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1 integer mean
Математика: целочисленное среднее -
2 integer mean
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3 mean
1) среднее значение || средний2) средний член3) способ; средство4) середина || срединный5) иметь в виду6) иметь значение; означать; значить•about the mean — вокруг среднего значения; относительно среднего
mean with respect to — значение, усреднённое по; среднее по...
- row mean- subgroup mean -
4 целочисленное среднее
integer mean мат.Русско-английский научно-технический словарь Масловского > целочисленное среднее
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5 целочисленное среднее
мат. integer meanБольшой англо-русский и русско-английский словарь > целочисленное среднее
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6 целочисленное среднее
Mathematics: integer meanУниверсальный русско-английский словарь > целочисленное среднее
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7 value
1) величина; значение; показатель2) ценность; стоимость3) нормировать4) цена || ценить; оценивать5) расценивать6) ценностный•equal in absolute value — мат. равный по модулю
spread in values — мат. разброс значений
- arithmetical mean value - average absolute value - average overall subsampling value - deficien value - high heating value - highly significant value - left invariant mean value - most probable value - nontrivial absolute value - optimum valueto possess [to take on] value — мат. принимать значение
- pH value- preset value - tabular value -
8 function
1) функция, действие || функционировать; действовать- essential functions - routine function - safety-related functions2) функциональное назначение; роль- circuit function - intrinsic function - metering function - primary function - robot function - planning function - service function - support function4) функциональный узел ( машины)5) матем. функциональная зависимость, функция- absolutely additive function - absolutely bounded function - absolutely continuous function - absolutely integrable function - absolutely monotone function - absolutely summable function - absolutely symmetric function - almost complex function - almost continuous function - almost convex function - almost everywhere defined function - almost everywhere finite function - almost invariant function - almost periodic function - almost recursive function - almost separably-valued function - almost separating function - almost universal function - analytically independent function - analytically representable function - approximately differentiable function - asymptotically differentiable function - asymptotically finite function - asymptotically uniformly optimal function - bounded below function - cellwise continuous function - circumferentially mean p-valent function - comparison function - complementary error function - complete analytic function - completely additive function - completely computable function - completely monotone function - completely multiplicative function - completely productive function - completely subadditive function - completely symmetrical function - completely undefined function - complex hyperbolic function - conditional risk function - countably multiplicative function - countably valued function - covariant function - cumulative distribution function - cumulative frequency function - deficiency function - double limit function - doubly periodic function - doubly recursive function - effectively computable function - effectively constant function - effectively decidable function - effectively variable function - elementarily symmetric function - entire function of maximum type - entire function of mean type - entire function of potential type - entire function of zero type - entire rational function - essentially increasing function - essentially integrable function - essentially real function - essentially smooth function - everywhere differentiable function - everywhere smooth function - expansible function - explicitly definable function - exponentially convex function - exponentially decreasing function - exponentially increasing function - exponentially multiplicative function - exponentially vanishing function - finitely mean valent function - finitely measurable function - function of appropriate behavior - function of bounded characteristic - function of bounded type - function of bounded variation - function of complex variable - function of exponential type - function of finite genus - function of finite variation - function of fractional order - function of infinite type - function of integral order - function of maximal type - function of minimal type - function of mixed variables - function of normal type - function of number theory - function of one variable - function of rapid descent - function of rapid growth - function of real variable - general universal function - geometric carrier function - implicitly definable function - incomplete dibeta function - incomplete gamma function - incomplete tribeta function - incompletely defined function - inductively defined function - inductively integrable function - infinitely divisible function - infinitely many-valued function - integral logarithmic function - inverse trigonometric function - inverted beta function - iterative function - joint correlation function - joint density function - linearly separable function - locally bounded function - locally constant function - locally holomorphic function - locally homogeneous function - locally integrable function - locally negligible function - locally regular function - locally summable function - logarithmic generating function - logarithmic integral function - logarithmically infinite function - logarithmically plurisubharmonic function - logarithmically subharmonic function - lower semicontinuous function - monotone non-decreasing function - monotone non-increasing function - multiply periodic function - multiply recursive function - negative definite function - negative infinite function - nontangentially bounded function - normalized function - normed function - nowhere continuous function - nowhere differentiable function - nowhere monotonic function - n-times differentiable function - n-tuply periodic function - numeralwise expressible function - numeralwise representable function - numerical function - numerically valued function - oblate spheroidal function - operating characteristic function - optimal policy function - parametrically definable function - partially symmetric function - piecewise constant function - piecewise continuously differentiable function - piecewise linear function - piecewise monotonic function - piecewise polynomial function - piecewise quadratic function - piecewise regular function - piecewise smooth function - pointwise approximated function - positive homogeneous function - positive infinite function - positive monotone function - positive monotonic function - positive semidefinite function - potentially calculable function - potentially recursive function - power series function - probability generating function - quadratically summable function - rapidly damped function - rapidly decreasing function - rapidly oscillatory function - recursively continuous function - recursively convergent function - recursively defined function - recursively differentiable function - recursively divergent function - recursively extensible function - relative distribution function - relative frequency function - representing function - reproducing kernel function - residual function - residue function - scalarwise integrable function - scalarwise measurable function - sectionally smooth function - simply periodic function - singly recursive function - slowly increasing function - slowly oscillating function - slowly varying function - smoothly varying function - solid spherical harmonic function - solid zonal harmonic function - steadily increasing function - stopped random function - strictly convex function - strictly decreasing function - strictly increasing function - strictly integrable function - strictly monotone function - strongly differentiable function - strongly holomorphic function - strongly integrable function - strongly measurable function - strongly plurisubharmonic function - totally additive function - totally continuous function - totally measurable function - totally multiplicative function - totally positive function - triangular function - uniformly best decision function - uniformly bounded function - uniformly definable function - uniformly differentiable function - uniformly homotopic function - uniformly integrable function - uniformly limited function - uniformly measurable function - uniformly smooth function - unit step function - unitary divisor function - upper measurable function - upper semicontinuous function - weakly analytic function - weakly continuous function - weakly differentiable function - weakly holomorphic function - weakly measurable function - weakly singular function - weighted random functiondomain of a function — область определения функции, область изменения независимой переменной
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9 величина
