18010066 dictionar-roman-englez

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Dictionar Roman-Englez de Termeni Matematici
A Ă Â B C D E F G H I Î J K L M N O P Q R S Ş T Ţ U V W X Y Z
A
abscisă - abscissa
absolut - absolute
aceleaşi semne - like signs
acurateţe - accuracy
admisibil - admissible
aduna - to add
adunare - addition
afirmaţie - statement
algebră - algebra
algoritm - algorithm
algoritm de divizare - algorithm for division, division algorithm
algoritmul lui Euclid - Euclidean algorithm
alternanţă - alternance
alternare - alteration
amplasare - disposition
amplitudine - amplitude
analiza - to analyze
analiză - analysis
analiză matematică - calculus
analogic - analogous, analogical
analogie - analogy
anula - to vanish
aplicată - applicate
aplicaţie - map, mapping
arbitrar - arbitrary
arc - arc
arccosinus - anticosine, arccosine
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arcsinus - antisine, arcsine
arctangentă - arctangent
argument - argument
argument al funcţiei - argument of a function
arie - area
arie a suprafeţei - surface area
asemănare - similarity, similitude
asimetric - asymmetric(al), unsymmetric
asimetrie - asymmetry
asimptotă - asymptote
asimptote ale hiperbolei - asymptotes of a hyperbola
axa x - x-axis
axă - axis
axă de coordonate - coordinate axis
axă de rotaţie - pivot
axă orizontală - horizontal axis
axă principală - major axis, principal axis
axă verticală - vertical axis
axiomă - axiom
B
bază - base, basis
bază ortogonală - orthogonal base
bază ortonormată - orthonormal basis
bilion - billion
binar - binary
bine definit - well-defined
binom - binomial
bisectoare - bisector, bisectrix
biunivoc - one-to-one
C
calcul - calculus, computation
calcula - to count
calculabil - computable
calculul determinantului - evaluation of determinant

canonic - canonical
determinarea extremului - hill climbing
câmp - field
cât - quotient, ratio
cel mai mare divizor comun
- greatest common divisor, greatest common
factor
cel mai mic multiplu comun - lowest common multiple
cel mai mic numitor comun - lowest common denominator
centru - centre, center
centru de rotaţie - pivot
centru al unei circumferinţe exînscrise - excentre, centre of the escribed circle
centrul circumferinţei circumscrise - circumcenter
centrul circumferinţei înscrise - incenter
cerc - circle
cercuri concentrice - concentric circles
cifră - digit
cilindru - cylinder
circumferinţă înscrisă - incircle, inscribed circle
circumferinţă unitară - unit circle
circumscris - escribed
coardă - chord
coeficient - coefficient
coeficient binomial - binomial coefficient
coeficient unghiular - slope
coincident - coincident
coliniaritate - collinearity
combinaţie - combination
comparare - comparation
comparaţie - comparation
con - cone
concavă - concave
condiţie - condition
condiţie iniţială - initial condition
condiţie necesară şi suficientă - necessary and sufficient condition
congruenţă - congruence
conjugat - adjoint, conjugate
consecinţă - corollary
constantă - constant
constantă de integrare - integration constant
continuitate - continuity
convex - convex
convexitate - convexity

coordonată - coordinate
coordonate afine - affine coordinates
coordonate carteziene - Cartesian coordinates
coplanar - coplanar
corolar - corollary
cosinus director - direction cosine
creşte - to increase
creştere - increment
criteriu - criterion
criteriu de divizibilitate - criterion for divisibility
cuantor - quantifier
cuantor existenţial - existential quantifier
cuantor universal - universal quantifier
cub - cube
cunoscut - known
cuplu - pair
cuplu ordonat - ordered pair
curbă - curve
curbă concavă - concave curve
curbă convexă - convex curve
curbă cubică - cubic, cubic curve
curbă integrală - integral curve
D
dacă şi numai dacă - if and only if
date - data
decizie - decision
deducţie - deduction
defini - to define
definit peste tot - everywhere defined
definiţie - definition
degenerat - degenerate
deîmpărţit - dividend
deînmulţit - multiplicand
delatare - dilatation, stretching
demonstra - to prove
demonstraţie - proof
dependent - dependent
derivabilitate - differentiability

derivată - derivative
derivată în punct - derivative at a point
descazut - minuend
descompunere - decomposition, expansion
descompunere binomială - binomial expansion
descompunere în factori - factoring, factorization
descompunere în factori primi - prime factorization
descompunere în fracţii elementare - partial-fraction expansion
descompunere a unei fracţii - decomposition of a fraction
descreşte - to decrease
determina - to determine
determinant - determinant
deviaţie - deviation
deviere - deviation
dezvoltare - expansion
dezvoltare a determinantului - expansion of a determinant
diagonală - diagonal
diagonală principală - main diagonal, principal diagonal
diametru - diameter
diferenţă - difference
diferenţiabilitate - differentiability
diferit - unequal
dimensiune - dimension
direct proporţional - directly proportional
direcţie - direction
discontinuu - discontinuous
discriminant - discriminant
dispărea - to vanish
distanţă - distance, way
distinct - distinct
divizare - division
divizibil {prin} - divisable {by}
divizor - divisor
divizor comun - common divisor, common factor
divizor propriu - proper factor
domeniu - domain, range
domeniu de definiţie - domain of definition
dreaptă - line
dreaptă numerică - number line
drept - straight
drepte neconcurente - skew lines

dreptunghi - rectangle
drum - way
dual - dual
E
echilateral - equilateral
echivalent - equivalent
ecuaţie - equation
ecuaţie algebrică - algebraic equation
ecuaţie a liniei drepte - equation of a straight line
ecuaţie a unei drepte cu coeficient
unghiular
- slope-intercept form of a straight line
equation
ecuaţie bipatrată - biquadratic equation
ecuaţie de ordinul întâi - first-order equation
ecuaţie exponenţială - exponential equation
ecuaţie liniară - linear equation
ecuaţie neliniară - non-linear equation
ecuaţie omogenă - homogeneous equation
ecuaţie de ordinul doi(patrată) - quadratic equation
element - element
element {al multimii} - member {of a set}
element de arie - differential of area, element of area
element de arie (al suprafeţei) - surface element
element diagonal - diagonal element
eliminare - elimination
eliminare prin substituţie - elimination by substitution
elipsă - ellipse
eroare - error
eroare de rotunjire - rounding error
esenţial - essential
estimaţie - estimation
evaluare - evaluation
exact - exact
exactitate - accuracy
excepţie - exclusion
exemplu - example
exînscris - escribed
exponent - degree, exponent, grade, power
exponenţial - exponential

expresie - expression
expresie algebrică - algebraic expression
expresie de sub integrală - integrand
extremal - extremal
extremum absolut - absolute extremum
F
factor - factor
familie - family
fascicul - pencil
fascicul de drepte - pencil of lines
faţă laterală - leg
figură circumscrisă - circumscribed figure
figură congruentă - equivalent figure
figuri congruente - congruent figures
flux - flux
focar - focus
formă generală - general form
formă parametrică - parametric form
formă standardă - standard form
formula binomului - binomial formula
formula coeficientului unghiular - slope formula
formula lui Leibniz - Leibniz rule
formula rădăcinilor ecuaţiei patrate - quadratic formula
formulă - formula
formulele jumătăţii unui unghi - half-angle formulas
fracţie - fraction
fracţie elementară - partial fraction
fracţie ordinară - common fraction
fracţie subunitară - proper fraction
fracţie supraunitară - improper fraction
fracţie zecimală - decimal fraction
fracţie zecimală finită - terminating decimal fraction
fracţie zecimală infinită
- infinite decimal fraction, non-terminating
decimal
fracţie zecimală periodică - periodic decimal fraction
fracţii cu numitori egali - similar fractions
funcţie - function
funcţie concavă - concave function

funcţie continuă - continuous function
funcţie de mai multe variabile - function of several variables
funcţie de o variabilă - function of a single variable
funcţie de variabilă complexă - function of a complex variable
funcţie descrescătoare - decreasing function
funcţie diferenţiabilă - differentiable function
funcţie discontinuă - discontinuous function
funcţie impară - odd-function
funcţie în scară
- inter-stage function, jump function, step
function
funcţie liniară - linear function
funcţie monoton crescătoare - monotone increasing function
funcţie monoton descrescătoare - monotone decreasing function
funcţie monotonă - monotonic function
funcţie pară - even function, symmetric function
funcţie periodică - periodic function
funcţie primitivă - primitive
funcţie raţională - rational function
funcţie signum - signum function
funcţie simetrică - symmetric function
funcţie trigonometrică - trigonometric function
fundamental - fundamental
G
general - general
geometrie - geometry
geometrie euclidiană - Euclidean geometry
grad - degree, grade
grad al polinomului - degree of a polinomial
H
hexaedru - hexahedron, hexaeder
hexagon - hexagon
hiperbolă - hyperbola
hiperbolic - hyperbolic

I
identitate - identity
imagine - image, map, mapping
impar - odd
implicaţie - implication
incertitudine - uncertainty
include - to include
incluziune - inclusion
incompatibil - inconsistent
incorect - incorrect
independent - independent
independenţă liniară - linear independency
inducţie - induction
inducţie completă - complete induction
inducţie matematică - mathematical induction
inecuaţie - inequality
inegal - unequal
infinit - infinite
inflexiune - inflexion
iniţial - initial
integrală - integral
integrare prin părţi - integration by parts
interdependenţă - interdependency
intersecţie - intersection
interval - interval
interval deschis - open interval
interval închis - closed interval
interval mărginit - bounded interval
interval semiînchis - semiclosed interval
invers - inverse, vice versa
invers proporţional - inversely proportional
ipotenuză - hypotenuse
ipoteză - hypothesis
ireductibilitate - irreductibility
Î

