Sentence examples for a point then the from inspiring English sources

But if there were such a point, then the path could be extended by having it pass through that point.

(ii Assume that a sequence in converges weakly to a point, then the following identity holds: (26).

It says that if in this space any closed-curve object, such as a rubber band, can be shrunk to a point, then the space is topologically equivalent to a sphere.

For example, in the setting of [9], if at the moment we reach a point, then the next iterate is an element of, where is the given mapping, which approximates the best approximation of in.

Following Browder [22], we say that a Banach space has a weakly continuous duality map if there exists a gauge for which the duality map is single valued and weak-to-weak* sequentially continuous (i.e., if is a sequence in weakly convergent to a point, then the sequence converges weakly* to ).

Let Y be a subvariety of X of dimension (m >0) mapping to a point: then the cohomology (or homology class, in view of Poincaré duality) class of Y is trivial, since the cohomology algebra of X and T are isomorphic.

She served the first game and lost, winning only a point, then lost the second game at love.

Fifth set: Federer* 6-3, 7-6, 4-6, 4-6, 2-3 Tsonga Federer starts well, going 40-love up, spoons his attempt at a backhand pass to give away a point then wins the game with a biffer of a smash.

Random scatter around zero axis is the expected pattern, but if cumulative values display a continuous increase or decrease towards a particular direction at a certain point, then the observation values are inspected from this point on.

He made a point, then, of lambasting the "pathetic spectacle" of rotten African leaders flying to summits in executive jets.

It is clear that if (V+W) has a fixed point, then the fixed point is a periodic solution of (1.2).