
<
January 3, 2014
Fifth International Workshop on Santilli's Iso, Geno, and HyperMathematics
Session 108 of ICNAAM 2014
http://www.icnaam.org/sessions_minisymposia.htm
PRWeb Release by VOCUS on the meeting
Santilli's Iso, Geno and HyperMathematics to be Developed at
the 21014 ICNAAM Conference in Greece
http://www.prweb.com/releases/2014/01/prweb11492321.htm
Organizers:
A. A. Bhalekar (India), Email: anabha@hotmail.com,
C. Corda (Italy), Email: cordac.galilei@gmail.com,
T. Vougiouklis (Greece), Email: tvougiou@eled.duth.gr.
OUTLINE OF ISOMATHJEMATICS
Let F(n, ⋅, I) be a numeric field of characteristic zero with
elements n, m, ... (real, complex and quaternionic numbers),
conventional associative product nm = n⋅m and multiplicative
unit I : I⋅n = n⋅I = n∀ n⋵F. In paper [1] of
1993, the ItalianAmerican scientist R. M. Santilli (CV) pointed
out that the ring F*(n*, ∗, I*) with elements n* = n⋅I*,
associativity preserving product n*∗m* = n*⋅T*⋅m*. and
generalized multiplicative unit I* = 1/T* , I*∗n* = n*∗I*
= n* ∀ n* ∈ F*, verifies all axioms of a numeric field
under the condition for I* of being invertible.
Santilli called the new fields F* isofields,, the new numbers
n* real, complex or quaternionic isonumbers, the new product
n*∗m* isoproduct, and the new unit I* isounit
where the prefix "iso" is used in the Greek meaning of being
"axiompreserving," In the same paper [1], Santilli discovered that
the isounit I* does not need to be an element of the original field,
and can be any desired nonsingular quantity, such as a number,
function, matrix, operator, etc. This led to the classification of
isonumbers of the first (second) kind depending on when the
isounit is (is not) an element of the original field.
The nontriviality of Santilli isonumbers should be indicated to
prevent predictable misjudgments. As an illustration, Santilli
isofields imply that prime numbers do not have an absolute meaning
since their numerical value depends on the assumed unit. Consider
the real isofields of the second kind F*(n, ∗, I*) where
n*≈n since I* ∈ F. Then, for I* = 3, the number 4 is a
prime number. Among various independent studies on Santilli isonumber
theory, we indicate monograph [2] by the Chinese mathematician CX.
Jiang and studies by the Italian physicist C. Corda [3] and Indian
Chemist A. A. Bhalekar [4].
In memoir [5] of 1996, Santilli identified the foundation of
isomathematics which is characterized by an isotopic lifting of
the totality of 20th century mathematics defined over a field of
characteristics zero, thus including the isotopies of functional
analysis, metric spaces, differential calculus, Lie's theory,
geometries, symmetries, topologies, etc. Particularly significant are
Santilli's stepbystep isotopies of the various branches of Lie's
theory with isoproduct [A, B]* = A∗B  B∗A which have
been constructed (when Santilli was at Harvard University in 1978
[6]) to characterize, apparently for the first time in a consistent
way, nonlinear, nonlocal and nonHamiltonian systems. Particularly
important is also Santilli's isodifferential calculus that
permitted the isotopies of Newton's, Hamilton's, Schroedinger,
Heisenberg's, Dirac's and other basic equations of physics. These
broader dynamical equations and their underlying isomathematics
characterize the isotopic branch of hadronic mechanics, or
isomechanics as a shot range covering of quantum mechanics to
avoid excessive linear, local and Hamiltonian approximations of
complex physical or chemical systems.
An important application and verification of isomathematics and
related isomechanics, for which the new mathematics was proposed for,
has been the first representation at the nonrelativistic and
relativistic levels of all characteristics of the neutron (and
not only its mass) in its synthesis from a proton and an electron in
the core of a star, p^{+} + e^{} → n + ν. In
this case, the conventional Schroedinger equation of quantum mechanics
does not yield physically meaningful solutions because the rest energy
of the neutron is higher by 0.782 MeV than the sum of the rest
energy of the proton and the electron, thus requiring a positive
binding energy which is anathema for quantum mechanics. Thanks to
their nounitary structure, the ShcroedingerSantilli isoequation for
the nonrelativistic treatment and the DiracSantilli is isoequation
for the relativistic treatment have permitted the removal of these
insufficiencies for the most fundamental nuclear synthesis in nature
(see the review by J. V. Kadeisvili [7]). Comprehensive treatments of
isomathematics, isomechanics and their applications in numerous fields
are available in Santilli's monographs [511]. For independent studies
we indicate monographs [1215] and quoted references by the
mathematicians Gr. Tsagas, D. S. Sourlas, J. V. Kadeisvili, R. M.
