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Collected Papers, Vol. II
  • Language: en
  • Pages: 202

Collected Papers, Vol. II

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Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry
  • Language: en
  • Pages: 84
Neutrosophic Methods in General Relativity
  • Language: en
  • Pages: 80

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...

Artificial Intelligence and Responsive Optimization
  • Language: en
  • Pages: 87
CONSIDERATIONS ON NEW FUNCTIONS IN NUMBER THEORY
  • Language: en
  • Pages: 20

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.

Computer Analysis of Number Sequences
  • Language: en
  • Pages: 86

Computer Analysis of Number Sequences

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Various Arithmetic Functions and their Applications
  • Language: en
  • Pages: 402

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.

Smarandache Function Journal, vol. 14/2004
  • Language: en
  • Pages: 418

Smarandache Function Journal, vol. 14/2004

A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.

Sequences of Numbers Involved in Unsolved Problems
  • Language: en
  • Pages: 141

Sequences of Numbers Involved in Unsolved Problems

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. The book contains 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, etc. ).