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CONTINUING THE REBIRTH OF THE
AMERICAN SCIENTIFIC LEADERSHIP, X:

Mathematical Foundations of Santilli Isotopies
Algebras, Groups and Geometries Vol. 32, pages 135-308 (2015)
available for free pdf download from the link
http://www.i-b-r.org/docs/Aversa-translation.pdf

This monograph was written after the achievement of maturity in the isotopies of all aspects of 20th century applied mathematics by Prof. R. M. Santilli (Curriculum, Prizes and Nominations, Scientific Archives) in the historical memoir, still recommended for study by non experts in the field, published in a special issue of the Rendiconti Circolo Matematico di Palermo entirely dedicated to Santilli isotopies
R. M. Santilli, "Nonlocal-Integral Isotopies of Differential Calculus, Mechanics and Geometries," published in the special issue Isotopies of Contemporary Mathematics, Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, 7-82 (1996), http://www.santilli-foundation.org/docs/Santilli-37.pdf

The above 1996 historical work, the English translation of the 2001 Spanish monograph, the monumental work on Santilli isotopies by Prof. Svetlin Georgiev of the Department of Mathematics of the Sorbonne University, Paris,
S. Georgiev Foundations of the IsoDifferential calculus. Volumes I, II, III, IV, and V, Nova Scientific Publisher (2014 on) and other contributions by important mathematicians, will be used as a textbooks for the

Ph. D. Course on IsoMathematics
as a covering of 20th century mathematics
http://www.i-b-r.org/Course-Santilli-IsoMathemathics-2015.pdf
under organization at selected departments of mathematics
with partial support by the R. M. Santilli Foundation
http://www.santilli-foundation.org
Application for financial support should be submitted to the
Email board(at)santilli-foundation(dot)org

APPLICATIONS OF ISOMATHEMATICS IN QUANTITATIVE SCIENCES
Among numerous novel applications permitted by isomathematics in all quantitative sciences, we quote:

*** The new class of isocryptograms with an infinite time for their resolution due to the continuous change of their isounit for a better protection against hackers of national, corporate and personal websites;

*** Convergence of perturbative isoseries at least 1,000 faster than 20th century series for a faster prediction of tornados and other increasingly alarming climactic events;

*** The first and only known optimization of the actual shape of objects moving within resistive media treatable via an isovariational principle;

*** Time invariant derivation of Hubble's law z = Hd from the primitive Lorentz-Santilli isosymmetry and its experimental verification via the loss (acquisition) of energy by light to cold (from hot) gases without any relative motion, known as Santilli IsoRedShift - IRS (IsoBlueShift - IBS), with confirmation of the lack of the expansion of the universe sustained by Einstein, Hubble, Fermi, Zwicky and other founders of 20th century sciences;

*** The first and only representation of the anomalous redshift of galactic stars via the admission of the real visible gas permeating all galaxies and the use of Santilli IBS in the vicinity of the galactic center and Santilli IRS for colder innergalactic gases;

*** The first and only invariant exact representation of the anomalous behavior of unstable hadrons with speed, the Bose-Einstein correlation and other particle physics events approximately treated with 20th century theories;

*** The first and only exact, nonrelativistic and relativistic isorepresentation of all characteristics of the neutron in its synthesis from the hydrogen under industrial development by the U. S. public company Thunder Energies Corporation whose stock is traded under the symbol TNRG;

*** The first and only known exact and time invariant representation of all nuclear magnetic moments and spins thanks to the representation of nuclear constituents as extended particles permitted by isomathematics and their deformation permitted by the Lorentz-Santilli isosymmetry;

*** The first and only known derivation from first axioms of the attractive force between two identical electrons in singlet valence couplings overcoming their Coulomb repulsion with exact representation of the binding energies of the hydrogen, water and other molecules;

*** Theoretical prediction and vast experimental verifications of the new chemical species of Santilli MagneCules with a bond intentionally weaker than the valence so as to achieve full combustion, whose new fuels under world wide production and sale by the U. S. public company Magnegas Corporation whose stock is traded at NASDAQ with the symbol MNGA

For a 750 page long, 2011 general review with 50 pages of prior reference, one can study the monograph

I. Gandzha and J. Kadeisvili, New Sciences for a New Era: Mathematical, Physical and Chemical Discoveries of Ruggero Maria Santilli, Sankata Printing Press, Nepal (2011),
http://www.santilli-foundation.org/docs/RMS.pdf

INVITATION FOR PAPERS

Richard Anderson
Trustee
The R. M. Santilli Foundation
Email: board(at)santilli-foundation(dot)org http://www.i-b-r.org/

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