Sentence examples for minimum point on from inspiring English sources

By Theorem 1.1 of [27], I has a minimum point on H, which is a critical point of I.

By Lemma 2.1 and Remark 2.1, ϕ has a minimum point on H T 1, which is a critical point of ϕ.

So J has a minimum point on (W_{p,T}^{1,2}), which is a critical point of J. Hence problem (1.1a - 1.1c 1.1a - 1.1cst one solution.

The investigation was based on measuring the loss in the drag reduction effectiveness which was manifested by a minimum point on the Fanning friction factor vs Reynolds number plot.

By Theorem 1.1 in [32], J has a minimum point on (W_{p,T}^{1,2}), which is a critical point of J. Hence problem (1.1a - 1.1c 1.1a - 1.1cst one weak solution.

Note that (W_{T}^{1,p(t)}) is reflexive Banach space, and the functional Φ is weakly lower semicontinuous, applying the least action principle (see [1], Theorem 1.1 and Corollary 1.1), Φ has a minimum point on (W_{T}^{1,p(t)}), which is a critical point of Φ.

Take as the global maximum point and global minimum point of on, respectively, then (3.28).

In view of, (3.5) implies that ; similar to the global minimum point of on Since it follows that there exists a constant such that Then we have (3.6).

Then y is a critical point of f, and f is convex; it follows that y is a global minimum point of f on D. (See, e.g., [15], p. 14, Theorem 1.17).

Let t ¯ be the global minimum point of x ( t ) on [ 0, T ].

Let t ¯, t ̲ be, respectively, the global maximum point and the global minimum point of x ( t ) on [ 0, T ] ; then x ′ ( t ¯ ) = 0, and we claim that ( ϕ ( x ′ ( t ¯ ) ) ) ′ ≤ 0. (2.6).