amount, size, magnitude* * *величина́ ж.1. (явление, свойство, напр. ток, напряжение, скорость и т. п.) quantityизмеря́ть величину́ — measure a quantityопределя́ть величину́ — define a quantityпренебрега́ть величино́й — neglect [ignore] a quantity2. ( значение) value, magnitudeвы́численная величина́ не о́чень точна́ — the calculated value is of limited accuracyна поря́док величины́ (больше, меньше) — by an order of magnitude (greater, smaller)поря́док величины́ — the order of (the) magnitude3. ( размер или размеры) sizeв натура́льную величину́ — life-size4. ( количество) amountна значи́тельную величину́ — by a large amountабсолю́тная величина́ ( комплексного числа) — absolute value, modulusаддити́вная величина́ — additive quantityана́логовая величина́ — analogue quantityбезразме́рная величина́ — non-dimensional [dimensionless] quantityбесконе́чно больша́я величина́ — infinite quantityбесконе́чно ма́лая величина́ — infinitesimal quantityвеличина́ ве́ктора, абсолю́тная — magnitude of a vectorве́кторная величина́ — vector quantityвзаи́мно незави́симые величи́ны — mutually independent variablesвзве́шенная величина́ — weighted quantityвспомога́тельная величина́ — auxiliary quantityвходна́я величина́1. input quantity2. input valueвходна́я, переме́нная величина́ — input variableвеличина́ вы́тяжки текст. — degree of draughtвыходна́я величина́1. output quantity2. output valueгармони́ческая величина́ — harmonic quantityграни́чная величина́ — boundary valueвеличина́ детона́ции ( топлива) — knock ratingдинами́ческая величина́ — dynamic quantityдискре́тная величина́ — discrete quantityдополни́тельная величина́ — complementдопуска́емая величина́ — allowable [permissible] valueза́данная величина́ — specified [predetermined] valueвеличина́ задаю́щая величина́ — specifying valueвеличина́ заря́да ВВ — size of an explosive chargeидеа́льная величина́ — ideal valueизмеря́емая величина́ — measurable quantityимено́ванная величина́ — denominate quantityинтегра́льная величина́ — integral quantityинформацио́нная величина́ — informational valueиррациона́льная величина́ — irrational quantityиско́мая величина́ — the unknown (quantity), the quantity sought forи́стинная величина́ — true valueколеба́тельная величина́ — oscillating quantityко́мплексная величина́ — complex quantityко́мплексно-сопряжё́нная величина́ — complex conjugateконе́чная величина́1. ( имеющая определённые зафиксированные пределы) finite quantity; ( окончательная) final quantity2. finite valueкоррели́рованная величина́ — correlated valueкрити́ческая величина́ — critical valueлокализо́ванная величина́ — local quantityмни́мая величина́ — imaginary quantityмоното́нная величина́ — monotonic [monotone] quantityмоното́нно возраста́ющая величина́ — monotone [monotonic] increasing quantityмоното́нно убыва́ющая величина́ — monotone [monotonic] decreasing quantityнаблюда́емая величина́ — observable valueнапра́вленная величина́ — directed quantityнатура́льная величина́ — actual [full] sizeвеличина́, не зави́сящая от объё́ма — volume-independent quantityнеизве́стная величина́ — the unknown (quantity)величина́ неопределё́нности — amount of uncertaintyнепреры́вная величина́ — analogue quantityнерегули́руемая величина́ — incontrolled quantityнесоизмери́мые величи́ны — incommensurable quantitiesнесу́щая величина́ — load-bearing [load-carrying] valueнеэлектри́ческая величина́ — nonelectric(al) quantityномина́льная величина́ — nominal [rated] valueнормиро́ванная величина́ — standardized valueвеличина́ нулево́го поря́дка — zeroth-order quantityобобщё́нная величина́ — generalized quantityобра́тная величина́ — reciprocal (quantity), inverse (value)обра́тно пропорциона́льные величи́ны — inversely proportional quantitiesограни́ченная величина́ — bounded quantityопо́рная величина́ — reference valueоптима́льная величина́ — optimal [optimum] valueотноси́тельная величина́ — relative valueотрица́тельная величина́ — negative (value)парциа́льная величина́ — partial quantityпарциа́льная, мо́льная величина́ — partial mole quantityпереме́нная величина́ — variable (quantity) (см. тж. переменная)периоди́ческая величина́ — periodic quantityпериоди́ческая, уравнове́шенная величина́ — balanced periodic quantityвеличина́ погре́шности — magnitude of errorвеличина́ поко́я — quiescent valueположи́тельная величина́ — positive (value)поро́говая величина́ — threshold (value)величина́ (второ́го, тре́тьего и т. п. [m2]) поря́дка ма́лости — (second, third, etc.) order infinitesimalпостоя́нная величина́ — constant (quantity) (см. тж. постоянная)постоя́нная во вре́мени величина́ — time-independent quantityпреде́льная величина́ — limiting valueпреде́льно постоя́нная величина́ — quantity constant in the limitпренебрежи́мо ма́лая величина́ — negligible [ignorable] quantityприближё́нная величина́ — approximate valueпроизво́дная величина́ — derivativeпря́мо пропорциона́льные величи́ны — directly proportional quantitiesпсевдопереме́нная величина́ — pseudovariableпсевдопериоди́ческая величина́ — pseudoperiodic quantityпсевдоскаля́рная ковариа́нтная величина́ — pseudoscalar covariantпульси́рующая величина́ — pulsating quantityразме́рная величина́ — denominate quantityрасчё́тная величина́ — design quantity, design variable, design parameterрегули́руемая величина́ — controlled quantity, controlled variableрегули́рующая величина́ — regulated condition, manipulated variableвеличина́ с ве́сом — weighted quantityсветова́я величина́ — photometric quantityсинусоида́льная, затуха́ющая величина́ — damped sinusoidal quantityсинусоида́льная, ко́мплексная величина́ — complex sinusoidal quantityскаля́рная величина́ — scalar (quantity)случа́йная величина́ — random [stochastic, chance] quantity, random [stochastic, chance] variable, variateслуча́йная, незави́симая величина́ — independent random variableслуча́йная, непреры́вная величина́ — continuous random variableсоизмери́мые величи́ны — commensurable quantitiesсопряжё́нная величина́ — conjugateсредневзве́шенная величина́ — weighted average, weighted meanсреднеквадрати́чная величина́ — root-mean-square [rms] valueсре́дняя величина́ — average [mean] valueстохасти́ческая величина́ — stochastic [random] variableсумма́рная величина́ — total valueуглова́я величина́ — angular valueуде́льная величина́ — specific quantityуправля́емая величина́ — controlled variable, controlled quantityуправля́ющая величина́ — controlling [manipulated] variable, controlling quantityура́вненная величина́ — adjusted quantityустанови́вшаяся величина́ — steady-state valueфакти́ческая величина́ — actual valueфизи́ческая величина́ — physical quantityфотометри́ческая величина́ — photometric quantityхарактеристи́ческая величина́ — characteristic quantityце́лая величина́ — integer quantityцифрова́я величина́ — digital quantityчи́сленная величина́ — numerical valueэлектри́ческая величина́ — electrical quantityэтало́нная величина́ — reference quantityэффекти́вная величина́ — effective value, root-mean-square [rms] value* * * -
10 aio
āio, verb. defect. The forms in use are: pres. indic. āio, ăis, ait—aiunt; subj. aias, aiat—aiant; imperf. indic. throughout, aiebam, aiebas, etc.; imper. ai, rare; part. pres. aiens, rare; once in App. M. 6, p. 178 Elm.; and once as P. a. in Cic. Top. 11, 49, v. below. Cic. wrote the pres. aiio, acc. to Quint. 1, 4, 11.—From ais with the interrog. part. ne, ain is used in colloquial language. For imperf. also aibas, Plaut. Trin. 2, 4, 28; Ter. Ad. 4, 2, 22:I.aibat,
Plaut. Trin. 4, 2, 33; 5, 2, 16:aibant,
id. ib. 1, 2, 175; 4, 2, 102; Ter. And. 3, 3, 3; ai is dissyl., but in the imper. also monosyl., Plaut. Truc. 5, 49; cf. Bentl. ad Ter. Ad. 4, 6, 5. Acc. to Prisc. 818 P., the pres. ait seems to take the place of a perf., but acc. to Val. Prob. 1482 P., there was a real perf. ai, aisti, ait;as aisti,
Aug. Ep. 54 and 174:aierunt,
Tert. Fuga in Persec. 6; the pres. inf. aiere is found in Aug. Trin. 9, 10 [cf. êmi = I say; Sanscr. perf. 3d sing. āha = he spake; ad ag ium, ad ag io; negare for ne ig are; Umbr. ai tu = dicito; Engl. aye = yea, yes, and Germ. ja], to say yes, to assent (opp. nego, to say no; with the ending - tumo, aiutumo; contract. autumo; opp. negumo; v. autumo).In gen.: vel ai vel nega, Naev. ap. Prisc. 473 P.:II.veltu mihi aias vel neges,
Plaut. Rud. 2, 4, 14:negat quis? nego. Ait? aio,
Ter. Eun. 2, 2, 21:Diogenes ait, Antipater negat,
Cic. Off. 3, 23:quasi ego id curem, quid ille aiat aut neget,
id. Fin. 2, 22; so id. Rab. Post. 12, 34.—Esp.A.To say, affirm, or assert something (while dicere signifies to speak in order to inform, and affirmare, to speak in affirmation, Doed. Syn. 4, 6 sq.—Therefore different from inquam, I say, I reply, since aio is commonly used in indirect, and inquam in direct discourse; cf. Doed. as cited above; Herz. ad Sall. C. 48, 3; and Ramsh. Gr. 800).a.In indirect discourse: insanam autem illam (sc. esse) aiunt, quia, etc., Pac. ap. Cic. Her. 2, 23, 36; Plaut. Capt. 1, 1, 3: Ch. Hodie uxorem ducis? Pa. Aiunt, they say so, id. ib. 2, 1, 21:b.ait hac laetitiā Deiotarum elatum vino se obruisse,
Cic. Deiot. 9:debere eum aiebat, etc.,
id. Verr. 2, 1, 18:Tarquinium a Cicerone immissum aiebant,
Sall. C. 48, 8:Vos sapere et solos aio bene vivere,
Hor. Ep. 1, 15, 45; id. S. 1, 2, 121; id. Ep. 1, 1, 88; 1, 7, 22.—In direct discourse: Ennio delector, ait quispiam, quod non discedit a communi more verborum;c.Pacuvio, inquit alius,
Cic. Or. 11, 36:Vos o, quibus integer aevi Sanguis, ait, solidaeque, etc.,
Verg. A. 2, 639; 6, 630; 7, 121;12, 156: O fortunati mercatores! gravis annis Miles ait,
Hor. S. 1, 1, 4; id. Ep. 1, 15, 40; 1, 16, 47; id. S. 2, 7, 72; 1, 3, 22.—With acc.:B.Causa optumast, Nisi quid pater ait aliud,
Ter. And. 5, 4, 47:Admirans ait haec,
Cat. 5, 3, 4; 63, 84:Haec ait,
Verg. A. 1, 297; v. B.—Simply to speak, and esp. in the form of transition, sic ait, thus he speaks or says (cf. the Hom. hôs phato):C.Sic ait, et dicto citius tumida aequora placat,
Verg. A. 1, 142; 5, 365; 9, 749.—Also of what follows: Sic ait in molli fixa toro cubitum: “Tandem,” etc.,
Prop. 1, 3, 34.—Ut ait quispiam (regularly in this order in Cic.), in quoting an unusual expression, as one says:D.ut ait Statius noster in Synephebis,
Cic. Sen. 7:ut ait Homerus,
id. ib. 10:ut ait Theophrastus,
id. Tusc. 1, 19, 45:ut ait Thucydides,
Nep. Them. 2:ut ait Cicero,
Quint. 7, 1, 51; 8, 6, 73; 9, 4, 40;9, 56, 60: ut Cicero ait,
id. 10, 7, 14; 12, 3, 11:ut Demosthenes ait,
id. 11, 1, 22:ut rumor ait,
Prop. 5, 4, 47: uti mos vester ait, Hor S. 2, 7, 79.—So without def. subject:ut ait in Synephebis,
Cic. Tusc. 1, 14, 31.—Aiunt, ut aiunt, quemadmodum or quod aiunt, in quoting a proverbial or technical phrase, as they say, as is said, as the saying is (Gr. to legomenon, hôs phasi; Fr. on dit;E.Germ. man sagt), either placed after it or interposed: eum rem fidemque perdere aiunt,
Plaut. Curc. 4, 2, 18: ut quimus, aiunt;quando, ut volumus, non licet,
Ter. And. 4, 5, 10:docebo sus, ut aiunt, oratorem eum,
Cic. de Or. 2, 57:Iste claudus, quemadmodum aiunt, pilam,
id. Pis. 28 B. and K. —Also in telling an anecdote:conspexit, ut aiunt, Adrasum quendam vacuā tonsoris in umbrā,
Hor. Ep. 1, 7, 49; 1, 17, 18.—In judic. lang.: ait lex, ait praetor, etc., the law, the prœtor says, i. e. prescribes, commands:F.ut ait lex Julia,
Dig. 24, 3, 64:Praetor ait, in eadem causā eum exhibere, etc.,
ib. 2, 9, 1:Aiunt aediles, qui mancipia vendunt, etc.,
ib. 21, 1, 1:Ait oratio, fas esse eum, etc.,
ib. 24, 1, 32 al. —Ain? = aisne? also often strengthened: ain tu? ain tute? ain tandem? ain vero? in conversational lang., a form of interrogation which includes the idea of surprise or wonder, sometimes also of reproof or sorrow, do you really mean so? indeed? really? is it possible? often only an emphatic what? Plaut. Ep. 3, 4, 73: Merc. Servus esne an liber? Sos. Utcumque animo conlibitumst meo. Merc. Ain vero? Sos. Aio enim vero, id. ib. 3, 4, 188; id. Am. 1, 1, 128: Phil. Pater, inquam, aderit jam hic meus. Call. Ain tu, pater? id. Most. 2, 1, 36; id. Ep. 5, 2, 33; id. Aul. 2, 2, 9; id. Curc. 2, 3, 44; Ter. Hec. 3, 4, 1; id. Eun. 3, 5, 19 al:G.Ain tu? Scipio hic Metellus proavum suum nescit censorem non fuisse?
