Research ArticleOpen accessIn the keywordsTHE COMPLEX STATISTICS PARADIGM AND THE LAW OF LARGE NUMBERSAbdo Abou JaoudeThe five basic axioms of Kolmogorov define the probability in the real set R and do not take into consideration the imaginary part which takes place in the complex set C, a problem that we are facing in applied mathematics. Whatever the probability distribution of the random variable in R is, the corresponding probability in the whole set C equals … …Journal of Mathematics and Statistics, Vol. 9, Issue 4 · 9 Oct 2013 · 8,199 accessesView PDFCite
Research ArticleOpen accessIn the keywordsPrediction in Complex Dimension Using Kolmogorov's Set of AxiomsAbdo Abou Jaoude, Khaled El-Tawil, Seifedine KadryProblem statement: The five basic axioms of Kolmogorov define the probability in the real set of numbers and do not take into consideration the imaginary part which takes place in the complex set of numbers, a problem that we are facing in many engineering systems. Approach: Evaluate the complex probabilities by considering supplementary new imaginary dimensions to the event occurring … …Journal of Mathematics and Statistics, Vol. 6, Issue 2 · 30 Jun 2010 · 8,519 accessesView PDFCite
Research ArticleOpen accessIn the abstractIterative Feedforward Control for Bearing-Free Multibody SystemsNicola Y. Bailey, Christopher Lusty, Patrick S. KeoghAutomated machinery and robotics are commonly conventional multibody systems containing bearing components, which exhibit uncertain, discontinuous and complex tribological characteristics. These generate wear and fundamentally limit the precision of small scale motion due to the tribological effects being difficult to compensate for using model-based active control. However, they can be eliminated through the replacement of traditional bearing joints with flexure … …Journal of Mechatronics and Robotics, Vol. 5, Issue 1 · 6 Dec 2021 · 6,477 accessesView PDFCite