Dict Rom Eng Matematică

5/28/2018 Dict Rom Eng Matematic

1/112

| Pagina principala| Ghidul utilizatorului| Rubrica candidatului| Curriculumurile scolare|

| Matematica competitiva| Matematica distractiva| Formule, dictionare| Avizuri|

|Pagini din istorie| Examene, teste| Bibliografie| Link-uri| Site map| Cartea Vizitatorilor

Dictionar Roman-Englez de Termeni Matematici

A BCDEFGHIJ KLMNOPQ RS#T&UVW X Y Z

Aabscis' - abscissaabsolut - absoluteacelea)i semne - like signsacurate+e - accuracyadmisibil - admissibleaduna - to addadunare - additionafirma+ie - statementalgebr' - algebra

algoritm - algorithmalgoritm de divizare - algorithm for division, division algorithmalgoritmul lui Euclid - Euclidean algorithmalternan+' - alternancealternare - alterationamplasare - dispositionamplitudine - amplitudeanaliza - to analyzeanaliz' - analysisanaliz'matematic' - calculus

analogic - analogous, analogicalanalogie - analogyanula - to vanishaplicat' - applicateaplica+ie - map, mappingarbitrar - arbitraryarc - arcarccosinus - anticosine, arccosine

Page 1 of 20Dictionar Roman-Englez

2/17/05http://math.ournet.md/formule/dic/roman.html
http://math.ournet.md/formule/dic/roman.htmlhttp://math.ournet.md/formule/dic/roman.html


2/112

arcsinus - antisine, arcsinearctangent' - arctangentargument - argumentargument al func+iei - argument of a functionarie - areaarie a suprafe+ei - surface areaasem'nare - similarity, similitudeasimetric - asymmetric(al), unsymmetricasimetrie - asymmetryasimptot' - asymptoteasimptote ale hiperbolei - asymptotes of a hyperbolaaxax - x-axisax' - axisax'de coordonate - coordinate axisax'de rota+ie - pivot

ax'orizontal' - horizontal axisax'principal' - major axis, principal axisax'vertical' - vertical axisaxiom' - axiom

Bbaz' - base, basisbaz'ortogonal' - orthogonal basebaz'ortonormat' - orthonormal basisbilion - billionbinar - binarybine definit - well-definedbinom - binomialbisectoare - bisector, bisectrixbiunivoc - one-to-one

Ccalcul - calculus, computationcalcula - to countcalculabil - computablecalculul determinantului - evaluation of determinant




3/112

canonic - canonicaldeterminarea extremului - hill climbingcmp - fieldct - quotient, ratio

cel mai mare divizor comun- greatest common divisor, greatest commonfactor

cel mai mic multiplu comun - lowest common multiplecel mai mic numitor comun - lowest common denominator centru - centre, center centru de rota+ie - pivotcentru al unei circumferin+e exnscrise - excentre, centre of the escribed circlecentrul circumferin+ei circumscrise - circumcenter centrul circumferin+ei nscrise - incenter cerc - circlecercuri concentrice - concentric circles

cifr' - digitcilindru - cylinder circumferin+'nscris' - incircle, inscribed circlecircumferin+'unitar' - unit circlecircumscris - escribedcoard' - chordcoeficient - coefficientcoeficient binomial - binomial coefficientcoeficient unghiular - slope

coincident - coincidentcoliniaritate - collinearitycombina+ie - combinationcomparare - comparationcompara+ie - comparationcon - coneconcav' - concavecondi+ie - conditioncondi+ie ini+ial' - initial conditioncondi+ie necesar')i suficient' - necessary and sufficient condition

congruen+' - congruenceconjugat - adjoint, conjugateconsecin+' - corollaryconstant' - constantconstant'de integrare - integration constantcontinuitate - continuityconvex - convexconvexitate - convexity




4/112

coordonat' - coordinatecoordonate afine - affine coordinatescoordonate carteziene - Cartesian coordinatescoplanar - coplanar corolar - corollarycosinus director - direction cosinecre)te - to increasecre)tere - incrementcriteriu - criterioncriteriu de divizibilitate - criterion for divisibilitycuantor - quantifier cuantor existen+ial - existential quantifier cuantor universal - universal quantifier cub - cubecunoscut - known

cuplu - pair cuplu ordonat - ordered pair curb' - curvecurb'concav' - concave curvecurb'convex' - convex curvecurb'cubic' - cubic, cubic curvecurb'integral' - integral curve

D

dac')i numai dac' - if and only ifdate - datadecizie - decisiondeduc+ie - deductiondefini - to definedefinit peste tot - everywhere defineddefini+ie - definition

degenerat - degeneratedemp'r+it - dividenddenmul+it - multiplicanddelatare - dilatation, stretchingdemonstra - to provedemonstra+ie - proof dependent - dependentderivabilitate - differentiability




5/112

derivat' - derivativederivat'n punct - derivative at a pointdescazut - minuenddescompunere - decomposition, expansiondescompunere binomial' - binomial expansiondescompunere n factori - factoring, factorizationdescompunere n factori primi - prime factorizationdescompunere n frac+ii elementare - partial-fraction expansiondescompunere a unei frac+ii - decomposition of a fractiondescre)te - to decreasedetermina - to determinedeterminant - determinantdevia+ie - deviationdeviere - deviationdezvoltare - expansion

dezvoltare a determinantului - expansion of a determinantdiagonal' - diagonaldiagonal'principal' - main diagonal, principal diagonaldiametru - diameter diferen+' - differencediferen+iabilitate - differentiabilitydiferit - unequaldimensiune - dimensiondirect propor+ional - directly proportional

direc+ie - directiondiscontinuu - discontinuousdiscriminant - discriminantdisp'rea - to vanishdistan+' - distance, waydistinct - distinctdivizare - divisiondivizibil {prin} - divisable {by}divizor - divisor divizor comun - common divisor, common factor divizor propriu - proper factor domeniu - domain, rangedomeniu de defini+ie - domain of definitiondreapt' - linedreapt'numeric' - number linedrept - straightdrepte neconcurente - skew lines




6/112

dreptunghi - rectangledrum - waydual - dual

E

echilateral - equilateralechivalent - equivalentecua+ie - equationecua+ie algebric' - algebraic equationecua+ie a liniei drepte - equation of a straight lineecua+ie a unei drepte cu coeficientunghiular

- slope-intercept form of a straight lineequation

ecua+ie bipatrat' - biquadratic equationecua+ie de ordinul nti - first-order equationecua+ie exponen+ial' - exponential equationecua+ie liniar' - linear equationecua+ie neliniar' - non-linear equationecua+ie omogen' - homogeneous equationecua+ie de ordinul doi(patrat') - quadratic equationelement - elementelement {al multimii} - member {of a set}element de arie - differential of area, element of area

element de arie (al suprafe+ei) - surface elementelement diagonal - diagonal elementeliminare - eliminationeliminare prin substitu+ie - elimination by substitutionelips' - ellipseeroare - error eroare de rotunjire - rounding error esen+ial - essentialestima+ie - estimation

evaluare - evaluationexact - exactexactitate - accuracyexcep+ie - exclusionexemplu - exampleexnscris - escribedexponent - degree, exponent, grade, power exponen+ial - exponential




7/112

expresie - expressionexpresie algebric' - algebraic expressionexpresie de sub integral' - integrandextremal - extremalextremum absolut - absolute extremum

Ffactor - factor familie - familyfascicul - pencilfascicul de drepte - pencil of linesfa+'lateral' - leg

figur'circumscris' - circumscribed figurefigur'congruent' - equivalent figurefiguri congruente - congruent figuresflux - fluxfocar - focusform'general' - general formform'parametric' - parametric formform'standard' - standard formformula binomului - binomial formulaformula coeficientului unghiular - slope formulaformula lui Leibniz - Leibniz ruleformula r'd'cinilor ecua+iei patrate - quadratic formulaformul' - formulaformulele jum't'+ii unui unghi - half-angle formulasfrac+ie - fractionfrac+ie elementar' - partial fractionfrac+ie ordinar' - common fractionfrac+ie subunitar' - proper fractionfrac+ie supraunitar' - improper fraction

frac+ie zecimal' - decimal fractionfrac+ie zecimal'finit' - terminating decimal fraction

frac+ie zecimal'infinit'- infinite decimal fraction, non-terminatingdecimal

frac+ie zecimal'periodic' - periodic decimal fractionfrac+ii cu numitori egali - similar fractionsfunc+ie - functionfunc+ie concav' - concave function




8/112

func+ie continu' - continuous functionfunc+ie de mai multe variabile - function of several variablesfunc+ie de o variabil' - function of a single variablefunc+ie de variabil'complex' - function of a complex variablefunc+ie descresc'toare - decreasing functionfunc+ie diferen+iabil' - differentiable functionfunc+ie discontinu' - discontinuous functionfunc+ie impar' - odd-function

func+ie n scar' - inter-stage function, jump function, stepfunction

func+ie liniar' - linear functionfunc+ie monoton cresc'toare - monotone increasing functionfunc+ie monoton descresc'toare - monotone decreasing functionfunc+ie monoton' - monotonic functionfunc+ie par' - even function, symmetric function

func+ie periodic' - periodic functionfunc+ie primitiv' - primitivefunc+ie ra+ional' - rational functionfunc+ie signum - signum functionfunc+ie simetric' - symmetric functionfunc+ie trigonometric' - trigonometric functionfundamental - fundamental

G

general - generalgeometrie - geometrygeometrie euclidian' - Euclidean geometrygrad - degree, gradegrad al polinomului - degree of a polinomial

H

hexaedru - hexahedron, hexaeder hexagon - hexagonhiperbol' - hyperbolahiperbolic - hyperbolic




9/112

Iidentitate - identityimagine - image, map, mapping

impar - oddimplica+ie - implicationincertitudine - uncertaintyinclude - to includeincluziune - inclusionincompatibil - inconsistentincorect - incorrectindependent - independentindependen+'liniar' - linear independency

induc+ie - inductioninduc+ie complet' - complete inductioninduc+ie matematic' - mathematical inductioninecua+ie - inequalityinegal - unequalinfinit - infiniteinflexiune - inflexionini+ial - initialintegral' - integralintegrare prin p'r+i - integration by parts

interdependen+' - interdependencyintersec+ie - intersectioninterval - intervalinterval deschis - open intervalinterval nchis - closed intervalinterval m'rginit - bounded intervalinterval seminchis - semiclosed intervalinvers - inverse, vice versainvers propor+ional - inversely proportional

ipotenuz' - hypotenuseipotez' - hypothesisireductibilitate - irreductibility




10/112

mp'r+i n dou'{n jum'tate} - to halvemp'r+ire f'r'rest - exact divisionn ntregime - wholen'l+ime - heightn'l+ime a triunghiului - altitude of a trianglenchis - closednclinare - slopenlocui - to replacenmul+i - to multiplynmul+ire - multiplicationnmul+itor - multiplier nscrie - to inscribe

K

kilogram - kilogram(me)kilometru - kilometre

Llatur'{a unui unghi} - side {of an angle}

latur'adiacent' - adjacent sidelege - lawlege asociativ' - associative lawlege comutativ' - commutative lawlege de compozitie - law of compositionlege distributiv' - distributive lawlegea ter+ului exclus - law of the excluded middlelem' - lemmalimit' - limit

limit'inferioar' - lower limitlimite de integrare - limits of integrationlinie de frac+ie - bar, vinculumliniar - linear liniaritate - linearitylinie dreapt' - straight-linelinie frnt' - brocken linelinie punctat' - dotted line




11/112

linie tangent' - tangent lineloc geometric al punctelor - geometric locuslocal - locallogaritm - logarithmlogaritm zecimal - common logslogaritm natural - natural logarithmlungime - lengthlungimea arcului - arc-length

Mm'rime - magnitudem'sur' - measure

m'surabil - measurablematematic' - mathematicsmatrice - matrixmatrice de transformare - matrix of the transformationmatrice diagonal' - diagonal matrixmatrice invers' - reciprocal matrixmatrice nul' - null-matrixmaxim - maximummaximum - maximummedian' - median {of a triangle}medie aritmetic' - mean, arithmetic meanmedie geometric' - geometric average, geometric mean,

mean proportionalmetoda elimin'rii - elimination methodmetoda induc+iei complete - principle of complete inductionmetru - meter minim - minimimminimum - minimummodul - module

monom - monommonoton - monotonousmuchie - edgemul+ime - setmul+ime de solu+ii - solution setmul+ime de valori - rangemul+ime universal' - universal setmul+ime vid' - empty set, null-set




12/112

multiplicare - multiplicatonmultiplicator - factor, multiplier multiplu - multiple, multiplexmultiplu comun - common multiplemutual - mutuallymutual disjuncte - mutually disjoint

Nnecunoscut' - unknownnedefinit - undefinednedegenerat - non-degneratenedescresc'tor - non-decreasing

nedeterminare - indeterminancy, uncertaintynedeterminat - indefinite, undeterminednegativ - negativeneglijabil - negligibleneliniar - non-linear nem'rginit - unboundedneomogen - inhomogeneousneperiodic - non-periodicnesimetric - non-symmetricnod - nodenormal' - normalnormal'la suprafa+' - normal to the surfacenum'r - number num'r complex - complex number num'r ntreg - integer number num'r ira+ional - irrational number num'r natural - natural number num'r par - even number num'r prim - prime number

num'r ra+ional - rational number num'r real - real number num'r transcendent - transcendental number num'r zecimal - decimal number num'r ordinal - ordinal number num'r'tor - numerator num'r'tor al frac+iei - term of a fractionnumere ntregi consecutive - consecutive integers




13/112

numere reciproc prime - coprime numbers, relatively prime numbersnumitor - denominator numitor comun - common denominator numitori diferi+i - unlike denominatorsnumitori identici - like denominators, same denominators

Ooblic - obliqueoctagon - octagonomogen - homogeneousordin - degree, exponentordin al derivatei - order of derivative

ordin al ecua+iei - order of equationordine - order ordonat' - ordinateorigine de coordonate - origin {of coordinates}orizontal - horizontaloval - oval

Ppar - evenparabol' - parabolaparabolic - parabolicparalel - parallelparalelepiped - parallelepipedparalelogram - parallelogramparametru - parameterparanteze figurate - braces

paranteze patrate - square brackets, bracketsparanteze rotunde - parenthesespatrat - quadrate, squarepatrulater - tetragonp'tratic - quadraticpentagon - pentagonperimertu - perimeterperioad' - period




14/112

perpendicular' - normal, perpendicularpicior al perpendicularei - foot {of a perpendicular}piramid' - pyramidplan - planeplan tangent - tangent planeplanxOy - xy-planeplanimetrie - plane geometry, planimetryplus - plus signpoliedru - polyhedronpoligoane asemenea - similar polygonspoligoane congruente - congruent polygonspoligon - polygonpoligon convex - convex polygonpoligon nscris - inscribed polygonpoligon regulat - equilateral polygon, regular polygon

polinom - polynomialposibilitate - possibilitypozitiv - positiveprecedent - precedingprecizie - accuracypreimagine - pre-imagepresupunere - assumptionprim'derivat' - first derivativeprincipal - principal

principiul dualitatii - duality principleprizm' - prismprocent - per centprodus - productprodus scalar - dot productprodus vectorial - cross-product, vector productprogresie - progressionprogresie aritmetic' - arithmetic progressionprogresie geometric' - geometric progressionproiec+ie - projectionpropor+ie - proportionpropozi+ie - proposition, statementproprietate - propertyproprietate asociativ' - associative propertypunct - dot, pointpunct de discontinuitate - point of discontinuitypunct de extrem - extremum point




15/112

punct de inflexiune - point of inflexionpunct diametral opus - diametrically opposite pointpunct focal - focal pointpunct izolat - acnodeputere - degree, grade, power

Rradian - radianradical - radical, radical signramur' - branchrang al unei matrici - rank of a matrixraport - ratio, relation

ra+ie a unei progresii aritmetice - common differencera+ie a unei progresii geometrice - common ratiora+ional - rationalraz' - radiusraz'vectoare - radius vector r'd'cin' - rootr'd'cin'dubl' - double rootr'd'cin'multipl' - repeated rootr'd'cin'patrat' - square rootr'd'cin'simpl' - simple rootr'd'cini conjugate - conjugate rootsreal - realreciproc - vice versareduce - to reducereducere termenilor asemenea - combine similar termsreductibil - reducibleregul' - ruleregula paralelogramului - parallelogram law, parallelogram rulerela+ie - relation

relativ - relativerepetat - multiplexreprezenta - to representrest - remainder, restrestric+ie - restrictionreuniune - unionrezolva - to solveridica la patrat - to square




16/112

ridica la putere - to raise to a power romb - lozenge, rhombus, rhombrota+ie - rotationrotunji - to round

Ssalt - jumpsatisface - to satisfyscalar - scalar sc'dere - subtractionsc'z'tor - subtrahendschem'bloc - flow chart

schema lui Horner - Horner's scheme, synthetic divisionschimb de variabil' - change of variablesecant' - secantsec+iune - cutsec+iune conic' - conic, conic sectionsec+iune conic'central' - central conicsec+iune conic'degenerat' - degenerate conicsec+iune conic'nedegenerat' - non-degenerate conic,

non-degenerate conic sectionsector circular - sector of a circlesegment - closed interval, intercept, segmentsegment de pe axax - x-interceptsegment liniar - line segment, straight-line segmentsegmente congruente - congruent segmentssemicerc - semi-circlesemidreapt' - raysemisfer' - hemispheresemn - signsemnul adun'rii - addition sign, plus sign

semnul r'd'cinii - radical, radical signsemnul sc'derii - minus {sign}sfer' - spheresimbol - symbolsimetric - symmetricsimetrie central' - central symmetrysimplifica - to cancelsimplificare - simplification




17/112

simplu - simplesinusoid' - sine curvesistem - systemsistem cartezian de coordonate - Cartesian coordinate systemsistem cu mai multe necunoscute - many-variable systemsistem de coordonate - coordinate systemsistem de ecua+ii liniare - system of linear equationsistem neortogonal de coordonate - non-orthogonal coordinate systemsistem omogen - homogeneous systemsistem ortogonal de coordonate - orthogonal coordnate systemsistem rectangular de coordonate - rectangular coordonate systemsolu+ie admisibil' - permissible solution, admissible solutionsolu+ie aproximativ' - approximate solutionsolu+ie complet' - complete solutionsolu+ie exact' - exact solution

solu+ie general' - general solutionsolu+ie nenul' - non-zero solutionsolu+ie netrivial' - non-trivial solutionsolu+ie nul' - zero solutionsolu+ie periodic' - periodic solutionsolu+ie unic' - unique solutionsolu+iona - to solvesolu+ionare {a unei probleme} - solution {of a problem}spa+iu - space

spa+iu euclidian - Euclidean spacestrict - strictstrict monoton - strongly monotonicsubstitui - to replacesubstitu+ie - substitutionsubstitu+ie invers' - back-substitutionsuma - to addsum' - sumsuprafa+' - surfacesuprafa+'de rota+ie - surface of revolutionsubmul+ime - subset

Ttangent' - tangentteorema lui Pythagoras - Pythagorean theorem




18/112

teorem' - theoremteorema fundamental'a aritmeticii - fundamental theorem of arithmeticteorema lui Bezout - factor theoremteorema lui Thales - intercept theoremteorema sinusurilor - law of sines, sine ruleteoria mul+imilor - set theoryteorie - theorytermen - termtermen al sumei - addend, summandtermen general - general termtermeni asemenea - similar termstetraedru - tetrahedrontot - wholetransforma - to transformtransformare de coordonate - transform of coordinates

translare - translationtransla+ie - bridgingtranzitivitate - transitivitytrapez - trapezoid, trapeziumtrigonometric - trigonometrictrigonometrie - trigonometrytrisec+ia unui unghi - trisection of the angletriunghi - triangletriunghi ascutunghic - acute triangle

triunghi asemenea - similar triangletriunghi dreptunghic - right triangletriunghi echilateral - equilateral triangletriunghi isoscel - isosceles triangletriunghi obtuzunghic - obtuse triangletriunghi scalen - scalene triangletriunghiular - triangular

U

unghi - angleunghi adiacent - adjacent angleunghi al'turat - adjacent angleunghi ascu+it - acute angle

unghi complementar {pn'la 90o} - complementary angle

- explementary angle




19/112

unghi complementar pn'la 360o

unghi de nclinare - slope angleunghi diedru - dihedral angleunghi drept - right angleunghi exterior {al triunghiului} - exteriar angle {of a triangle}

unghi interior - interior angleunghi nscris - inscribed angleunghi ntins - straight angleunghi la baz'a triunghiului - base angle {of a triangle}unghi la centru - central angleunghi obtuz - obtuse angleunghi plin - straight ahgle

unghi suplimentar pn'la 360o - conjugate angle

unghiuri adiacente suplimentare - adjacent supplementary anglesunghiuri alterne - alternate anglesunghiuri alterne externe - alternate exterior angles

unghiuri alterne interne- alternate interior angles, opposite interiorangles

unghiuri congruente - congruent anglesunghiuri corespondente - corresponding anglesunghiuri opuse la vrf - vertex angles

unghiuri suplimentare {pn'la 180o} - supplementary angles

unic - singleunicitate - uniqueness

unitate - unitunivoc - unambiguous

Vvalabil - validvalid - validvaloare - valuevaloare absolut' - absolute valuevaloare absolut'a num'rului complex - absolute value of a complex numbervaloare ini+ial' - initial valuevaloare medie - average, average valuevaloare limit' - limit valuevariabil' - variablevariabil'independent' - independent variable




20/112



|Pagini din istorie| Examene, teste| Bibliografie| Link-uri| Site map| Cartea Vizitatorilor|

vrf - vertexvector - vector vector coplanar - coplanar vector vector de baz' - base vectorvector normal - normal vector vector nul - null-vector vector unitar - unit vector vector tangent unitar - unit tangent vector veridicitate - truthverifica - to verifyvertical - verticalvitez' - speed, velocityvolum - volume

Zzecimal - decimalzero - zero

Bibliografie




21/112




Dictionar Englez-Roman de Termeni Matematici

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Aabscissa - abscis'absolute - absolutabsolute extremum - extremum absolutabsolute value - valoare absolut'absolute value of a complex number - valoare absolut'a num'rului complexaccuracy - precizie, exactitate, acurate+eacnode - punct izolatacute angle - unghi ascu+itacute triangle - triunghi ascu+itunghic

add - a aduna, a sumaaddend - termen al sumeiaddition - adunareaddition sign - semnul adun'riiadjacent angle - unghi adiacent, unghi al'turatadjacent side - latur 'adiacent'adjacent supplementary angles - unghiuri adiacente suplimentareadjoint - conjugatadmissible - admisibiladmissible solution - solu+ie admisibil'

affine coordinates - coordonate afinealgebra - algebr 'algebraic equation - ecua+ie algebric'algebraic expression - expresie algebric'algorithm - algoritmalgorithm for division - algoritm de divizarealternance - alternan+'alteration - alternare

Page 1 of 22Dictionar Englez-Roman

2/17/05http://math.ournet.md/formule/dic/engl.html
http://math.ournet.md/formule/dic/engl.htmlhttp://math.ournet.md/formule/dic/engl.html


22/112

alternate angles - unghiuri alternealternate exterior angles - unghiuri alterne externealternate interior angles - unghiuri alterne internealtitude of a triangle - n'l+ime a triunghiuluiamplitude - amplitudineanalogous - analogicanalogical - analogicanalogy - analogieanalysis - analiz'analyze - a analizaangle - unghianticosine - arccosinusantisine - arcsinusapplicate - aplicat'approximate solution - solu+ie aproximativ'

arbitrary - arbitrar arc - arcarccosine - arccosinusarc-length - lungimea arculuiarcsine - arcsinusarctangent - arctangent'area - arieargument - argumentargument of a function - argument al func+iei

arithmetic mean - medie aritmetic'arithmetic progression - progresie aritmetic'associative law - lege asociativ'associative property - proprietate asociativ'assumption - presupunereasymmetric(al) - asimetricasymmetry - asimetrieasymptote - asimptot'asymptotes of a hyperbola - asimptote ale hiperboleiaverage - valoare medieaverage value - valoare medieaxiom - axiom'axis - ax'

B




23/112

back-substitution - substitu+ie invers'bar - linie de frac+iebase - baz'base angle {of a triangle} - unghi la baz'a triunghiuluibase vector - vector de baz'basis - baz'billion - bilionbinary - binarbinomial - binombinomial coefficient - coeficient binomialbinomial expansion - descompunere binomial'binomial formula - formula binomuluibiquadratic equation - ecua+ie bipatrat'bisector - bisectoarebisectrix - bisectoare

bounded interval - interval m'rginitbraces - paranteze figuratebrackets - paranteze patratebranch - ramur'bridging - transla+iebrocken line - linie frnt'

Ccalculus - analiz'matematic', calculcancel - a simplificacanonical - canonicCartesian coordinate system - sistem cartezian de coordonateCartesian coordinates - coordonate cartezienecentral angle - unghi la centrucentral conic - sec+iune conic'central'central symmetry - simetrie central'

centre - centrucentre of the escribed circle - centru unei circumferin+e exnscrisecenter - centruchange of variable - schimb de variabil'chord - coard'circle - cerccircumcenter - centrul circumferin+ei circumscrisecircumscribed figure - figur 'circumscris'




