The transcendental method in the theory of neutron slowing down

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

“…Thus, the obtained analytical solutions, in addition to having a theoretical value, possess potential for practical application. The theoretical accuracy of the STFT 13,14,24,26 is unlimited, and, therefore, extreme precision is attainable with this approach (See Table I). Advantage of the Perovich method is evident comparing to conventional analytical and numerical methods.…”

“…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.…”

“…Mathematical form of the relationship between the equilibrium critical thickness and material parameters can be reduced to a transcendental equation (6). 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.…”

An inverse problem of temperature estimation for the combination of the linear and nonlinear resistances

“…Let us note that the nonlinear functional equation (4) is analytically solvable by application of the Special Trans Function Theory. [3][4][5][6][7][8][9][10] We remark that equation (4) has two real solutions (Y < 1, T > β and Y > 1, T < β), but the subject matter of this paper is the first solution (Y < 1, T > β). The second solution, Y > 1, T < β, will be subject of one of the fore coming papers.…”

“…1 In this paper some different thermistors-linear resistances structures have been employed in unknown ambient temperature intervals estimation analytically, for given boundaries of the equivalent resistances of above noted structures, by the application of the STF Theory. [3][4][5][6][7][8][9] Let us consider, now, both nonlinear resistances structures in more details.…”