Slavica M. Perovich

The transcendental method in the theory of neutron slowing down

The transcendental method for finding the exact analytical closed-form solution to the linear unidimensional integral equation of neutron slowing down with energy-dependent cross-section in an infinite homogeneous medium is studied in some detail. An original method of genesis of the isomorphic integral form of the process, and genesis of the general form of the analytical solution is applied. This, together with the exact solution of the transcendental equation of order one also determined, constitutes the exact solution of the problem. The numerical results obtained for different magnitudes of absorption rates and for different moderator masses show agreement with more conventional solutions, like those of Teichmann (1961) and Sengupta (1974). The conditions for the existence of the exact solutions are discussed.

On the analytical solution of some families of transcendental equations

The problem of finding the exact analytical closed-form solution of some families of transcendental equations is studied, in some detail, by the Special Trans Function Theory (STFT). The mathematical genesis of the analytical closed-form solution is presented, and the structure of the theoretical derivation, proofs and numerical results confirm the validity and base principle of the STFT. Undoubtedly, the proposed analytical approach implies the qualitative improvement of the conventional analytical and numerical methods.

Reply to the comment on the transcendental method

For comment see Miranovic, ibid., vol.28, p.4189 (1995) Using an unconventional mathematical approach and analysis of the precision of solution by a new formula for the representation of number in the transcendental method, we indicate that the objection given in the comment most probably shows a lack of understanding and misapprehension. Undoubtedly, the transcendental equation of the neutron slowing down (Perovich 1992) has an analytical closed-form solution. This solution is exact according to the new closed-form representation of numbers with the desired accuracy. The numerical results, obtained for different magnitudes of the transcendental parameter B(u), support the validity and basic principles of the transcendental method.

Concerning the analytical solution of the dispersive equation in the linear transport theory

Abstract The transcendental method for finding the analytical closed-form solution to the dispersive equation in the Linear Transport Theory is studied in some detail. The mathematical genesis of general form of the analytical solution is presented. This solution is exact according to the new closed-form representation of the numbers with desired accuracy in the transcendental method theory. This approach implies the qualitative improvement of the more conventional method such as successive approximations. The numerical results, obtained for different magnitudes of the cross section parameter c, support the validity and basic principles of the transcendental method. The conditions for the existence of the exact solution are discussed.

On the Exact Analytical Solutions of Certain Lambert Transcendental Equations

The subject matter of this paper is the Special Trans Functions Theory (STFT) in finding the exact analytical closed form solutions (the new special tran functions) of certain Lambert transcendental equations. Note that these Lambert transcendental equations frequently appear in applied physics and engineering domain. The structure of the theoretical derivations, proofs, and numerical results confirms validity and basic principles of the STFT. Undoubtedly, the proposed exact analytical approach implies the qualitative improvements of the conventional methods and techniques.

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

The problem of finding an exact analytical closed-form solution of some families of transcendental equations, which describe the equilibrium critical thickness of misfit dislocation generation in epitaxial thin films, is studied in some detail by the Special Trans Functions Theory (STFT). A novel STFT mathematical approach with an analytical closed-form solution is presented. Structure of the STFT exact solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. The proposed STFT analytical approach shows qualitative improvement in theoretical sense (a novel gradient coefficient genesis), and, in accuracy when compared to the conventional analytical and numerical methods.

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

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 Nonlinear Functional Equations

The problem of finding the exact analytical closed‐form solution of some families of non‐linear functional equations is studied, in some detail, by the Special Trans Function Theory (STFT). The mathematical genesis of the analytical closed‐form solutions and the structure of theoretical derivation, are presented. Undoubtedly, the proposed analytical theory implies the qualitative improvement of the conventional approaches.

The STFT in an Exponential Function Approximation

The paper proposed an original method for an exponential function linear approximation, based upon recently developed Special Trans Function Theory—STFT, Perovich S.M. (1992–2007). It moves the exponential function analysis from the classical MacLaurins series and the field of numerical methods to the field of the STFT. The appropriate simulations have been realized in Matlab and some numerical and graphical results are given.

The special trans function theory to the AM detector transfer factor analytical analysis

The special trans function theory (STFT) for finding the exact analytical closed-form solution to the AM detector transfer factor is studied in some detail. The AM detector transfer factor, as function of the different parameters, is analytically analyzed. Obtained numerical and graphical results confirm validity and base principle of the STFT.