24/112

closed - nchisclosed interval - interval nchis, segmentcoefficient - coeficientcoincident - coincidentcollinearity - coliniaritatecombination - combina+iecombine similar terms - reducere a termenilor asemeneacommon denominator - numitor comuncommon difference - ra+ie a unei progresii aritmeticecommon divisor - divizor comuncommon factor - divizor comuncommon fraction - frac+ie ordinar'common logs - logaritm zecimalcommon multiple - multiplu comuncommon ratio - ra+ie a unei progresii geometrice

commutative law - lege comutativ'comparation - compara+ie, comparare

complementary angle - unghi complementar {pn'la 90o}complete induction - induc+ie complet'complete solution - solu+ie complet'complex number - num'r complexcomputable - calculabilcomputation - calculconcave - concav'

concave curve - curb'concav'concave function - func+ie concav'concentric circles - cercuri concentricecondition - condi+iecone - concongruence - congruen+'congruent angles - unghiuri congruentecongruent figures - figuri congruentecongruent polygons - poligoane congruente

congruent segments - segmente congruenteconic - sec+iune conic'conic section - sec+iune conic'conjugate - conjugat

conjugate angle - unghi suplimentar pn'la 360o

conjugate roots - r 'd'cini conjugateconsecutive integers - numere ntregi consecutiveconstant - constant'




25/112

continuity - continuitatecontinuous function - func+ie continu'convex - convexconvex curve - curb'convex'convex polygon - poligon convexconvexity - convexitatecoordinate - coordonat'coordinate axis - ax'de coordonatecoordinate system - sistem de coordonatecoplanar - coplanar coplanar vector - vector coplanar coprime numbers - numere reciproc primecorollary - consecin+', corolarcorresponding angles - unghiuri corespondentecount - a calcula

criterion - criteriucriterion for divisibility - criteriu de divizibilitatecross-product - produs vectorialcube - cubcubic - curb'cubic'cubic curve - curb'cubic'curve - curb'cut - sec+iunecylinder - cilindru

Ddata - datedecimal - zecimaldecimal fraction - frac+ie zecimal'decimal number - num'r zecimaldecision - decizie

decomposition - descompuneredecomposition of a fraction - descompunere a unei frac+iidecrease - a descre)tedecreasing function - func+ie descrescatoarededuction - deduc+iedefine - a definidefinition - defini+iedegenerate - degenerat




26/112

degenerate conic - sec+iune conic'degenerat'degree - putere, ordin, grad, exponentdegree of a polinomial - grad al polinomuluidenominator - numitor dependent - dependentderivative - derivat'derivative at a point - derivat'n punctdeterminant - determinantdetermine - a determinadeviation - devia+ie, devierediagonal - diagonal'diagonal element - element diagonaldiagonal matrix - matrice diagonal'diameter - diametrudiametrically opposite point - punct diametral opus

difference - diferen+'differentiability - derivabilitate, diferen+iabilitatedifferentiable function - func+ie diferen+iabil'differential of area - element de ariedigit - cifr 'dihedral angle - unghi diedrudilatation - delataredimension - dimensiunedirection - direc+ie

direction cosine - cosinus director directly proportional - direct propor +ionaldiscontinuous - discontinuudiscontinuous function - func+ie discontinu'discriminant - discriminantdisposition - amplasaredistance - distan+'distinct - distinctdistributive law - lege distributiv'dividend - demp'r+itdivisable {by} - divizibil {prin}division - divizaredivision algorithm - algoritm de divizaredivisor - divizor domain - domeniudomain of definition - domeniu de defini+iedot - punct




27/112

dot product - produs scalar dotted line - linie punctat'double root - r 'd'cin'dubl'dual - dualduality principle - principiul dualit'+ii

Eedge - muchieelement - elementelement of area - element de arieelimination - eliminareelimination by substitution - eliminare prin substitu+ie

elimination method - metoda elimin'riiellipse - elips'empty set - mul+ime vid'equation - ecua+ieequation of a straight line - ecua+ie a liniei drepteequilateral - echilateralequilateral polygon - poligon regulatequilateral triangle - triunghi echilateralequivalent - echivalentequivalent figure - figur 'congruent'error - eroareescribed - circumscris, exnscrisessential - esen+ialestimation - estima+ieEuclidean algorithm - algoritmul lui EuclidEuclidean geometry - geometrie euclidian'Euclidean space - spa+iu euclidianevaluation - evaluareevaluation of determinant - calculul determinantului

even - par even function - func+ie par'even number - num'r pareverywhere defined - definit peste totexact - exactexact division - mp'r+ire f'r'restexact solution - solu+ie exact'example - exemplu




28/112

excentre - centru al unei circumferin+e exnscriseexclusion - excep+ieexistential quantifier - cuantor existen+ialexpansion - descompunere, dezvoltareexpansion of a determinant - dezvoltare a determinantului

explementary angle - unghi complementar pn'la 360o

exponent - exponent, ordinexponential - exponen+ialexponential equation - ecua+ie exponen+ial'expression - expresieexterior angle {of a triangle} - unghi exterior {al triunghiului}extremal - extremalextremum point - punct de extremum

Ffactor - factor, multiplicator factor theorem - teorema lui Bezoutfactoring - descompunere n factorifactorization - descompunere n factorifamily - familiefield - cmpfirst derivative - prim

'derivat

'first-order equation - ecua+ie de ordinul ntiflow chart - schem'blocflux - fluxfocal point - punct focalfocus - focar foot {of a perpendicular} - picior al perpendiculareiformula - formul'fraction - frac+iefunction - func+ie

function of a complex variable - func+ie de variabil'complex'function of a single variable - func+ie de o variabil'function of several variables - func+ie de mai multe variabilefundamental - fundamentalfundamental theorem of arithmetic - teorem'fundamental'a aritmeticii




29/112

Ggeneral - generalgeneral form - form'general'

general solution - solu+ie general'general term - termen generalgeometric average - medie geometric'geometric locus - loc geometric al punctelor geometric mean - medie geometric'geometric progression - progresie geometric'geometry - geometriegrade - grad, exponent, puteregreatest common divisor - cel mai mare divizor comun

greatest common factor - cel mai mare divizor comun

Hhalf-angle formulas - formule ale jum't'+ii unui unghihalve - a mp'r+i n dou'{n jum'tate}height - n'l+imehemisphere - semisfer '

hexagon - hexagonhexaeder - hexaedruhexahedron - hexaedruhill climbing - determinarea extremuluihomogeneous - omogenhomogeneous equation - ecua+ie omogen'homogeneous system - sistem omogenhorizontal - orizontalhorizontal axis - ax'orizontal'Horner's scheme - schema lui Horner hyperbola - hiperbol'hyperbolic - hiperbolichypotenuse - ipotenuz'hypothesis - ipotez'

I




30/112

identity - identitateif and only if - dac')i numai dac'image - imagine

implication - implica+ieimproper fraction - frac+ie supraunitar'incenter - centrul circumferin+ei nscriseincircle - circumferin+'nscris'include - a includeinclusion - incluziuneinconsistent - incompatibilincorrect - incorectincrease - a cre)te

increment - cre)tereindefinite - nedeterminatindependent - independentindependent variable - variabil'independent'indeterminancy - nedeterminareinduction - induc+ieinequality - inecua+ieinfinite - infinitinfinite decimal fraction - frac+ie zecimal'infinit'

inflexion - inflexiuneinhomogeneous - neomogeninitial - ini+ialinitial condition - condi+ie ini+ial'initial value - valoare ini+ial'inscribe - a nscrieinscribed angle - unghi nscrisinscribed circle - circumferin+'nscris'inscribed polygon - poligon nscrisinteger number - num'r ntreg

integral - integral'integral curve - curb'integral'integrand - expresie de sub integral'integration by parts - integrare prin p'r+iintegration constant - constant'de integrareinter-stage function - func+ie n scar'intercept - segmentintercept theorem - teorema lui Thales




31/112

interdependency - interdependen+'interior angle - unghi interior intersection - intersec+ieinterval - intervalinverse - inversinversely proportional - invers propor +ionalirrational number - num'r ira+ionalirreductibility - ireductibilitateisosceles triangle - triunghi isoscel

Jjump - salt

jump function - func+ie n scar'

Kkilogram(me) - kilogramkilometre - kilometruknown - cunoscut

Llaw - legelaw of composition - lege de compozi+ielaw of sines - teorema sinusurilor law of the excluded middle - legea ter +ului exclusleast common denominator - cel mai mic numitor comunleast common multiple - cel mai mic multiplu comun

leg - fa+'lateral'Leibniz rule - formula lui Leibnizlemma - lem'length - lungimelike denominators - numitori identicilike signs - acelea)i semnelimit - limit'limit value - valoare limit'




32/112

limits of integration - limite de integrareline - dreapt'line segment - segment liniar linear - liniar linear equation - ecua+ie de gradul nti (liniar')linear function - func+ie liniar'linear independency - independen+'liniar'linearity - liniaritatelocal - locallogarithm - logaritmlower limit - limit'inferioar'lowest common denominator - cel mai mic numitor comunlowest common multiple - cel mai mic multiplu comunlozenge - romb

