Sentence examples for be proven by classical from inspiring English sources

The following theorem can be proven by classical techniques; we refer the reader to [2, 4, 5] for sketches of the proofs.

For later use of this paper, in the following we first give some results on the existence of traveling fronts of (1.4) which can be proved by classical methods (see [4, 5]).

The existence and regularity of the unique solution w can be proved by applying classical methods, for instance, the method of continuity (see [29]).

It is discussed proof-theoretically how tautologies in purely implicational classical logic can be proved by polynomially sized derivations when their minimal counterpart is exponentially sized.

"These practices have been proven by time".

The theorem was proven by Boris Trakhtenbrot (1950).

All recurrences were proven by biopsy.

Metastases were proven by biopsy.

CFSGS was proven by biopsy.

Two solutions are obtained by Theorem 3, and the existence of the third solution is proved by the classical linking theorem (see [19, 20]) and Galerkin approximation.

The famous 148 Letters of Phalaris were proved by the great English classical scholar Richard Bentley, in his Dissertation on the Letters of Phalaris (1699), to have been written much later by a sophist or rhetorician, possibly Adrianus of Tyre (d. c. ad 193).