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Galambos, J. and Simonelli, I. (1996) Bonferroni-Type Inequalities with Applications, Probability and Its Applications. Springer-Verlag, New York, x+269.

has been cited by the following article:

  • TITLE: Undulatory Theory with Paraconsistent Logic (Part II): Schrödinger Equation and Probability Representation

    AUTHORS: João Inácio Da Silva Filho

    KEYWORDS: Paraconsistent Logic, Wave Theory, Quantum Mechanics, Paraquantum Logic, Schrödinger Equation

    JOURNAL NAME: Journal of Quantum Information Science, Vol.6 No.3, August 12, 2016

    ABSTRACT: Part I of this study proved that the Paraconsistent Annotated Logic using two values (PAL2v), known as the Paraquantum Logic (PQL), can represent the quantum by a model comprising two wave functions obtained from interference phenomena in the 2W (two-wave) region of Young’s experiment (double slit). With this model represented in one spatial dimension, we studied in the Lattice of the PQL, with their values represented in the set of complex numbers, the state vector of unitary module and its correspondence with the two wave functions. Based on these considerations, we applied the PQL model for obtaining Paraquantum logical states ψ related to energy levels, following the principles of the wave theory through SchrÖdinger’s equation. We also applied the probability theory and Bonferroni’s inequality for demonstrating that quantum wave functions, represented by evidence degrees, are probabilistic functions studied in the PQL Lattice, confirming that the final Paraquantum Logic Model is well suited to studies involving aspects of the wave-particle theory. This approach of quantum theory using Paraconsistent logic allows the interpretation of various phenomena of Quantum Mechanics, so it is quite promising for creating efficient models in the physical analysis and quantum computing processes.