Cic. Att. 6, 1; 4, 5 al.:ain tute,
Plaut. Truc. 1, 2, 90:ain tandem ita esse, ut dicis?
id. Aul. 2, 4, 19; so id. As. 5, 2, 47; id. Trin. 4, 2, 145; Ter. And. 5, 3, 4:ain tandem? insanire tibi videris, quod, etc.,
Cic. Fam. 9, 21 Manut.; id. Att. 6, 2.—Also with a plur. verb (cf. age with plur. verb, s. v. ago, IV. a.):ain tandem? inquit, num castra vallata non habetis?
Liv. 10, 25.—Quid ais? (as in conversation).—a.With the idea of surprise, astonishment, Ti legeis (cf. Quid dixisti? Ter. And. 3, 4, 14; id. Eun. 5, 6, 16, Ti eipas); what do you say? what? Merc. Quis herus est igitur tibi? Sos. Amphitruo, quicum nuptast Alcumena. Merc. Quid ais? Quid nomen tibist? Plaut. Am. 1, 1, 208; so Ter. And. 4, 1, 42; id. Heaut. 5, 1, 27.—b.When one asks [p. 79] another for his meaning, opinion, or judgment, what do you mean? what do you say or think? Th. Ita me di ament, honestust. Pa. Quid tu ais, Gnatho? Num quid habes, quod contemnas? Quid tu autem, Thraso? Ter. Eun. 3, 2, 21: Hunc ais? Do you mean this man? (= dicis, q. v., II.) Pers. 4, 27.—c.When one wishes to try or prove another, what is your opinion? what do you say? Sed quid ais? quid Amphitruoni [dono] a Telebois datumst? Plaut. Am. 1, 1, 262.—Hence, * āiens, entis, P. a., affirming, affirmative (usu. affirmativus):negantia contraria aientibus,
Cic. Top. 11, 49. -
11 nombre
nombre [nɔ̃bʀ]masculine noun• s'accorder en nombre [terme] to agree in number• est-il du nombre des reçus ? is he among those who passed?* * *nɔ̃bʀnom masculin1) Linguistique, Mathématique number2) ( quantité) numberêtre en nombre inférieur — [troupes, joueurs] to be fewer in number; [groupe] to be smaller
être en nombre supérieur — [troupes, joueurs] to be greater in number; [groupe] to be bigger
dans le nombre (colloq) il y aura bien quelqu'un qui me prêtera de l'argent — surely one of them will lend me some money
3) ( grande quantité) numbers (pl)être écrasé or succomber sous le nombre — ( de personnes) to be overcome by sheer weight of numbers; (de dossiers, lettres) to be defeated by the sheer volume
sans nombre — [ennemis] countless; [ennuis] endless
•Phrasal Verbs:* * *nɔ̃bʀ nm1) (= chiffre) numberTreize est un nombre impair. — Thirteen is an odd number.
2) (= quantité)* * *nombre ⇒ Les nombres nm1 Math, Ling, Sci number; un nombre à deux chiffres a two-digit number; nombre positif/négatif positive/negative number; la théorie des nombres number theory; la loi des grands nombres the law of large numbers; s'accorder en genre et en nombre to agree in gender and number;2 ( quantité) number; le nombre des chômeurs the number of unemployed; le nombre croissant/décroissant the increasing/decreasing ou falling number; un certain nombre de some; être égal en nombre or en nombre égal to be equal in number; être inférieur en nombre or en nombre inférieur [troupes, joueurs] to be fewer in number; [groupe] to be smaller; être supérieur en nombre or en nombre supérieur [troupes, joueurs] to be greater in number; [groupe] to be bigger; nous sommes en nombre suffisant pour there are enough of us to; dans le nombre○ il y aura bien quelqu'un qui me prêtera de l'argent surely one of them will lend me some money; ils sont du nombre de ceux qui they are among those who; ils étaient au nombre de 30 there were 30 of them;3 ( grande quantité) numbers (pl); être écrasé or succomber sous le nombre ( de personnes) to be overcome by sheer weight of numbers; (de dossiers, lettres) to be defeated by the sheer volume; subir la loi du nombre to be overcome by sheer weight of numbers; sans nombre [ennemis, personnes] countless; [ennuis] endless; bon nombre de a good many; nombre de fois many times;nombre aléatoire Ordinat random number; nombre algébrique algebraic number; nombre atomique atomic number; nombre d'Avogadro Avogadro's number ou constant; nombre cardinal cardinal number; nombre complexe complex (number); nombre décimal decimal; nombre entier whole number; nombre entier naturel natural number; nombre entier relatif integer; nombre fractionnaire fraction; nombre au hasard = nombre aléatoire; nombre hétérogène mixed number; nombre imaginaire Ordinat imaginary number; nombre impair odd number; nombre irrationnel irrational number; nombre de Mach Mach (number); nombre de masse nucleon ou mass number; nombre d'or Art golden section; nombre ordinal ordinal number; nombre pair even number; nombre parfait perfect number; nombre premier prime number; nombre rationnel rational number; nombre réel real number.[nɔ̃br] nom masculin1. MATHÉMATIQUES [généralement] numberun nombre de trois chiffres a three-digit ou three-figure numbernombre entier whole number, integer2. [quantité] numberinférieur/supérieur en nombre inferior/superior in number ou numbersun grand nombre de a lot of, a great number of, a great many3. [masse] numbersvaincre par le nombre to win by sheer weight ou force of numbersdans le nombre, il y en aura bien un pour te raccompagner there's bound to be one of them who will take you hometous ceux-là n'ont été invités que pour faire nombre those people over there have just been invited to make up the numbersnombre d'or golden section ou mean————————Nombres nom masculin plurielau nombre de locution prépositionnelletu peux me compter au nombre des participants you can count me among the participants, you can count me indu nombre de locution prépositionnelleétiez-vous du nombre des invités? were you amongst ou one of those invited?————————sans nombre locution adjectivale -
12 moment
1) момент, время2) мат. момент•- centroidal moment of inertia - equivalent moment of inertia - moment of a frequency distribution - moment of a support - negative pitching moment -
13 estimator
1) оценка3) сметчик4) статистика, используемая в качестве оценки5) таксатор•- almost invariant estimator - almost unbiased estimator - asymptotically efficient estimator - asymptotically normal estimator - asymptotically optimal estimator - asymptotically robust estimator - asymptotically sufficient estimator - asymptotically unbiased estimator - conditional mean estimator - conditionally unbiased estimator - functionally uniform consistent estimator - maximum probability estimator - minimum contrast estimator - minimum entropy estimator - minimum local bias estimator - minimum risk estimator - minimum variance estimator - nearly unbiased estimator - studentized robust estimator - uncorrelated estimators - uniformly best constant risk estimator - uniformly consistent estimator - uniformly minimum risk estimator - uniformly minimum variance unbiased estimator - uniformly unbiased estimator - weighted least squares estimatorrestricted least squares weighted by mean estimator — ограниченная оценка по методу наименьших квадратов, взвешенная по среднему
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14 arithmetic
̘. ̈n.əˈrɪθmətɪk
1. сущ. арифметика;
счет
2. прил.;
= arithmeticalарифметика - four operations of * четыре действия арифметики (разговорное) арифметика, знание арифметики - his * is poor в арифметике он слаб, арифметика у него хромает (разговорное) учебник арифметики (компьютерное) арифметическое устройство (ЭВМ) расчет(ы) - faulty political * неоправдавшиеся политические расчеты арифметический;
числовойaddress ~ вчт. адресная арифметикаarithmetic = arithmetical ~ арифметика;
счетarithmetic = arithmetical arithmetical: arithmetical арифметический;
arithmetical mean среднее арифметическое;
arithmetical progression арифметическая прогрессияbinary ~ вчт. двоичная арифметикаdecimal ~ вчт. десятичная арифметикаdouble-precision ~ вчт. арифметика с двойной точностьюexternal ~ вчт. внешняя арифметикаinteger ~ вчт. целочисленная арифметикаinternal ~ вчт. внутренняя арифметикаinterval ~ вчт. интервальная арифметикаmachine ~ вчт. машинная арифметикаmental ~ счет в уме mental ~ устный счет mental: ~ производимый в уме, мысленный;
mental arithmetic (или calculations) счет в уме;
mental reservation мысленная оговоркаmodular ~ вчт. арифметика в остаточных классахparallel ~ вчт. параллельная арифметикаtable ~ вчт. табличная арифметикаБольшой англо-русский и русско-английский словарь > arithmetic
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15 MPI
