GRANTS FOR INNOVATIVE TEACHING IN
MATHEMATICS, PHYSICS AND CHEMISTRY
- Richard Anderson
Trustee, The R. M. Santilli Foundation
http://www.santilli-foundation.org/
http://www.world-lecture-series.org/

Following the success of the new 21st century sciences "beyond Einstein" presented this year at

Third International Conference on the Lie-admissible
Treatment of Irreversible Processes
Kathmandu University, Nepal, January 4 to 8, 2011
http://www.ku.edu.np/iclatip/
with proceedings available in free pdf download
http://www.santilli-foundation.org/docs/Nepal-2011.pdf

San Marino Workshop on Astrophysics and Cosmology for
Matter and Antimatter September 5 to 9, 2011
http://www.workshops-hadronic-mechanics.org/
with lectures for free view or download from the link
http://www.world-lecture-series.org/san-marino-2011

CNAAM 2011, Halkidiki, Greece, 19-25 September 2011
http://www.icnaam.org/index.htm

the confirmation by CERN/GRAN SASSO of superluminal
speeds as previously presented at the 2011 San Marino Workshop
by G. Nimtz, A. Kholmetskii, R. M. Santilli, et al
http://www.bbc.co.uk/news/science-environment-15791236

Prof. R. M. Santilli recent announcement
Super/Sub-luminal speeds verify SR axioms
http://www.santilli-foundation.org/sr-axioms.php

our Foundation will support the organization and conduction in mid 2012 of a
Post Ph. D. Seminar Course on Hadronic Mechanics
Besides the teaching by the founders, our Foundation is seeking additional
teachers for selected topics in mathematics, physics and chemistry
specified below (grant rules at bottom).

I. INNOVATIVE TEACHING IN MATHEMATICS
I-1. Santilli isonumber theory
A teacher, expert in number theory, is needed to present the new numeric fields with arbitrary (non singular) multiplicative unit, called Santilli isounit, and show that they verify the conventional axioms of numerical fields under a simple redefinition of the multiplication, first introduced by Prof. Santilli in Ref. [1] below. Due to the preservation of the conventional numerical axioms, the new numbers were called by Prof. Santilli "isonumbers" where the prefix "iso" is intended in the Greek meaning of preserving the original axioms. The teacher should additionally present some of the implications of isonumbers worked out by Prof. Jing in Ref. [2], and indicate some applications, e.g., to the new isocryuptograms, that is, cryptograms defined over Santilli isofields in such a way to admit an infinite number of possible isounits (applications to physics will be presented by physicists).

[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.santilli-foundation.org/docs/Santilli-34.pdf

[2] Chun-Xuan Jiang, Foundations of Santilli Isonumber Theory,
International Academic Press (2001),
http://www.i-b-r.org/docs/jiang.pdf

I-2. Isospaces, isofunctional analysis, and isodifferenial calculus.
With reference to the seminal memoir [3], a teacher expert in functional analysis and differential calculus is needed for a presentation on the isotopies of conventional vector, metric or pseudo-metric spaces, called isospaces, essentially given by the reformulation of conventional spaces over Santilli isofields, i.e., a redefinition admitting Santilli isounit as the right and left unit at all levels. The teaching should then pass to an outline of isofunctional analysis, initiated by Prof. J. V. Kadeisvili, A Aringazin et al, consisting of functions defined on isospaces that admit Santilli isounit as the right and left unit. Finally, the teaching should include a presentation of the isodifferential calculus, first introduced by Prof. Santilli in Ref. [3], which is also given by the redefinition of the ordinary differential calculus in such a a way to admit Santilli isounit when depending on the variable of differentiation.

