Sentence examples for a sharp result from inspiring English sources

In this paper, we prove a sharp result on left-invertibility of the these operators.

It would be interesting to establish whether this is the case, and, if it is not necessary, whether one can derive a sharp result.

We then consider the spectra of Bernoulli convolutions and obtain a sharp result which extends the corresponding result of Jorgensen, Kornelson and Shuman.

We establish conditions providing almost sure asymptotic periodicity of the solution (X(n)) for (|L|=1) and (|L|<1), where (L:=prod_{i=0}^{K-1}a(i)). A sharp result on the asymptotic periodicity of (X(n)) is also proved.

(7) In Proposition 2, Section 6.2, we present a sharp result, which proves that, under some additional assumptions on g, condition (sigmainboldsymbol {l}_{2}) is necessary and sufficient for the asymptotic periodicity of (X(n)) in form (6), when (L=1), and in form (7), when (L=-1).

The onset of breakthrough causes a sharp result in the increase of torque signal and simultaneous roll-off of the feed force signal (shown as stage 3 in Figure 2 [ 18, 19]).

An example is shown in which such a control design method provides a sharper result than the control design using existing IQC techniques.

So we have a slightly sharp result.

Thus, a quite sharp result of the classical Hilbert inequality for double series is obtained.

This is a sharp contrasting result between local and global games, since the class of Groves mechanisms is neutral.

We obtain a number of sharp results concerning the existence of tangential limits for functions in the spaces.