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The refractive index n and the extinction coefficient k can be obtained by the Cauchy model, which is useful for dielectric materials (with exponential absorption), far from the absorption bands [39].
Cauchy model is useful to know the refractive index (n) and the extinction coefficient ( k) for dielectric materials (with exponential absorption), far from the absorption bands [36], by the equations n = a + b λ 2 + c λ 4 (3) k = d exp e λ. (4).
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A functionally graded piezoelectric strip with exponential material gradation is under consideration.
In this regard, a heterogeneous FG viscoelastic plate with exponential material gradation in the x-direction and two circular cutouts as shown in Figure 1 is considered.
Time history of the longitudinal displacement component of the node (x = 2, y = 0) of the heterogeneous viscoelastic plate with exponential material properties variations is shown in Figure 7.
Moreover, the improvement of the characteristics of materials with time is nearly exponential.
Exponential growth combined with exponential decline explains lifetime performance evolution in individual and human species.
All proposed control laws achieve asymptotic stability with exponential convergence.
This leads to neutral functional differential equations with exponential nonlinearities.
But new AIDS epidemics are emerging with exponential speed in Eastern and Central Europe, in India and China, and throughout Southeast Asia, Latin America and the Caribbean.
Existing approaches are restricted to processes with exponential time distribution.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com