[3] R. M. Santilli, "Nonlocal-Integral Isotopies of Differential Calculus, Mechanics
and Geometries," in Isotopies of Contemporary Mathematical Structures,
P. Vetro Editor, Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, 7-82 (1996),
http://www.santilli-foundation.org/docs/Santilli-37.pdf

[4] R. M. Falcon Ganfornina and J. Nunez Valdes, Fundamentos de la Isoteoria de Lie-Santilli,
International Academic Press (2001),
http://www.i-b-r.org/docs/spanish.pdf

I-3. Lie-Santilli isotheory
The 20th century formulation of Lie's theory is notoriously linear, local-differential and Hamiltonian. By contrast, the majority of systems in the physical reality are nonlinear, nonlocal and non-Hamiltonian, that is, containing variationally nonselfadjoint forces that, by conception, are not representable with a Hamiltonian. Thanks to the preceding isotopies of numerical fields, metric spaces, functional analysis and differential calculus, Prof. Santilli has achieve ed a reformulation of Lie's theory, today known as Lie-Santilli isotheory, that is indeed directly applicable to nonlinear, nonlocal and non-Hamiltonian systems, while preserving the original Lie axioms at the abstract level. A teacher, expert in Lie's theory, is needed to present the various branches of the Lie-Santilli isotheory, including isoassociative enveloping algebras, isoalgebras, isogroups and their representation as available in the publications below.

[5] R. M. Santilli, Elements of Hadronic Mechanics.Volume I
Ukraine Academy of Sciences, Kiev, second edition 1995,
http://www.santilli-foundation.org/docs/Santilli-300.pdf

[6] D. S. Sourlas and G. T. Tsagas, Mathematical Foundation of the Lie-Santilli Theory,
Ukraine Academy of Sciences 91993),
http://www.santilli-foundation.org/docs/santilli-70.pdf

[7] J. V. Kadeisvili, Santilli's Isotopies of Contemporary Algebras, Geometries and Relativities,
Ukraine Academy of Sciences, Second edition (1997)
http://www.santilli-foundation.org/docs/Santilli-60.pdf

I-4. Tsagas-Sourlas-Santilli-Ganfornsxina-Valdes (TSSGV) isotopology
20th century applied sciences are based on the Euclidean and other topologies that are local-differential, thus being solely applicable to a finite number of point-like particles. 21st century problems require the characterization of a finite number of extended, therefore generally non spherical and deformable particles that, as such, require a structurally broader topology with far reaching mathematical and physical implication. This new topology has been first studied by Profs. Tsagas and Sourlas [8], then by Prof. Santilli [[3], then by Profs. Ganformina and Valdes [9] and it is today called the TSSGV isotopology. A teacher, expert in 20th century topologies, is needed for the teaching of the TSSGV isotopology.

]8\ G. Tsagas, ''Studies on the classification of Lie-Santilli algebras," Algebras, Groups and
GeometriesVol. 13, 129- (1996). available from the link
http://www.santilli-foundation.org/docs/Tsagas.pdf

[9] Raul M. Falcon Ganfornina and Juan Nunez Valdes, ``Studies on the Tsagas-Sourlas-Santilli
Isotopology," Algebras, Groups and Geometries {\bf 20}, 1 (2003),
http://www.santilli-foundation.org/docs/isotopologia.pdf

I-5. Hilbert-Myung-Santilli isospaces
20th century formulations of quantum mechanics are based on the theory of linear operators on a Hilbert space defined over a field of complex numbers. However, physical problems of interest in the 21st century are strictly nonlinear, thus preventing the use of conventional Hilbert spaces due to a number of problematic aspects, such as the inability to study composite systems with non;linear interactions due to the violation of the superposition principle and other shortcomings. An axiom preserving lifting of Hilbert spaces capable of consistent treatment of nonlinear, as well as nonlocal-integral and nonpotential/non-Hamiltonian interactions (via their embedding in Santilli's isounit) has been achieved by Prof. Santilli in 10982 in collaboration with the mathematician Prof. H. C. Myung [10] and then studied in details in various works (see Ref. [11]). A teacher, expert in Hilbert spaces, is needed for a presentation on the covering Hilbert-Myung-Santilli isospaces and some of their important implications, such as the achievement of strong convergent for the isotopic image of conventionally divergent expansions, the Dirac-Myung-Santilli isodelta function also studied by Prof. M. Nishioka [12] and other important features.

