Concerning exact analytical STFT solutions to some families of inverse problems in engineering material theory

On the exact analytical solution of some families of equilibrium critical thickness transcendental equations

“…Tables I and II show From a theoretical point of view, solutions (26) for h c can be found with an arbitrary order of accuracy by taking appropriate values of x and [u/a]. It is not difficult to see that the analytical solution (26) gives impressive results which confirm successful application of the STFT. In an exact way, the number of accurate digits in the practical applicable h c is in accordance with the physical requirements of exactness.…”

“…Let us note that Eq. (6) has two real solutions: z > (for z>1) and z < (for z<1), 19,21,26 which are presented in Fig. 1.…”

“…26 is also applicable for derivation of the analytical closed-form solution to equation (8) for Z>1 (trans > ( β)), but for the appropriate equation for identification (EQID) in a form of an integral equation. Note that in the aforementioned outline of the special trans functions (trans < ( β) and trans > ( β)) derivation, some of its most elementary properties are discussed.…”

“…In this section, as above mentioned, the problem of finding an exact analytical closed-form solution to the transcendental equation (6) using the Special Trans Functions Theory, [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] will be discussed in detail.…”

“…Perovich's Special Trans Functions Theory (STFT) has been proved to be a very powerful theory for solving transcendental equations and obtaining exact analytical closed-form solutions without any assumptions, hypotheses nor any additional proofs, [13][14][15][16][17][18][19][20][21][22][23] as opposed to the approaches presented in papers. 1,7 Examples of its application are shown in papers concerning the calculation of the closed-form solutions in some families of transcendental equations, 19 Lambert transcendental equation, 24 engineering materials, 26 theory of neutron slowing down, 13,14 linear transport theory, 17,23,27 Plutonium temperature estimation, 21 temperature estimation, 22 nonlinear circuit theory 15 and Hopfield neuron analysis, 18 as well as solar cell analysis 20,25 etc. Note that, also, a broad class of nonlinear functional equations of the transcendental type which appear in Refs.…”