împărţi în două {în jumătate} - to halve
împărţire fără rest - exact division
în întregime - whole
înălţime - height
înălţime a triunghiului - altitude of a triangle
închis - closed
înclinare - slope
înlocui - to replace
înmulţi - to multiply
înmulţire - multiplication
înmulţitor - multiplier
înscrie - to inscribe
K
kilogram - kilogram(me)
kilometru - kilometre
L
latură {a unui unghi} - side {of an angle}
latură adiacentă - adjacent side
lege - law
lege asociativă - associative law
lege comutativă - commutative law
lege de compozitie - law of composition
lege distributivă - distributive law
legea terţului exclus - law of the excluded middle
lemă - lemma
limită - limit
limită inferioară - lower limit
limite de integrare - limits of integration
linie de fracţie - bar, vinculum
liniar - linear
liniaritate - linearity
linie dreaptă - straight-line
linie frântă - brocken line
linie punctată - dotted line

linie tangentă - tangent line
loc geometric al punctelor - geometric locus
local - local
logaritm - logarithm
logaritm zecimal - common logs
logaritm natural - natural logarithm
lungime - length
lungimea arcului - arc-length
M
mărime - magnitude
măsură - measure
măsurabil - measurable
matematică - mathematics
matrice - matrix
matrice de transformare - matrix of the transformation
matrice diagonală - diagonal matrix
matrice inversă - reciprocal matrix
matrice nulă - null-matrix
maxim - maximum
maximum - maximum
mediană - median {of a triangle}
medie aritmetică - mean, arithmetic mean
medie geometrică - geometric average, geometric mean,
mean proportional
metoda eliminării - elimination method
metoda inducţiei complete - principle of complete induction
metru - meter
minim - minimim
minimum - minimum
modul - module
monom - monom
monoton - monotonous
muchie - edge
mulţime - set
mulţime de soluţii - solution set
mulţime de valori - range
mulţime universală - universal set
mulţime vidă - empty set, null-set

multiplicare - multiplicaton
multiplicator - factor, multiplier
multiplu - multiple, multiplex
multiplu comun - common multiple
mutual - mutually
mutual disjuncte - mutually disjoint
N
necunoscută - unknown
nedefinit - undefined
nedegenerat - non-degnerate
nedescrescător - non-decreasing
nedeterminare - indeterminancy, uncertainty
nedeterminat - indefinite, undetermined
negativ - negative
neglijabil - negligible
neliniar - non-linear
nemărginit - unbounded
neomogen - inhomogeneous
neperiodic - non-periodic
nesimetric - non-symmetric
nod - node
normală - normal
normală la suprafaţă - normal to the surface
număr - number
număr complex - complex number
număr întreg - integer number
număr iraţional - irrational number
număr natural - natural number
număr par - even number
număr prim - prime number
număr raţional - rational number
număr real - real number
număr transcendent - transcendental number
număr zecimal - decimal number
număr ordinal - ordinal number
numărător - numerator
numărător al fracţiei - term of a fraction
numere întregi consecutive - consecutive integers

numere reciproc prime - coprime numbers, relatively prime numbers
numitor - denominator
numitor comun - common denominator
numitori diferiţi - unlike denominators
numitori identici - like denominators, same denominators
O
oblic - oblique
octagon - octagon
omogen - homogeneous
ordin - degree, exponent
ordin al derivatei - order of derivative
ordin al ecuaţiei - order of equation
ordine - order
ordonată - ordinate
origine de coordonate - origin {of coordinates}
orizontal - horizontal
oval - oval
P
par - even
parabolă - parabola
parabolic - parabolic
paralel - parallel
paralelepiped - parallelepiped
paralelogram - parallelogram
parametru - parameter
paranteze figurate - braces
paranteze patrate - square brackets, brackets
paranteze rotunde - parentheses
patrat - quadrate, square
patrulater - tetragon
pătratic - quadratic
pentagon - pentagon
perimertu - perimeter
perioadă - period

perpendiculară - normal, perpendicular
picior al perpendicularei - foot {of a perpendicular}
piramidă - pyramid
plan - plane
plan tangent - tangent plane
plan xOy - xy-plane
planimetrie - plane geometry, planimetry
plus - plus sign
poliedru - polyhedron
poligoane asemenea - similar polygons
poligoane congruente - congruent polygons
poligon - polygon
poligon convex - convex polygon
poligon înscris - inscribed polygon
poligon regulat - equilateral polygon, regular polygon
polinom - polynomial
posibilitate - possibility
pozitiv - positive
precedent - preceding
precizie - accuracy
preimagine - pre-image
presupunere - assumption
primă derivată - first derivative
principal - principal
principiul dualitatii - duality principle
prizmă - prism
procent - per cent
produs - product
produs scalar - dot product
produs vectorial - cross-product, vector product
progresie - progression
progresie aritmetică - arithmetic progression
progresie geometrică - geometric progression
proiecţie - projection
proporţie - proportion
propoziţie - proposition, statement
proprietate - property
proprietate asociativă - associative property
punct - dot, point
punct de discontinuitate - point of discontinuity
punct de extrem - extremum point

punct de inflexiune - point of inflexion
punct diametral opus - diametrically opposite point
punct focal - focal point
punct izolat - acnode
putere - degree, grade, power
R
radian - radian
radical - radical, radical sign
ramură - branch
rang al unei matrici - rank of a matrix
raport - ratio, relation
raţie a unei progresii aritmetice - common difference
raţie a unei progresii geometrice - common ratio
raţional - rational
rază - radius
rază vectoare - radius vector
rădăcină - root
rădăcină dublă - double root
rădăcină multiplă - repeated root
rădăcină patrată - square root
rădăcină simplă - simple root
rădăcini conjugate - conjugate roots
real - real
reciproc - vice versa
reduce - to reduce
reducere termenilor asemenea - combine similar terms
reductibil - reducible
regulă - rule
regula paralelogramului - parallelogram law, parallelogram rule
relaţie - relation
relativ - relative
repetat - multiplex
reprezenta - to represent
rest - remainder, rest
restricţie - restriction
reuniune - union
rezolva - to solve
ridica la patrat - to square

ridica la putere - to raise to a power
romb - lozenge, rhombus, rhomb
rotaţie - rotation
rotunji - to round
S
salt - jump
satisface - to satisfy
scalar - scalar
scădere - subtraction
scăzător - subtrahend
schemă bloc - flow chart
schema lui Horner - Horner's scheme, synthetic division
schimb de variabilă - change of variable
secantă - secant
secţiune - cut
secţiune conică - conic, conic section
secţiune conică centrală - central conic
secţiune conică degenerată - degenerate conic
secţiune conică nedegenerată - non-degenerate conic,
non-degenerate conic section
sector circular - sector of a circle
segment - closed interval, intercept, segment
segment de pe axa x - x-intercept
segment liniar - line segment, straight-line segment
segmente congruente - congruent segments
semicerc - semi-circle
semidreaptă - ray
semisferă - hemisphere
semn - sign
semnul adunării - addition sign, plus sign
semnul rădăcinii - radical, radical sign
semnul scăderii - minus {sign}
sferă - sphere
simbol - symbol
simetric - symmetric
simetrie centrală - central symmetry
simplifica - to cancel
simplificare - simplification

simplu - simple
sinusoidă - sine curve
sistem - system
sistem cartezian de coordonate - Cartesian coordinate system
sistem cu mai multe necunoscute - many-variable system
sistem de coordonate - coordinate system
sistem de ecuaţii liniare - system of linear equation
sistem neortogonal de coordonate - non-orthogonal coordinate system
sistem omogen - homogeneous system
sistem ortogonal de coordonate - orthogonal coordnate system
sistem rectangular de coordonate - rectangular coordonate system
soluţie admisibilă - permissible solution, admissible solution
soluţie aproximativă - approximate solution
soluţie completă - complete solution
soluţie exactă - exact solution
soluţie generală - general solution
soluţie nenulă - non-zero solution
soluţie netrivială - non-trivial solution
soluţie nulă - zero solution
soluţie periodică - periodic solution
soluţie unică - unique solution
soluţiona - to solve
soluţionare {a unei probleme} - solution {of a problem}
spaţiu - space
spaţiu euclidian - Euclidean space
strict - strict
strict monoton - strongly monotonic
substitui - to replace
substituţie - substitution
substituţie inversă - back-substitution
suma - to add
sumă - sum
suprafaţă - surface
suprafaţă de rotaţie - surface of revolution
submulţime - subset
T
tangentă - tangent
teorema lui Pythagoras - Pythagorean theorem

teoremă - theorem
teorema fundamentală a aritmeticii - fundamental theorem of arithmetic
teorema lui Bezout - factor theorem
teorema lui Thales - intercept theorem
teorema sinusurilor - law of sines, sine rule
teoria mulţimilor - set theory
teorie - theory
termen - term
termen al sumei - addend, summand
termen general - general term
termeni asemenea - similar terms
tetraedru - tetrahedron
tot - whole
transforma - to transform
transformare de coordonate - transform of coordinates
translare - translation
translaţie - bridging
tranzitivitate - transitivity
trapez - trapezoid, trapezium
trigonometric - trigonometric
trigonometrie - trigonometry
trisecţia unui unghi - trisection of the angle
triunghi - triangle
triunghi ascutunghic - acute triangle
triunghi asemenea - similar triangle
triunghi dreptunghic - right triangle
triunghi echilateral - equilateral triangle
triunghi isoscel - isosceles triangle
triunghi obtuzunghic - obtuse triangle
triunghi scalen - scalene triangle
triunghiular - triangular
U
unghi - angle
unghi adiacent - adjacent angle
unghi alăturat - adjacent angle
unghi ascuţit - acute angle
unghi complementar {până la 90o} - complementary angle
- explementary angle

unghi complementar până la 360o
unghi de înclinare - slope angle
unghi diedru - dihedral angle
unghi drept - right angle
unghi exterior {al triunghiului} - exteriar angle {of a triangle}
unghi interior - interior angle
unghi înscris - inscribed angle
unghi întins - straight angle
unghi la bază a triunghiului - base angle {of a triangle}
unghi la centru - central angle
unghi obtuz - obtuse angle
unghi plin - straight ahgle
unghi suplimentar până la 360o - conjugate angle
unghiuri adiacente suplimentare - adjacent supplementary angles
unghiuri alterne - alternate angles
unghiuri alterne externe - alternate exterior angles
unghiuri alterne interne
- alternate interior angles, opposite interior
angles
unghiuri congruente - congruent angles
unghiuri corespondente - corresponding angles
unghiuri opuse la vârf - vertex angles
unghiuri suplimentare {până la 180o} - supplementary angles
unic - single
unicitate - uniqueness
unitate - unit
univoc - unambiguous
V
valabil - valid
valid - valid
valoare - value
valoare absolută - absolute value
valoare absolută a numărului complex - absolute value of a complex number
valoare iniţială - initial value
valoare medie - average, average value
valoare limită - limit value
variabilă - variable
variabilă independentă - independent variable

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vârf - vertex
vector - vector
vector coplanar - coplanar vector
vector de bază - base vector
vector normal - normal vector
vector nul - null-vector
vector unitar - unit vector
vector tangent unitar - unit tangent vector
veridicitate - truth
verifica - to verify
vertical - vertical
viteză - speed, velocity
volum - volume
Z
zecimal - decimal
zero - zero
Bibliografie