[10] H. C. Myung and R. M. Santilli, Hadronic Journal Vol. 5, pages 1277-1366 (1982).
http://www.santilli-foundation.org/docs/Santilli-201.pdf

[11] R. M. Santilli, Elements of Hadronic Mechanics, Volume II
Ukraine Academy of Sciences, Kiev, second edition 1995,
http://www.santilli-foundation.org/docs/Santilli-301.pdf

[12] M. Nishioka, Lettere Nuovo Cimento Vol. 39, pages 369-372 (1984),
http://www.santilli-foundation.org/docs/Santilli-202.pdf

II. INNOVATIVE TEACHING IN PHYSICS
Theoretical physicists experts in classical mechanics, quantum mechanics and scattering theory are needed to teach the following selected topics:

II-1. Foundations of classical and operator hadronic mechanics
Recall the true Lagrange and Hamilton equations, those with external terms necessary for the representation of irreversible processes; recall the 'No Reduction Theorems" establishing the impossibility of the elimination of external terms in the reduction of classical irreversible systems to their elementary constituents; recall that the brackets of the time evolution with external terms violate the conditions to constitute an algebra; review Santilli's Lie-isotopic, Lie-admissible and hyper-structural formulations of the true Lagrange and Hamilton equations (for single valued closed non-Hamiltonian, single valued non-Hamiltonian irreversible; and multivalued irreversible systems, respectively) in such a way to admit a consistent algebras in the brackets of the time evolution; show the universality of the derivation of the Lagrange-Santilli and Hamilton-Santilli equations from an action principle via the the use of the anew differential calculus; review the unique and unambiguous hadronization of these classical mechanics (that are universal for noncanonical systems) into corresponding nonunitary branches of hadronic mechanics (that are universal for nonunitary theories); review the corresponding classes of Schroedinger-Santilli, Heisenberg-Santilli and Dirac-Santilli iso-, geno- and hyper-equations; show that hadronic mechanics is a new realization of the abstract axioms of quantum mechanics permitted by Santilli new is-, geno-, and hyper- mathematics; prove the full causality of non-relativistic and relativistic hadronic mechanics via the Galileo-Santilli and the Lorentz-Poincare'-Santilli symmetries, respectively; show that hadronic mechanics is a "completion" of quantum mechanics mostly according to Einstein, Podolsky and Rosen; show the revisions necessary for Bell's inequality under causal and invariant non-Hamiltonian, thus nonunitary interactions and the consequential revision of local realism. Recommended general reference and vast literature quoted therein:

[13] R. M. Santilli, Elements of Hadronic Mechanics, Volume II
Ukraine Academy of Sciences, Kiev, second edition 1995,
http://www.santilli-foundation.org/docs/Santilli-301.pdf

II.2. Rutherford-Santilli synthesis of neutrons from H-atoms inside stars
Initiate the study via a quantitative representation of "all" characteristics of the pi-0 (including charge radius, meanlife, etc. and not the mass alone) in its known synthesis e^+ + e^- => pi-0 first achieved by Santilli in 1978 in Section 5 of Ref. [14]; show the inconsistency of Schroedinger equation since the rest energy of the pi-0 is much bigger than the sum of c the rest energies of the original particles thus requiring an inconsistent large "positive binding energy"; show the necessity of a nonunitary generalization of quantum mechanics for the considered synthesis that lead to Santilli's 1978 proposal for the covering hadronic mechanics; and review in detail the 1978 analytic solution in Section 5 of Ref. [14]. Pass then to the review of the nonrelativistic [14] and relativistic [15] synthesis of the neutron inside stars p^+ + e^- => n + ? with ensuing new model today known as Rutherford-Santilli neutron; show again the inconsistency of Schroedinger equation due to the need for a "positive binding energy"; review Santilli's isotopies of the SU(2)-spin symmetry for extended spinning particles on a Hilbert-Myung-Santilli isospace over Santilli's isofield of complex numbers; show the dramatic differences for Rutherford's synthesis in first treating the proton as a point-particle and then its treatment as an extended charge distribution with a hyperdense medium in its in terior; show in the latter case the constrained character of the electron compressed within the hyperdense medium inside the proton with consequential null total angular momentum and the spin of the neutron coinciding with that of the proton; review the experiments on the laboratory synthesis of the neutron from a hydrogen gas; show the impossibility for extended protons and neutrons to identify the spin, let alone the energy needed to characterize the hypothetical neutrino; shows the need for Santilli's alternative aetherino (or etherino) longitudinal impulse (not a particle!) propagating through the aether with consistent reaction p^+ + a + e^- => n without the neutrino [18]; show the compatibility of Santilli's aetherino hypothesis with ongoing experiments claiming the "detection of (undetectable) neutrinos"; conclude by indicating the basically new energies without radiations and other energies that are derivable from quantitative representation of Rutherford's synthesis of the neutron (see memoir [19] for a general review)

