As a part of its science-based activities, the Faculty of Natural and Applied Sciences (FNAS), Department of Mathematics and Statistics at Notre Dame University-Louaize Shouf Campus (NDU-SC), organized on Monday, March 26, 2018, a lecture in mathematics titled, "The Complex Probability Paradigm and Analytic Nonlinear Prognostic for Vehicle Suspension Systems,” delivered by Dr. Abdo Abou Jaoude, full-time assistant professor at the FNAS. Dr. Abou Jaoude discussed his latest findings that serve to further develop his new field on the complex probability paradigm in the presence of SC Director Fr. Naji Khalil and a number of faculty, staff, and students.
Dr. Abou Jaoude explained the five basic axioms of Andrey N. Kolmogorov, which define the probability in the real set R and do not take into consideration the imaginary part M, which takes place in the complex set C = R + M, a problem faced in applied and pure mathematics. The objective here is to evaluate the complex probabilities by considering supplementary new imaginary dimensions to the event occurring in the "real" laboratory. He added that whatever the probability distribution of the random variable in R is, the corresponding probability in the whole set C is always equal to one, so the outcome of the random experiment in C can be predicted totally and perfectly. The result indicates that chance and luck in R is replaced now by total determinism in C. This is the consequence of the fact that the probability in C is got by subtracting the chaotic factor from the degree of our knowledge of the stochastic system.
This novel complex probability paradigm was thus applied to the concepts of degradation and the remaining useful lifetime of a vehicle suspension system in the nonlinear damage accumulation case; hence, to the field of prognostic. It followed directly from the newly-added axioms. The result was elaborated throughout this lecture. In addition, the lecture further developed the new field of the complex probability paradigm, which considers all random variables in the complex set C. Consequently, this application proves that this complex extension is successful and fruitful.
The audience appreciated Dr. Abou Jaoude’s contributions to the new field in applied and pure mathematics and expressed much interest in learning more about it.