Matematica pentru toti

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®Ą. 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 y(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. This value was found to be cos(p/17).
admite
la fel admite	The function h(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®Ą 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 W. 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 S_r^-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 h may have a different distribution.
altfel	This definition also makes use of the abstraction principle, but in another way.
altfel zis	Otherwise speaking [f_n(x)] = [g_n(x)] if and only if {f_n(x)}~{g_n(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=j(a).
ambiguu	This ambiguity does not lead to misunderstanding.
aminti
amintim că	We recall that the compensator gⁿ of the measure of jumps mⁿ 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 A_t.
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 q 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, ..., t_n are arranged in ascending [descending] order.
arăta
arată	Fig.12 depicts the slope of the line Dx versus Dt.
vom arăta	We shall show that in this case p must divide b.
este arătat	The slope of the line Dx versus Dt 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 x(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 1^o 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, S_2k-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 m related to k by the relation m=4pk.
astfel	Thus the following theorem has been proved. The factors m and k are related as follows: m=4pk.
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, g , 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 y(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 F_m(x,u_m) 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 m more accurately.
se atribuie sens	Analogous meaning is attached to the notation D[0,Ą).

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 R_m-semisimple rings are strongly R_m-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 y(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 w(t) is stochastic in character (or in nature). Noise w(t) is of a stochastic character (or nature).
avea valoarea
are valoarea	The derivative F'(x) has the value 0 at the point 0.

Aforisme
Ştiinţele matematice, ştiinţele naturale şi ştiinţele umanitare pot fi numite, respectiv şi ştiinţe supranaturale, ştiinţe naturale şi ştiinţe nenaturale.

L. D. Landau

Adevărul matematic, indiferent unde, la Paris sau la Toulouse, este unul şi acelaşi.

Blaise Pascal

O glumă matematică reuşită este mai bună decât o duzină de lucrări mediocre; ea este, totodată şi cea mai bună matematică.

John E. Littlewood

Când doi oameni, având fiecare câte un măr, fac schimb, ei vor rămâne cu câte un măr fiecare, dar când doi oameni fac schimb de idei, aceasta înseamnă că ... ei n-au mere.

Din aritmetica schimbului

Matematica seamănă cu o moară: dacă veţi turna în ea boabe de grâu, veţi obţine făină, dar dacă veţi turna în ea tărâţe, tărâţe şi veţi obţine.

A. Huxley

Reputaţia unui matematician se bazează pe cantitatea de demonstraţii, pe care le-a inventat (cu alte cuvinte: lucrările deschizătorilor de căi întotdeauna au fost greoaie).

A. S. Bezikovici

O demonstraţie se numeşte strictă, dacă strictă o consideră majoritatea matematicienilor.

Morris Kline

Dacă teorema aşa şi n-a putut fi demonstrată, atunci ea devine axiomă.

Euclid

Cel mai mare neadevăr este adevărul înţeles greşit.

William James

Rectorul Institutului Politehnic din Zürich îmi spune:
– Nu este totul pierdut, tinere. Ai căzut la examen? Acelaşi lucru s-a întâmplat şi cu Giuseppe Verdi, care n-a reuşit la examenele de la Conversatorul din Milano.

Albert Einstein

Oamenii de geniu se împart în trei categorii: genii de speţa întâia, care pot fi apreciaţi pe când se află încă în viaţa, genii de speţa a doua, care sunt apreciaţi după moarte, şi genii de speţa a treia, care nu sunt înţeleşi de omenire niciodată.

Stanislaw Lem

Studiile reprezintă ceia ce rămâne, când uiţi totul ce ai învăţat la şcoală.

Albert Einstein

Universitatea dezvoltă toate aptitudinile, inclusiv şi prostia.

A. P. Cehov

După părerea mea, printre cele mai mari descoperiri, realizate în ultimul timp de către raţiunea omului este, la sigur, arta de a judeca despre cărţi, fără a le citi.

G. K. Lichtenberg

Întotdeauna este plăcut să observi, cum alţii comit greşelile pe care singur le făceai cândva.

John E. Littlewood

Taci, atâta timp cât nu poţi spune mai mult decât tăcerea.

Pythagoras

Cercetarea fundamentală este ceia ce faci, când nu ştii ceia ce ai de gând a face.

Charles Wilson

Dumneavoastră doar nu sunteţi matematician? Nu. Prin urmare, nici nu am ce discuta. Eu discut numai cu acei care posedă metoda analizei matematice.

Anatole France

În fiecare ştiinţă este numai atâta ştiinţă adevărată, câtă matematică conţine.

Immanuel Kant

Matematica pentru toti

joi, 17 noiembrie 2011

Dictionar Matematic Roman-Englez de Fraze Uzuale - litera A

Unele "legi" importante şi glumeţe

Regula regulelor

Legea problemelor

Criteriul criteriilor

Postulatul ipotezelor

Principiul rezultatului final

Teorema despre adâncimea băltoacei

Legea I a disrutei

Legea II a diaputei

Definiţia plagiatului şi a cercetării

Postulatul experienţei de lucru

Postulatele de bază ale experimentelor

AFORISME

Probleme gluma