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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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'
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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'
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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
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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
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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
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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
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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
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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
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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'
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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
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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
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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'
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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
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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'
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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
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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
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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
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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
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volume - volum
Wway - drum, distant'well-defined - bine definitwhole - tot, n ntregime
Xx-axis - axaxx-intercept - segment de pe axaxxy-plane - planxOy
Y-axis - axay
Z
z-axis - axazzero - zerozero solution - solu+ie nul'
Bibliografie
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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.
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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
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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).
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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)
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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),
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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
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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
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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
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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 $i n cazul ...In the same manner as in the case ofconvergence toa Wiener process, one can easily deduce the followingresult.In the case of distributions, as in the case offunctions,
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the following properties hold true.
ca urmare Such a solution does not exist in consequence(or onaccount) of (6) and Remark 4.
calcula As is easy to calculate... sunt calculate The coefficients of expansion (9) are evaluated(or
computed) from formulas (5). cum este u$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
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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.
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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.
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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.
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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
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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
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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).
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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
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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