Sentence examples for sharp relation from inspiring English sources

A sharp relation is obtained as a lower bound of the squared norm of second fundamental form in terms of the warping function and the slant angle.

In this paper, we study warped product submanifolds of nearly cosymplectic manifolds in which the base manifold is slant and thus we derive a sharp relation for the squared norm of the second fundamental form.

We establish a sharp relation between the rate of convergence of the eigenvalues as the singular pole is approaching a boundary point and the number of nodal lines of the eigenfunction of the limiting problem, i.e. of the Dirichlet-Laplacian, ending at that point.

Then, we determine sharp inclusion relations between α-modulation spaces and Lp-Sobolev spaces, and between α-modulation spaces and local Hardy spaces.

PPT was defined as a sharp sensation in relation to gentle needle placement in a painful area.

Black Scenarios – For the years 2015 2024, the average cost per ton of consumed fuel converges to $8.62, a sharp reduction in relation to BAU state, mainly due to high cost of EUA for these scenarios.

b) Coronal image in the same patient showing a large intraorbital fluid collection with a thick enhancing rim and sharp angles in relation to the orbital wall (long arrow).

The partial closure coincided with a sharp downturn in relations between the two countries.

Ukraine's new president, Viktor F. Yanukovich, promised a sharp improvement in relations with Russia on Friday, five years after the Orange Revolution chilled ties between the neighbors.

The Bush administration's plans to place parts of the missile defense system in Poland and the Czech Republic, which were once part of the Soviet military alliance, led to a sharp deterioration of relations between Washington and Moscow.

The trial led to a sharp deterioration in relations between Ukraine and the West, and there were subsequent efforts to prosecute Ms. Tymoshenko on charges of tax evasion and embezzlement.