Mmagnitude - m'rimemain diagonal - diagonal'principal'major axis - ax'principal'many-variable system - sistem cu mai multe necunoscutemap - imagine, aplica+iemapping - imagine, aplica+iemeter - metrumathematical induction - induc+ie matematic'mathematics - matematic'matrix - matricematrix of the transformation - matrice de transformaremaximum - maximum, maximmean - medie aritmetic'mean proportional - medie geometric'measurable - m'surabil

measure - m'sur'median {of a triangle} - median'member {of a set} - element {al mul+imii}minimum - minimum, minimminuend - desc'zutminus {sign} - semnul sc'deriimodule - modulmonom - monom




33/112

monotone decreasing function - func+ie monoton descresc'toaremonotone increasing function - func+ie monoton cresc'toaremonotonic function - func+ie monoton'monotonous - monotonmultiple - multiplumultiplex - multiplu, repetatmultiplicand - denmul+itmultiplication - nmul+ire, multiplicaremultiplier - nmul+itor, multiplicatormultiply - a nmul+imutually - mutualmutually disjoint - mutual disjuncte

N

natural logarithm - logaritm naturalnatural number - num'r naturalnecessary and sufficient condition - condi+ie necesar')i suficient'negative - negativnegligible - neglijabilnode - nodnon-decreasing - nedescresc'tornon-degnerate - nedegeneratnon-degenerate conic - sec+iune conic'nedegenerat'non-degenerate conic section - sec+iune conic'nedegenerat'non-linear - neliniar non-linear equation - ecua+ie neliniar'non-orthogonal coordinate system - sistem neortogonal de coordonatenon-periodic - neperiodicnon-symmetric - nesimetricnon-terminating decimal - frac+ie zecimal'infinit'non-trivial solution - solu+ie netrivial'

non-zero solution - solu+ie nenul'normal - normal', perpendicular'normal to the surface - normal'la suprafa+'normal vector - vector normalnull-vector - vector nulnull-matrix - matrice nul'null-set - mul+ime vid'number - num'r




34/112

number line - dreapt'numeric'numerator - num'r'tor

Ooblique - oblicobtuse angle - unghi obtuzobtuse triangle - triunghi obtuzunghicoctagon - octagonodd - impar odd-function - func+ie impar'one-to-one - biunivocopen interval - interval deschis

opposite interior angles - unghiuri alterne interioareorder - ordineorder of derivative - ordin al derivateiorder of equation - ordinul ecua+ieiordered pair - cuplu ordonatordinal number - num'r ordinalordinate - ordonat'origin {of coordinates} - origine de coordonateorthogonal base - baz'ortogonal'orthogonal coordnate system - sistem ortogonal de coordonateorthonormal basis - baz'ortonormat'oval - oval

Ppair - cupluparabola - parabol'

parabolic - parabolicparallel - paralelparallelepiped - paralelepipedparallelogram - paralelogramparallelogram law - regula paralelogramuluiparallelogram rule - regula paralelogramuluiparameter - parametruparametric form - form'parametric'




35/112

parentheses - paranteze rotundepartial fraction - frac+ie elementar'partial-fraction expansion - descompunere n frac+ii elementarepencil - fasciculpencil of lines - fascicul de dreptepentagon - pentagonper cent - procentperimeter - perimertuperiod - perioad'periodic decimal fraction - frac+ie zecimal'periodic'periodic function - func+ie periodic'periodic solution - solu+ie periodic'permissible solution - solu+ie admisibil'perpendicular - perpendicular'pivot - ax'de rota+ie, centru de rota+ie

plane - planplane geometry - planimetrieplanimetry - planimetrieplus sign - semnul adun'rii, pluspoint - punctpoint of discontinuity - punct de discontinuitatepoint of inflexion - punct de inflexiunepolygon - poligonpolyhedron - poliedru

polynomial - polinompositive - pozitivpossibility - posibilitatepower - putere, exponentpre-image - preimaginepreceding - precedentprime factorization - descompunere n factori primiprime number - num'r primpimitive - func+ie primitiv'principal - principalprincipal axis - ax'principal'principal diagonal - diagonal'principal'principle of complete induction - metoda induc+iei completeprism - prizm'product - produsprogression - progresieprojection - proiec+ie




36/112

proof - demonstra+ieproper factor - divizor propriuproper fraction - frac+ie subunitar'property - proprietateproportion - propor+ieproposition - propozi+ieprove - a demonstrapyramid - piramid'Pythagorean theorem - teorema lui Pythagoras

Qquadrate - patrat

quadratic - p'traticquadratic equation - ecua+ie de gradul al doilea (patrat')quadratic formula - formula r 'd'cinilor ecua+iei de gradul al doilea

(ecua+iei patrate)quantifier - cuantor quotient - ct

Rradian - radianradical - radical, semnul r 'd'ciniiradical sign - radical, semnul r 'd'ciniiradius - raz'radius vector - raz'vectoareraise to a power - a ridica la putererange - mul+ime de valori, domeniurank of a matrix - rang al unei matrici

ratio - ct, raportrational - ra+ionalrational function - func+ie ra+ional'rational number - num'r ra+ionalray - semidreapt'real - realreal number - num'r realreciprocal matrix - matrice invers'




37/112

rectangle - dreptunghirectangular coordonate system - sistem rectangular de coordonatereduce - a reducereducible - reductibilregular polygon - poligon regulatrelation - rela+ie, raportrelative - relativrelatively prime numbers - numere reciproc primeremainder - restrepeated root - r 'd'cin'multipl'replace - a substitui, a nlocuirepresent - a reprezentarest - restrestriction - restric+ierhomb - romb

rhombus - rombright angle - unghi dreptright triangle - triunghi dreptunghicroot - r 'd'cin'rotation - rota+ieround - a rotunjirounding error - eroare de rotunjirerule - regul'

Ssame denominators - numitori identicisatisfy - a satisfacescalar - scalar scalene triangle - triunghi scalensecant - secant'sector of a circle - sector circular

segment - segmentsemi-circle - semicercsemiclosed interval - interval seminchisset - mul+imeset theory - teoria mul+imilorside {of an angle} - latur '{a unui unghi}sign - semnsignum function - func+ia signum




38/112

similar fractions - frac+ii cu numitori egalisimilar polygons - poligoane asemeneasimilar terms - termeni asemeneasimilar triangle - triunghi asemeneasimilarity - asem'naresimilitude - asem'naresimple - simplusimple root - r 'd'cin'simpl'simplification - simplificaresine curve - sinusoid'sine rule - teorema sinusurilor single - unicsingle root - r 'd'cin'simpl'skew lines - drepte neconcurenteslope - nclinare, coeficient unghiular

slope angle - unghi de nclinareslope formula - formula coeficientului unghiular slope-intercept form of a straight lineequation

- ecua+ie a unei drepte cu coeficientunghiular

solution {of a problem} - solu+ie {a unei probleme}solution set - mul+ime de solu+iisolve - a solu+iona, a rezolvaspace - spa+iuspeed - vitez'

sphere - sfer 'square - patrat, a ridica la patratsquare brackets - paranteze patratesquare root - r 'd'cin'patrat'standard form - form'standard'statement - propozi+ie, afirma+iestep function - func+ie n scar'straight - dreptstraight angle - unghi ntins, unghi plinstraight-line - linie dreapt'

straight-line segment - segment liniar stretching - delatarestrict - strictstrongly monotonic - strict monotonsubset - submul+imesubstitution - substitu+iesubtraction - sc'deresubtrahend - sc'z'tor




39/112

sum - sum'summand - termen al sumei

supplementary angles - unghiuri suplimentare {pn'la 180o}surface - suprafat'surface area - arie a suprafe+ei

surface element - element de arie {al suprafe+ei}surface of revolution - suprafa+'de rota+iesymbol - simbolsymmetric - simetricsymmetric function - func+ie simetric', func+ie par'synthetic division - schema lui Horner system - sistemsystem of linear equations - sistem de ecua+ii liniare

Ttangent - tangent'tangent line - linie tangent'tangent plane - plan tangentterm - termenterm of a fraction - num'r'tor al frac+ieiterminating decimal fraction - frac+ie zecimal'finit'

tetragon - patrulater tetrahedron - tetraedrutheorem - teorem'theory - teorietranscendental number - num'r transcendenttransform - a transformatransform of coordinates - transformare de coordonatetransitivity - tranzitivitatetranslation - translaretrapezium - trapez

trapezoid - trapeztriangle - triunghitriangular - triunghiular trigonometric - trigonometrictrigonometric function - func+ie trigonometric'trigonometry - trigonometrietrisection of the angle - trisec+ie a unui unghitruth - veridicitate




