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infinite series seri-ye bikarân (#) Fr.: série infinie A series with infinitely many terms, in other words a series that has no last term, such as 1 + 1/4 + 1/9 + 1/16 + · · · + 1/n^{2} + ... . The idea of infinite series is familiar from decimal expansions, for instance the expansion π = 3.14159265358979... can be written as π = 3 + 1/10 + 4/10^{2} + 1/10^{3} + 5/10^{4} + 9/10^{5} + 2/10^{6} + 6/10^{7} + 5/10^{8} + 3/10^{9} + 5/10^{10} + 8/10^{11} + ... , so π is an "infinite sum" of fractions. See also → finite series. |
infinite set hangard-e bikarân Fr.: ensemble infini A set which can be put in a one-to-one correspondence with part of itself. |
infinitesimal bikarânxord Fr.: infinitésimal General: Indefinitely or exceedingly small. Infinitesimal, coined by Ger. philosopher and mathematician Baron Gottfried Wilhelm von Leibniz (1646-1716) from N.L. infinitesim(us) "infinite in rank," from infinit(us), → infinite, + -esimus suffix of ordinal numerals + → -al. Bikarânxord, from bikarân "unbounded, unlimited, infinite," from bi- "without" + karân "boundary, side, end" (variants karâné, kenâr, from Mid.Pers. karân, karânak, kenâr "edge, limit, boundary," Av. karana- "side, boundary, end") + xord "minute, little, small" (from Mid.Pers. xvart, xôrt "small, insignificant;" Av. ādra- "weak, dependent;" Skt. ādhrá- "small, weak, poor," nādh "to be oppressed;" Gk. nothros "sluggish;" PIE base *nhdhro-). |
infinitesimal calculus afmârik-e bikarânxord Fr.: calcul infinitésimal The body of rules and processes by means of which continuously varying magnitudes are dealt with in → calculus. The combined methods of mathematical analysis of → differential calculus and → integral calculus. → infinitesimal, → calculus. |
infinitive karpâyé Fr.: infinitif The nominal form of the verb which expresses the idea of action or state without indicating person, number, or tense. Contraction of L. infinitivus modus "unlimited, indefinite mood," from L. infinitus, → infinite. Karpâyé, literally "action base," from kar-, → verb, + pâyé, → base. |
infinity bipâyân (#), bipâyâni (#) Fr.: infini, infinité That quantity which is greater than any assignable quantity. Noun form of → infinite. |
infix darvand Fr.: infixe An → affix that is inserted within a root or stem. From L. infixus p.p. of infigere "to fasten in," from in- + figere "fasten." Darvand, from dar- "in" + vand, → affix. |
inflate pandâmidan Fr.: s'enfler To become inflated; to increase, especially suddenly and substantially. → inflation, → inflatory model. Inflate, from L. inflatus p.p. of inflare "to blow into, puff up," from → in- "into" + flare "to blow." Pandâmidan "to swell," from pandâm [Mo'in] "swelling;" Borujerdi panâm, panam "swellig;" Malâyeri panomidan "to swell;" Laki penamiyen "to swell;" Hamadâni pandumidan "swelling of the eye or other parts of the body;" Kermâni padum kerdan "to swell," padum "swelled; fat, corpulent;" Tâleši pandâm, pandom "swelling;" Gilaki pandâm kudan "rising of river water caused by flood;" cf. Gk. pneuma "wind; breath," from pnein "to blow; to breathe;" PIE base *pneu- "to breathe." Related terms in other Indo-European languages: O.E. fnaeran "to breathe heavily," fneosan "to snort, sneeze;" M.H.G. pfnusen, pfnehen "to breathe, pant, sniff, snort, sneeze;" Norw. fnysa "to breeze;" M.Du. fniesen, Du. fniezen "to sneeze;" O.H.G. niosan, Ger. niesen "to sneeze." |
inflation pandâm Fr.: inflation 1) General: The act of inflating; the state of being inflated. Verbal noun of → inflate. |
inflationary model model-e pandâmi Fr.: modèle d'inflation A class of → Big Bang models of the Universe that include a finite period of accelerated expansion in their early histories. Such an event would have released enormous energy, stored until then in the vacuum of space-time. The horizon of the Universe expanded, temporarily, much faster than the speed of light. → inflaton field. |
inflaton inflaton Fr.: inflaton The hypothetical → particle that mediates the hypothetical → inflaton field. From inflat-, from → inflaton field, + particle suffix → -on. |
