When the cushion deforms, it creates a band of contact in the specimen that is nearly hydrostatic, which is extremely useful in calculations that assume a uniform load distribution.
The data in these articles all result in values of α > 90°, which indicates that the octahedra are squashed, but unfortunately the precision of the data as reported is not sufficiently high to be useful in calculations of the a parameter.
The analysis of the results demonstrates that any slenderness ratio is useful in the calculation of the elastic constants, although in some cases the third natural frequency should be used.
The training ANN model with the Levenberg Marquardt (LM) algorithm provides more accurate prediction and is quite useful in the calculation of tool chip interface temperature when compared with the trained RA method in machining.
In any plane triangle ABC, if a, b, and c are the sides opposite angles A, B, and C, respectively, then The formula is especially useful in making calculations using logarithms.
One should note that, if we put p = 2 in Definition 1.1, we will obtain the spaces B α and B α, 0. Remark 1.2 ( p, α ) -Bloch space is very useful in some calculations in this paper and it can be also used to study some other operators like integral operators (see [12]).
It is shown below that this value of n is much larger than necessary, because Chebyshev's inequality is not sufficiently precise to be useful in numerical calculations.
To describe the random variability of soil properties, polygonal probability distributions are proposed, which are especially useful in sumulation calculations.
Quantum-chemical methods, with the explicit inclusion of solvation free energy into the framework of the MO SCF method, are useful tools for predicting thermodynamic properties and phase behavior of some substances to an accuracy useful in engineering calculations.