Dictionar Englez-Roman de Termeni Matematici
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A
abscissa - abscisă
absolute - absolut
absolute extremum - extremum absolut
absolute value - valoare absolută
absolute value of a complex number - valoare absolută a numărului complex
accuracy - precizie, exactitate, acurateţe
acnode - punct izolat
acute angle - unghi ascuţit
acute triangle - triunghi ascuţitunghic
add - a aduna, a suma
addend - termen al sumei
addition - adunare
addition sign - semnul adunării
adjacent angle - unghi adiacent, unghi alăturat
adjacent side - latură adiacentă
adjacent supplementary angles - unghiuri adiacente suplimentare
adjoint - conjugat
admissible - admisibil
admissible solution - soluţie admisibilă
affine coordinates - coordonate afine
algebra - algebră
algebraic equation - ecuaţie algebrică
algebraic expression - expresie algebrică
algorithm - algoritm
algorithm for division - algoritm de divizare
alternance - alternanţă
alteration - alternare
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alternate angles - unghiuri alterne
alternate exterior angles - unghiuri alterne externe
alternate interior angles - unghiuri alterne interne
altitude of a triangle - înălţime a triunghiului
amplitude - amplitudine
analogous - analogic
analogical - analogic
analogy - analogie
analysis - analiză
analyze - a analiza
angle - unghi
anticosine - arccosinus
antisine - arcsinus
applicate - aplicată
approximate solution - soluţie aproximativă
arbitrary - arbitrar
arc - arc
arccosine - arccosinus
arc-length - lungimea arcului
arcsine - arcsinus
arctangent - arctangentă
area - arie
argument - argument
argument of a function - argument al funcţiei
arithmetic mean - medie aritmetică
arithmetic progression - progresie aritmetică
associative law - lege asociativă
associative property - proprietate asociativă
assumption - presupunere
asymmetric(al) - asimetric
asymmetry - asimetrie
asymptote - asimptotă
asymptotes of a hyperbola - asimptote ale hiperbolei
average - valoare medie
average value - valoare medie
axiom - axiomă
axis - axă
B

back-substitution - substituţie inversă
bar - linie de fracţie
base - bază
base angle {of a triangle} - unghi la bază a triunghiului
base vector - vector de bază
basis - bază
billion - bilion
binary - binar
binomial - binom
binomial coefficient - coeficient binomial
binomial expansion - descompunere binomială
binomial formula - formula binomului
biquadratic equation - ecuaţie bipatrată
bisector - bisectoare
bisectrix - bisectoare
bounded interval - interval mărginit
braces - paranteze figurate
brackets - paranteze patrate
branch - ramură
bridging - translaţie
brocken line - linie frântă
C
calculus - analiză matematică, calcul
cancel - a simplifica
canonical - canonic
Cartesian coordinate system - sistem cartezian de coordonate
Cartesian coordinates - coordonate carteziene
central angle - unghi la centru
central conic - secţiune conică centrală
central symmetry - simetrie centrală
centre - centru
centre of the escribed circle - centru unei circumferinţe exînscrise
center - centru
change of variable - schimb de variabilă
chord - coardă
circle - cerc
circumcenter - centrul circumferinţei circumscrise
circumscribed figure - figură circumscrisă

closed - închis
closed interval - interval închis, segment
coefficient - coeficient
coincident - coincident
collinearity - coliniaritate
combination - combinaţie
combine similar terms - reducere a termenilor asemenea
common denominator - numitor comun
common difference - raţie a unei progresii aritmetice
common divisor - divizor comun
common factor - divizor comun
common fraction - fracţie ordinară
common logs - logaritm zecimal
common multiple - multiplu comun
common ratio - raţie a unei progresii geometrice
commutative law - lege comutativă
comparation - comparaţie, comparare
complementary angle - unghi complementar {până la 90o}
complete induction - inducţie completă
complete solution - soluţie completă
complex number - număr complex
computable - calculabil
computation - calcul
concave - concavă
concave curve - curbă concavă
concave function - funcţie concavă
concentric circles - cercuri concentrice
condition - condiţie
cone - con
congruence - congruenţă
congruent angles - unghiuri congruente
congruent figures - figuri congruente
congruent polygons - poligoane congruente
congruent segments - segmente congruente
conic - secţiune conică
conic section - secţiune conică
conjugate - conjugat
conjugate angle - unghi suplimentar până la 360o
conjugate roots - rădăcini conjugate
consecutive integers - numere întregi consecutive
constant - constantă

continuity - continuitate
continuous function - funcţie continuă
convex - convex
convex curve - curbă convexă
convex polygon - poligon convex
convexity - convexitate
coordinate - coordonată
coordinate axis - axă de coordonate
coordinate system - sistem de coordonate
coplanar - coplanar
coplanar vector - vector coplanar
coprime numbers - numere reciproc prime
corollary - consecinţă, corolar
corresponding angles - unghiuri corespondente
count - a calcula
criterion - criteriu
criterion for divisibility - criteriu de divizibilitate
cross-product - produs vectorial
cube - cub
cubic - curbă cubică
cubic curve - curbă cubică
curve - curbă
cut - secţiune
cylinder - cilindru
D
data - date
decimal - zecimal
decimal fraction - fracţie zecimală
decimal number - număr zecimal
decision - decizie
decomposition - descompunere
decomposition of a fraction - descompunere a unei fracţii
decrease - a descreşte
decreasing function - funcţie descrescatoare
deduction - deducţie
define - a defini
definition - definiţie
degenerate - degenerat

degenerate conic - secţiune conică degenerată
degree - putere, ordin, grad, exponent
degree of a polinomial - grad al polinomului
denominator - numitor
dependent - dependent
derivative - derivată
derivative at a point - derivată în punct
determinant - determinant
determine - a determina
deviation - deviaţie, deviere
diagonal - diagonală
diagonal element - element diagonal
diagonal matrix - matrice diagonală
diameter - diametru
diametrically opposite point - punct diametral opus
difference - diferenţă
differentiability - derivabilitate, diferenţiabilitate
differentiable function - funcţie diferenţiabilă
differential of area - element de arie
digit - cifră
dihedral angle - unghi diedru
dilatation - delatare
dimension - dimensiune
direction - direcţie
direction cosine - cosinus director
directly proportional - direct proporţional
discontinuous - discontinuu
discontinuous function - funcţie discontinuă
discriminant - discriminant
disposition - amplasare
distance - distanţă
distinct - distinct
distributive law - lege distributivă
dividend - deîmpărţit
divisable {by} - divizibil {prin}
division - divizare
division algorithm - algoritm de divizare
divisor - divizor
domain - domeniu
domain of definition - domeniu de definiţie
dot - punct

dot product - produs scalar
dotted line - linie punctată
double root - rădăcină dublă
dual - dual
duality principle - principiul dualităţii
E
edge - muchie
element - element
element of area - element de arie
elimination - eliminare
elimination by substitution - eliminare prin substituţie
elimination method - metoda eliminării
ellipse - elipsă
empty set - mulţime vidă
equation - ecuaţie
equation of a straight line - ecuaţie a liniei drepte
equilateral - echilateral
equilateral polygon - poligon regulat
equilateral triangle - triunghi echilateral
equivalent - echivalent
equivalent figure - figură congruentă
error - eroare
escribed - circumscris, exînscris
essential - esenţial
estimation - estimaţie
Euclidean algorithm - algoritmul lui Euclid
Euclidean geometry - geometrie euclidiană
Euclidean space - spaţiu euclidian
evaluation - evaluare
evaluation of determinant - calculul determinantului
even - par
even function - funcţie pară
even number - număr par
everywhere defined - definit peste tot
exact - exact
exact division - împărţire fără rest
exact solution - soluţie exactă
example - exemplu

excentre - centru al unei circumferinţe exînscrise
exclusion - excepţie
existential quantifier - cuantor existenţial
expansion - descompunere, dezvoltare
expansion of a determinant - dezvoltare a determinantului
explementary angle - unghi complementar până la 360o
exponent - exponent, ordin
exponential - exponenţial
exponential equation - ecuaţie exponenţială
expression - expresie
exterior angle {of a triangle} - unghi exterior {al triunghiului}
extremal - extremal
extremum point - punct de extremum
F
factor - factor, multiplicator
factor theorem - teorema lui Bezout
factoring - descompunere în factori
factorization - descompunere în factori
family - familie
field - câmp
first derivative - primă derivată
first-order equation - ecuaţie de ordinul întâi
flow chart - schemă bloc
flux - flux
focal point - punct focal
focus - focar
foot {of a perpendicular} - picior al perpendicularei
formula - formulă
fraction - fracţie
function - funcţie
function of a complex variable - funcţie de variabilă complexă
function of a single variable - funcţie de o variabilă
function of several variables - funcţie de mai multe variabile
fundamental - fundamental
fundamental theorem of arithmetic - teoremă fundamentală a aritmeticii

G
general - general
general form - formă generală
general solution - soluţie generală
general term - termen general
geometric average - medie geometrică
geometric locus - loc geometric al punctelor
geometric mean - medie geometrică
geometric progression - progresie geometrică
geometry - geometrie
grade - grad, exponent, putere
greatest common divisor - cel mai mare divizor comun
greatest common factor - cel mai mare divizor comun
H
half-angle formulas - formule ale jumătăţii unui unghi
halve - a împărţi în două {în jumătate}
height - înălţime
hemisphere - semisferă
hexagon - hexagon
hexaeder - hexaedru
hexahedron - hexaedru
hill climbing - determinarea extremului
homogeneous - omogen
homogeneous equation - ecuaţie omogenă
homogeneous system - sistem omogen
horizontal - orizontal
horizontal axis - axă orizontală
Horner's scheme - schema lui Horner
hyperbola - hiperbolă
hyperbolic - hiperbolic
hypotenuse - ipotenuză
hypothesis - ipoteză
I

identity - identitate
if and only if - dacă şi numai dacă
image - imagine
implication - implicaţie
improper fraction - fracţie supraunitară
incenter - centrul circumferinţei înscrise
incircle - circumferinţă înscrisă
include - a include
inclusion - incluziune
inconsistent - incompatibil
incorrect - incorect
increase - a creşte
increment - creştere
indefinite - nedeterminat
independent - independent
independent variable - variabilă independentă
indeterminancy - nedeterminare
induction - inducţie
inequality - inecuaţie
infinite - infinit
infinite decimal fraction - fracţie zecimală infinită
inflexion - inflexiune
inhomogeneous - neomogen
initial - iniţial
initial condition - condiţie iniţială
initial value - valoare iniţială
inscribe - a înscrie
inscribed angle - unghi înscris
inscribed circle - circumferinţă înscrisă
inscribed polygon - poligon înscris
integer number - număr întreg
integral - integrală
integral curve - curbă integrală
integrand - expresie de sub integrală
integration by parts - integrare prin părţi
integration constant - constantă de integrare
inter-stage function - funcţie în scară
intercept - segment
intercept theorem - teorema lui Thales

