The solutions of natural and forced vibrations are worked out by using the formulas obtained in the present study.
It is therefore possible to obtain a good approximation of the distribution of ΔS using the formulas obtained under the simpler substitution models.
Here, examples are presented of calculations of the piezomagnetic signals arising from the propagation of Rayleigh waves, using the formula obtained above.
Using (3.3) and the formulas obtained in [3], we deduce the second order of the BT bifurcation normal form as follows.
We estimated the age of individuals using eye lens mass and the formula obtained by Boujard (1982) from a population of A. scherman, geographically close to our study area.
A prediction profiler was also built on Excel Software version 10.0 (Microsoft Corporation) using the prediction formula obtained from the model developed for glycaemic responses.
Using the formulas 9, we obtain begin{aligned} A =left| frac{ tau circ Theta )"}{[ tau circ Theta )']^2}right|le, Cfrac{|1-overline{a} Theta |^4}{|1-overline{a}Theta |^3}+ C' |1-overline{a} Theta |^2 ; frac{|Theta "|}{|Theta '|^2}.
Hence, the stress distribution of any angle can be obtained using the formulas above.
The expectations are obtained using the formulas: cf I, u = ∑ j ∑ e, d ∑ < e, d > → i ; i ∈ I, u c i · p e, d, j, i cg I, T = ∑ j ∑ e, d ∑ < e, d > → i ; i ∈ I, T c i · p e, d, j, i Under k =1 all expectations equal the number of events or the cost values.
It is obvious that problem (42) match the framework of the problem (5), thus the solution of (42) can be obtained by using the formulas in Section 2.2.