inflaton field meydân-e inflaton Fr.: champ inflaton A hypothetical → scalar field that provides a theoretical basis for → inflation in the early → Big Bang history of the → Universe. The inflaton field would fill space with the same energy at every point. In general, the scalar field can vary with time and space, though to a first approximation everywhere in the Universe will have the same value at any time. The field has a particle associated with it, called → inflaton, just as the → electromagnetic field is associated with the → photon. The inflaton field is characterized also by a → negative pressure that would yield a tremendous → repulsive gravity during a brief lapse of time. In the earliest moments of the Universe, space is uniformly filled with an inflaton field, whose value places it higher up on its → potential energy curve. The inflaton's → potential energy would drop in a tiny fraction of a second, on the order of 10^{-35} seconds. And yet, during that brief instant, space would expand by a colossal factor, of at least 10^{30}. |
inflect darcaftidan Fr.: mettre une désinence à, fléchir 1) General: To bend in, to turn from a direct line or course. From M.E. inflecten, from L. inflectere "to bend in, bow, curve," figuratively, "to change," from → in- + flectere "to bend, to curve," of uncertain origin. |
inflection darcafteš Fr.: inflexion A change in the form of a word to indicate a change in such grammatical features as tense, person, gender, case, number, voice, or mood. A general term for → declension and → conjugation. Verbal noun of → inflect. |
inflection point noqte-ye darcafteš Fr.: point d'inflexion A point on a → curve at which the → tangent changes direction, from rotating in one sense to rotating in the opposite sense. → inflection; → point. |
inflectional darcafteši Fr.: désinentiel, flexionnel Of, relating to, or characterized by the use of → inflection, e.g. → inflectional affix. → inflection + → -al. |
inflectional affix vand-e darcafteši Fr.: affixe inflexionnelle An → inflection that is added at the end of a root word. In English there are eight inflectional affixes, which are all suffixes. They always follow derivational suffixes and do not change the category of a word. → inflectional + → affix. |
inflow dartacân Fr.: afflux, débit entrant 1) The act or process of flowing in or into. Something that flows
in or into. Opposite of → outflow. |
influence 1) hanâyeš (#) ; 2) hanâyidan (#) Fr.: 1) influence; 2) influencer, influer 1) The act or power of producing an → effect,
especially inconspicuously; the effect of power exerted. M.E., from O.Fr. influence, from L. influentia "stellar emanation" (it was thought an ethereal liquid flowed from the stars and affected the destiny of humans), also "a flow of water, a flowing in," from L. influentem (nominative influens), pr.p. of influere "to flow into," from → in- "into, in, on, upon" + fluere "to flow;" PIE base *bhleu- "to swell, overflow;" cf. Gk. phluein "to boil over, bubble up," phlein "to abound." Hanâyeš "influence" (Borhân-e Qâte'; Kasravi). We suggest the following origin for this word: ultimately from Proto-Ir. *ha-nai "to conduct, direct, guide, lead," from *ham-naiH-, from prefix *ham- "together," also an intensive prefix, → com-, + *naiH- "to lead, conduct, guide;" cf. Av. naii- (naŷ-) "to lead, guide," naiieiti "leads;" O.Pers. nay- "to lead, bring" anaya "leads;" Mid.Pers. nidan, ônidan, nay- "to lead, bring;" Sogd. n'y- "to lead;" Choresmian (prefixed, + *apa-) bny- "to remove;" Skt. nī- "to lead," náyati "leads." In dialects: Anâraki niye "to bring, lead;" Kurd. (prefixed) ânin, inân, (with prefix ham-) hânin, hênân "to bring, lead to," Tâleši ânân, ânoe "to bring together two edges;" Zazaki ân- "to bring;" Qohrudi hunda, hun- "to bring, lead;" Târi niya-, neg- "to lead;" Lasgardi (prefixed) bin- "to bring, carry;" Qomi niyé, Tafreši neyé "a jab or poke used for leading the cattle;" see also → relate. |
inform azdâyidan (#) Fr.: informer 1) To impart → knowledge of a fact or circumstance. Inform, from M.E. informen, from O.Fr. enformer, from L. informare "to shape, form; to form an idea of," from → in- "into" + → forma "form." Azdâyidan, from Mid.Pers. azdênidan "to inform," from azd "information, proclamation; known" (loaned into Arm. azd), from O.Pers. azdā "known," azdā kar "to become known;" Av. azdā "known;" Sogdian 'zd' "informed, known;" cf. Skt. addhā' "manifestly; certainly, truly," addhāti "sage." |
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