Sentence examples for formula due to a from inspiring English sources
Last month, the state Department of Education said it is underfunding many school districts under the SFRA formula due to a lack of revenue.
We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schrödinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation, generalizes to higher dimensions.
We can assume without loss of generality that a belief set includes a single formula, due to the finiteness assumption.
After finding τ ( x ) and ν ( x ), the solution of problem T1 defined in Ω 2 by a formula due to Cauchy [4] or Darboux (see (43)).
The formula obtained is an extension of an index formula due to Fedosov.
Our proofs make essential use of techniques based on a logarithmic Sobolev inequality, Rosen's inequality (proved via a new Fenchel Young inequality), and a very precise asymptotic formula due to Hartman and Wintner.
The results are derived with the help of generalization of a quadratic transformation formula due to Kummer very recently obtained by Kim et al. Several identities, including one obtained earlier by Krattenthaler and Rao, follow special cases of our main findings.
Since the number of cases is very large to study with FEM even with modern machines, the use of a recent simple approximate formula due to Greenwood based on the stress field in the absence of the hole is first attempted, and compared with a full FEM analysis in sample cases.
Taking into account the adjusted formula due to the assumption of unequal expectations, we instead find an effect size of r = 0.64, still quite strong, but logically interpretable and meaningful.
Sialic acid is also an ingredient in powdered infant formula due to its association with brain development.
