Sentence examples for 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.

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

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.

In all, the only sharp inverse relationship detected at early adult life (4-months) between miR-34a and its target, SIRT1, is observed in plasma.

1UP.com's Andrew Pfister applauded the character dialogues as being "intelligent, subtle and sharp"; the relationships between characters were lauded as well.

It is observed that dykes trending east west show branching and sharp cross-cutting relationship.

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

Of the couple's relationship, Sharp has stated, "Some guys might think being married to someone as famous as Rosie is a tough position, but I don't, I'm very proud of her".