1) Общая лексика: epidemic hysteria, mass psychogenic illness2) Медицина: многоразмерный опросник боли (Multidimentional Pain Inventory), ЛПУ (лечебно-профилактическое учреждение), Myocardial performance index, Master Patient Index3) Американизм: Modified Policy Iteration4) Военный термин: man-portable illuminator, maximum permissible intake, mean point of impact, military police investigator, military procurement instruction, missile periodic inspection5) Техника: Max Planck Institute, major program issues, multipath interference, multipoint injection, (magnetic particle inspection) МПД6) Автомобильный термин: multi port injection, многоточечный впрыск7) Биржевой термин: Marginal Propensity To Invest9) Сокращение: Magnetic Particle Inspection, Mail Processing Infrastructure (2003 funding LAN successor for Remote Encoding, completed by 2007), Multiprotocol Interface, Multidimentional Pain Inventory, Multi Point Injection10) Вычислительная техника: Multibus II Peripheral Interface, Multiple Protocol Interface, Multiprocessor Interconnect Bus, Message Passing Interface (SMP, Cluster), Message Passing Interface11) Нефть: main plant item, Main Production Island12) Генетика: маннозофосфатизомераза13) Биохимия: Mannose Phosphate Isomerase14) Биотехнология: Message passage interface15) Фирменный знак: Meeting Professionals International16) Глоссарий компании Сахалин Энерджи: magnetic particle [powder] inspection17) Океанография: Marine Pollution Incident, Max- Planck Institute for Meteorology18) Сахалин Ю: magnetic particle examination19) Сахалин А: (magnetic particle inspection) магнитопорошковая дефектоскопия20) Расширение файла: Multiprecision Integer21) Программное обеспечение: Matlab Parallel Interface -
16 MPi
1) Общая лексика: epidemic hysteria, mass psychogenic illness2) Медицина: многоразмерный опросник боли (Multidimentional Pain Inventory), ЛПУ (лечебно-профилактическое учреждение), Myocardial performance index, Master Patient Index3) Американизм: Modified Policy Iteration4) Военный термин: man-portable illuminator, maximum permissible intake, mean point of impact, military police investigator, military procurement instruction, missile periodic inspection5) Техника: Max Planck Institute, major program issues, multipath interference, multipoint injection, (magnetic particle inspection) МПД6) Автомобильный термин: multi port injection, многоточечный впрыск7) Биржевой термин: Marginal Propensity To Invest9) Сокращение: Magnetic Particle Inspection, Mail Processing Infrastructure (2003 funding LAN successor for Remote Encoding, completed by 2007), Multiprotocol Interface, Multidimentional Pain Inventory, Multi Point Injection10) Вычислительная техника: Multibus II Peripheral Interface, Multiple Protocol Interface, Multiprocessor Interconnect Bus, Message Passing Interface (SMP, Cluster), Message Passing Interface11) Нефть: main plant item, Main Production Island12) Генетика: маннозофосфатизомераза13) Биохимия: Mannose Phosphate Isomerase14) Биотехнология: Message passage interface15) Фирменный знак: Meeting Professionals International16) Глоссарий компании Сахалин Энерджи: magnetic particle [powder] inspection17) Океанография: Marine Pollution Incident, Max- Planck Institute for Meteorology18) Сахалин Ю: magnetic particle examination19) Сахалин А: (magnetic particle inspection) магнитопорошковая дефектоскопия20) Расширение файла: Multiprecision Integer21) Программное обеспечение: Matlab Parallel Interface -
17 sequence
1) очерёдность; порядок следования3) геол. стратиграфический разрез4) серия, комплекс•- absolutely divergent sequence - absolutely limited sequence - absolutely summable sequence - absolutely unbiased sequence - adjusted homology sequence - asymptotically convergent sequence - asymptotically isotropic sequence - asymptotically lattice sequence - compactly divergent sequence - completely reversible sequence - conditionally divergent sequence - decimal geometric sequence - delicately divergent sequence - discretely convergent sequence - essentially convergent sequence - essentially finite sequence - essentially periodic sequence - everywhere dense sequence - infinitely large sequence - infinitely proceeding sequence - infinitely small sequence - integral stationary sequence - inverse sequence - inverted sequence - linearly independent sequence - locally convergent sequence - metrically convergent sequence - metrically transitive sequence - monotonically decreasing sequence - monotonically increasing sequence - never increasing sequence - numerical sequence - projectively realizable sequence - properly divergent sequence - rapid acquisition sequence - rapidly decreasing sequence - rapidly increasing sequence - recursively defined sequence - recursively divergent sequence - recursively enumerable sequence - relatively compact sequence - sequence of prime numbers - sequence of principal indices - slowly decreasing sequence - slowly increasing sequence - slowly oscillating sequence - stochastically compact sequence - stochastically stable sequence - strictly increasing sequence - strictly measurable sequence - strictly monotonic sequence - strongly convergent sequence - strongly downward sequence - strongly stationary sequence - strongly summable sequence - totally increasing sequence - totally monotone sequence - two-taile sequence - two-way infinite sequence - unconditionally divergent sequence - uniformly divergent sequence - uniformly integrable sequence - weakly convergent sequence -
18 sum
1) сумма; итог || суммировать, складывать; подводить итог3) резюмировать•sum over sum — мат. сумма вдоль подпространства
sum taken over — сумма, взятая по…
to sum up — резюмировать, суммировать
to sum with respect to — суммировать по...
- free sum- rank sum- regression sum of squares- risk sum- row sum- sum of squares for contrasts- unit sum -
19 ab
ăb, ā, abs, prep. with abl. This IndoEuropean particle (Sanscr. apa or ava, Etr. av, Gr. upo, Goth. af, Old Germ. aba, New Germ. ab, Engl. of, off) has in Latin the following forms: ap, af, ab (av), au-, a, a; aps, abs, as-. The existence of the oldest form, ap, is proved by the oldest and best MSS. analogous to the prep. apud, the Sanscr. api, and Gr. epi, and by the weakened form af, which, by the rule of historical grammar and the nature of the Latin letter f, can be derived only from ap, not from ab. The form af, weakened from ap, also very soon became obsolete. There are but five examples of it in inscriptions, at the end of the sixth and in the course of the seventh century B. C., viz.:I.AF VOBEIS,
Inscr. Orell. 3114;AF MVRO,
ib. 6601;AF CAPVA,
ib. 3308;AF SOLO,
ib. 589;AF LYCO,
ib. 3036 ( afuolunt =avolant, Paul. ex Fest. p. 26 Mull., is only a conjecture). In the time of Cicero this form was regarded as archaic, and only here and there used in account-books; v. Cic. Or. 47, 158 (where the correct reading is af, not abs or ab), and cf. Ritschl, Monum. Epigr. p. 7 sq.—The second form of this preposition, changed from ap, was ab, which has become the principal form and the one most generally used through all periods—and indeed the only oue used before all vowels and h; here and there also before some consonants, particularly l, n, r, and s; rarely before c, j, d, t; and almost never before the labials p, b, f, v, or before m, such examples as ab Massiliensibus, Caes. B. C. 1, 35, being of the most rare occurrence.—By changing the b of ab through v into u, the form au originated, which was in use only in the two compounds aufero and aufugio for abfero, ab-fugio; aufuisse for afuisse, in Cod. Medic. of Tac. A. 12, 17, is altogether unusual. Finally, by dropping the b of ab, and lengthening the a, ab was changed into a, which form, together with ab, predominated through all periods of the Latin language, and took its place before all consonants in the later years of Cicero, and after him almoet exclusively.—By dropping the b without lengthening the a, ab occurs in the form a- in the two compounds a-bio and a-perio, q. v.—On the other hand, instead of reducing ap to a and a, a strengthened collateral form, aps, was made by adding to ap the letter s (also used in particles, as in ex, mox, vix). From the first, aps was used only before the letters c, q, t, and was very soon changed into abs (as ap into ab):abs chorago,
Plaut. Pers. 1, 3, 79 (159 Ritschl):abs quivis,
Ter. Ad. 2, 3, 1:abs terra,
