Open AccessUse of Exponential Functions in the Evaluations of Stochastic Variables in the Ionizing Radiation Field
Author(s) -
Terman Frometa-Castillo
Publication year - 2018
Publication title -
applied physics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9647
pISSN - 1916-9639
DOI - 10.5539/apr.v10n3p34
Subject(s) - probabilistic logic , exponential function , random variable , ionizing radiation , mathematics , simple (philosophy) , computer science , type (biology) , differential equation , differential (mechanical device) , statistical physics , statistics , physics , mathematical analysis , irradiation , nuclear physics , thermodynamics , philosophy , ecology , epistemology , biology
To show that some deficiencies arisen can occur as result of owing to the stochastic processes/effects (SP/Es) in areas of ionizing radiations have not been probabilistically treated nor modeled, because they use exponential functions (EFs) derived from unnecessary differential equations (DEs) or unnecessary definition; and 2) to discuss some statistical models project (SMp) proposals of new probabilistic functions (PFs) that have probabilistic foundations, and will overcome the quoted problems.The following results were obtained: 1) Determination of deficiencies due to use of EFs in evaluations of the following SP/Es: cell survival attenuation of radiation, radioactive decay and radioactivity; and 2) The SMp formulations for these SP/Es.The previous SP/Es have not been probabilistically treated nor modelled, since they use EFs that are non-PFs, and some of them are derived from unnecessary solutions of DEs or unnecessary definition. These differential equations used in the derivations do not represent physic properties of the SP/Es, but are simply a mathematic property of the EFs modelling their respective SP/Es. The SMp proposes PFs that will be able to model SP/Es with simple and homogeneous functions using the three types of SP/Es. The SMp models will represent new PFs, where the probability of a random variable X is expressed as PX = p(y), instead of x; and the stochastic region is limited by two 0% and/or 100%-deterministic regions. The SMp treats the radioactivity as a SP/E SMp type P2, and considers there is no need of its current definition.