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Neutrosophic Methods in General Relativity
Neutrosophy is a theory developed by Florentin Smarandache in 1995 as a generalization of dialectics, which studies the origin, nature and properties of neutralities. This book applies neutrosophic method to the General Theory of Relativity, aiming to discover new effects hidden before.Studying Einstein's basic space-time, neutrosophic method displays new trajectories and particles never considered before. Such trajectories/particles are of two "mixed" kinds, which are (1) common for sub-light mass-bearing particles and massless photons (non-isotropic/isotropic trajectories) and (2) common for massless photons and super-light mass-bearing tachyons (isotropic/non-isotropic trajectories). As i...
CONSIDERATIONS ON NEW FUNCTIONS IN NUMBER THEORY
New functions are introduced in number theory, and for each one a general description, examples, connections, and references are given.
Various Arithmetic Functions and their Applications
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes, so on, have been extracted from the Archives of American Mathematics (University of Texas at Austin) and Arizona State University (Tempe): "The Florentin Smarandache papers" special collections, and Arhivele Statului (Filiala Vâlcea & Filiala Dolj, Romania). This book was born from the collaboration of the two authors, which started in 2013. The first common work was the volume "Solving Diophantine Equations", published in 2014. The contribution of the authors can be summarized as follows: Florentin Smarandache came with his extraordinary ability to propose new areas of study in number theory, and Octavian Cira - with his algorithmic thinking and knowledge of Mathcad.
Neutrosophic Logic, Wave Mechanics, and Other Stories (Selected Works 2005-2008)
There is beginning for anything; we used to hear that phrase.The same wisdom word applies to us too. What began in 2005 asa short email on some ideas related to interpretation of the WaveMechanics results in a number of papers and books up to now.Some of these papers can be found in Progress in Physics orelsewhere.Our purpose here is to present a selection of those papers in acompilation which enable the readers to find some coherentideas which appeared in those articles. For this reason, theordering of the papers here is based on categories of ideas.
Smarandache Notions, Vol. 14
Papers concerning any of the Smarandache type functions, sequences, numbers, algorithms, inferior/superior f-parts, magic squares, palindromes, functional iterations, semantic paradoxes, Non-Euclidean geometries, manifolds, conjectures, open problems, algebraic structures, neutrosophy, neutrosophic logic/set/probability, hypothesis that there is no speed barrier in the universe, quantum paradoxes, etc. have been selected for this volume. Contributors are from Australia, China, England, Germany, India, Ireland, Israel, Italy, Japan, Malaysia, Morocco, Portugal, Romania, Spain, USA. Most of the papers are in English, a few of them are in Spanish, Portuguese, or German.