Falcon Ganfornina, J. Nunez Valdes, S. Georgiev, and others.
OUTLINE OF GENOMATHEMATICS
Santilli has dedicated his research life to the representation of
irreversible systems due to their evident significant for
energyreleasing processes. The research initiated during his graduate
studies at the University of Turin, Italy, in the mid 1960s. Santilli
recognized that 20th century theories are reversible over time because
based on Lie algebras whose product is invariant under
antiHermiticity [A, B] = AB  BA = [A, B]^{+}. As a
condition to assure irreversibility over time, Santilli therefore
searched for a covering of Lie algebras whose product is neither
antisymmetric nor symmetric, selected Lieadmissible algebras
according to the American mathematician A. A. Albert [16], and
published in 1967 paper [17] the embedding of Lie algebras into
covering Lieadmissible algebras illustrated with the first
formulation of (p,q)deformations (A, B) = pAB  qBA that was later on
followed by a large number of papers in the simpler deformations AB 
qBA.
Also during his Ph. D. thesis, Santilli proved a No Reduction
Theorem according to which macroscopic irreversible systems cannot
be consistently reduced to a finite number of quantum mechanical
particles all in reversible conditions.Alternatively, Santilli No
reduction Theorem implies that known thermodynamical laws cannot be
consistently eliminated via the reduction of systems to quantum
mechanical events. The theorem established that macroscopic
irreversibility, rather than "disappearing" at the elementary particle
level, originate instead at the ultimate structure of physical
systems, thus establishing the need for their quantitative studies
preferably as a covering of reversible quantum descriptions.
Mathematical maturity in the formulation of Lieadmissible treatments
was initiated with paper [1] of 1993 in which Santilli discovered
that, besides the unit of a field being an arbitrary nonsingular
quantity, the multiplication can be ordered either to the right n>m
or to the left n<m while preserving all axioms of a field. This
allowed Santilli to introduce the forward genofields
F^{>}(n^{>}, >, I^{>}) with
forward real, complex or quaternionic genonumbers
n^{>} = n⋅I^{>}, forward genoproduct
n^{>}>m^{>} =
n^{>}⋅S⋅m^{>}, and forward
genounit I^{>} = 1/ S, with conjugate backward
genofields^{<}F(^{<}n, <,
^{<}I), ^{<}I = 1 / R. The property R≠S then
assures the lack of violation of causality and other physical laws in
the representation of energy releasing processes.
Genomathematics is characterized by the dual, forward and
backward genotopies of 20th century mathematics over a field of
characteristic zero, thus including the forward and backward
genotopies of numbers, functional analysis, differential calculus,
metric spaces, algebras, geometries, topologies, etc. which
genotopies, to be consistent, must be formulated over a basic
genofield. The Lieadmissible covering of Lie algebras [6(b)] is
characterized by two universal enveloping genoassociative algebras,
one for the product ordered to the right and one to the left,
resulting in a genobimodular structure namely, a bimodular
structure with action to the right A>) = HS) and to the left
(<H = (RA, R≠S. Such a genobimodule characterizes a
Lieadmissible algebra with product (A, B) = ARB  BSA first
identified by Santilli in 1978 [6], with genoequations i dA/dt = (A,
H) = A<H  H<A = ARH  HSA. These equations are at the
foundation of the genotopic branch of hadronic mechanics, or
genomechanics, that has already permitted the scientific
identification and industrial development of new fuels and energies
by U. S. publicly traded companies and their foreign associates.
A presentation of Lieadmissible formulations as of 1995 is available
in Refs. [6,8,9,10, 11]. The latest presentation is available in
memoir [18] of 2006. Among a numbers of independent studies in
Lieadmissible treatments we mention refs. [1927] by the physicists
S. Adler, P. Roman, H. C. Myung, J. Ellis, E. Mavromatos, D. V.
Nanopoulos, J. Dunning Davies, A. A. Bhalekar, V. M. Tangde and
others. Additional more recent references are available in the
Proceedings of the Third International Conference on Lieadmissible
Treatments of Irreversible Processes[28].