Cato, R. R. 51;and in compounds: aps-cessero,
Plaut. Trin. 3, 1, 24 (625 R.); id. ib. 3, 2, 84 (710 R): abs-condo, abs-que, abs-tineo, etc. The use of abs was confined almost exclusively to the combination abs te during the whole ante-classic period, and with Cicero till about the year 700 A. U. C. (=B. C. 54). After that time Cicero evidently hesitates between abs te and a te, but during the last five or six years of his life a te became predominant in all his writings, even in his letters; consequently abs te appears but rarely in later authors, as in Liv. 10, 19, 8; 26, 15, 12;and who, perhaps, also used abs conscendentibus,
id. 28, 37, 2; v. Drakenb. ad. h. l. (Weissenb. ab).—Finally abs, in consequence of the following p, lost its b, and became ds- in the three compounds aspello, as-porto, and as-pernor (for asspernor); v. these words.—The late Lat. verb abbrevio may stand for adbrevio, the d of ad being assimilated to the following b.The fundamental signification of ab is departure from some fixed point (opp. to ad. which denotes motion to a point).In space, and,II.Fig., in time and other relations, in which the idea of departure from some point, as from source and origin, is included; Engl. from, away from, out of; down from; since, after; by, at, in, on, etc.I.Lit., in space: ab classe ad urbem tendunt, Att. ap. Non. 495, 22 (Trag. Rel. p. 177 Rib.):b.Caesar maturat ab urbe proficisci,
Caes. B. G. 1, 7:fuga ab urbe turpissima,
Cic. Att. 7, 21:ducite ab urbe domum, ducite Daphnim,
Verg. E. 8, 68. Cicero himself gives the difference between ab and ex thus: si qui mihi praesto fuerit cum armatis hominibus extra meum fundum et me introire prohibuerit, non ex eo, sed ab ( from, away from) eo loco me dejecerit....Unde dejecti Galli? A Capitolio. Unde, qui cum Graccho fucrunt? Ex Capitolio, etc., Cic. Caecin. 30, 87; cf. Diom. p. 408 P., and a similar distinction between ad and in under ad.—Ellipt.: Diogenes Alexandro roganti, ut diceret, si quid opus esset: Nunc quidem paululum, inquit, a sole, a little out of the sun, Cic. Tusc. 5, 32, 92. —Often joined with usque:illam (mulierem) usque a mari supero Romam proficisci,
all the way from, Cic. Clu. 68, 192; v. usque, I.—And with ad, to denote the space passed over: siderum genus ab ortu ad occasum commeant, from... to, Cic. N. D. 2, 19 init.; cf. ab... in:venti a laevo latere in dextrum, ut sol, ambiunt,
Plin. 2, 47, 48, § 128.Sometimes with names of cities and small islands, or with domus (instead of the usual abl.), partie., in militnry and nautieal language, to denote the marching of soldiers, the setting out of a flcet, or the departure of the inhabitants from some place:c.oppidum ab Aenea fugiente a Troja conditum,
Cic. Verr. 2, 4, 33:quemadmodum (Caesar) a Gergovia discederet,
Caes. B. G. 7, 43 fin.; so id. ib. 7, 80 fin.; Sall. J. 61; 82; 91; Liv. 2, 33, 6 al.; cf.:ab Arimino M. Antonium cum cohortibus quinque Arretium mittit,
Caes. B. C. 1, 11 fin.; and:protinus a Corfinio in Siciliam miserat,
id. ib. 1, 25, 2:profecti a domo,
Liv. 40, 33, 2;of setting sail: cum exercitus vestri numquam a Brundisio nisi hieme summa transmiserint,
Cic. Imp. Pomp. 12, 32; so id. Fam. 15, 3, 2; Caes. B. C. 3, 23; 3, 24 fin.:classe qua advecti ab domo fuerant,
Liv. 8, 22, 6;of citizens: interim ab Roma legatos venisse nuntiatum est,
Liv. 21, 9, 3; cf.:legati ab Orico ad M. Valerium praetorem venerunt,
id. 24, 40, 2.Sometimes with names of persons or with pronouns: pestem abige a me, Enn. ap. Cic. Ac. 2, 28, 89 (Trag. v. 50 Vahl.):B.Quasi ad adulescentem a patre ex Seleucia veniat,
Plaut. Trin. 3, 3, 41; cf.:libertus a Fuflis cum litteris ad Hermippum venit,
Cic. Fl. 20, 47:Nigidium a Domitio Capuam venisse,
id. Att. 7, 24:cum a vobis discessero,
id. Sen. 22:multa merces tibi defluat ab Jove Neptunoque,
Hor. C. 1, 28, 29 al. So often of a person instead of his house, lodging, etc.: videat forte hic te a patre aliquis exiens, from the father, i. e. from his house, Ter. Heaut. 2, 2, 6:so a fratre,
id. Phorm. 5, 1, 5:a Pontio,
Cic. Att. 5, 3 fin.:ab ea,
Ter. And. 1, 3, 21; and so often: a me, a nobis, a se, etc., from my, our, his house, etc., Plaut. Stich. 5, 1, 7; Ter. Heaut. 3, 2, 50; Cic. Att. 4, 9, 1 al.Transf., without the idea of motion. To designate separation or distance, with the verbs abesse, distare, etc., and with the particles longe, procul, prope, etc.1.Of separation:2.ego te afuisse tam diu a nobis dolui,
Cic. Fam. 2, 1, 2:abesse a domo paulisper maluit,
id. Verr. 2, 4, 18, § 39:tum Brutus ab Roma aberat,
Sall. C. 40, 5:absint lacerti ab stabulis,
Verg. G. 4, 14.—Of distance:3.quot milia fundus suus abesset ab urbe,
Cic. Caecin. 10, 28; cf.:nos in castra properabamus, quae aberant bidui,
id. Att. 5, 16 fin.; and:hic locus aequo fere spatio ab castris Ariovisti et Caesaris aberat,
Caes. B. G. 1, 43, 1:terrae ab hujusce terrae, quam nos incolimus, continuatione distantes,
Cic. N. D. 2, 66, 164:non amplius pedum milibus duobus ab castris castra distabant,
Caes. B. C. 1, 82, 3; cf. id. lb. 1, 3, 103.—With adverbs: annos multos longinque ab domo bellum gerentes, Enn. ap. Non. 402, 3 (Trag. v. 103 Vahl.):cum domus patris a foro longe abesset,
Cic. Cael. 7, 18 fin.; cf.:qui fontes a quibusdam praesidiis aberant longius,
Caes. B. C. 3, 49, 5:quae procul erant a conspectu imperii,
Cic. Agr. 2, 32, 87; cf.:procul a castris hostes in collibus constiterunt,
Caes. B. G. 5, 17, 1; and:tu procul a patria Alpinas nives vides,
Verg. E. 10, 46 (procul often also with simple abl.;v. procul): cum esset in Italia bellum tam prope a Sicilia, tamen in Sicilia non fuit,
Cic. Verr. 2, 5, 2, § 6; cf.:tu apud socrum tuam prope a meis aedibus sedebas,
id. Pis. 11, 26; and:tam prope ab domo detineri,
id. Verr. 2, 2, 3, § 6.—So in Caesar and Livy, with numerals to designate the measure of the distance:onerariae naves, quae ex eo loco ab milibus passuum octo vento tenebatur,
eight miles distant, Caes. B. G. 4, 22, 4; and without mentioning the terminus a quo: ad castra contenderunt, et ab milibus passunm minus duobus castra posuerunt, less than two miles off or distant, id. ib. 2, 7, 3; so id. ib. 2, 5, 32; 6, 7, 3; id. B. C. 1, 65; Liv. 38, 20, 2 (for which:duo milia fere et quingentos passus ab hoste posuerunt castra,
id. 37, 38, 5). —To denote the side or direction from which an object is viewed in its local relations,=a parte, at, on, in: utrum hacin feriam an ab laeva latus? Enn. ap. Plaut. Cist. 3, 10 (Trag. v. 38 Vahl.); cf.:II.picus et cornix ab laeva, corvos, parra ab dextera consuadent,
Plaut. As. 2, 1, 12: clamore ab ea parte audito. on this side, Caes. B. G. 3, 26, 4: Gallia Celtica attingit ab Sequanis et Helvetiis flumen Rhenum, on the side of the Sequani, i. e. their country, id. ib. 1, 1, 5:pleraque Alpium ab Italia sicut breviora ita arrectiora sunt,
on the Italian side, Liv. 21, 35, 11:non eadem diligentia ab decumuna porta castra munita,
at the main entrance, Caes. B. G. 3, 25 fin.:erat a septentrionibus collis,
on the north, id. ib. 7, 83, 2; so, ab oriente, a meridie, ab occasu; a fronte, a latere, a tergo, etc. (v. these words).Fig.A.In time.1.From a [p. 3] point of time, without reference to the period subsequently elapsed. After:2.Exul ab octava Marius bibit,
Juv. 1,40:mulieres jam ab re divin[adot ] adparebunt domi,
immediately after the sucrifice, Plaut. Poen. 3, 3, 4:Caesar ab decimae legionis cohortatione ad dextrum cornu profectus,
Caes. B. G. 2, 25, 1:ab hac contione legati missi sunt,
immediately after, Liv. 24, 22, 6; cf. id. 28, 33, 1; 40, 47, 8; 40, 49, 1 al.:ab eo magistratu,
after this office, Sall. J. 63, 5:a summa spe novissima exspectabat,
after the greatest hope, Tac. A. 6, 50 fin. —Strengthened by the adverbs primum, confestim, statim, protinus, or the adj. recens, immediately after, soon after:ut primum a tuo digressu Romam veni,
Cic. Att. 1, 5, 4; so Suet. Tib. 68:confestim a proelio expugnatis hostium castris,
Liv. 30, 36, 1:statim a funere,
Suet. Caes. 85;and followed by statim: ab itinere statim,
id. ib. 60:protinus ab adoptione,
Vell. 2, 104, 3:Homerus qui recens ab illorum actate fuit,
soon after their time, Cic. N. D. 3, 5; so Varr. R. R. 2, 8, 2; Verg. A. 6, 450 al. (v. also primum, confestim, etc.).—Sometimes with the name of a person or place, instead of an action: ibi mihi tuae litterae binae redditae sunt tertio abs te die,
