Sentence examples for classical existence from inspiring English sources

However, constructive analysis remains on the fringes of the mathematical mainstream, probably because most mathematicians accept classical existence proofs and see no need for the additional mathematical baggage involved in carrying out analysis constructively.

Lemma 2.1 is the classical existence theorem of global attractor by Temam [17].

In this paper, the classical existence result for ε-approximate equilibrium problems is proved in the framework of the Hadamard space (nonlinear space).

He showed that many of the classical existence and uniqueness theorems for second-order discrete boundary value problems extend to the fraction-order case.

Through a priori estimates, we have established the classical existence theorems under appropriate domain convexity hypotheses for both (i) strictly regular A and semilinear or concave ({mathcal {G}}), and (ii) regular A and uniformly concave ({mathcal {G}}).

Our main concerns in this paper are second derivative estimates under natural "strict regularity" conditions on the augmenting matrices, together with accompanying gradient and Hölder estimates, which then lead to classical existence theorems.

There is no separate verb "to exist" in classical Greek; existence was expressed by means of the verb "to be".

Besides Yablo's paradox and a game theoretic version of Mirimanoff's paradox, several classical results (existence of a non r.e.

(3) They addressed the classical problem of existence and uniqueness of (3).

Chew and Flordeliza, in [5], generalized the classical Carathéodory's existence theorem on the Cauchy problem (x^{prime}=f t, x)) with (x 0)=0).

Since the classical solutions admit existence of the stress concentrations and plasticization, but do not take them into calculation, an attempt was made to investigate them and to introduce them into the design process, proposing a controlled degree of plasticization.