OUTLINE OF HYPERMATHEMATICS
Hypermathematics is the most general mathematics that can be
currently conceived by the human mind. It is based on multivalued,
forward and backward hyperlifting of genomathematics via
hyperoperations called "hopes" verifying the axioms of the Hv
hyperstructures by the Greek mathematician T. Vougiouklis (see
paper [29] of 2013 and references quoted therein). Hypermathematics
admits as particular cases the preceding geno and isomathematics and
characterizes the hyperstructural branch of hadronic mechanics,
also calledhypermechanics [9, 18]. It should be noted that
hypermathematics achieves compatibility with our sensory perception
because it is multivalued rather than "multidimensional" as
it is the case for various theories. A primary aim of hypermathematics
is to stimulate a new era in the study of biological structures, such
as the DNA, whose complexity is outside realistic capabilities of
20th century mathematics as well as isomathematics and
genomathematics. Monograph [30] by I. Gandzha and J. V. Kadeisvili
is suggested for a general independent review.
FINANCIAL SUPPORT FOR PARTICIPATION
Scientist interested in participating are suggested to apply for
financial support by sending via email a one page motivation and the
CV to
The R. M. Santilli Foundation
http://www.santillifoundation.org/
http://www.worldlectureseries.org/
Email: board(at)santillifoundation(dot)org
Deadline for applications: August 15, 2014
REFERENCES
[1] R. M. Santilli, "Isonumbers and Genonumbers of Dimensions 1, 2, 4,
8, their Isoduals and Pseudoduals, and ;Hidden Numbers; of Dimension
3, 5, 6, 7," Algebras, Groups and Geometries Vol. 10, 273 (1993),
http://www.santillifoundation.org/docs/Santilli34.pdfbr>
[2] ChunXuan Jiang, Foundations of Santilli Isonumber Theory,
International Academic Press (2001),
http://www.ibr.org/docs/jiang.pdf
[3] C. Corda, (a) "Introductionto Santilli isonumbers American Institute of Physics Conf. Proc. 1479 , 1013 (2012); and (b) "Introduction to
Santilli isomathematics", American Institute of Physics Conf. Proc. 1558, 685 (2013)
http://www.santillifoundation.org/docs/Cordaisomathematics.pdf
[4] A. A. Bhalekar, "Santilli's New Mathematics for Chemists and
Biologists. An Introductory Acount,", CACAA, 3(1), 1586 (2014)
http://www.santillifoundation.org/docs/BhalekarMath2013.pdf
[5] R. M. Santilli, "NonlocalIntegral Isotopies of Differential
Calculus, Mechanics and Geometries," in Isotopies of Contemporary
Mathematical Structures, P. Vetro Edi tor, Rendiconti Circolo
Matematico Palermo, Suppl. Vol. 42, 782 (1996),
http://www.santillifoundation.org/docs/Santilli37.pdf
[6] R. M. Santilli, Foundation of Theoretical Mechanics, Volume
(a) I (1978) and (b) II (1982) SpringerVerlag, Heidelberg, Germany,
http://www.santillifoundation.org/docs/Santilli209.pdf
http://www.santillifoundation.org/docs/santilli69.pdf
[7] J. V. Kadeisvili, "The RutherfordSantilli Neutron," Hadronic
Journal , 31, 1114 (2008)
http://www.ibr.org/RutherfordSantilliII.pdf
[8] R. M. Santilli, Isotopic Generalizations of Galilei and
Einstein Relativities, Volumes (a) I and (b) II, International
Academic Press (1991) ,
http://www.santillifoundation.org/docs/Santilli01.pdf
http://www.santillifoundation.org/docs/Santilli61.pdf
[9] R. M. Santilli, Elements of Hadronic Mechanics, Volumes I
and II Ukraine Academy of Sciences, Kiev, second edition 1995,
http://www.santillifoundation.org/docs/Santilli300.pdf
http://www.santillifoundation.org/docs/Santilli301.pdf
[10] R. M. Santilli, Hadronic Mathematics, Mechanics and
Chemistry,, Vol. I [a], II [b], III [c], IV [d] and [e],
International Academioc Press, (2008), available as free downlaods
from
http://www.ibr.org/HadronicMechanics.htm
[11] R. M. Santilli, Foundations of Hadronic Chemistry, with
Applications to New Clean Energies and Fuels, Kluwer Academic
Publishers (2001),
http://www.santillifoundation.org/docs/Santilli113.pdf
.
[12] S. Sourlas and G. T. Tsagas, Mathematical Foundation of the
LieSantilli Theory, Ukraine Academy of Sciences (1993),
http://www.santillifoundation.org/docs/santilli70.pdf
[13] J. V. Kadeisvili, Santilli's Isotopies of Contemporary
Algebras, Geometries and Relativities, Ukraine Academy of
Sciences, Second edition (1997),
http://www.santillifoundation.org/docs/Santilli60.pdf
[14] R. M. Falcon Ganfornina and J. Nunez Valdes, Fundamentos de la
Isoteoria de Lie Santilli, International Academic Press (2001),
http://www.ibr.org/docs/spanish.pdf
[15] S. Georgiev and J. V. Kadeisvili, Foundations of the
IsoDifferential Calculus, Vol. I, to appear.
