Sentence examples for cases of the conjecture from inspiring English sources

(He'd already solved some special cases of the conjecture).

Besides, various cases of the conjecture were proved by Cellina [4] and Fryszkowski [5].

We investigate special cases of the conjecture and prove that the conjecture holds for some of them.

The cases of the conjecture in dimensions one and two were handled in the 19th century, and Stephen Smale solved the cases where n ≥ 5 in 1961.

In the case of the conjecture (C^*(1/2)) we proceed in a similar fashion.

Building on work by the 1990 Fields Medalist, Russian Vladimir Drinfeld, Lafforgue established one important case of the Langlands conjectures.

Also some special cases of Alspach Conjecture are solved in this article.

Both (first-order) contraction mappings and the rth-order contraction mappings defined in Theorem 1.3 are special cases of the now-proven generalised Banach contraction conjecture (see Jachymski [8], Merryfield-Stein [9] and Arvanitakis [10]).

We then present complete verifications of the conjecture in 48 varied cases with real quadratic base fields.

In a 200-page paper he marshaled enough powerful mathematical machinery to prove one special case of the Taniyama-Weil conjecture, valid for "semistable" elliptic curves, and that was enough to imply Fermat's last theorem.

Special cases of the generalized (t,k -design problem include well-known conject,k -design-designs, degree sequences of graproblem hypergraphs, and partincludeiner systems.