Sentence examples for on certain line from inspiring English sources

We show that if such an extremal function is in (C^{3}), then it is affine on certain line segments that foliate the domain D. Thus one can further approach all such problems by specifically looking for such foliations.

Similarly, Burkholder has noted that his extremal function (7) is affine on certain line segments.

For example, in [1], p.687, (9.7), it is observed that a certain extremal biconcave function is affine on certain line segments.

First, we will geometrically prove that (A(x_{1},x_{2})) is constant on certain line segments that are maximal and then we use this fact to show that u is affine on each such segment.

In various papers of Burkholder, it has been pointed out that certain functions discovered there are affine on certain line segments, apparently without the realization that this is a general property of this type of extremal functions.

We show that if such an extremal function is in (C^{3}), then it is affine on certain line segments that foliate the domain D. This structural result represents a very preliminary step in a larger program of determining maximal ζ-convex functions in certain Banach spaces.

And I'd observe the emphasis he would put on certain lines, and then stare at the audience.

Here again we face another expression of fuzziness as one, two and even three choices appeared on certain lines after collecting all the answers of the survey.

On side changes during a match, his routine included stepping on certain lines and avoiding others.

"I think journalists get hung up on certain lines of what's ethical more than the readers".

Third, Murdoch's papers' support was highly conditional on certain lines not being crossed and on certain policies, mostly notably on relaxing cross-media ownership rules, being adopted.