "at" + ludere "to play," from ludus "a game, play;" PIE base *leid- "to play, jest."
In an optical system, the point to which light rays are converged (real image) or
from which they appear to diverge (virtual image) after reflection or refraction.
From O.Fr. image, from L. imaginem (nom. imago) "copy, picture, likeness " from stem of imitari "to copy, imitate," from im-, stem of imitare "to copy, imitate" + -ago noun suffix.
Tasvir, loan from Ar.
Fr.: addition d'images
The process of adding several usually low-exposure images to create an image having a significantly higher signal/noise ratio.
Fr.: correction de l'image brouillée
A technique using a mathematical model of the blurring process to recover the original, sharp image. See also → blurred image.
Fr.: formation de l'image
The meeting of light rays emanating from an object after crossing an optical system.