The Department of Mathematics and Statistics at the Faculty of Natural and Applied Sciences (FNAS) Notre Dame University-Louaize Shouf Campus (NDU-SC) hosted on Monday, October 23, 2017, a lecture titled, “The Complex Probability Paradigm and Analytic Linear Prognostic for Vehicle Suspension Systems,” and delivered by Dr. Abdo Abou Jaoude. Dr. Abou Jaoude discussed before an audience of mathematics and engineering students his latest findings that would help develop further the new field of the Complex Probability Paradigm.
Dr. Abou Jaoude took the floor to explain 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 that we are facing 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. Dr. Abou Jaoude 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 system.
Thus, this novel complex probability paradigm was applied to the concepts of degradation and the remaining useful lifetime of a vehicle suspension system in the linear damage accumulation case hence to the field of prognostic, and it followed directly from the newly added axioms. This result was elaborated throughout this lecture. In addition, this lecture developed more the new field of the “Complex Probability Paradigm” that considers all the random variables in the complex set C. Consequently, this application proves that this complex extension is successful and fruitful.
Students appreciated Dr. Abou Jaoude’s contributions to the new field in applied and pure mathematics and expressed much interest in learning more about it.