40/112

Uunambiguous - univoc

unbounded - nem'rginituncertainty - incertitudine, nedeterminareundefined - nedefinitundetermined - nedeterminatunequal - inegal, diferitunion - reuniuneunique solution - solu+ie unic'uniqueness - unicitateunit - unitate

unit circle - circumferin+'unitar'unit tangent vector - vector tangent unitar unit vector - vector unitar universal quantifier - cuantor universaluniversal set - mul+ime universal'unknown - necunoscut'unlike denominators - numitori diferi+iunsymmetric - asimetric

Vvalid - valid, valabilvalue - valoarevanish - a se anula, a disp'reavariable - variabil'vector - vector vector product - produs vectorialvelocity - vitez'verify - a verificavertex - vrf vertex angles - unghiuri opuse la vrf vertical - verticalvertical axis - ax'vertical'vice versa - invers, reciprocvinculum - linie de frac+ie




42/112




43/112




Dictionar Matematic Roman-Englez de Fraze Uzuale

A BCDEFGH IJK LMNOPQ RS#T&UVW X Y Z

Aabia The superscripts are hardly(or scarcely) visible.abordare Amore careful approachis needed.

absolut analog In complete analogywith the result, we may provethat ...

accentua atenie

se accentuiaz!atenie asupra In this section, emphasis is placed(or attention isfocussed) onautonomous systems.

accepta o ipotez! to accept a hypothesis

aceia$i The numbers +8 and +3 have likesigns.No two polynomials can have all their roots alike(orthe same) unless they differ by a numerical factor.

acela$i The preceding discussion may be summed up bysaying that the arithmetic for complex numbers ismuch the sameas that for real numbers.

acum We nowwant to letj.For the presentwe content ourselves withdemonstrating the assertions just made concerning thesets GandH.

ar!ta acum este u$or de ar!tat c! We can now easily show that...

adecvat The model fitsthe process under study adequately.

adeveri

se adevere$te c! Thus the martingale (t) turns out tobe a processwith independent increments.

s-a adeverit a fi This proved to bea bigger problem than originallyanticipated.

Page 1 of 70Fraze uzuale

2/17/05http://math.ournet.md/formule/fraze/fraze.html
http://math.ournet.md/formule/fraze/fraze.htmlhttp://math.ournet.md/formule/fraze/fraze.html


44/112

This value was found to becos(/17).

admite

la fel admite The function (t) also admitsdecomposition of theform (4).

adresa

ne adres!m la We now turn tothe task of considering thecontinuous-parameter supermarlingales.

aduce

demonstraia este adus! The proofof the theorem is givenin [8].

aduna

adun!m Now write down these inequalities for n, n+1, ..., n+mand addthem to obtain the estimation (6).

afirma

afirm! The fundamental theorem of arithmetic assertsthat

every integer greater than 1 can be factored in one andonly one way, apart from order, as the product ofpositive prime numbers.Bohm [2] claimsthat there is such a thing as theprimacy of metaphysics in connection with biology.

afirmaie

afirmaie mai general! A more general statementcan be found in [15]. afirmaie necesar! Approaching the limit asNwe obtain the

required assertion. afirmaie reciproc! The converse of(5) is false.

The converse ofthis statementis known to be false.However, if we are concerned only with versions of agiven process, the converseholds in the followingsense.

afla

a afla We are now in a position to determine(or to find)the value ofx*.

ajunge

ajungem la ... Thus we arrive atthe following conclusion[definition, equation, theorem, assertion, result].

ajutor

cu ajutorul By means ofthe equivalence relation we get thedecomposition of the set of all oriented segments intodisjoint classes such that segments in the same classare equivalent and segments in different classes arenot equivalent.When formalizing the notions of probability theory,the first fundamental assumption is that the results ofexperiments can be described by means ofa certain




45/112

set .The data were obtained with the help(or with theaid) ofa digitizer.Both problems are solved byconstructing a right-handinverse matrix S

r-1of S.

alt Anotherway to approach the problem is to take aTaylor series expansion ofg(t). alt! Any term may be transposed from one member of

equation to the other, provided its sign is changed.The random variable may have a differentdistribution.

altfel This definition also makes use of the abstractionprinciple, but in another way.

altfel zis Otherwise speaking [fn(x)] = [gn(x)] if and only if

{fn(x)}~{g

n(x)}.

am!nunit

mai am!nunit These operations are discussed in more detailin nextsection.

ambele Bothestimates are quite rough.But the functionsfandgare bothcontinuous, andthus the two functions coincide.Multiplying the twosides of (4) by cosmxandintegrating, we obtain ...

ambele p!ri The two sidesof Young's inequality

are equal if and only

if b=(a).

ambiguu This ambiguitydoes not lead to misunderstanding.

aminti

amintim c! We recall thatthe compensator nof the measure ofjumps nis non-negative.

Recall thatLis generated by all processes whosetrajectories are right-continuous and have right limits.

analiza

pentru a analiza To analysethe equation, it is convenient to go over tonon-dimensional variables.

este analizat! To analysethe equation, it is convenient to go over tonon-dimensional variables.The sum Sis analysedanalogously.

analogic The proof of (11) is completely analogousto that of(10).




46/112

analogic cu ... We shall introduce distributions in a way analogousto thatused in the Cantor theory when generalizingrational to real numbers.

analogie The analogueof the Fermat's theorem is also valid.

anume In this particular case only one side of the triangle,namelyBC, has traces within the limits of thedrawing.If Sconsists of a single elementx, thenR(x), namelythe smallest subring containingx, is commutative.The extended solutions have the property II, namelyof uniform continuity.

aparatul matematic mathematical apparatus(or tools/ techniques)a body of mathematics

aparine

aparine la The processX(t) falls intoone of the following threeclasses depending on its asymptotic behaviour.This equation falls amongthe so-called renewalequations.

care nu aparine This equation contradicts the assumption that Gcontains points not belonging toD.

ap!rea

apare The problem arisesof finding the conditions underwhich the distributionp(u) is unimodal.

aplica

s!aplic!m Let us applythis result to the case of an increasing

processAt. pot fi aplicate Formulas (1) and (2) may be employedon condition

that the contour Chas no loops. se poate de aplicat Sincepis of the form 1+4m, Corollary 2.5 is

applicableand hencep=x2+y2.

aproape The temperature was observed to be nearzero. aproape de The angle is closed to45 deg. aproape peste tot The Lebesque-integrable functions are equal if and

only if they have the same values almost everywhere.

aproape toate Nearly allscientific problems deal with quantities andrelations among them. aproape toi It is easy to verify thatf(x)


47/112

to be t2.

aranja n ordine cresc!toare[descresc!toare] sunt aranjai n ordine cresc!-

toare[descresc!toare]The jump moments t1, t2, ..., tnare arranged in

ascending[descending] order.

ar!ta

arat! Fig.12 depictsthe slope of the line xversus t. vom ar!ta We shall showthat in this casepmust divide b. este ar!tat The slope of the line xversus tis shown

schematically in Fig.12. pentru a ar!ta c! To show that q and r are unique, suppose that q'

and r' is any pair of integers for which a=bq'+r', 0r'< b.

cum este ar!tat mai sus As has been shown above, the processX tis a

continuousL2-martingale.

arbitrar Let (t) be an arbitraryquasi-potential.Suppose this is true for an arbitraryn.

argument This is aconvincing reasonfor the study of stochasticequations of the form.This reasonsuggests that the solution to Eqn (17) isunique.

argumente There are doubtful pointsin the above reasoning.

aritmetic! Arithmeticis the elementary branch of mathematicsdealing with the properties of numbers and theiroperations.

asigura

asigur! Property 1oensuresthe feasibility of the addition.

The MIS furnishes(or supplies) data formanagement.

asociat

asociat!cu(referitoare la) The error is associated with(or is due to) theinaccuracy in computations.The study is concerned withlinear functionals of

supercritical processes.The first problem isdirectly related topartialdifferential equations.Further extension of the notion of a stochastic integralis connected withthe extension of the notion ofconvergence.

asociat laThe polynomialR(t) corresponding tothis functionby (6) is almost everywhere nonzero.The space, S2k-1, and the projective metric,L(r,s),




48/112

associated withit will play an important part in thefuture.It is convenient to replace kby a new factor relatedtokby the relation =4k.

astfelThusthe following theorem has been proved.The factors and kare related as follows: =4k.

astfel nct LetXbe a space such thatfrom every open cover wecan select a finite cover.We break up the component a into severalcomponents in such a way thatAandBnow belongto different components.We select a basis in the underlying space such that...Specifically, the parameter can be chosen so thatthedistribution is unimodal.The model is soconstructed asto allow furthermodification and improvement.

astfel ... ca We take a point on the line such that...

astfel ... nct We take a point on the line such that...Applying Lemma 20.3 ktimes, we infer that thereexists a periodic function G0(x) withG0

(k)=g(x).

a$a numitIn applications we often come across the so-calledHeaviside function.

a$a ... pentru care We take a point on the line such that...

a$adar Thus, the integral on the right-hand side of (5) can beanalytically continued to the whole domain.The last formula becomesp(la+mq)=b, so thatp|b.

