The phrase "a refinement for" is correct and usable in written English.
It can be used when discussing improvements or enhancements made to a particular process, idea, or product.
Example: "The team proposed a refinement for the existing software to enhance its user interface."
Alternatives: "an improvement to" or "a modification for".
If transport to a secondary compartment is expected, this compartment has also to be addressed by a risk assessment at tier 2. The refined n-PEC-assessment at tier 2 comprises two aspects: on the one hand, a refinement for the initial compartment (n-PECini refined), and on the other hand an assessment for a second compartment if the ENM might be transported into it (n-PECsec comp).
In this section, we give a refinement for Carleman's inequality (see Corollary 4.4).
Now, in order to obtain a refinement for the Cauchy-Schwarz inequality, we first assume in (18) that p q = p + q.
Mathias Wien found a difference of 1 to 2 between successive temporal levels and a refinement for the key pictures [9].
A refinement for America's Cup racing limited J-boats to 87 feet on the waterline but allowed for huge "overhangs" at bow and stern that dip into the water when the boats heel in the wind.
Hermite-Hadamard's inequality provides a refinement for Jensen's inequality, namely, for a convex function (f: Isubsetmathbb{R} rightarrowmathbb{R}), f biggl(frac{a+b}{2} biggr) leqfrac{1}{b-a}int _{a}^{b}f(x),dx leqfrac {f(a)+f(b)}{2}quad text{for any } a,bin I. (2) We refer the reader to Section 2 for further details regarding these inequalities.
While observed instabilities are identified as numeric in nature and are eliminated accordingly, their very occurrence highlights the need for a refinement of the model for future studies.
First, we give a refinement of (9) for two pairs of operators.
But by 1877 the Trinidad Guardian newspaper was calling for "a refinement of our vulgar tastes".
But she also called for a refinement of Lebanon's human trafficking law and greater awareness among judges and law enforcement on how to apply the law.
In the following theorem, we show a refinement of inequality (15) for the Hilbert-Schmidt norm.