interdependency - interdependenţă
interior angle - unghi interior
intersection - intersecţie
interval - interval
inverse - invers
inversely proportional - invers proporţional
irrational number - număr iraţional
irreductibility - ireductibilitate
isosceles triangle - triunghi isoscel
J
jump - salt
jump function - funcţie în scară
K
kilogram(me) - kilogram
kilometre - kilometru
known - cunoscut
L
law - lege
law of composition - lege de compoziţie
law of sines - teorema sinusurilor
law of the excluded middle - legea terţului exclus
least common denominator - cel mai mic numitor comun
least common multiple - cel mai mic multiplu comun
leg - faţă laterală
Leibniz rule - formula lui Leibniz
lemma - lemă
length - lungime
like denominators - numitori identici
like signs - aceleaşi semne
limit - limită
limit value - valoare limită

limits of integration - limite de integrare
line - dreaptă
line segment - segment liniar
linear - liniar
linear equation - ecuaţie de gradul întâi (liniară)
linear function - funcţie liniară
linear independency - independenţă liniară
linearity - liniaritate
local - local
logarithm - logaritm
lower limit - limită inferioară
lowest common denominator - cel mai mic numitor comun
lowest common multiple - cel mai mic multiplu comun
lozenge - romb
M
magnitude - mărime
main diagonal - diagonală principală
major axis - axă principală
many-variable system - sistem cu mai multe necunoscute
map - imagine, aplicaţie
mapping - imagine, aplicaţie
meter - metru
mathematical induction - inducţie matematică
mathematics - matematică
matrix - matrice
matrix of the transformation - matrice de transformare
maximum - maximum, maxim
mean - medie aritmetică
mean proportional - medie geometrică
measurable - măsurabil
measure - măsură
median {of a triangle} - mediană
member {of a set} - element {al mulţimii}
minimum - minimum, minim
minuend - descăzut
minus {sign} - semnul scăderii
module - modul
monom - monom

monotone decreasing function - funcţie monoton descrescătoare
monotone increasing function - funcţie monoton crescătoare
monotonic function - funcţie monotonă
monotonous - monoton
multiple - multiplu
multiplex - multiplu, repetat
multiplicand - deînmulţit
multiplication - înmulţire, multiplicare
multiplier - înmulţitor, multiplicator
multiply - a înmulţi
mutually - mutual
mutually disjoint - mutual disjuncte
N
natural logarithm - logaritm natural
natural number - număr natural
necessary and sufficient condition - condiţie necesară şi suficientă
negative - negativ
negligible - neglijabil
node - nod
non-decreasing - nedescrescător
non-degnerate - nedegenerat
non-degenerate conic - secţiune conică nedegenerată
non-degenerate conic section - secţiune conică nedegenerată
non-linear - neliniar
non-linear equation - ecuaţie neliniară
non-orthogonal coordinate system - sistem neortogonal de coordonate
non-periodic - neperiodic
non-symmetric - nesimetric
non-terminating decimal - fracţie zecimală infinită
non-trivial solution - soluţie netrivială
non-zero solution - soluţie nenulă
normal - normală, perpendiculară
normal to the surface - normală la suprafaţă
normal vector - vector normal
null-vector - vector nul
null-matrix - matrice nulă
null-set - mulţime vidă
number - număr

number line - dreaptă numerică
numerator - numărător
O
oblique - oblic
obtuse angle - unghi obtuz
obtuse triangle - triunghi obtuzunghic
octagon - octagon
odd - impar
odd-function - funcţie impară
one-to-one - biunivoc
open interval - interval deschis
opposite interior angles - unghiuri alterne interioare
order - ordine
order of derivative - ordin al derivatei
order of equation - ordinul ecuaţiei
ordered pair - cuplu ordonat
ordinal number - număr ordinal
ordinate - ordonată
origin {of coordinates} - origine de coordonate
orthogonal base - bază ortogonală
orthogonal coordnate system - sistem ortogonal de coordonate
orthonormal basis - bază ortonormată
oval - oval
P
pair - cuplu
parabola - parabolă
parabolic - parabolic
parallel - paralel
parallelepiped - paralelepiped
parallelogram - paralelogram
parallelogram law - regula paralelogramului
parallelogram rule - regula paralelogramului
parameter - parametru
parametric form - formă parametrică

parentheses - paranteze rotunde
partial fraction - fracţie elementară
partial-fraction expansion - descompunere în fracţii elementare
pencil - fascicul
pencil of lines - fascicul de drepte
pentagon - pentagon
per cent - procent
perimeter - perimertu
period - perioadă
periodic decimal fraction - fracţie zecimală periodică
periodic function - funcţie periodică
periodic solution - soluţie periodică
permissible solution - soluţie admisibilă
perpendicular - perpendiculară
pivot - axă de rotaţie, centru de rotaţie
plane - plan
plane geometry - planimetrie
planimetry - planimetrie
plus sign - semnul adunării, plus
point - punct
point of discontinuity - punct de discontinuitate
point of inflexion - punct de inflexiune
polygon - poligon
polyhedron - poliedru
polynomial - polinom
positive - pozitiv
possibility - posibilitate
power - putere, exponent
pre-image - preimagine
preceding - precedent
prime factorization - descompunere în factori primi
prime number - număr prim
pimitive - funcţie primitivă
principal - principal
principal axis - axă principală
principal diagonal - diagonală principală
principle of complete induction - metoda inducţiei complete
prism - prizmă
product - produs
progression - progresie
projection - proiecţie

proof - demonstraţie
proper factor - divizor propriu
proper fraction - fracţie subunitară
property - proprietate
proportion - proporţie
proposition - propoziţie
prove - a demonstra
pyramid - piramidă
Pythagorean theorem - teorema lui Pythagoras
Q
quadrate - patrat
quadratic - pătratic
quadratic equation - ecuaţie de gradul al doilea (patrată)
quadratic formula - formula rădăcinilor ecuaţiei de gradul al doilea
(ecuaţiei patrate)
quantifier - cuantor
quotient - cât
R
radian - radian
radical - radical, semnul rădăcinii
radical sign - radical, semnul rădăcinii
radius - rază
radius vector - rază vectoare
raise to a power - a ridica la putere
range - mulţime de valori, domeniu
rank of a matrix - rang al unei matrici
ratio - cât, raport
rational - raţional
rational function - funcţie raţională
rational number - număr raţional
ray - semidreaptă
real - real
real number - număr real
reciprocal matrix - matrice inversă

rectangle - dreptunghi
rectangular coordonate system - sistem rectangular de coordonate
reduce - a reduce
reducible - reductibil
regular polygon - poligon regulat
relation - relaţie, raport
relative - relativ
relatively prime numbers - numere reciproc prime
remainder - rest
repeated root - rădăcină multiplă
replace - a substitui, a înlocui
represent - a reprezenta
rest - rest
restriction - restricţie
rhomb - romb
rhombus - romb
right angle - unghi drept
right triangle - triunghi dreptunghic
root - rădăcină
rotation - rotaţie
round - a rotunji
rounding error - eroare de rotunjire
rule - regulă
S
same denominators - numitori identici
satisfy - a satisface
scalar - scalar
scalene triangle - triunghi scalen
secant - secantă
sector of a circle - sector circular
segment - segment
semi-circle - semicerc
semiclosed interval - interval semiînchis
set - mulţime
set theory - teoria mulţimilor
side {of an angle} - latură {a unui unghi}
sign - semn
signum function - funcţia signum

similar fractions - fracţii cu numitori egali
similar polygons - poligoane asemenea
similar terms - termeni asemenea
similar triangle - triunghi asemenea
similarity - asemănare
similitude - asemănare
simple - simplu
simple root - rădăcină simplă
simplification - simplificare
sine curve - sinusoidă
sine rule - teorema sinusurilor
single - unic
single root - rădăcină simplă
skew lines - drepte neconcurente
slope - înclinare, coeficient unghiular
slope angle - unghi de înclinare
slope formula - formula coeficientului unghiular
slope-intercept form of a straight line
equation
- ecuaţie a unei drepte cu coeficient
unghiular
solution {of a problem} - soluţie {a unei probleme}
solution set - mulţime de soluţii
solve - a soluţiona, a rezolva
space - spaţiu
speed - viteză
sphere - sferă
square - patrat, a ridica la patrat
square brackets - paranteze patrate
square root - rădăcină patrată
standard form - formă standardă
statement - propoziţie, afirmaţie
step function - funcţie în scară
straight - drept
straight angle - unghi întins, unghi plin
straight-line - linie dreaptă
straight-line segment - segment liniar
stretching - delatare
strict - strict
strongly monotonic - strict monoton
subset - submulţime
substitution - substituţie
subtraction - scădere
subtrahend - scăzător

sum - sumă
summand - termen al sumei
supplementary angles - unghiuri suplimentare {până la 180o}
surface - suprafată
surface area - arie a suprafeţei
surface element - element de arie {al suprafeţei}
surface of revolution - suprafaţă de rotaţie
symbol - simbol
symmetric - simetric
symmetric function - funcţie simetrică, funcţie pară
synthetic division - schema lui Horner
system - sistem
system of linear equations - sistem de ecuaţii liniare
T
tangent - tangentă
tangent line - linie tangentă
tangent plane - plan tangent
term - termen
term of a fraction - numărător al fracţiei
terminating decimal fraction - fracţie zecimală finită
tetragon - patrulater
tetrahedron - tetraedru
theorem - teoremă
theory - teorie
transcendental number - număr transcendent
transform - a transforma
transform of coordinates - transformare de coordonate
transitivity - tranzitivitate
translation - translare
trapezium - trapez
trapezoid - trapez
triangle - triunghi
triangular - triunghiular
trigonometric - trigonometric
trigonometric function - funcţie trigonometrică
trigonometry - trigonometrie
trisection of the angle - trisecţie a unui unghi
truth - veridicitate

U
unambiguous - univoc
unbounded - nemărginit
uncertainty - incertitudine, nedeterminare
undefined - nedefinit
undetermined - nedeterminat
unequal - inegal, diferit
union - reuniune
unique solution - soluţie unică
uniqueness - unicitate
unit - unitate
unit circle - circumferinţă unitară
unit tangent vector - vector tangent unitar
unit vector - vector unitar
universal quantifier - cuantor universal
universal set - mulţime universală
unknown - necunoscută
unlike denominators - numitori diferiţi
unsymmetric - asimetric
V
valid - valid, valabil
value - valoare
vanish - a se anula, a dispărea
variable - variabilă
vector - vector
vector product - produs vectorial
velocity - viteză
verify - a verifica
vertex - vârf
vertex angles - unghiuri opuse la vârf
vertical - vertical
vertical axis - axă verticală
vice versa - invers, reciproc
vinculum - linie de fracţie