Every element in Thas norm at least equal to 1, sothere must be one of them, , which is of leastpositive norm.Sincepis of the form 1+4m, Corollary 2.5 isapplicable and hencep=x2+y2.ThereforeP(x,s,t,A) saitsfies the Chapman-Kolmogorov equation.

Consequently,

ata$a la poate fi ata$at la The processX(t) may be placed(or put) intoone of

the following three classes depending on itsasymptotic behaviour.

atinge

atinge maximum[minimum]The function (x) reaches its maximum[minimum]atx*=3h/2.Let b1(s,w) coincide with thezfor which the




49/112

minimumof the function |B(s,w)z|, |z|=1, isattainedand let b2(s,w) coincide withzfor which the

above function attainsits maximum.

atinge scopul

de a atinge scopul In order to attain the purpose, we shall not availourselves of the methods of functional analysis.

este atins scopul This aim is attained(or objective is accomplished)by introducing non-dimensional variablesx' = x/x0

andy' = y/y0.

atinge

se atinge Evidently, if the inf in (1.5) is attainedat a certainpoint , then the inf

m(x,u

m) is also attained at that

point.

atrage atenia

s!atrag!atenia The reader should take notice ofthe fact that the scaleparameter adoes not enter into the expression for G(u).It is necessary to payspecial attention tothebehaviour ofF(x) at infinity.

se atrage atenia Recently much attention(or thought/consideration) has been givento the study of thediffusion processes.

atribui sens

pentru a atribui sens To attach a meaning tothe solution of this stochasticequation, we must define the measure moreaccurately.

se atribuie sens Analogous meaning is attached tothe notationD[0,).

atribui valoarea

atribuim valoarea We assign the value0 to this state. valori pot fi atribuite A variable is a quantity to which an unlimited number

of values can be assignedin an investigation.

automat It follows automaticallythat theseRm-semisimple

rings are stronglyRm

-semisimple.

auxiliar As a preliminary to the proof of the theorem, we shalldiscuss several auxiliaryassertions.

avantaj

avantaje To appreciate the merits(or the advantages) of thistheory, it suffices to observe that ...

avantaj principalThe main(or principal/ major) advantageof this




50/112

approach is that it enables the results of the previouschapter to be extended to the case underconsideration.

avea

avem Since a satisfies (1), we haveY1=Y2.

nu are For instance, the functionhas nota derivative at

the point 0.The prime numberppossess nofactors other than 1and p.

poate avea It follows that the solution can haveonly a finitenumber of zeros inD.

nu poate avea It follows that the solution cannot havemore than afinite number of zeros inD.

avea de-a face

avem de-a face In this section we dealonly withrational integers.

avea intenia

vom avea intenia In this section we are going tomodify our definitionof distribution so as to obtain a notion equivalent tothat of S. Sobolyev and L. Schwartz.

avea loc

aceast!nu poate avea loc This cannot be, for l/pis not a rational number. aceast!are loc n cazul This happens to be the case forthose equations in

which Sincreases.

avea maxim[minim] are maxim[minim] The function (x) has a maximum[minimum] at the

pointx*=3h/2.

avea neajunsul

au neajunsul These equations possess afundamental defect(ordemerit/ draw back/ disadvantage).

are neajunsul His hypothesis has limitationsof its own.

avea nevoie de

vom avea nevoie de In order to achieve this, we shall needsome material

from elementary number theory.avea o form!...

are o form!... Equation (3.2) is of thefollowing form...

avea o mare importan!

are o mare importan! In applications the following theorem is of greatimportance.

avea sens




51/112

dac!are sens

The symbol , if it is meaningful, always

represents a number. nu are sens If the common part is empty, the difference has no

sense.

avea soluie unic!

are soluie unic! Equation (7) has a unique solution.

avea un caracter

are un caracter Noise (t) isstochastic in character(or in nature).Noise (t) is of astochastic character(or nature).

avea valoarea

are valoarea The derivativeF'(x) has the value0 at the point 0.

Bbaza pe

se bazeaz!pe The proof is based onthe ideas of Kunita andWatanabe [36].The previous analysis proceeds fromthe assumptionthat the classM*contains the classM2,.

bineneles It is clear thatthe definitions and properties givenbelow can be extended to -algebras.

biunivocitate Hence from (6) and the remark concerning theone-to-one-nessof the correspondence, relation (8)yieldsF=0.

Cca de obicei As usual, we use continuous versions of (4).

ca $i n As inthe example discussed above, we can easilyprove the following proposition.

ca $i n cazul ...In the same manner as in the case ofconvergence toa Wiener process, one can easily deduce the followingresult.In the case of distributions, as in the case offunctions,




52/112

the following properties hold true.

ca urmare Such a solution does not exist in consequence(or onaccount) of (6) and Remark 4.

calcula As is easy to calculate... sunt calculate The coefficients of expansion (9) are evaluated(or

computed) from formulas (5). cum este u$or de calculat as is easy to calculateas is easy to evaluate

calcula integral!dea-lungulcurbei

to take the integral along a curve

calcula integral!pe domeniu to take the integral over a domain

care In classical analysis there have been considered severalsequences of functions whichare distributionallyconvergent to (x).Choose inD

2

any function thattends to infinity as

x0. c!rui A variable is a quantity to whichan unlimited number

of values can be assigned in an investigation. al c!rui LetAbe a strongly positive operator whosedomain of

definition does not depend on t. care este Consider the function (y), which isa periodical

distribution coinciding with (y) for |y| < 1/2.

caz

caz particular This formula can be considered as a particular caseof

formula (14). cazul considerat In the case under considerationthe process (t) is

continuous.Let us generalize equation (6) to the case underdiscussion.

c!uta

vom c!uta We shall seeka solution to (12) in the formz(t,u) =x(t)y(u).

sunt c!utate It is convenient, in solving problems, to use letters forthe numders which are sought.

c!utat! The sought-forquantityMis involved in the equationreciprocally.The desiredvalue of mcan be determined fromconition (4).

care va fi c!utat! Consider the equation (3), wheref(t) is the function tobe found.Here v*is the value of vto be determined.

c!utare




53/112

n c!utarea In looking(or in search) forthe optimal solution wediscovered that ...

cteva To see this, we shall prove severallemmas.A fewwords should be said about physical meaning ofthis parameter.Someother examples of fundamental sequences will

be given after the following lemma. cteva modalit!i There is more than one wayto approach the problem.

ce For instance, the Dirac delta distribution cannot beidentified with any continuous function, whichwill beproved in Section 8.

cel mai bine The nature of this problem can bestbe made plain byexamples.

cel mai mare divizor comun(CMMDC)

The greatest common divisor(GCD) of two integershand kis the largest positive factor common to both hand k.

cel mai mic multiplu comun(CMMMC)

Twelve is the least common multiple(LCM) of 3 and4.

cel mult The set of the points of discontinuity off(t) is at(the)mostcountable.

cel puin Formula (7) is true under the hypothesis that at leastone of the integrals on the left-hand side is meaningful.

cercetare

cercetare profund! the in-depth study

cercetare ulterioar! To determine whether these ideals coincide, we mustmake a further studyof the polynomials.

cere

se cere It is requiredto estimate in the best possible mannerthe value of a random variable .

se cere ntrebarea It istherefore reasonable to askfor which classes of"integers" the fundamental theorem holds, and forwhich it does not.

cerin!mai puternic! The processMt, satisfies the conditions of (1) with the

stronger requirementthat be anL2-

martingale.

chiar n cazul cnd This example shows that the ordinary derivative doesnot always coincide with the distributional derivative,even whenthe ordinary derivative wrists everywhereexcept at one point.

ciThus we need not 8, but9 parameters to describe thesystem.




