Titlebook: Mathematics of Particle-Wave Mechanical Systems; James M. Hill Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive

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James M. HillProposes a novel mathematical model to address the issues of dark energy and matter in modern physics.Develops a fully Lorentz invariant reformulation of Newton‘s second law of motion.Invites readers

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Introduction,particle-wave mechanical systems which are mechanical systems incorporating both particle and wave energies. The chapter closes with a brief plan of the text and two tables of the major symbols and basic equations.

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Special Relativity,he fundamental notion of Lorentz transformations and the importance of invariance with respect to frames that are moving with constant relative velocity. The following section highlights the Einstein addition of velocities law which is an immediate consequence of the notion of invariance under Lorentz transformations.

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Derivations and Formulae, In the final section of this chapter, for the sake of completeness, we present an alternative derivation that is based on the hyperbolic representation . rather than the trigonometric representation .. The following chapter deals with Lorentz invariances and functional dependence of the assumed underlying linear forces . and . given by (.).

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Book 2022t basic of all mechanical principles is Newton’s second law, and conventionally, energy is just energy whether particle or wave energy. In this monograph, Louis de Broglie’s idea of simultaneous existence of both particle and associated wave is developed, with a novel proposal to account for mass an

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ormulation of Newton‘s second law of motion.Invites readers Despite successes of modern physics, the existence of dark energy and matter is indicative that conventional mechanical accounting is lacking. The most basic of all mechanical principles is Newton’s second law, and conventionally, energy is