Sentence examples for validity of formula from inspiring English sources

Ma and Earn (2006) have recently discussed various aspects related to the derivation and validity of formula (3), and Andreasen (2011) has studied the effects of population heterogeneity on the size of epidemic.

The theoretical results are close to the simulation results, thereby demonstrating the validity of Formulae (24) and (33).

Details of the connection between structural rules of Gentzen-Style sequent calculi and their dialogical counterparts are given in Section 4. As a legacy from the philosophical stance of the fathers of the dialogical approach, the systems of dialogical logic are usually constructive procedures to prove the validity of formulas.

Since the validity of formulas like $\forall x \ Px \rightarrow \exists x Px$ or $\exists x (Px \rightarrow Px)$ is largely a byproduct of what may strike one as an ad hoc stipulation, one may be motivated to expand the range of model-theoretic interpretations in order to allow for a model with an empty domain of discourse.

Since the length of a formula is finite, it is enough to test a finite number of translations in order to determine if a formula of L is valid in L. Thus, checking the validity of a formula of L is equivalent to performing a finite number of finitary tests.

Finally, a modified formula for the maximum tension reinforcement ratio ρmax is suggested instead of that recommended by Eurocode 8, which takes into consideration the effect of high strength concrete, where the validity of this formula is checked by a comparative study with other formulas for ρmax.

The validity of proposed formula was checked against the results from parametric study and the experiments.

The objective of this study is to check the validity of the formula.

The objective is to identify the limits of the validity of each formula.

One numerical example is presented to verify the validity of the formula; numerical simulations are compared against literature data (wind tunnel test results) for a benchmark building structure.

The validity of the formula is confirmed by reproducing the experimental data for Prandtl number of liquid water at various temperatures.