Sentence examples for get refinements from inspiring English sources

In such a way, they get refinements and converses of numerous mean inequalities for Hilbert space operators.

In particular, we get refinements of the Sobolev embedding theorems, Trudinger's limiting embedding as well as embeddings of Sobolev spaces into space ofλ-Hölder-continuous functions including the result of Brézis and Wainger.

In [2], Feng used the following inequalities to get refinements of (1): f ( a + b 2 ) ≤ 1 b − a ∫ a b f ( t ) d t ≤ 1 4 ( f ( a ) + 2 f ( a + b 2 ) + f ( b ) ) ≤ f ( a ) + f ( b ) 2, where f is a real-valued function which is convex on the interval [ a, b ].

With Orazio you get refinement, but at no time does it turn into smallness".

To get refinement around a certain point in the domain, a node is fixed at that point and several rings of decreasing node type are defined around it.

Heneghan reports of four triggers for a diagnosis that often occurs early in the consultation, which get refined during the later refinement stage: spot diagnosis, self-labelling, the presenting complaints and pattern recognition [ 9].

In this paper, we use a similar method to [2, 3] and we get different refinements of (1).

We use a similar method to (Feng in J. Inequal. Appl. 2012 18, 2012; Wang in J. Inequal. Appl. 2013:420132013) and we get different refinements of the Heinz inequalities for matrices.

Of course, we can get such refinement and reversions in all other cases for p, s and r, s.

Remark 2.8 From the inequalities (24 - 27 24 - 27q < s ), we get the reforement for inequalities obtained from Theorem 1.2 and reversion when ( q > s ).

In general, given m partitions (mathcal {P}_{1}), …, (mathcal {P}_{m}), it is possible to get a refinement by computing the intersection of them as (mathcal {P}' = bigcap _{i=1}^{m} mathcal {P}_{i}) [6].