Sentence examples for a sharp relationship from inspiring English sources

He has established a sharp relationship between the squared norm of the second fundamental form and the warping function.

In [4], Chen extended the notion of Ricci curvature to k-Ricci curvature for a Riemannian manifold and established a sharp relationship between k-Ricci curvatures and the shape operator and also a sharp relationship between k-Ricci curvatures and the squared mean curvature for an n-dimensional Riemannian submanifold in a real space form M ¯ with constant sectional curvature c.

In [4], Chen established a sharp relationship involving the Ricci curvature and the squared mean curvature for an arbitrary n-dimensional Riemannian submanifold of a real space form of constant sectional curvature c, Ric ( X ) ≤ ( n − 1 ) c + n 2 4 ∥ H ∥ 2, (23).

Especially, Chen in [2] obtained the sharp relationship between norm of the squared mean curvature and the warping function f of the warped product (M_{1}times _{f}M_{2}) isometrically immersed in a real space form, i.e., we have the following.

It consists of fine lamellae of ferrite and austenite which show a sharp Kurdjumov Sachs orientation relationship with each other.

Nichols raised the bar into the stratosphere with his very first film, an adaptation of Edward Albee's vinegar-sharp relationship satire.

Birtwistle and his librettist, David Harsent, stay remarkably close to the detail of the myth but, as well as giving an extra dimension to the Minotaur himself, they also give a sharp twist to the relationship between the other protagonists.

McCain and his aides draw a sharp distinction between his relationship to Hagee and Barack Obama's ties to the Rev. Jeremiah Wright Jr. "I didn't attend Pastor Hagee's church for 20 years," the candidate told reporters on his Straight Talk Express.

In each analysis we found a sharp increase in the relationship between chronic conditions and adjusted odds of the composite outcome.

29 Our results showed a very sharp, positive relationship between the number of smokers in the household and the likelihood that a youth would smoke.

He has been living in Paris on and off since the sixties, and is a sharp observer of France's relationship to the Arab world.