Sentence examples for are sharp in the from inspiring English sources

So the conclusion of Theorem 1.9, Corollary 1.10 may occur and our results are sharp in the special cases.

All the above inequalities are sharp in the sense that there are examples of functions for which each equality case is realized.

Furthermore, the conditions are sharp in the sense that they are equivalent toLpsolvability for a special class of operators which arise in then=2 case.

It is shown that these lower bounds are sharp in the power scale in the case of S2, the unit sphere in R3.

The coefficient 1 in the second inequality and the constant 1 4 in the last inequality are sharp in the sense that they cannot be replaced by a smaller quantity.

One implication of these examples is that the ranges of p are sharp in the recent results obtained in [4], [5] for non-divergence type elliptic and parabolic equations in a half space with the Dirichlet or Neumann boundary condition when the coefficients do not have any regularity in a tangential direction.

Even though, similar peaks are observed in both the spectra, the spectral peaks are sharper in the case of purified MWNT.

England have been sharp in the field.

Sabathia has been sharp in the three outings, striking out 23 and walking only 4.

Goalie Marc-Andre Fleury was sharp in the first period, in which the Wings outshot the Pens by 19-11.

In the Hindi, Tamil, Telugu, Marathi and Bengali blogospheres, the rise of female bloggers has been sharp in the past two or three years, especially in small-town and rural India.