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volume - volum
W
way - drum, distantă
well-defined - bine definit
whole - tot, în întregime
X
x-axis - axa x
x-intercept - segment de pe axa x
xy-plane - plan xOy
Y
y-axis - axa y
Z
z-axis - axa z
zero - zero
zero solution - soluţie nulă
Bibliografie

of 22Dictionar Englez-Roman

Dictionar Matematic Roman-Englez de Fraze Uzuale
A Ă Â B C D E F G H I Î J K L M N O P Q R S Ş T Ţ U V W X Y Z
A
abia The superscripts are hardly (or scarcely) visible.
abordare A more careful approach is needed.
absolut analog In complete analogy with the result, we may prove
that ...
accentua atenţie
se accentuiază atenţie asupra In this section, emphasis is placed (or attention is
focussed) on autonomous systems.
accepta o ipoteză to accept a hypothesis
aceiaşi The numbers +8 and +3 have like signs.
No two polynomials can have all their roots alike (or
the same) unless they differ by a numerical factor.
acelaşi The preceding discussion may be summed up by
saying that the arithmetic for complex numbers is
much the same as that for real numbers.
acum We now want to let j→∞.
For the present we content ourselves with
demonstrating the assertions just made concerning the
sets G and H.
arăta
acum este uşor de arătat că We can now easily show that ...
adecvat The model fits the process under study adequately.
adeveri
se adevereşte că Thus the martingale ψ(t) turns out to be a process
with independent increments.
s-a adeverit a fi This proved to be a bigger problem than originally
anticipated.
Page 1 of 70Fraze uzuale
2/17/05http://math.ournet.md/formule/fraze/fraze.html

This value was found to be cos(π/17).
admite
la fel admite The function η(t) also admits decomposition of the
form (4).
adresa
ne adresăm la We now turn to the task of considering the
continuous-parameter supermarlingales.
aduce
demonstraţia este adusă The proof of the theorem is given in [8].
aduna
adunăm Now write down these inequalities for n, n+1, ..., n+m
and add them to obtain the estimation (6).
afirma
afirmă The fundamental theorem of arithmetic asserts that
every integer greater than 1 can be factored in one and
only one way, apart from order, as the product of
positive prime numbers.
Bohm [2] claims that there is such a thing as the
primacy of metaphysics in connection with biology.
afirmaţie
afirmaţie mai generală A more general statement can be found in [15].
afirmaţie necesară Approaching the limit as N→∞ we obtain the
required assertion.
afirmaţie reciprocă The converse of (5) is false.
The converse of this statement is known to be false.
However, if we are concerned only with versions of a
given process, the converse holds in the following
sense.
afla
a afla We are now in a position to determine (or to find)
the value of x*.
ajunge
ajungem la ... Thus we arrive at the following conclusion
[definition, equation, theorem, assertion, result].
ajutor
cu ajutorul By means of the equivalence relation we get the
decomposition of the set of all oriented segments into
disjoint classes such that segments in the same class
are equivalent and segments in different classes are
not equivalent.
When formalizing the notions of probability theory,
the first fundamental assumption is that the results of
experiments can be described by means of a certain

set Ω.
The data were obtained with the help (or with the
aid) of a digitizer.
Both problems are solved by constructing a right-hand
inverse matrix Sr
-1 of S.
alt Another way to approach the problem is to take a
Taylor series expansion of g(t).
altă Any term may be transposed from one member of
equation to the other, provided its sign is changed.
The random variable η may have a different
distribution.
altfel This definition also makes use of the abstraction
principle, but in another way.
altfel zis Otherwise speaking [fn(x)] = [gn(x)] if and only if
{fn(x)}~{gn(x)}.
amănunţit
mai amănunţit These operations are discussed in more detail in next
section.
ambele Both estimates are quite rough.
But the functions f and g are both continuous, and
thus the two functions coincide.
Multiplying the two sides of (4) by cosmx and
integrating, we obtain ...
ambele părţi The two sides of Young's inequality
are equal if and only
if b=ϕ(a).
ambiguu This ambiguity does not lead to misunderstanding.
aminti
amintim că We recall that the compensator γn of the measure of
jumps µn is non-negative.
Recall that L is generated by all processes whose
trajectories are right-continuous and have right limits.
analiza
pentru a analiza To analyse the equation, it is convenient to go over to
non-dimensional variables.
este analizată To analyse the equation, it is convenient to go over to
non-dimensional variables.
The sum S is analysed analogously.
analogic The proof of (11) is completely analogous to that of
(10).

analogic cu ... We shall introduce distributions in a way analogous
to that used in the Cantor theory when generalizing
rational to real numbers.
analogie The analogue of the Fermat's theorem is also valid.
anume In this particular case only one side of the triangle,
namely BC, has traces within the limits of the
drawing.
If S consists of a single element x, then R(x), namely
the smallest subring containing x, is commutative.
The extended solutions have the property II, namely
of uniform continuity.
aparatul matematic mathematical apparatus (or tools / techniques)
a body of mathematics
aparţine
aparţine la The process X(t) falls into one of the following three
classes depending on its asymptotic behaviour.
This equation falls among the so-called renewal
equations.
care nu aparţine This equation contradicts the assumption that G
contains points not belonging to D.
apărea
apare The problem arises of finding the conditions under
which the distribution p(u) is unimodal.
aplica
să aplicăm Let us apply this result to the case of an increasing
process At.
pot fi aplicate Formulas (1) and (2) may be employed on condition
that the contour C has no loops.
se poate de aplicat Since p is of the form 1+4m, Corollary 2.5 is
applicable and hence p=x2+y2.
aproape The temperature was observed to be near zero.
aproape de The angle θ is closed to 45 deg.
aproape peste tot The Lebesque-integrable functions are equal if and
only if they have the same values almost everywhere.
aproape toate Nearly all scientific problems deal with quantities and
relations among them.
aproape toţi It is easy to verify that f(x)<C for almost all x.
aproximativ acelaşi As the numbers of the molecules moving in opposite
directions are much the same, it is natural to
assume ...
aproximaţie
în primă aproximaţie
As (or in) a first approximation, x(t) may be chosen

to be t2.
aranja în ordine crescătoare
[descrescătoare]
sunt aranjaţi în ordine crescă-
toare [descrescătoare]
The jump moments t1, t2, ..., tn are arranged in
ascending [descending] order.
arăta
arată Fig.12 depicts the slope of the line ∆x versus ∆t.
vom arăta We shall show that in this case p must divide b.
este arătat The slope of the line ∆x versus ∆t is shown
schematically in Fig.12.
pentru a arăta că To show that q and r are unique, suppose that q'
and r' is any pair of integers for which a=bq'+r', 0
≤ r' < b.
cum este arătat mai sus As has been shown above, the process X t is a
continuous L2-martingale.
arbitrar Let ξ(t) be an arbitrary quasi-potential.
Suppose this is true for an arbitrary n.
argument This is a convincing reason for the study of stochastic
equations of the form.
This reason suggests that the solution to Eqn (17) is
unique.
argumente There are doubtful points in the above reasoning.
aritmetică Arithmetic is the elementary branch of mathematics
dealing with the properties of numbers and their
operations.
asigura
asigură Property 1o
ensures the feasibility of the addition.
The MIS furnishes (or supplies) data for
management.
asociat
asociată cu (referitoare la) The error is associated with (or is due to) the
inaccuracy in computations.
The study is concerned with linear functionals of
supercritical processes.
The first problem is directly related to partial
differential equations.
Further extension of the notion of a stochastic integral
is connected with the extension of the notion of
convergence.
asociat la
The polynomial R(t) corresponding to this function
by (6) is almost everywhere nonzero.
The space, S2k-1, and the projective metric, L(r,s),

associated with it will play an important part in the
future.
It is convenient to replace k by a new factor µ related
to k by the relation µ=4πk.
astfel
Thus the following theorem has been proved.
The factors µ and k are related as follows: µ=4πk.
astfel încât Let X be a space such that from every open cover we
can select a finite cover.
We break up the component a into several
components in such a way that A and B now belong
to different components.
We select a basis in the underlying space such that ...
Specifically, the parameter can be chosen so that the
distribution is unimodal.
The model is so constructed as to allow further
modification and improvement.
astfel ... ca We take a point on the line such that ...
astfel ... încât We take a point on the line such that ...
Applying Lemma 20.3 k times, we infer that there
exists a periodic function G0(x) with G0
(k)=g(x).
aşa numit
In applications we often come across the so-called
Heaviside function.
aşa ... pentru care We take a point on the line such that ...
aşadar Thus, the integral on the right-hand side of (5) can be
analytically continued to the whole domain.
The last formula becomes p(la+mq)=b, so that p|b.
Every element in T has norm at least equal to 1, so
there must be one of them, γ , which is of least
positive norm.
Since p is of the form 1+4m, Corollary 2.5 is
applicable and hence p=x2+y2.
Therefore P(x,s,t,A) saitsfies the Chapman-
Kolmogorov equation.
Consequently,
ataşa la
poate fi ataşat la The process X(t) may be placed (or put) into one of
the following three classes depending on its
asymptotic behaviour.
atinge
atinge maximum [minimum]
The function ψ(x) reaches its maximum [minimum]
at x*=3h/2.
Let b1(s,w) coincide with the z for which the

minimum of the function | B(s,w) z |, | z |=1, is
attained and let b2(s,w) coincide with z for which the
above function attains its maximum.
atinge scopul
de a atinge scopul In order to attain the purpose, we shall not avail
ourselves of the methods of functional analysis.
este atins scopul This aim is attained (or objective is accomplished)
by introducing non-dimensional variables x' = x/x0
and y' = y/y0.
atinge
se atinge Evidently, if the inf in (1.5) is attained at a certain
point , then the inf Φm(x,um) is also attained at that
point.
atrage atenţia
să atragă atenţia The reader should take notice of the fact that the scale
parameter a does not enter into the expression for G
(u).
It is necessary to pay special attention to the
behaviour of F(x) at infinity.
se atrage atenţia Recently much attention (or thought /
consideration) has been given to the study of the
diffusion processes.
atribui sens
pentru a atribui sens To attach a meaning to the solution of this stochastic
equation, we must define the measure µ more
accurately.
se atribuie sens Analogous meaning is attached to the notation D
[0,∞).
atribui valoarea
atribuim valoarea We assign the value 0 to this state.
valori pot fi atribuite A variable is a quantity to which an unlimited number
of values can be assigned in an investigation.
automat It follows automatically that these Rm-semisimple
rings are strongly Rm-semisimple.
auxiliar As a preliminary to the proof of the theorem, we shall
discuss several auxiliary assertions.
avantaj
avantaje To appreciate the merits (or the advantages) of this
theory, it suffices to observe that ...
avantaj principal
The main (or principal / major) advantage of this

