Therefore, even if we were to derive analogous expressions for the variance of these quantities, it would not appear sensible to use them to furnish symmetric confidence intervals around the point estimate.
Then in 1907 the Russian mathematician Gury Vasilyevich Kolosov, and independently in 1914 the British engineer Charles Edward Inglis, derived the analogous solution for stresses around an elliptical hole.
The proposed equations are derived from analogous formulas for debris clouds originated by impacts on simple aluminum plates, by applying proper corrections to account for different materials effects and different behavior of sandwich panels compared to plates of same material.
The inequalities derived are analogous to the L2 Morse inequalities of Novikov and Shubin and the asymptotic L2 Morse inequalities of an inexact Morse 1-form as derived by Mathai and Shubin.
Using that fact the authors in [11] derived the analogous results of Theorem 1.8 and Corollary 1.9 for discrete case, and here, similarly as in the previous section, we get the following results.
Via the matrix method [30], we derived an analogous contingency table that could be expected to be observed under the given sensitivity and specificity specifications.
These data corroborate our earlier results derived from analogous breedings of two other GlyR β-transgenic spa/ spa lines, in which we never observed a phenotypic modification in non-transgenic littermates (Hartenstein et al. 1996; Hartenstein 1996).
By similar arguments, we can derive an analogous formula for Caputo fractional derivative, i.e., Theorem 3.9 Let α > 0, β ∈ ( − 1, ∞ ) and s, t ∈ T be such that t > s.
We next derive an analogous result for tκ/2Px(T>t), with κ="1+α−n/2, where T is the exit time from Ω. Lastly, we deduce the renormalized Yaglom limit for the process conditioned on survival.
Derivation of linear operators, relating the stress-resultants to their related displacements or deformations in each of the layers of the pipe, as well as the process of deriving an analogous linear operator to represent the behavior of the pipe as a whole, are clearly presented, highlighting interesting mathematical aspects and their associated physical meaning.
