We study Santilli’s isomathematics for the generalization of modern mathematics via the isomultiplication a× ̂a=abT ̂ and isodivision a÷ ̂b=a/b I ̂, where the new multiplicative unit I ̂≠1 is called Santilli isounit, T ̂I ̂=1, and T ̂ is the inverse of the isounit, while keeping unchanged addition and subtraction, , In this paper, we introduce the isoaddition a+ ̂b=a+b+0 ̂ and the isosubtraction a- ̂b=a-b-0 ̂ where the additive unit 0 ̂≠0 is called isozero, and we study Santilli isomathem,atics formulated with the four isooperations (+ ̂,- ̂,× ̂,÷ ̂). We introduce, apparently for the first time, Santilli’s isoprime theory of the first kind and Santilli’s isoprime theory of the second kind. We also provide an example to illustrate the novel isoprime isonumbers
| Published in |
American Journal of Modern Physics (Volume 4, Issue 5-1)
This article belongs to the Special Issue Issue I: Foundations of Hadronic Mathematics |
| DOI | 10.11648/j.ajmp.s.2015040501.12 |
| Page(s) | 17-23 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Isoprimes, Isomultiplication, Isodivision, Isoaddition, Isosubtraction
| [1] | R. M. Santilli, Isonumbers and genonumbers of dimension 1, 2, 4, 8, their isoduals and pseudoduals, and “hidden numbers” of dimension 3, 5, 6, 7, Algebras, Groups and Geometries 10, 273-322 (1993). |
| [2] | Chun-Xuan Jiang, Foundations of Santilli’s isonumber theory, Part I: Isonumber theory of the first kind, Algebras, Groups and Geometries, 15, 351-393(1998). |
| [3] | Chun-Xuan Jiang, Foundations of Santilli’s isonumber theory, Part II: Isonumber theory of the second kind, Algebras Groups and Geometries, 15, 509-544 (1998). |
| [4] | Chun-Xuan Jiang, Foundations of Santilli’s isonumber theory. In: Foundamental open problems in sciences at the end of the millennium, T. Gill, K. Liu and E. Trell (Eds) Hadronic Press, USA, 105-139 (1999). |
| [5] | Chun-Xuan Jiang, Foundations of Santilli’s isonumber theory, with applications to new cryptograms, Fermat’s theorem and Goldbach’s conjecture, International Academic Press, America- Europe- Asia (2002) (also available in the pdf file http: // www. i-b-r. org/jiang. Pdf) |
| [6] | B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Ann. Math.,167,481-547(2008). |
| [7] | E. Szemerédi, On sets of integers containing no elements in arithmetic progression, Acta Arith., 27, 299-345(1975). |
| [8] | H. Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions, J. Analyse Math., 31, 204-256 (1977). |
| [9] | W. T. Gowers, A new proof of Szemerédi’s theorem, GAFA, 11, 465-588 (2001). |
| [10] | B. Kra, The Green-Tao theorem on arithmetic progressions in the primes: an ergodic point of view, Bull. Amer. Math. Soc., 43, 3-23 (2006). |
APA Style
Chun-Xuan Jiang. (2015). Santilli’s Isoprime Theory. American Journal of Modern Physics, 4(5-1), 17-23. https://doi.org/10.11648/j.ajmp.s.2015040501.12
ACS Style
Chun-Xuan Jiang. Santilli’s Isoprime Theory. Am. J. Mod. Phys. 2015, 4(5-1), 17-23. doi: 10.11648/j.ajmp.s.2015040501.12
AMA Style
Chun-Xuan Jiang. Santilli’s Isoprime Theory. Am J Mod Phys. 2015;4(5-1):17-23. doi: 10.11648/j.ajmp.s.2015040501.12
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Download@article{10.11648/j.ajmp.s.2015040501.12,
author = {Chun-Xuan Jiang},
title = {Santilli’s Isoprime Theory},
journal = {American Journal of Modern Physics},
volume = {4},
number = {5-1},
pages = {17-23},
doi = {10.11648/j.ajmp.s.2015040501.12},
url = {https://doi.org/10.11648/j.ajmp.s.2015040501.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.s.2015040501.12},
abstract = {We study Santilli’s isomathematics for the generalization of modern mathematics via the isomultiplication a× ̂a=abT ̂ and isodivision a÷ ̂b=a/b I ̂, where the new multiplicative unit I ̂≠1 is called Santilli isounit, T ̂I ̂=1, and T ̂ is the inverse of the isounit, while keeping unchanged addition and subtraction, , In this paper, we introduce the isoaddition a+ ̂b=a+b+0 ̂ and the isosubtraction a- ̂b=a-b-0 ̂ where the additive unit 0 ̂≠0 is called isozero, and we study Santilli isomathem,atics formulated with the four isooperations (+ ̂,- ̂,× ̂,÷ ̂). We introduce, apparently for the first time, Santilli’s isoprime theory of the first kind and Santilli’s isoprime theory of the second kind. We also provide an example to illustrate the novel isoprime isonumbers},
year = {2015}
}
TY - JOUR T1 - Santilli’s Isoprime Theory AU - Chun-Xuan Jiang Y1 - 2015/08/11 PY - 2015 N1 - https://doi.org/10.11648/j.ajmp.s.2015040501.12 DO - 10.11648/j.ajmp.s.2015040501.12 T2 - American Journal of Modern Physics JF - American Journal of Modern Physics JO - American Journal of Modern Physics SP - 17 EP - 23 PB - Science Publishing Group SN - 2326-8891 UR - https://doi.org/10.11648/j.ajmp.s.2015040501.12 AB - We study Santilli’s isomathematics for the generalization of modern mathematics via the isomultiplication a× ̂a=abT ̂ and isodivision a÷ ̂b=a/b I ̂, where the new multiplicative unit I ̂≠1 is called Santilli isounit, T ̂I ̂=1, and T ̂ is the inverse of the isounit, while keeping unchanged addition and subtraction, , In this paper, we introduce the isoaddition a+ ̂b=a+b+0 ̂ and the isosubtraction a- ̂b=a-b-0 ̂ where the additive unit 0 ̂≠0 is called isozero, and we study Santilli isomathem,atics formulated with the four isooperations (+ ̂,- ̂,× ̂,÷ ̂). We introduce, apparently for the first time, Santilli’s isoprime theory of the first kind and Santilli’s isoprime theory of the second kind. We also provide an example to illustrate the novel isoprime isonumbers VL - 4 IS - 5-1 ER -
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