i. e. after their departure from you, Cic. Att. 5, 3, 1: in Italiam perventum est quinto mense a Carthagine Nov[adot ], i. e. after leaving (=postquam a Carthagine profecti sunt), Liv. 21, 38, 1:secundo Punico (bello) Scipionis classis XL. die a securi navigavit,
i. e. after its having been built, Plin. 16, 39, 74, § 192. —Hence the poct. expression: ab his, after this (cf. ek toutôn), i. e. after these words, hereupon, Ov. M. 3, 273; 4, 329; 8, 612; 9, 764.With reference to a subsequent period. From, since, after:b.ab hora tertia bibebatur,
from the third hour, Cic. Phil. 2, 41:infinito ex tempore, non ut antea, ab Sulla et Pompeio consulibus,
since the consulship of, id. Agr. 2, 21, 56:vixit ab omni aeternitate,
from all eternity, id. Div. 1, 51, 115:cum quo a condiscipulatu vivebat conjunctissime,
Nep. Att. 5, 3:in Lycia semper a terrae motu XL. dies serenos esse,
after an earthquake, Plin. 2, 96, 98, § 211 al.:centesima lux est haec ab interitu P. Clodii,
since the death of, Cic. Mil. 35, 98; cf.:cujus a morte quintus hic et tricesimus annus est,
id. Sen. 6, 19; and:ab incenso Capitolio illum esse vigesumiun annum,
since, Sall. C. 47, 2:diebus triginta, a qua die materia caesa est,
Caes. B. C. 1, 36.—Sometimes joined with usque and inde:quod augures omnes usque ab Romulo decreverunt,
since the time of, Cic. Vat. 8, 20:jam inde ab infelici pugna ceciderant animi,
from the very beginning of, Liv. 2, 65 fin. —Hence the adverbial expressions ab initio, a principio, a primo, at, in, or from the beginning, at first; v. initium, principium, primus. Likewise ab integro, anew, afresh; v. integer.—Ab... ad, from (a time)... to:ab hora octava ad vesperum secreto collocuti sumus,
Cic. Att. 7, 8, 4; cf.:cum ab hora septima ad vesperum pugnatum sit,
Caes. B. G. 1, 26, 2; and:a quo tempore ad vos consules anni sunt septingenti octoginta unus,
Vell. 1, 8, 4; and so in Plautus strengthened by usque:pugnata pugnast usque a mane ad vesperum,
from morning to evening, Plaut. Am. 1, 1, 97; id. Most. 3, 1, 3; 3, 2, 80.—Rarely ab... in: Romani ab sole orto in multum diei stetere in acie, from... till late in the day, Liv. 27, 2, 9; so Col. 2, 10, 17; Plin. 2, 31, 31, § 99; 2, 103, 106, § 229; 4, 12, 26, § 89.Particularly with nouns denoting a time of life:B.qui homo cum animo inde ab ineunte aetate depugnat suo,
from an early age, from early youth, Plaut. Trin. 2, 2, 24; so Cic. Off. 2, 13, 44 al.:mihi magna cum co jam inde a pueritia fuit semper famillaritas,
Ter. Heaut. 1, 2, 9; so,a pueritia,
Cic. Tusc. 2, 11, 27 fin.; id. Fam. 5, 8, 4:jam inde ab adulescentia,
Ter. Ad. 1, 1, 16:ab adulescentia,
Cic. Rep. 2, 1:jam a prima adulescentia,
id. Fam. 1, 9, 23:ab ineunte adulescentia,
id. ib. 13, 21, 1; cf.followed by ad: usque ad hanc aetatem ab incunte adulescentia,
Plaut. Trin. 2, 2, 20:a primis temporibus aetatis,
Cic. Fam. 4, 3, 3:a teneris unguiculis,
from childhood, id. ib. 1, 6, 2:usque a toga pura,
id. Att. 7, 8, 5:jam inde ab incunabulis,
Liv. 4, 36, 5:a prima lanugine,
Suet. Oth. 12:viridi ab aevo,
Ov. Tr. 4, 10, 17 al.;rarely of animals: ab infantia,
Plin. 10, 63, 83, § 182.—Instead of the nom. abstr. very often (like the Greek ek paioôn, etc.) with concrete substantives: a pucro, ab adulescente, a parvis, etc., from childhood, etc.:qui olim a puero parvulo mihi paedagogus fuerat,
Plaut. Merc. 1, 1, 90; so,a pausillo puero,
id. Stich. 1, 3, 21:a puero,
Cic. Ac. 2, 36, 115; id. Fam. 13, 16, 4 (twice) al.:a pueris,
Cic. Tusc. 1, 24, 57; id. de Or. 1, 1, 2 al.:ab adulescente,
id. Quint. 3, 12:ab infante,
Col. 1, 8, 2:a parva virgine,
Cat. 66, 26 al. —Likewise and in the same sense with adject.: a parvo, from a little child, or childhood, Liv. 1, 39, 6 fin.; cf.:a parvis,
Ter. And. 3, 3, 7; Cic. Leg. 2, 4, 9:a parvulo,
Ter. And. 1, 1, 8; id. Ad. 1, 1, 23; cf.:ab parvulis,
Caes. B. G. 6, 21, 3:ab tenero,
Col. 5, 6, 20;and rarely of animals: (vacca) a bima aut trima fructum ferre incipit,
Varr. R. R. 2, 1, 13.In other relations in which the idea of going forth, proceeding, from something is included.1.In gen. to denote departure, separation, deterring, avoiding, intermitting, etc., or distance, difference, etc., of inanimate or abstract things. From: jus atque aecum se a malis spernit procul, Enn. ap. Non. 399, 10 (Trag. v. 224 Vahl.):2.suspitionem et culpam ut ab se segregent,
Plaut. Trin. 1, 2, 42:qui discessum animi a corpore putent esse mortem,
Cic. Tusc. 1, 9, 18:hic ab artificio suo non recessit,
id. ib. 1, 10, 20 al.:quod si exquiratur usque ab stirpe auctoritas,
Plaut. Trin. 1, 2, 180:condicionem quam ab te peto,
id. ib. 2, 4, 87; cf.:mercedem gloriae flagitas ab iis, quorum, etc.,
Cic. Tusc. 1, 15, 34:si quid ab illo acceperis,
Plaut. Trin. 2, 2, 90:quae (i. e. antiquitas) quo propius aberat ab ortu et divina progenie,
Cic. Tusc. 1, 12, 26:ab defensione desistere,
Caes. B. C. 2, 12, 4:ne quod tempus ab opere intermitteretur,
id. B. G. 7, 24, 2:ut homines adulescentis a dicendi studio deterream,
Cic. de Or. 1, 25, 117, etc.—Of distance (in order, rank, mind, or feeling):qui quartus ab Arcesila fuit,
the fourth in succession from, Cic. Ac. 1, 12, 46:tu nunc eris alter ab illo,
next after him, Verg. E. 5, 49; cf.:Aiax, heros ab Achille secundus,
next in rank to, Hor. S. 2, 3, 193:quid hoc ab illo differt,
from, Cic. Caecin. 14, 39; cf.:hominum vita tantum distat a victu et cultu bestiarum,
id. Off. 2, 4, 15; and:discrepare ab aequitate sapientiam,
id. Rep. 3, 9 fin. (v. the verbs differo, disto, discrepo, dissideo, dissentio, etc.):quae non aliena esse ducerem a dignitate,
Cic. Fam. 4, 7:alieno a te animo fuit,
id. Deiot. 9, 24 (v. alienus). —So the expression ab re (qs. aside from the matter, profit; cf. the opposite, in rem), contrary to one's profit, to a loss, disadvantageous (so in the affirmative very rare and only ante-class.):subdole ab re consulit,
Plaut. Trin. 2, 1, 12; cf. id. Capt. 2, 2, 88; more frequently and class. (but not with Cicero) in the negative, non, haud, ab re, not without advantage or profit, not useless or unprofitable, adcantageous:haut est ab re aucupis,
Plaut. As. 1, 3, 71:non ab re esse Quinctii visum est,
Liv. 35, 32, 6; so Plin. 27, 8, 35; 31, 3, 26; Suet. Aug. 94; id. Dom. 11; Gell. 18, 14 fin.; App. Dogm. Plat. 3, p. 31, 22 al. (but in Ter. Ad. 5, 3, 44, ab re means with respect to the money matter).In partic.a.To denote an agent from whom an action proceeds, or by whom a thing is done or takes place. By, and in archaic and solemn style, of. So most frequently with pass. or intrans. verbs with pass. signif., when the active object is or is considered as a living being: Laudari me abs te, a laudato viro, Naev. ap. Cic. Tusc. 4, 31, 67: injuria abs te afficior, Enn. ap. Auct. Her. 2, 24, 38:b.a patre deductus ad Scaevolam,
Cic. Lael. 1, 1:ut tamquam a praesentibus coram haberi sermo videretur,
id. ib. 1, 3:disputata ab eo,
id. ib. 1, 4 al.:illa (i. e. numerorum ac vocum vis) maxime a Graecia vetere celebrata,
id. de Or. 3, 51, 197:ita generati a natura sumus,
id. Off. 1, 29, 103; cf.:pars mundi damnata a rerum natura,
Plin. 4, 12, 26, § 88:niagna adhibita cura est a providentia deorum,
Cic. N. D. 2, 51 al. —With intrans. verbs:quae (i. e. anima) calescit ab eo spiritu,
is warmed by this breath, Cic. N. D. 2, 55, 138; cf. Ov. M. 1, 417: (mare) qua a sole collucet, Cic. Ac. 2, 105:salvebis a meo Cicerone,
i. e. young Cicero sends his compliments to you, id. Att. 6, 2 fin.:a quibus (Atheniensibus) erat profectus,
i. e. by whose command, Nep. Milt. 2, 3:ne vir ab hoste cadat,
Ov. H. 9, 36 al. —A substantive or adjective often takes the place of the verb (so with de, q. v.):levior est plaga ab amico quam a debitore,
Cic. Fam. 9, 16, 7; cf.:a bestiis ictus, morsus, impetus,
id. Off. 2, 6, 19:si calor est a sole,
id. N. D. 2, 52:ex iis a te verbis (for a te scriptis),
id. Att. 16, 7, 5:metu poenae a Romanis,
Liv. 32, 23, 9:bellum ingens a Volscis et Aequis,
id. 3, 22, 2:ad exsolvendam fldem a consule,
id. 27, 5, 6.—With an adj.:lassus ab equo indomito,
Hor. S. 2, 2, 10:Murus ab ingenic notior ille tuo,
Prop. 5, 1, 126:tempus a nostris triste malis,
time made sad by our misfortunes, Ov. Tr. 4, 3, 36.—Different from per:vulgo occidebantur: per quos et a quibus?