approach is that it enables the results of the previous
chapter to be extended to the case under
consideration.
avea
avem Since a satisfies (1), we have Y 1=Y 2.
nu are For instance, the function
has not a derivative at
the point 0.
The prime number p possess no factors other than ± 1
and ± p.
poate avea It follows that the solution can have only a finite
number of zeros in D.
nu poate avea It follows that the solution cannot have more than a
finite number of zeros in D.
avea de-a face
avem de-a face In this section we deal only with rational integers.
avea intenţia
vom avea intenţia In this section we are going to modify our definition
of distribution so as to obtain a notion equivalent to
that of S. Sobolyev and L. Schwartz.
avea loc
această nu poate avea loc This cannot be, for l/p is not a rational number.
această are loc în cazul This happens to be the case for those equations in
which S increases.
avea maxim [minim]
are maxim [minim] The function ψ(x) has a maximum [minimum] at the
point x*=3h/2.
avea neajunsul
au neajunsul These equations possess a fundamental defect (or
demerit / draw back / disadvantage).
are neajunsul His hypothesis has limitations of its own.
avea nevoie de
vom avea nevoie de In order to achieve this, we shall need some material
from elementary number theory.
avea o formă ...
are o formă ... Equation (3.2) is of the following form ...
avea o mare importanţă
are o mare importanţă In applications the following theorem is of great
importance.
avea sens

dacă 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 soluţie unică
are soluţie unică Equation (7) has a unique solution.
avea un caracter
are un caracter Noise ω(t) is stochastic in character (or in nature).
Noise ω(t) is of a stochastic character (or nature).
avea valoarea
are valoarea The derivative F'(x) has the value 0 at the point 0.
B
baza pe
se bazează pe The proof is based on the ideas of Kunita and
Watanabe [36].
The previous analysis proceeds from the assumption
that the class M* contains the class M2,∞.
bineînţeles It is clear that the definitions and properties given
below can be extended to σ-algebras.
biunivocitate Hence from (6) and the remark concerning the
one-to-one-ness of the correspondence, relation (8)
yields F=0.
C
ca de obicei As usual, we use continuous versions of (4).
ca şi în As in the example discussed above, we can easily
prove the following proposition.
ca şi în cazul ...
In the same manner as in the case of convergence to
a Wiener process, one can easily deduce the following
result.
In the case of distributions, as in the case of functions,

the following properties hold true.
ca urmare Such a solution does not exist in consequence (or on
account) 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 uşor de calculat as is easy to calculate
as is easy to evaluate
calcula integrală dea-lungul
curbei
to take the integral along a curve
calcula integrală pe domeniu to take the integral over a domain
care In classical analysis there have been considered several
sequences of functions which are distributionally
convergent to δ(x).
Choose in D2 any function that tends to infinity as
x→0.
cărui A variable is a quantity to which an unlimited number
of values can be assigned in an investigation.
al cărui Let A be a strongly positive operator whose domain of
definition does not depend on t.
care este Consider the function λ(y), which is a periodical
distribution coinciding with δ(y) for | y | < 1/2.
caz
caz particular This formula can be considered as a particular case of
formula (14).
cazul considerat In the case under consideration the process α(t) is
continuous.
Let us generalize equation (6) to the case under
discussion.
căuta
vom căuta We shall seek a solution to (12) in the form
z(t,u) = x(t) y(u).
sunt căutate It is convenient, in solving problems, to use letters for
the numders which are sought.
căutată The sought-for quantity M is involved in the equation
reciprocally.
The desired value of m can be determined from
conition (4).
care va fi căutată Consider the equation (3), where f(t) is the function to
be found.
Here v* is the value of v to be determined.
căutare

în căutarea In looking (or in search) for the optimal solution we
discovered that ...
câteva To see this, we shall prove several lemmas.
A few words should be said about physical meaning of
this parameter.
Some other examples of fundamental sequences will
be given after the following lemma.
câteva modalităţi There is more than one way to approach the problem.
ce For instance, the Dirac delta distribution cannot be
identified with any continuous function, which will be
proved in Section 8.
cel mai bine The nature of this problem can best be made plain by
examples.
cel mai mare divizor comun
(CMMDC)
The greatest common divisor (GCD) of two integers
h and k is the largest positive factor common to both h
and k.
cel mai mic multiplu comun
(CMMMC)
Twelve is the least common multiple (LCM) of 3 and
4.
cel mult The set of the points of discontinuity of f(t) is at (the)
most countable.
cel puţin Formula (7) is true under the hypothesis that at least
one of the integrals on the left-hand side is meaningful.
cercetare
cercetare profundă the in-depth study
cercetare ulterioară To determine whether these ideals coincide, we must
make a further study of the polynomials.
cere
se cere It is required to estimate in the best possible manner
the value of a random variable ξ.
se cere întrebarea It is therefore reasonable to ask for which classes of
"integers" the fundamental theorem holds, and for
which it does not.
cerinţă mai puternică The process Mt, satisfies the conditions of (1) with the
stronger requirement that be an L2-
martingale.
chiar în cazul când This example shows that the ordinary derivative does
not always coincide with the distributional derivative,
even when the ordinary derivative wrists everywhere
except at one point.
ci
Thus we need not 8, but 9 parameters to describe the
system.

ciocni cu
ne ciocnim cu In applications we often come across the so-called
Heaviside function.
cititor The reader will find it a useful exercise to supply the
details of the proof.
clasic In classical analysis there have been considered
several sequence of functions which are
distributionally convergent to δ(x).
clar
este clar că Clearly, the sum, difference and product of such
integers are of the same form.
It is clear that a and -a are both in the set A.
intuitiv este clar It is clear intuitively that every collection, finite or
infinite, of non-negative integers contains a smallest
one.
coeficientul pe lângă
the coefficient of smth.
the coefficient multiplying smth.
coeficientul pe lângă
termenul
superior
A polinomial is monic if its leading coefficent is 1.
coincide
coincide cu For an arbitrary function F(x) satisfying conditions 1) -
6) there exists a unique probability measure whose
distribution function coincides with F(x).
The characteristic through A is the same as the one
through B.
complet satisfăcător Completely satisfactory solution of the functional
problem is given in [6].
completa
este completată It is assumed that σ-algebra F0 is completed (or
augmented) by all P-null sets.
complicat The problem of optimization is, in general, more
complicated.
Integration of equation (3.2) represents a rather
involved boundary-value problem.
conclude From a>b and b>c we conclude that a>c.
condiţie
condiţia asupra This result was established in another way under
somewhat weaker conditions on the diffusion
coefficients.
condiţiile conform cărora The problem arose of finding the conditions under
which the distribution p(t) is unimodal.

condiţie de convergenţă la The condition for convergence to a Wiener process is
stated in the next section.
condiţie de existenţă şi
unicitate a soluţiei
Let the coefficients of equation (9) satisfy the
condition for the existence and uniqueness of the
solution.
condiţii exacte pentru The exact conditions for equilibria to exist and be
stable are examined.
condiţie mai fină The tangent bundle of the manifolds provides a
sharper necessary condition.
condiţii sunt verificate Assume that conditions (5) and (20) are satisfied.
If the conditions of Theorem 10 are satisfied and,
moreover, A(ϕ,t) is continuously differentiable, then ...
Let the conditions of Theorem 4 be satisfied and the
function be twice continuously differentiable.
alte condiţii fiind aceleaşi The distinction between (14) and (15) is that the
variable x entering into (15) depends on ω, other
things being equal.
în condiţia că Thus, the function f(x) is uniquely determined,
provided that it exists everywhere.
Any term may be transposed from one member of
equation to the other, providing its sign is changed.
The abstraction principle can be applied to sets of
arbitrary elements provided there exists an
equivalence relation ~.
These functions are locally Riemann-integrable under
(or on) the condition that their values are equal at all
points of continuity.
în condiţiile teoremei Under the conditions of Theorem 6.1 the limit
exists and is differentiable.
conduce
conduce la ecuaţia This reasoning yields a simple equation.
confirma ipoteza to verify a hypothesis
conform
conform algoritmului The classes can be formed by the FLAMENCO
algorithm.
conform criteriului By the Eisenstein's criterion, the polynomial xn-2 is
irreducible over the field of rational numbers.
conform definiţiei Then, by definition, ...
conform ipotezei inducţiei By the induction hypothesis, the theorem is true for f
(x).
conform lemei By Lemma 2.3, the sequence {gn(x)} is fundamental.
conform presurunerii
By assumption, E(1)=0.
By the assumption of the lemma, the solution to (1) is
positive.

