Sentence examples for which is a refinement of from inspiring English sources

But all of us have this fear, this vertiginous alienation, this sudden mid-life awakening to an astonished sense that we don't know who we are or how we got here, which is a refinement of the fear of death.

which is a refinement of (1.1).

In [2], Dragomir established the following theorem which is a refinement of the first inequality of (1.1).

In [6], Yang and Hong established the following theorem which is a refinement of the second inequality in (1.1).

Theorem 6 and Remark 1(2) applied to functions f ( z ) = z p and g ( z ) = z q give the following corollary, which is a refinement of [[29], Corollary 3.3].

We give an analogue of the Bessel inequality and we state a simple formulation of the Grüss type inequality in inner product -modules, which is a refinement of it.

The ANN can predict a value for solubility, which is a refinement on the original qualitative duties of Hume-Rothery's Rules.

Inkbox's two-week tattoos made waves when the company debuted its product on Kickstarter last year – Toronto-based founders Tyler and Braden Handley raised nearly $300,000 for their organic limited-time body art invention, which was a refinement of their original product offering that cut application time to just 10 minutes.

The other one is MEA, maximum expected accuracy folding, which is a recent refinement of MFE folding.

Applying the previous lemma on the convex function defined earlier f = ⦀ A ν X B 1 − ν + A 1 − ν X B ν ⦀. on the interval [ μ, 1 − μ ] when 0 ≤ μ ≤ 1 2 and on the interval [ 1 − μ, μ ] when 1 2 ≤ μ ≤ 1, we obtain the following refinement of the first inequality (1.1) which is a kind of refinements of Theorem 1 in a paper Kittaneh [5] and Theorem 1 in a paper of Feng [3].

Applying the Lemma 1 to the function f = ⦀ A ν X B 1 − ν + A 1 − ν X B ν ⦀ on the interval [ μ, 1 2 ] when 0 ≤ μ ≤ 1 2, and on the interval [ 1 2, μ ] when 1 2 ≤ μ ≤ 1, we obtain the following theorem, which is a kind of refinements of Theorem 3 in a paper Kittaneh [5] and Theorem 3 in a paper of Feng [3].