by whom and upon whose orders? Cic. Rosc. Am. 29, 80 (cf. id. ib. 34, 97: cujus consilio occisus sit, invenio; cujus manu sit percussus, non laboro); so,ab hoc destitutus per Thrasybulum (i. e. Thrasybulo auctore),
Nep. Alc. 5, 4.—Ambiguity sometimes arises from the fact that the verb in the pass. would require ab if used in the active:si postulatur a populo,
if the people demand it, Cic. Off. 2, 17, 58, might also mean, if it is required of the people; on the contrary: quod ab eo (Lucullo) laus imperatoria non admodum exspectabatur, not since he did not expect military renown, but since they did not expect military renown from him, Cic. Ac. 2, 1, 2, and so often; cf. Rudd. II. p. 213. (The use of the active dative, or dative of the agent, instead of ab with the pass., is well known, Zumpt, § 419. It is very seldom found in prose writers of the golden age of Roman liter.; with Cic. sometimes joined with the participles auditus, cognitus, constitutus, perspectus, provisus, susceptus; cf. Halm ad Cic. Imp. Pomp. 24, 71, and ad ejusdem, Cat. 1, 7 fin.; but freq. at a later period; e. g. in Pliny, in Books 2-4 of H. N., more than twenty times; and likewise in Tacitus seventeen times. Vid. the passages in Nipperd. ad Tac. A. 2, 49.) Far more unusual is the simple abl. in the designation of persons:deseror conjuge,
Ov. H. 12, 161; so id. ib. 5, 75; id. M. 1, 747; Verg. A. 1, 274; Hor. C. 2, 4, 9; 1, 6, 2;and in prose,
Quint. 3, 4, 2; Sen. Contr. 2, 1; Curt. 6, 7, 8; cf. Rudd. II. p. 212; Zumpt ad Quint. V. p. 122 Spalding.—Hence the adverbial phrase a se=uph heautou, sua sponte, of one's own uccord, spontaneously:ipsum a se oritur et sua sponte nascitur,
Cic. Fin. 2, 24, 78:(urna) ab se cantat quoja sit,
Plaut. Rud. 2, 5, 21 (al. eapse; cf. id. Men. 1, 2, 66); so Col. 11, 1, 5; Liv. 44, 33, 6.With names of towns to denote origin, extraction, instead of gentile adjectives. From, of:c.pastores a Pergamide,
Varr. R. R. 2, 2, 1:Turnus ab Aricia,
Liv. 1, 50, 3 (for which Aricinus, id. 1, 51, 1):obsides dant trecentos principum a Cora atque Pometia liberos,
Liv. 2, 22, 2; and poet.: O longa mundi servator ab Alba, Auguste, thou who art descended from the old Alban race of kings (=oriundus, or ortus regibus Albanis), Prop. 5, 6, 37.In giving the etymology of a name: eam rem (sc. legem, Gr. nomon) illi Graeco putant nomine a suum cuique tribuendo appellatam, ego nostro a legendo, Cic. Leg. 1, 6, 19: annum intervallum regni fuit: id ab re... interregnum appellatum, Liv. 1, 17, 6:d.(sinus maris) ab nomine propinquae urbis Ambracius appellatus,
id. 38, 4, 3; and so Varro in his Ling. Lat., and Pliny, in Books 1-5 of H. N., on almost every page. (Cf. also the arts. ex and de.)With verbs of beginning and repeating: a summo bibere, in Plaut. to drink in succession from the one at the head of the table:e.da, puere, ab summo,
Plaut. As. 5, 2, 41; so,da ab Delphio cantharum circum, id Most. 1, 4, 33: ab eo nobis causa ordienda est potissimum,
Cic. Leg. 1, 7, 21:coepere a fame mala,
Liv. 4, 12, 7:cornicem a cauda de ovo exire,
tail-foremost, Plin. 10, 16, 18:a capite repetis, quod quaerimus,
Cic. Leg. 1, 6, 18 al.With verbs of freeing from, defending, or protecting against any thing:f.a foliis et stercore purgato,
Cato, R. R. 65 (66), 1:tantumne ab re tuast oti tibi?
Ter. Heaut. 1, [p. 4] 1, 23; cf.:Saguntini ut a proeliis quietem habuerant,
Liv. 21, 11, 5:expiandum forum ab illis nefarii sceleris vestigiis,
Cic. Rab. Perd. 4, 11:haec provincia non modo a calamitate, sed etiam a metu calamitatis est defendenda,
id. Imp. Pomp. 6, 14 (v. defendo):ab incendio urbem vigiliis munitam intellegebat,
Sall. C. 32:ut neque sustinere se a lapsu possent,
Liv. 21, 35, 12:ut meam domum metueret atque a me ipso caveret,
Cic. Sest. 64, 133.With verbs of expecting, fearing, hoping, and the like, ab =a parte, as, Cic. Att. 9, 7, 4: cum eadem metuam ab hac parte, since I fear the same from this side; hence, timere, metuere ab aliquo, not, to be afraid of any one, but, to fear something (proceeding from) from him:g.el metul a Chryside,
Ter. And. 1, 1, 79; cf.:ab Hannibale metuens,
Liv. 23, 36; and:metus a praetore,
id. 23, 15, 7;v. Weissenb. ad h. l.: a quo quidem genere, judices, ego numquam timui,
Cic. Sull. 20, 59:postquam nec ab Romanis robis ulla est spes,
you can expect nothing from the Romans, Liv. 21, 13, 4.With verbs of fastening and holding:h.funiculus a puppi religatus,
Cic. Inv. 2, 51, 154:cum sinistra capillum ejus a vertice teneret,
Q. Cic. Pet. Cons. 3.Ulcisci se ab aliquo, to take vengeance on one:i.a ferro sanguis humanus se ulciscitur,
Plin. 34, 14, 41 fin.Cognoscere ab aliqua re to knoio or learn by means of something (different from ab aliquo, to learn from some one):j.id se a Gallicis armis atque insignibus cognovisse,
Caes. B. G. 1, 22.Dolere, laborare, valere ab, instead of the simple abl.:k.doleo ab animo, doleo ab oculis, doleo ab aegritudine,
Plaut. Cist. 1, 1, 62:a morbo valui, ab animo aeger fui,
id. Ep. 1, 2, 26; cf. id. Aul. 2, 2, 9:a frigore et aestu ne quid laborent,
Varr. R. R. 2, 2, 17; so,a frigore laborantibus,
Plin. 32, 10, 46, § 133; cf.:laborare ab re frumentaria,
Caes. B. G. 7, 10, 1; id. B. C. 3, 9; v. laboro.Where verbs and adjectives are joined with ab, instead of the simple abl., ab defines more exactly the respect in which that which is expressed by the verb or adj. is to be understood, in relation to, with regard to, in respect to, on the part of:l.ab ingenio improbus,
Plaut. Truc. 4, 3, 59:a me pudica'st,
id. Curc. 1, 1, 51:orba ab optimatibus contio,
Cic. Fl. 23, 54; ro Ov. H. 6,156: securos vos ab hac parte reddemus, Planc. ap. Cic. Fam. 10, 24 fin. (v. securus):locus copiosus a frumento,
Cic. Att. 5, 18, 2; cf.:sumus imparati cum a militibas tum a pecunia,
id. ib. 7, 15 fin.:ille Graecus ab omni laude felicior,
id. Brut. 16, 63:ab una parte haud satis prosperuin,
Liv. 1, 32, 2 al.;so often in poets ab arte=arte,
artfully, Tib. 1, 5, 4; 1, 9, 66; Ov. Am. 2, 4, 30.In the statement of the motive instead of ex, propter, or the simple abl. causae, from, out of, on account of, in consequence of: ab singulari amore scribo, Balb. ap. Cic. Att. 9, 7, B fin.:m.linguam ab irrisu exserentem,
thrusting out the tongue in derision, Liv. 7, 10, 5:ab honore,
id. 1, 8; so, ab ira, a spe, ab odio, v. Drak. ad Liv. 24, 30, 1: 26, 1, 3; cf. also Kritz and Fabri ad Sall. J. 31, 3, and Fabri ad Liv. 21, 36, 7.Especially in the poets instead of the gen.:n.ab illo injuria,
Ter. And. 1, 1, 129:fulgor ab auro,
Lucr. 2, 5:dulces a fontibus undae,
Verg. G. 2, 243.In indicating a part of the whole, for the more usual ex, of, out of:o.scuto ab novissimis uni militi detracto,
Caes. B. G. 2, 25, 1:nonnuill ab novissimis,
id. ib.; Cic. Sest. 65, 137; cf. id. ib. 59 fin.: a quibus (captivis) ad Senatum missus (Regulus).In marking that from which any thing proceeds, and to which it belongs:p.qui sunt ab ea disciplina,
Cic. Tusc. 2, 3, 7:ab eo qui sunt,
id. Fin. 4, 3, 7:nostri illi a Platone et Aristotele aiunt,
id. Mur. 30, 63 (in imitation of oi upo tinos).To designate an office or dignity (with or without servus; so not freq. till after the Aug. period;q.in Cic. only once): Pollex, servus a pedibus meus,
one of my couriers, Cic. Att. 8, 5, 1; so,a manu servus,
a secretary, Suet. Caes. 74: Narcissum ab eplstulis ( secretary) et Pallantem a rationibus ( accountant), id. Claud. 28; and so, ab actis, ab admissione, ab aegris, ab apotheca, ab argento, a balneis, a bibliotheca, a codicillis, a jumentis, a potione, etc. (v. these words and Inscr. Orell. vol. 3, Ind. xi. p. 181 sq.).The use of ab before adverbs is for the most part peculiar to later Latinity:► a.a peregre,
Vitr. 5, 7 (6), 8:a foris,
Plin. 17, 24, 37; Vulg. Gen, 7, 16; ib. Matt. 23, 27:ab intus,
ib. ib. 7, 15:ab invicem,
App. Herb. 112; Vulg. Matt. 25, 32; Cypr. Ep. 63, 9: Hier. Ep. 18:a longe,
Hyg. Fab. 257; Vulg. Gen. 22, 4; ib. Matt. 26, 58:a modo,
ib. ib. 23, 39;Hier. Vit. Hilar.: a nune,
Vulg. Luc. 1, 48:a sursum,
ib. Marc. 15, 38.Ab is not repeated like most other prepositions (v. ad, ex, in, etc.) with pron. interrog. or relat. after subst. and pron. demonstr. with ab:b.Arsinoen, Stratum, Naupactum...fateris ab hostibus esse captas. Quibus autem hostibus? Nempe iis, quos, etc.,
Cic. Pis. 37, 91:a rebus gerendis senectus abstrahit. Quibus? An iis, quae in juventute geruntur et viribus?