[16] A. A. Albert,"Onthepowerassociativerings,"Trans.Amer.Math.Soc.,64,
552593 (1948).
[17] R. M. Santilli, "Embedding of
LiealgebrasintoLieadmissiblealgebras, " Nuovo Ci mento, 51, 570
(1967)
http://www.santillifoundation.org/docs/Santilli54.pdf
[18] R. M. Santilli, "Lieadmissible invariant representation of
irreversibility for matter and antimatter at the classical and
operator levels," Nuovo Cimento B 121, 443 (2006),
http://www.santillifoundation.org/docs//LieadmissNCBI.pdf
[19] S. Adler, Phys. Rev. 17, 3212 (1978)
[20] P. Roman and R. M. Santilli, "A Lieadmissible model for
dissipative plasma," Let tere Nuovo Cimento 2, 449455 (l969)
[21] H. C. Myung and R. M. Santilli, "Bimodulargenotopic Hilbert
Space Formulation of the Interior Strong Problem," Hadronic J. 5,
13671404 (l982).
[22] J. Fronteau, R. M. Santilli andA. TellezArenas, "Lieadmissible
structure of statis tical mechanics," Hadronic Journal 3, 130145
(1979).
[23] J. Ellis, N. E. Mavromatos and D. V. Nanopoulos in Proceedings of
the Erice Sum mer School, 31st Course: From Superstrings to the
Origin of SpaceTime, World Scientific (1996).
[24] J. DunningDavies, "Lieadmissible formulation of
thermodynamoical laws," ZZZZZZZZZZ to be completed.
[25] J. DunningDavies, (a) "Thermodynamics of Antimatter via
Santilli's Isodualities", Found. Phys. Lett., 12(6), 593599 (1999);
(b) "The Thermodynamics Associated with Santilli's Hadronic
Mechanics",, Prog. Phys., 4, 2426 (2006).
[26] A. A. Bhalekar, (a) "Santilli's Lieadmissible mechanics. The
only option commensurate with irreversibility and nonequilibrium
thermodynamics", AIP Conf. Proc., 1558, 702706 (2013); (b)
"Genononequilibrium thermodynamics.I. Background and preparative
aspects", CACAA, 2(4), 313366 (2013); (c) "On the GenoGPITT
framework", AIP Conf. Proc., 1479, 10021005 (2012); (c) "Studies
of Santilli's isotopic, genotopic and isodual four directions of
time", AIP Conf. Proc., 1558, 697701 (2013).
http://www.santillifoundation.org/docs/RhodesGreeceAAB.pdf
http://www.santillifoundation.org/docs/TimeArrowsAAB2.pdf
http://www.santillifoundation.org/docs/ANIL%20BHALEKARRhodesI.pdf
http://www.santillifoundation.org/docs/ANIL%20BHALEKARRhodesII.pdf
[27] V. M. Tangde, (a) "Advances in hadronic chemistry and its
applications", CACAA, 2(4), 367392 (2013); (b) "Elementary and
brief introduction of hadronic chemistry", AIP Conf. Proc., 1558, 652656 (2013).
http://www.santillifoundation.org/docs/paper244.pdf
http://www.santillifoundation.org/docs/Tangde.pdf
http://www.santillifoundation.org/docs/hadronicchemistry2013.pdf
http://www.santillifoundation.org/docs/Vijay%20TangdeHadronicChemistry.pdf
[28] C. Corda, editor, {\it Proceedings of the 2011 International Conference on
Lieadmissible Formulations for Irreversible Processes,} Kathmandu
University, Nepal (2011)
http://www.santillifoundation.org/docs/Nepal2011.pdf
[29] R. M. Santilli and T. Vougiouklis, (a) "Isotopies, Genotopies, Hyperstructures and their Applications,"Prooc. Int. Workshop in Monderoduni: New Frontiers in Hyperstructures and Related Algebras, Hadronic Press (1996), 177188; and (b) "Lieadmissible hyper
algebras," Italian Journal of Pure and Applied Mathematics, Vol. 31, pages 239254 (2013)
http://www.santillifoundation.org/Lieadmhyperstr.pdf
[30] 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.santillifoundation.org/docs/RMS.pdf
**********************************