Since ... by hypothesis, (4) is a bounded sequence.
conform proprietăţii By property (4) of norms, every element in T has
norm at least equal to 1, so there must be one of them,
γ, which is of least positive norm.
conform teoremei By Theorem 1.1, we can find q and r so that b=dq+r,
0 ≤ r < d.
consecinţă
consecinţă din To complete the proof of the lemma, we use the
corollary of Lemma 2.
este o consecinţă The inequality f(x)≤0 is a direct consequence of the
system fi(x)≤0, i=l, 2, ..., n.
consecutiv When an expression contains parentheses within
parentheses, they may be removed in succession,
beginning with the innermost.
considera
considerăm Consider the rational number a/b.
poate fi considerată The problem can be approached in many different
ways.
să considerăm Let us now consider the case a>1.
Consider now the case a>1.
sunt considerate Several other functions, very useful from the practical
point of view, are considered in the following section.
Some properties of the operator L are dealt with in the
next chapter.
considerată An integral part of the creative approach to the
problem under consideration (or under study) is the
analysis of its similarity to and difference from the
analogous problems.
poate fi considerat ca C (R+) can be regarded as a complete separable
metric space under the topology of uniform
convergence.
în lucrare se consideră The paper deals with the theory of distributions of
finite order.
considera acum
considerăm acum We now consider the process η(t).
Consider now the process η(t).
considera de la început
vom considera de la început Consider first the simplest case where a=0.
We will first confine our attention to discrete-
parameter martingales.
considera util

considerăm util We find it useful to define a new concept of
conjugacy and to discuss its relation to the old.
considerabil mai simplu Theorems IV and VI are considerably simpler than
the analogous theorems in the differential calculus.
consideraţie We now turn to the task of considering the
continuous-parameter stochastic processes.
The consideration (or discussion) of this problem in
more detail shows that ...
We must now subject the concept of equivalence to a
somewhat closer scrutiny.
Further inspection (or examination) of Fig.1 discloses
that there are two points of inflection on the curve.
consta
constă în ... The abstraction principle consists (or lies) in the
identification of objects (mathematical entities) which
have a common property.
construcţie By a slight change in the method of (7), the
construction of such functions is easily carried out.
construi
pentru a construi The abstraction principle is often applied in
mathematics to construct new notions.
continuu
In the case under consideration the process α(t) is
continuous at every point of the interval (c,d).
continuă din dreapta după t Ft is continuous from the right (or right-continuous)
in t if for all t ≥ 0 .
contrazice
ce contrazice So π is a unit, contrary to the hypothesis.
So p|L, contradicting the fact that L is prime.
această contrazice This contradicts r ≥ 0.
contrazice presupunerii This equation contradicts the assumption that G
contains a point not belonging to D.
This contradicts the hypothesis that k→∞ and that (6)
holds for all l<km.
contribui
pentru a contribui la
răspândirea
This series of expository presentations of the best
thoughts and keenest researches in pure and applied
mathematics is intended to contribute to the
dissemination of mathematical knowledge.
conţine
se conţine The subgroup Pn is contained in the centralizer of the
element p in B.

conţine proprietăţi The following list contains the fundamental
properties of the norm.
convenabil
convenabilă In some cases the following complex form of
trigonometrical series is advantageous.
mai convenabil It is more convenient to break up the experiment into
three phases.
este convenabil It is convenient to call two Gaussian integers
associates if α=εβ, where ε is a unit.
va fi convenabil It will be convenient to define the convergence of fn
(x) in the following sense.
deseori este convenabil It is often convenient to establish the position of
points by giving their coordinates.
conveni
vom conveni We shall agree to write A(x,t)∈S if A(x,t) is a process
with independent increments.
converge
converge absolut The series (1) converges absolutely.
converge aproape peste tot to converge almost everywhere
converge în medie to converge in (the) mean
converge în probabilitate to converge in probability
converge uniform Thus the series (4) converges uniformly.
convinge
ne convingem că Make (or be) sure that the coefficients have no
common factors other than +1.
To complete the proof, check that ...
Before applying Theorem 10.7, check to see that there
is an α in A such that ...
a se convinge în To prove the convergence X n→M, it suffices to make
sure that ...
trebuie să se convingă că The investigator must assure himself that the errors
are within the admissible limits.
pentru a se convinge în ... To see that if θ satisfies an equation
anxn + an-1xn-1 + ... + a0 = 0, then there is a rational r
such that rθ is an algebraic rational, observe that an
θ
satisfies (3).
To be certain that c is the required element, check
that D[c,A]>0.
pentru a se convinge în
aceasta
To see this, notice that Powell's frequency function is
identical with our function Φb(x).

se poate de convins că Then, similarly as has been done in [1], one ascertains
that the limit function satisfies the equation (4).
este uşor de convins că It is easy to make sure that ϕ(x) is convex on [c,∞).
coordona
se coordonează The theory checks well (or agrees / is in good
agreement) with experiment.
The hypothesis fits the experimental data.
This conjecture is in line with that of Seidenberg.
corect This definition is correct; since the sequence {pn
(m)
(x)} is fundamental.
corectitudinea definiţiei To verify the correctness of this definition, we must
prove that ...
corespondenţă biunivocă The one-to-one correspondence established above
makes it unnecessary to distinguish between functions
f(x) and distributions [f(x)].
crescător
crescătoare There is an increasing sequence of integers km such
that ...
strict crescător Introduce a strictly increasing funstion g(x) defined
on [0,∞).
creşte
creşte monoton după t Ft monotonically increases in t, that is Fs⊂ Ft, for
s<t.
cu ... ce tinde ... Each summand on the right of (12) becomes
vanishingty small with (or as) n→∞.
cub al numărului When a is used three times as a factor, the product is
called the third power of a, or the cube of a.
cunoaşte
cum noi deja cunoaştem Since, as we already know, all these trigonometrical
integrals vanish, we obtain formula (5).
cunoscut cu The reader acquainted with the Lebesgue integrals
can interpret formula (1) in a still wider sense, viz. as
the equality almost everywhere.
este cunoscut că It is well known that for an arbitrary function F(x)
satisfying conditions 1) - 6) there exists a unique
probability measure whose distribution function
coincides with F(x).
cum este cunoscut
As is well known, the nth partial sum of the series
is nothing else

than the Dirichlet kernel .
este bine cunoscut It is well known that there exist sequences {Tn} and
{Sn} such that ηn=Tn-Sn.
este cunoscută ca This relation is known as the Biot-Savart law.
cuvânt
cu alte cuvinte To put it in another way, the gross weight W can be
represented as W=Wst+We+Wp.
D
da
dă The repeated application of relation (2.1) yields ...
The following theorem provides the description of the
everywhere dense set E.
dăm We give (or present) below a synthesis of various
approaches available.
da posibilitate
dă posibilitate The martingale approach enables us (or permits) to
suggest a new method for constructing solutions of
stochastic differential equations.
Knowledge of the numerical values of a and b offers a
means of (or makes possible) determining ...
This method makes it possible to tackle the boundary-
value problem under discussion.
The main advantage of this approach is that it enables
the results of the previous chapter to be extended to the
case under consideration.
da restul de la împărţire
dă restul de la împărţire Every integer a leaves a remainder r, 0 ≤ r < m, on
division by m.
dacă In the course of the proof of the theorem we have
described the method for determining the functions
Φn (x0, ..., xn) if X is locally compact.
dacă acesta este cazul If this is the case, the deterministic approach is quite
suited for this purpose.
dacă acesta există Hence, it follows that the representation of f(x) in the
form (4), if it exists, is unique.

dacă este necesar The integer k can be, if necessary, replaced by any
greater integer.
dacă n-ar fi Were is not for the discontinous coefficient,the
problem would be much simpler.
dacă nu If there is no such ζ, we write max f = ∞.
Unless otherwise stated, condition (2) will always be
assumed to be in force.
dacă numai Thus, the function f(x) is uniquely determined,
provided (that) it exists everywhere.
dacă şi numai dacă R is a realization of η(t) if and only if ...
dacă şi numai dacă există The martingale ξ(t) is uniformly integrable if and only
if there exists a random variable η such that E |η| <
∞ and ξ(t) = E {η | Ft}.
dacă ..., atunci Evidently, if the inf in (1.5) is attained at a certain point
, then the inf Φm(x,um) is also attained at that point.
dacă ... nu Unless u is a power of 2, this can always be done.
dar Element ξ belongs to V, whereas (or and) ζ belongs to
W.
This value is negative — not positive.
dar atunci But then we could proceed from the pair (x, y) to a still
smaller in the same way as from (x1, y1) to (x2, y2).
dar nu With time the number of particles increases, rather
than remains constant.
date iniţiale the initial (or the input) data
datorită Delacherie and Meyer are well known for their book
'Stochastic Processes and Potentials'.
Mathematics, due to (or owing to / because of) its
abstract nature, finds wide application in most spheres
of human activity.
de aceea For this reason the points belonging to Ω are called
elementary events.
Conversely, if N=1, we have a+b=1, so that either a=0
or b=0.
Every element in T has norm at least equal to 1, so there
must be one of them, g, which is of least positive norm.
de asemenea
Observe also that |Dn(s)| ≤ C logn.
From equation (3) we find, as well,
.
If α and β belong to F, so do α+β, α−β, αβ, and α/β if

β≠0.
de fapt In fact, this follows from the consideration that the
sequence gn(x) is bounded for x>0.
Since these are continuous processes, we actually
have ...
de fiecare dată când In stating rules, letters are used to represent not only the
numbers to be found, but also the numbers that must be
given whenever the rule is applied.
de k ori Applying Lemma 20.3 k times, we infer that there
exists a periodic function G0(x) with G0
(k)(x)=g(x).
Differentiating formula (8) k times, we obtain the
equality ...
de la The Arab notation has been in use since the XVI
century.
Prof. Romanov is giving a course of lectures on chaos
and bifurcations in room 406, commencing October 1.
In order to start from the very beginning, we introduce
first the basic notions and concepts of the theory of
measurements.
From this time on, the density function decreases.
We shall start with the basic notions and concepts of
the theory of measurements.
de unde Setting (*) we obtain (**), whence, in view of
inequality (1), ...
The author does not explain from whence the estimate
(7) emerges.
deduce
deducem Applying Lemma 20.3 k times, we infer (or deduce)
that there exists a periodic function G0(x) with G0
(k)=g
(x).
deducem ecuaţia We derive (or deduce) the equation for the
distribution of cell size at division and the distribution
of generation time.
defini
definim Define unit and prime just as we did for the Gaussian
integer.
definită The function h(x) is defined at every point of the
interval [c,d].
The variable, whose value is determined once the
value of the independent variable is given, is called the
dependent variable.
bine definită