[14] R. M. Santilli, "Need of subjecting to an experimental verification the validity within a hadron
of Einstein special relativity and Pauli exclusion principle," Hadronic J. Vol. 1, 574-901 (1978), available in free pdf download from
http://www.santilli-foundation.org/docs/Santilli-73.pdf

[151] R. M. Santilli, "Apparent consistency of Rutherford's hypothesis on the neutron as a
compressed hydrogen atom," Hadronic J. Vol. 13, 513-531 (1990)
www.santilli-foundation.org/docs/ Santilli-21.pdf

[16] R. M. Santilli, "Recent theoretical and experimental evidence on the synthesis of the neutron,"
Communication of the JINR, Dubna, Russia, No. E4-93-252 (1993), published in the Chinese
J. System Eng. and Electr. Vol. 6, 177 (1995,
http://www.santilli-foundation.org/docs/Santilli-18.pdf

[17] C. Borghi, C. Giori C. and A. Dall'Olio,(Russian) Phys. Atomic Nuclei, Vol. 56, 205 (1993).
R. M. Santilli, "Apparent confirmation of Don Borghi's experiment toward the synthesis of neutron
from protons and electrons," Hadronic Journal Vol. 30, 709 (1997).
http://www.neutronstructure.org/neutron-synthesis.htm

[18] R. M. Santilli, "The etherino and/or the Neutrino Hypothesis?" Found. Phys. Vol. 37, p. 670 (2007)
www.santilli-foundation.org/docs/EtherinoFoundPhys.pdf

[19] J. V. Kadeisvili, ''The Rutherford-Santilli Neutron," Hadronic J. Vol. 31, 1 (2008),
http://www.i-b-r.org/Rutherford-Santilli-II.pdf
also available in htlm format from the website
http://www.i-b-r.org/Rutherford-Santilli-neutron.htm

II-3. Santilli classical and operator isodual theory of antimatter
Recall the large scientific imbalance of the 20th century for which matter was studied at all levels, from Newton to second quantization, while antimatter was solely studied in second quantization; show the complete inability by Einstein's special and general relativities to represent neutral antiparticles; show the necessity for Newtonian, Minkowskian and Riemannian representation of neutral antimatter; shows the need of a new mathematics for the classical representation of neutral antimatter; review Santilli's isodual mathematics with negative units; review Santilli isodual classical and operator mechanics; shows the equivalence of isoduality and charge conjugation at the operator level; show that the achievement of a classical representation of neutral antimatter implies necessary physical differentiation between light emitted by matter and antimatter; review Santilli isodual elm waves and photons and their cosmological implications for the possible future detection of antimatter galaxies and stars; show the compatibility of the isodual theory of antimatter with all available classical and operator experimental data on antimatter; show the prediction by the isodual theory of antimatter of gravitational repulsion of antimatter in the field of matter or vice versa; review Santilli's 1994 proposed resolutory experiments to measure the gravity of positrons in a horizontal vacuum and supercooled tube on Earth; review the proposed experiments to establish or deny the existence of Santilli isodual light. Main reference and vast literature quoted therein:

[20] Isodual Theory of Antimatter with Application to Antigravity,
Grand Unification and the Spacetime Machine,
R.M.Santilli, Springer 2001
http://www.santilli-foundation.org/docs/santilli-79.pdf

II-4. Nonunitary Lie-isotopic and Lie-admissible scattering theories of hadronic mechanics
Show that the reduction to point-like abstractions of the scattering region for high energy processes is a philosophic conception outside realities due to the hyperdense character of the scattering regions and the absence in nature of 'point-like wavepackets"; show the necessary emergence in the interior of the scattering region of contact, zero-range, nonlinear, nonlocal and non-Hamiltonian interactions with consequential impossibility for the conventional relativistic scattering theory to be exactly valid for high energy scattering processes; review the foundations of the nonunitary, fully causal and time invariant Lie-isotopic and Lie-admissible scattering theory of hadronic mechanics; show the necessary mutation of the rest energy of virtual or intermediate particles in scattering processes, thus dismissing 20th century beliefs on the mass of the Higgs boson and similar hypothetical particles; show the irreconcilable insufficiencies of Feynman's diagrams for high energy inelastic scattering processes; show the inconsistencies of Feynman';s diagrams for particle-antiparticle annihilation whenever mediated by a particle or an antiparticle; shows the necessity of new vistas for high energy hyperdense scattering regions without mediation by hypothetical new particles; show the representation by the new nonunitary scattering theory of events impossible for the conventional unitary theory, such as the synthesis of hadrons from lighter particles; show the predictions of the scattering theory. of hadronic mechanics. Main recent reference (see monograph [13] for the status of the research in 1995)

[21] Nonunitary Lie-isotopic and Lie-admissible scattering theories of hadronic mechanics,"
Papers
I, II, III, IV and V, by R. M. Santilli and A. O. E. Animalu, in the
Proceedings of the Third International Conference on the Lie-Admissible Treatment
of Irreversible Processes, C. Corda, Editor, Kathmandu University (2011)
http://www.santilli-foundation.org/docs/Isoscattering-I.pdf
http://www.santilli-foundation.org/docs/Isoscattering-II.pdf
http://www.santilli-foundation.org/docs/Isoscattering-III.pdf
http://www.santilli-foundation.org/docs/Isoscattering-IV.pdf
http://www.santilli-foundation.org/docs/Isoscattering-V.pdf

II-5. Experimental verifications of hadronic mechanics in classical mechanics, particle physics, nuclear physics, superconductivity, astrophysics and cosmology, the novel intermediate fusions without radiations, and other applications of hadronic mechanics
To be taught by Santilli and his associates

III. INNOVATIVE TEACHING IN CHEMISTRY
Theoretical chemists experts in quantum chemistry are needed to teach the following selected topics:

III.1. Introduction to hadronic chemistry
Show that the 20th century notion of valence is a pure nomenclature without technical content because lacking an equation representing the bond in a way consistent with experimental evidence; prove that two identical electrons in single valence coupling repel each other according to quantum mechanics; prove that, according to 20th century notion of orbitals, all substances are predicted as being paramagnetic in dramatic disagreement with evidence; review the lack of exact representation by quantum chemistry from first axiomatic principles of the hydrogen and other molecules; show the prediction, in general, by quantum chemistry axioms without manipulations of the wrong signs, let alone the wrong values of electric and magnetic moments of the water and other molecules; show that the screening of the Coulomb potential via the multiplication of an arbitrary function fitted from the data causes the loss of quantized orbits, with consequential inability of still claiming the validity of "quantum chemistry", the breaking of the basic Galilean and other symmetries and the violation of other quantum mechanical principles; show the necessity of admitting the presence in valence electron pairing of contact, zero-range, nonlinear, nonlocal and non-Hamiltonian interactions due to mutual penetration of extended wavepackets of the electrons; show the structural impossibility for an exact representation of electron valence couplings by quantum mechanics and chemistry in favor of the covering hadronic mechanics and chemistry; outline the isotopic and genotopic lifting of quantum chemistry via single and dual nonunitary transforms, respectively; show the insufficiencies of quantum chemistry for the representation of irreversible chemical reactions in favor of the Lie-admissible branch of hadronic chemistry. main reference:

[22] Foundations of Hadronic Chemistry, with Applications to New Clean Energies and Fuels,
R. M. Santilli, Kluwer Academic Publishers (2001),
http: //www.santilli-foundation.org/docs/Santilli-113.pdf.

III.2. Santilli-Shillady hadronic model of the hydrogen molecule
Review the model of the hydrogen molecules according to hadronic chemistry first achieved by Santilli and Shillady in 1999 ]23]; show its numerically exact representation of the binding energy of the H2 molecule, its diamagnetic character and other features; show the achievement of these results thanks to strongly attractive valence bond permitted by the non-hamiltonian interactions of hadronic chemistry; show the consequential reduction (in first approximation) of the hydrogen molecule to a restricted three-body system characterized by the two protons and the strongly bonded valence electron pair in singlet coupling; review the exact analytic solution by R. Perez-Enriquez, R. Riera, A.K. Aringazin and M.G. Kucherenko ]24,25].

[23] "A new isochemical model of the hydrogen molecule,"
R. M. Santilli and D. D. Shillady, Intern. J. Hydrogen Energy Vol. 24, pages 943-956 (1999)
www.santilli-foundation.org/docs/Santilli-135.pdf

[24] "Exact analytic solution of the restricted three-body Santilli-Shillady model of the hydrogen
molecule, " R. Perez-Enriquez and R. Riera, Progress in Physics Vol. 2, 34-41 (2007)
(physics/0001056)v www.santilli-foundation.org/docs/3body2.pdf

[25] "Exact variational solution of the restricted three-body Santilli-Shillady model of the hydrogen
molecule," A.K. Aringazin and M.G. Kucherenko, Hadronic J. Vol. 23, 1-56 (2000) (physics/
0001056)www.santilli-foundation.org/docs/3body.pdf

III.3. Santilli-Shillady hadronic model of the water molecule
Review the model of the water molecule from first axiomatic principle of hadronic chemistry without adulterations or arbitrary screening functions first achieved by Santilli and Shillady in 2000 [26]; show the representation of the binding energy of the water molecule exact to the desired decimal; show the exact representation of the sign and values of the electric and magnetic polarizations;; show that the Santilli-Shillady model of molecules permits a reduction of computer time at least of the order of 1000 due to the strong convergence of otherwise weakly convergent series; outline the implications of the Santilli-Shillady molecular model for the 21st century chemistry.

[26] "A new isochemical model of the water molecule,"
R. M. Santilli and D. D. Shillady, Intern. J. Hydrogen Energy Vol. 25, 173-183 (2000)
www.santilli-foundation.org/docs/Santilli-39.pdf

III-4. The new chemical species of magnecules, the novel magnecular combustion, and their industrial; applications
To be taught by Santilli and his associates.

TEACHING GRANTS
Each accepted teacher is expected to write a review paper on his/her topic so as to show the acquisition of the necessary knowledge in the field, and then be a teacher at the indicated Seminar Course in mid 2012. Our Foundation will provide a first grant of $3,000 for the writing of the review paper, $1,500 payable at initiation and the balance at the reception of a draft of the paper. An additional grant will be provided for teaching at the Seminar Course, for the payment of travel, lodging and other expenses. The review papers will be published in advance of the course for their availability to interested students and participants.

Interested teachers should contact me by email with the identification of his/her field of expertise, the selected topic as listed above and include the CV

Thanks for your interest and best regards

Richard Anderson
Trustee The R. M. Santilli Foundation
Email: board@santilli-foundation.org

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