54/112

ciocni cu

ne ciocnim cu In applications we often come acrossthe so-calledHeaviside function.

cititor The readerwill find it a useful exercise to supply thedetails of the proof.

clasic In classicalanalysis there have been consideredseveral sequence of functions which aredistributionally convergent to (x).

clar

este clar c! Clearly, the sum, difference and product of suchintegers are of the same form.It is clear thataand -aare both in the setA.

intuitiv este clar It is clear intuitivelythat every collection, finite orinfinite, of non-negative integers contains a smallestone.

coeficientul pe lng! the coefficient ofsmth.the coefficient multiplyingsmth.

coeficientul pe lng!termenul

superior

A polinomial is monic if its leading coefficentis 1.

coincide

coincide cu For an arbitrary functionF(x) satisfying conditions 1) -6) there exists a unique probability measure whosedistribution function coincides withF(x).The characteristic throughAis the same asthe onethroughB.

complet satisf!c!tor Completely satisfactorysolution of the functionalproblem is given in [6].

completa

este completat! It is assumed that -algebraF0is completed(or

augmented) by allP-null sets.

complicat The problem of optimization is, in general, morecomplicated.Integration of equation (3.2) represents a ratherinvolvedboundary-value problem.

conclude From a>band b>cwe concludethat a>c.

condiie

condiia asupra This result was established in another way undersomewhat weaker conditions onthe diffusioncoefficients.

condiiile conform c!rora The problem arose of finding the conditions underwhichthe distributionp(t) is unimodal.




55/112

condiie de convergen!la The condition for convergence toa Wiener process isstated in the next section.

condiie de existen!$iunicitate a soluiei

Let the coefficients of equation (9) satisfy thecondition for the existence and uniqueness of thesolution.

condiii exacte pentru The exact conditions forequilibria to exist and be

stable are examined. condiie mai fin! The tangent bundle of the manifolds provides a

sharpernecessary condition. condiii sunt verificate Assume that conditions(5) and (20) are satisfied.

If the conditionsof Theorem 10 are satisfiedand,moreover,A(,t) is continuously differentiable, then ...Let the conditionsof Theorem 4 be satisfiedand thefunction be twice continuously differentiable.

alte condiii fiind acelea$i The distinction between (14) and (15) is that thevariablexentering into (15) depends on , otherthings being equal.

n condiia c! Thus, the functionf(x) is uniquely determined,provided thatit exists everywhere.Any term may be transposed from one member ofequation to the other, providingits sign is changed.The abstraction principle can be applied to sets ofarbitrary elements providedthere exists anequivalence relation ~.These functions are locally Riemann-integrable under(or on) the conditionthat their values are equal at allpoints of continuity.

n condiiile teoremei Under the conditions of Theorem6.1 the limit

exists and is differentiable.

conduce

conduce la ecuaia This reasoning yieldsa simple equation.

confirma ipoteza to verify a hypothesis

conform

conform algoritmului The classes can be formed by theFLAMENCOalgorithm.

conform criteriului By theEisenstein's criterion, the polynomialxn-2 is

irreducible over the field of rational numbers. conform definiiei Then, by definition, ... conform ipotezei induciei By the induction hypothesis, the theorem is true forf

(x). conform lemei By Lemma2.3, the sequence {gn(x)} is fundamental.

conform presuruneriiBy assumption,E(1)=0.By the assumptionof the lemma, the solution to (1) ispositive.




56/112

Since ... by hypothesis, (4) is a bounded sequence. conform propriet!ii By property(4) of norms, every element in Thas

norm at least equal to 1, so there must be one of them,, which is of least positive norm.

conform teoremei By Theorem1.1, we can find qand rso that b=dq+r,0 r < d.

consecin!

consecin!din To complete the proof of the lemma, we use thecorollary ofLemma 2.

este o consecin! The inequalityf(x)0 is adirect consequenceof thesystemf

i(x)0, i=l, 2, ..., n.

consecutiv When an expression contains parentheses withinparentheses, they may be removed in succession,beginning with the innermost.

considera consider!m Considerthe rational number a/b. poate fi considerat! The problem can be approachedin many different

ways. s!consider!m Let usnow considerthe case a>1.

Considernow the case a>1.

sunt considerate Several other functions, very useful from the practicalpoint of view, are consideredin the following section.Some properties of the operatorLare dealt within thenext chapter.

considerat! An integral part of the creative approach to theproblem under consideration(or under study) is theanalysis of its similarity to and difference from theanalogous problems.

poate fi considerat ca C(R+

) can be regarded asa complete separable

metric space under the topology of uniformconvergence.

n lucrare se consider! The paper deals withthe theory of distributions offinite order.

considera acum consider!m acum We now considerthe process (t).

Consider nowthe process (t).

considera de la nceput

vom considera de la nceput Consider firstthe simplest case where a=0.We will first confineour attention todiscrete-parameter martingales.

considera util




57/112

consider!m util We find it usefulto define a new concept ofconjugacy and to discuss its relation to the old.

considerabil mai simplu Theorems IV and VI are considerably simplerthanthe analogous theorems in the differential calculus.

consideraie We now turn to the task of consideringthecontinuous-parameter stochastic processes.The consideration(or discussion) of this problem inmore detail shows that ...We must now subject the concept of equivalence to asomewhat closer scrutiny.Further inspection(or examination) of Fig.1 disclosesthat there are two points of inflection on the curve.

consta

const!n ... The abstraction principle consists(or lies) intheidentification of objects (mathematical entities) whichhave a common property.

construcie By a slight change in the method of (7), theconstructionof such functions is easily carried out.

construi

pentru a construi The abstraction principle is often applied inmathematics to constructnew notions.

continuuIn the case under consideration the process (t) iscontinuousat every point of the interval (c,d).

continu!din dreapta dup!t Ftis continuous from the right(or right-continuous)

in t if for all t!0 .

contrazice

ce contrazice So is a unit, contrary tothe hypothesis.Sop|L, contradictingthe fact thatLis prime.

aceast!contrazice This contradictsr!0.

contrazice presupunerii This equation contradicts the assumptionthat Gcontains a point not belonging toD.This contradicts the hypothesisthat kand that (6)holds for all l


58/112

conine propriet!i The following list containsthe fundamentalpropertiesof the norm.

convenabil

convenabil! In some cases the following complex form of

trigonometrical series is advantageous.

mai convenabil It is more convenientto break up the experiment intothree phases.

este convenabil It is convenientto call two Gaussian integersassociates if =, where is a unit.

va fi convenabil It will be convenientto define the convergence offn

(x) in the following sense. deseori este convenabil It is often convenientto establish the position of

points by giving their coordinates.

conveni

vom conveni We shall agreeto writeA(x,t)SifA(x,t) is a processwith independent increments.

converge

converge absolut The series (1) converges absolutely. converge aproape peste tot to converge almost everywhere converge n medie to converge in(the) mean converge n probabilitate to converge in probability converge uniform Thus the series (4) converges uniformly.

convinge ne convingem c! Make(or be) sure thatthe coefficients have nocommon factors other than +1.To complete the proof, check that...Before applying Theorem 10.7, check to see thatthereis an inAsuch that ...

a se convinge n To prove the convergenceX nM, it suffices to makesure that...

trebuie s!se conving!c! The investigator must assure himself thatthe errorsare within the admissible limits.

pentru a se convinge n ... To see thatif satisfies an equationa

nxn+ a

n-1xn-1+ ... + a0= 0, then there is a rational r

such that ris an algebraic rational, observe that an

satisfies (3).To be certain thatcis the required element, checkthatD[c,A]>0.

pentru a se convinge naceasta

To see this, notice that Powell's frequency function isidentical with our function

b(x).




59/112

se poate de convins c! Then, similarly as has been done in [1], one ascertainsthatthe limit function satisfies the equation (4).

este u$or de convins c! It is easy to make sure that(x) is convex on [c,).

coordona

se coordoneaz! The theory checks well(or agrees/ is in good

agreement) withexperiment.The hypothesis fitsthe experimental data.This conjecture is in line withthat of Seidenberg.

corect This definition is correct; since the sequence {pn

(m)

(x)} is fundamental.

corectitudinea definiiei To verify the correctness ofthis definition, we mustprove that ...

coresponden!biunivoc! The one-to-one correspondenceestablished abovemakes it unnecessary to distinguish between functions

(x) and distributions [f(x)].cresc!tor

cresc!toare There is an increasingsequence of integers km

such

that ... strict cresc!tor Introduce a strictly increasingfunstiong(x) defined

on [0,).

cre$te

cre$te monoton dup!t Ftmonotonically increases int, that isF

sF

t, for

s


60/112

than the Dirichlet kernel .

este bine cunoscut It is well knownthat there exist sequences {Tn} and

{Sn} such that

n=T

n-S

n.

este cunoscut!ca This relation is known asthe Biot-Savart law.

cuvnt

cu alte cuvinte To put it in another way, the gross weight Wcan berepresented as W=W

st+W

e+W

p.

Dda

d! The repeated application of relation (2.1) yields...The following theorem providesthe description of theeverywhere dense setE.

d!m We give(or present) below

Dict Rom Eng Matematică

Documents

Transcript of Dict Rom Eng Matematică