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

Abstract

The subject of the theoretical analysis presented in this paper is an analytical approach to the temperature estimation, as an inverse problem, for different thermistors – linear resistances structures: series and parallel ones, by the STFT - Special Trans Functions Theory (S.M. Perovich). The mathematical formulae genesis of both cases is given. Some numerical and graphical simulations in MATHEMATICA program have been realized. The estimated temperature intervals for strongly determined values of the equivalent resistances of the nonlinear structures are given, as well

Concerning an analytical solution of some families of Kepler’s transcendental equation

“…5 polynomialization of Kepler's equation through Chebyshev polynomial expansion of the sine is presented. , Hopfield neuron analysis 14 some families of transcendental equations, 8,12,15,20,[23][24][25]38 solar cell analysis, 16,21,35 Plutonium temperature estimation, 8,17,36 ambient temperature estimation, 18,11 Lambert transcendental equations analysis, 8,20 as well as in problem in engineering materials, 22,34,40,41 ect. The biggest impact of this work is in the usage of a new STF theory approach in formulae genesis for the determining position (r, v) in time t. All investigations and analysis of the value E in this paper have been consistently accomplished with the usage of STF theory.…”

The Special Trans Functions Theory for the Degree of Nuclear Fuel Burn-Up Estimation

“…(3)) is solvable using the Special Tran Function Theory [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Let us note that Perovich's Special Tran Functions Theory (STFT), has been proved to be a very powerful theory for solving transcendental equations, some integral and integro-differential equations, and, obtaining exact analytical closed-form solutions.…”

“…Let us note that Perovich's Special Tran Functions Theory (STFT), has been proved to be a very powerful theory for solving transcendental equations, some integral and integro-differential equations, and, obtaining exact analytical closed-form solutions. Examples of STFT application are shown in articles concerning the closed-form solution genesis in: the theory of neutron slowing down [ [6], [7], [16]], the nonlinear circuit theory [ [8], [16], [22]], the linear transport theory [ [9], [16], [20]], the Hopfield neuron analysis [11], some families of transcendental equations analysis [ [12], [16], [17]], the solar cell theoretical analysis [ [13], [18], [22]], the Plutonium temperature estimation [14], the ambient temperature estimation [ [15], [16]], the Lambert transcendental equations analysis [ [16], [17], [23]], as well as in the problem in the engineering materials [19], [21], [22]], etc.…”

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

“…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.…”