id. Sen. 6:a Jove incipiendum putat. Quo Jove?
id. Rep. 1, 36, 56:res publica, quascumque vires habebit, ab iis ipsis, quibus tenetur, de te propediem impetrabit,
id. Fam. 4, 13, 5.—Ab in Plantus is once put after the word which it governs: quo ab, As. 1, 1, 106.—c.It is in various ways separated from the word which it governs:d.a vitae periculo,
Cic. Brut. 91, 313:a nullius umquam me tempore aut commodo,
id. Arch. 6, 12:a minus bono,
Sall. C. 2, 6:a satis miti principio,
Liv. 1, 6, 4:damnis dives ab ipsa suis,
Ov. H. 9, 96; so id. ib. 12, 18; 13, 116.—The poets join a and que, making aque; but in good prose que is annexed to the following abl. (a meque, abs teque, etc.):e.aque Chao,
Verg. G. 4, 347:aque mero,
Ov. M. 3, 631:aque viro,
id. H. 6, 156:aque suis,
id. Tr. 5, 2, 74 al. But:a meque,
Cic. Fam. 2, 16, 1:abs teque,
id. Att. 3, 15, 4:a teque,
id. ib. 8, 11, §7: a primaque adulescentia,
id. Brut. 91, 315 al. —A Greek noun joined with ab stands in the dat.: a parte negotiati, hoc est pragmatikê, removisse, Quint. 3, 7, 1.III.In composition ab,1.Retains its original signif.: abducere, to take or carry away from some place: abstrahere, to draw auay; also, downward: abicere, to throw down; and denoting a departure from the idea of the simple word, it has an effect apparently privative: absimilis, departing from the similar, unlike: abnormis, departing from the rule, unusual (different from dissimilis, enormis); and so also in amens=a mente remotus, alienus ( out of one's senses, without self-control, insane): absurdus, missounding, then incongruous, irrational: abutor (in one of its senses), to misuse: aborior, abortus, to miscarry: abludo; for the privative force the Latin regularly employs in-, v. 2. in.—2.It more rarely designates completeness, as in absorbere, abutor ( to use up). (The designation of the fourth generation in the ascending or descending line by ab belongs here only in appearance; as abavus for quartus pater, great-great-grandfather, although the Greeks introduced upopappos; for the immutability of the syllable ab in abpatrnus and abmatertera, as well as the signif. Of the word abavus, grandfather's grandfather, imitated in abnepos, grandchild's grandchild, seems to point to a derivation from avi avus, as Festus, p. 13 Mull., explains atavus, by atta avi, or, rather, attae avus.) -
20 long
1. n долгий срок; длительный период; большой промежуток времениfor long — надолго, на большой срок
before long — скоро, в ближайшее время
it is long since we saw him — мы уже давно его не видели, прошло много времени с тех пор, как мы его видели
he may not endure long — он, вероятно, долго не продержится
2. n стих. долгий слогlong term — долгий срок; долгосрочный
long memory — долгая память, хорошая память
3. n фон. долгий гласный4. n муз. лонга5. n бирж. покупатель ценных бумагlong elephant — ширина рулона обойной бумаги,8
foolscap long folio — формат писчей бумаги,5Х40,6 см
6. n бирж. спекулянт, играющий на повышение7. n бирж. брюки8. n бирж. большие роста9. a длинныйat long range — на большом расстоянии; с большого расстояния
a long way about — крюк, объезд
10. a редк. высокий, долговязый11. a долгий, продолжительный, длительныйLong Service and Good Conduct Medal — медаль «За долголетнюю и безупречную службу»
for a long time — долго, давно; надолго
a long time ago — много времени тому назад; давным-давно
12. a имеющий такую-то длину; длиной в …13. a имеющий такую-то продолжительность; продолжительностью в …an hour long — продолжающийся один час, часовой
as long as life endures — пока есть жизнь, пока человек жив
long swing hip beat — с большого маха вис лежа на н.ж.
14. a отдалённый15. a фин. долгосрочный16. a медленный, медлительный17. a томительный, скучныйthe long hours dragged slowly by — долгие, томительные часы тянулись так медленно
long, unlively debate — длинные, скучные дебаты
18. a разг. большойlong drink — «большой стакан»
19. a разг. удлинённый, продолговатый20. a разг. грам. полный21. a разг. целыйlong mile — добрая миля, не меньше мили
22. a разг. богатый; сильныйhe is long on common sense — здравый смысл — его сильная сторона
long ears — глупость;
a long dozen — тринадцать;
long head — проницательность; предусмотрительность
to take long views — проявлять предусмотрительность, быть дальновидным
in the long run — в конечном счёте; в результате
23. adv долго; длительно24. adv давно; долгое времяlong ago — давно; давным-давно
25. adv усил. полностью; с начала до концаall day long — целый день; день-деньской
long house — длинный вигвам; общий дом нескольких семейств
26. adv бирж. на повышениеso long as — если только, при условии, что
long mark — знак долготы,
27. v страстно желать; стремитьсяСинонимический ряд:1. boring (adj.) boring; long-winded; prolix; tedious; verbose; wordy2. lengthy (adj.) attenuated; dragging; drawn out; drawn-out; elongate; elongated; extended; extensive; interminable; lengthy; long-drawn-out; longsome; overlong; prolonged; protracted; unending3. age (noun) aeon; aeons; age; ages; blue moon; coon's age; dog's age; donkey's years; eternity4. ache (verb) ache; covet; crave; desire; dream; hanker; hanker for; hunger; itch; long for; lust; pant; pine; pine for; sigh; suspire; thirst; wish; yearn; yearn for; yenАнтонимический ряд:brief; compact; compressed; concise; condensed; curt; disdain; ephemeral; evanescent; fleeting; forgo; interesting; laconic; pithy; short
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Logarithm — The graph of the logarithm to base 2 crosses the x axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3) … Wikipedia
mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… … Universalium
Quantile — Quantiles are points taken at regular intervals from the cumulative distribution function of a random variable. Dividing ordered data into q essentially equal sized data subsets is the motivation for q quantiles; the quantiles are the data values … Wikipedia
Harmonic divisor number — This article is about harmonic divisor numbers. For meanings of harmonic number, see harmonic number (disambiguation). In mathematics, a harmonic divisor number, or Ore number (named after Øystein Ore who defined it in 1948), is a positive… … Wikipedia
Rounding — This article is about numerical rounding. For lip rounding in phonetics, see Labialisation. For other uses, see Rounding (disambiguation). Rounding a numerical value means replacing it by another value that is approximately equal but has a… … Wikipedia
Number theory — A Lehmer sieve an analog computer once used for finding primes and solving simple diophantine equations. Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers (the… … Wikipedia
Arithmetic function — In number theory, an arithmetic (or arithmetical) function is a real or complex valued function ƒ(n) defined on the set of natural numbers (i.e. positive integers) that expresses some arithmetical property of n. [1] An example of an arithmetic… … Wikipedia
Binomial distribution — Probability distribution name =Binomial type =mass pdf cdf Colors match the image above parameters =n geq 0 number of trials (integer) 0leq p leq 1 success probability (real) support =k in {0,dots,n}! pdf ={nchoose k} p^k (1 p)^{n k} ! cdf =I {1… … Wikipedia