The integral is well defined in
accordance with the above definition.
definit anterior Using the Haar family {gn} defined above, we
introduce functions {hn}.
pozitiv definit A complex-valued function f(x) is called positive
definite if for any n and complex numbers zj
definire
în definirea In defining K(x) we have made use of our assumption
that b(x)=0 for x<a.
definiţie In the definition of the mth derivative we can replace
the polynomials pn(x) by functions fn(x).
din definiţie From the definition it follows at once that G(u)
satisfies condition (2).
definiţie echivalentă It is possible to give an equivalent definition of
integral (1) as the limit of sums (2).
definiţie exactă A precise definition is given below.
demonstra
demonstrează This proves that d is a factor shared by both a and b.
pentru a demonstra To prove the theorem, it suffices to show that ...
este demonstrată Since Nρ<Nα, the inequality (3) is established.
pentru a demonstra To prove this, interchange the order of integration in
the double integral in (6), after which all the integrals
except (8) can be evaluated exactly by appropriate
change of variables.
To prove the theorem, note first that neither a nor b can
be zero.
nu este ce demonstra If p|a, there is nothing to prove.
se poate de demonstrat că It may be proved that if ...
de la început vom demonstra We shall first prove the following two lemmas.
înainte de a demonstra
teorema
Before proving the theorem we illustrate its
applications.
trebuie să demonstrăm că We must prove that the two factorizations differ at
most in the order in which the primes appear.
demonstrare
în procesul demonstrării In the course of the proof of this theorem we have
made use of the following lemma.
demonstraţie

fără demonstraţie We shall assume without proof the following theorem.
denumire The name 'distribution' is due to L. Schwartz, who
developed the theory in 1945 and later.
deoarece This cannot be, for 1/p is not a rational number.
In the theory of distributions a distinction between the
trigonometrical series and the Fourier series is
unnecessary since each convergent trigonometrical
series is an expansion of a periodic distribution.
Because (3), we have ...
deoarece în caz contrar All numbers amn can be arranged in a sequence {bk}
convergent to b0, for otherwise it would suffice to
neglect a finite number of initial terms a1n, a2n, ..., apn
to get a contradiction to property (5).
deoarece ..., atunci Since the functions w are solutions of this equation, the
difference of any two of them may be regarded as the
solution of a certain linear differential equation.
deosebi
se deosebeşte prin The function f(x) differs from F(x)(k-1)by a constant.
se deosebesc prin We must prove that the two factorizations differ at
most in the order in which the primes appear.
se deosebesc una de alta prin The equation f'(x) = g'(x) holds if and only if the
distributions f(x) and g(x) differ from each other by a
constant function.
deosebire
spre deosebire de ... The absolute value of a number a, as distinguished
from its algebraic value, is represented by |a|.
As opposed to (or as distinct from / in contrast to)
the real case, any polynomial always has a root in the
field of complex numbers.
In fundamental contrast to M. R. Stein, we have
preferred the algebraic approach.
deosebit
este deosebit de importantă The case of a linear substitution is especially
important (or is of particular importance) for us.
depinde
care nu depinde de To this end, we establish first that there exists a
constant L not depending on s and n such that ...
nu depinde de alegere The distribution (1) does not depend on the choice of
the indefinite integral ψ(x).
depinde esenţial de In this new definition the fact that the choice of the
integer k depends on the interval [a,b] is essential.
depinde monoton de t
Let (2) be a family of finite stopping times which are

monotonically dependent on t and right-continuous in
t.
deriva
deriva ... după x To differentiate v(t,x) with respect to x.
deriva ... în raport cu x To take the derivative of v(t,x,u) with respect to x.
derivând In fact, by differentiating (3) we obtain ...
Hence, by successive differentiation we obtain ...
derivând de k ori Differentiating formula (8) k times, we obtain the
equality ...
derivând succesiv Hence by successive differentiation we obtain ...
derivata după x A derivative of u(t,x,u) with respect to x.
deschide
deschide posibilităţi The interpretative approach opens perspectives in that
direction.
deschiderea parantezelor the removal of parentheses
descompune în factori to expand the number into factors
to factor the number
to present smth in a factor form
to factor smth into components
descompune în serie
descompunem în serie Expand function ϕ(x) in a Taylor series.
descompunem în serie în
raport cu x
Expand function u(t,x,u) into a Taylor series about x.
poate fi descompusă în serie Under certain conditions a continuous function can be
expanded into a Fourier-Bessel series.
Function f(x) can be expanded as an infinite power
series.
descompunere
Any supermartingale ζ(t) has exactly one
decomposition of the form ζ(t)=µ(t)-α(t).
descompunere în 6 = 2*3 = 3*2 are the only factorizations of 6 into
positive prime factors.
descompunere în fracţii
elementare
The decomposition of a fraction into partial
fractions.
descompunere în serie Hence, we obtain the expansion of ctgx:
ctgx = 2(sin2x + sin4x + sin6x + ...).
descrescător Let {an} be a decreasing sequence and {bn} an
increasing sequence of numbers.
descriere formală A formal description of the basic notions is usually
based on the set-theoretical model of probability theory
developed by A. N. Kolmogorov in 1929.
descris

descris anterior We now show how the method described above can be
extended to move the existence of µ.
descrisă de ecuaţie We will consider only those systems whose evolution is
given by the equation of form (8).
desemna
desemnează The symbol Fn(x)→ will denote that the sequence
{Fn(x)} converges almost uniformly to a function.
desen
pe desen In Fig.11 the planes π1 and π2 are shown as coinciding.
din desen se vede că In Fig.10 it is seen that ...
în limitele desenului In this particular case only one side of the triangle,
namely BC, has traces within the limits of the
drawing.
deşi It is possible that the ordinary derivative does not exist,
although the distributional derivative has a value at this
point.
detaliat
mai detaliat It is necessary to consider this problem in greater
detail.
detaliile The details can be found in most texts on the theory of
equations, for example in the book of Thomas listed in
bibliography.
The Introduction gives details concerning the
application of stochastic differential equations in
natural sciences.
determina
determină Two sequences {fn(x)} and {gn(x)} determine the same
distribution if and only if they are equivalent.
determinat cu exactitate de The indefinite integral is determined up to a constant.
Integrating f(x) k times, we obtain a locally integrable
function F(x), which is determined up to a polynomial
of degree less than k.
deveni
devine The relation of equivalence is then transformed into
the usual equality.
With this terminology Theorem 1.5 becomes
meaningful for the Gaussian integers.
dezacord This explains the discrepancy in behaviour of the two
functions.
diferenţă

unică diferenţă între The only difference among them is the order of
appearance of the factors.
diferi
diferă de The function f(x) differs from F(k-1)(x) by a constant.
The proof is not like that of Theorem 5.6.
diferite de Consider the numbers which are different from 0 and
±1.
The prime numbers p possess no factors other than ±1
and ± p.
dificil
este mai dificil It is slightly more difficult to see that
dificultate
dificultate poate fi trecută This difficulty can be remedied by a slight restatement
of the fundamental theorem to include negative
numbers.
din nou Now we can, once again, use the arguments analogous
to those presented in Section II.
direct This inequality can be proved directly (or
immediately) using (7) and Lemma 9 in Section 1.
direcţie
în aceea direcţie The interpretative approach opens perspectives in that
direction.
discontinuitate de speţa întâia
[a doua]
With probability 1 ξ(t) has no discontinuities of the
first [second] kind.
discuta
discutăm In Chapter 8 we discuss the filtering problem.
nu va fi discutată The validity of this assumption will not be debated
here.
distinge
pentru a distinge The one-to-one correspondence established above
makes it unnecessary to distinguish between functions
f(x) and distributions [f(x)].
distingere In the theory of distributions a distinction between the
trigonometrical series and the Fourier series is
unnecessary since each convergent trigonometrical
series is an expansion of a periodic distribution.
distribuţie comună the joint (or simultaneous) distribution
divide
se divid
Then the numbers 1, 2, ..., p-1 fall into pairs such that

the product of any pair is congruent to 1 modulo p.
se divide The procedure is then broken down (or divided /
subdivided) into the three steps: ...
se divide prin Nine is a multiple of three.
divizibil
sunt divizibile prin All the terms on the right are divisible by p.
domeniu de definiţie Let A be a strongly positive operator whose domain of
definition does not depend on G.
dori
dorit Passing to the limit in (6) we obtain the desired result.
This is exactly the wanted decomposition.
este de dorit It is desirable in many applications that the function Xt
be also measurable.
după ce To prove this, interchange the order of integration in the
double integral in (6), after which all the integrals
E
ecuaţie
din ecuaţia From equation (2) we find that ...
ecuaţie cu n necunoscute the equation in n unknowns
ecuaţie de gradul n the equation of degree n
ecuaţie iniţială the input equation
ecuaţie în raport cu
(necunoscuta) x
the equation in (the unknown) x
ecuaţie rezolvabilă în raport
cu x
the equation solvable for x
editarea The publication of this monograph was made possible
due to ...
He has over 70 published works.
efectua
pot fi efectuate The calculations can be carried out (or performed) in
the same way as in Section 15.
de a efectua transformarea On many occasions it is useful to take the Laplace
transform of equation (15).
egal
sunt egali The vectors and are equal in magnitude.

elabora
era elaborată The statistical theory has been developed quite
recently.
elementar The solution of equation (5) is obtained in an
elementary manner by expanding function x(t) in a
Fourier series.
elibera
să ne eliberăm de But here we need only free ourselves of the term V(x)
*µ.
enunţul problemei The most general statement of the problem can be
formulated as follows.
evident A more exact answer to the question requires
apparently (or evidently) a refinement of the
definition of a system.
este evident It is obvious (or evident) that Xt is progressively
measurable.
Obviously (or evidently / apparently), the above
theorem hot index set is taken to be a finite interval
[0,T ] instead of R+.
eveniment We note that any subset of Ω is called an event.
eveniment sigur the sure event
evident The proof of this property is obvious since b=0.
Applying Theorem 12.3 to the obvious equality (*) we
get ...
evita
pentru a evita confuzii To avoid possible confusion, the continuity condition
will be restated in each case.
pentru a evita neînţelegeri To avoid misunderstanding, we may call the first kind
of intervals (including end-points) the closed intervals
and the second kind the open intervals.
pentru a evita repetări în
viitor
To avoid repetitions in future, we present here basic
concepts and definitions.
exact
exact unul Any prime Π divides exactly one positive rational
prime p.
mai exact More precisely, we shall assume that the following
condition is satisfied.
exactitate
cu exactitate de
Then we can write for the division-size density function
(up to a normalization factor) .
The factors in product (4) are determined uniquely
except for order.

Factorization of any positive integer is unique to within
the order of factors.
The fundamental theorem of arithmetic asserts that
every integer greater than 1 can be factored in one and
only one way, apart from as the product of positive
prime numbers.
excepţie
cu excepţia The function ν possesses the property (1) for all ω and t
except for some sets of measure 0.
To prove this, interchange the order of integration in the
double integral in (6), after which all the integrals
exclude
se exclude The second of these possibilities is excluded, for r(x) is
in T.
exclude posibilitate This approach excludes the possibility of considering
the equations having solutions which belong to a more
general class of numbers.
exemplu Another example of the abstraction principle is the
Cantor definition of a real number.
Let us first look at some simple examples.
de exemplu For instance (or for example), the coefficient of
variation, CV, of size at division is typically 10% and
the CV of age at division is typically 20% or more.
As an example, let α=5 and β=1+2i.
prin exemple The nature of this problem can best be made plain by
examples.
We shall explain it by means of examples.
exemplu interesant We shall construct an interesting example of such a
process in this chapter.
exemplu tipic The polynomials Bn(t) are typical examples of
generalized Brownian functionals.
unele exemple Some other examples of fundamental sequences will
be given after the following lemma.
în calitate de exemplu As an example, consider the primitive polynomials
x2+3 and 3x2+7x-11.
exista
există limita With probability 1 there exists the limit
.
existenţă The existence of the Wiener process follows easily
from the Kolmogorov's criterion.
explica

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