NEUTROSOPHIC LOGIC, WAVE MECHANICS, AND OTHER STORIES

There is beginning for anything; we used to hear that phrase. The same wisdom word applies to the authors too. What began in 2005 as a short email on some ideas related to interpretation of the Wave Mechanics results in a number of papers and books up to now. Some of these papers can be found in Progress in Physics or elsewhere. It is often recognized that when a mathematician meets a physics-inclined mind then the result is either a series of endless debates or publication. In this story, authors preferred to publish rather than perish. Therefore, the purpose with this book is to present a selection of published papers in a compilation which enable the readers to find some coherent ideas which appear in those articles. For this reason, the ordering of the papers here is based on categories of ideas

Unfolding the Labyrinth: Open Problems in Mathematics, Physics, Astrophysics, and Other Areas of Science

Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation. The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plau-sible solutions, it is merely to keep the fun of readers in discovering the answers by themselves.Comment: 139 pages, many figure

Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review

The present review analyzes classes of exact solutions for the convection and thermal diffusion equations in the Boussinesq approximation. The exact integration of the Oberbeck–Boussinesq equations for convection and thermal diffusion is more difficult than for the Navier–Stokes equations. It has been shown that the exact integration of the thermal diffusion equations is carried out in the Lin–Sidorov–Aristov class. This class of exact solutions is a generalization of the Ostroumov–Birikh family of exact solutions. The use of the class of exact solutions by Lin–Sidorov–Aristov makes it possible to take into account not only the inhomogeneity of the pressure field, the temperature field and the concentration field, but also the inhomogeneous velocity field. The present review shows that there is a class of exact solutions for describing the flows of incompressible fluids, taking into account the Soret and Dufour cross effects. Accurate solutions are important for modeling and simulating natural, technical and technological processes. They make it possible to find new physical mechanisms of momentum transfer for the design of new types of equipment. © 2023 by the authors

Higher spin quaternion waves in the Klein-Gordon theory

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d'Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories