Sentence examples for crucial theorem from inspiring English sources

We start our work by proving the following crucial Theorem.

The crucial theorem is then that regular maps between affine varieties are continuous with respect to the Zariski topology.

In our crucial Theorem 2.3, we prove a nonexistence result for (1.10), under suitable weighted integrability assumptions on.

So it is crucial in Theorems 2, 4 and 5.

Pappus cites the solution to the duplication of the cube as one of the three most crucial geometrical theorems for practical mechanics (Math. Coll. 1028. 18 21).

The crucial assumption in Theorem 1 is the so-called solvability criterion (13).

The crucial assumption in Theorem 4 is the assumption of positive definiteness of the matrix (S [a_{1},b,c,rho,h,g_{,h,g_{1},g_{2},beta,zeta ]).

The crucial assumption in Theorem 1 is the assumption of positive definiteness of the matrix S 1 ( g, h, β, ξ ).

First, we are going to characterize the behavior of z near the (relative) boundary of its domain, which is crucial for the theorem to follow.

It plays a crucial role in proving Theorem 4. Copyright © 2007 by Horacio Arlo-Costa.

In studying the weighted approximation, the following theorem is crucial.