Hyperstructures in Lie-Santilli Admissibility and Iso-Theories

In the quiver of hyperstructures Professor R. M. Santilli, in early 90'es, tried to find algebraic structures in order to express his pioneer Lie-Santilli's Theory. Santilli's theory on 'isotopies' and 'genotopies', born in 1960's, desperately needs 'units e' on left or right, which are nowhere singular, symmetric, real-valued, positive-defined for n-dimensional matrices based on the so called isofields.These elements can be found in hyperstructure theory, especially in $H_v$-structure theory introduced in 1990. This connection appeared first in 1996 and actually several $H_v$-fields, the e-hyperfields, can be used as isofields or genofields so as, in such way they should cover additional properties and satisfy more restrictions. Several large classes of hyperstructures as the P-hyperfields, can be used in Lie-Santilli's theory when multivalued problems appeared, either in finite or in infinite case. We review some of these topics and we present the Lie-Santilli admissibility in Hyperstructures

Studies on the classical determinism predicted by A. Einstein, B. Podolsky and N. Rosen

In this paper, we continue the study initiated in preceding works of the argument by A. Einstein, B. Podolsky and N. Rosen according to which quantum mechanics could be “completed” into a broader theory recovering classical determinism. By using the previously achieved isotopic lifting of applied mathematics into isomathematics and that of quantum mechanics into the isotopic branch of hadronic mechanics, we show that extended particles appear to progressively approach classical determinism in the interior of hadrons, nuclei and stars, and appear to recover classical determinism at the limit conditions in the interior of gravitational collaps

Finite H_v-Fields with Strong-Inverses

The largest class of hyperstructures is the class of H v -structures. This is the class of hyperstructures where the equality is replaced by the non-empty intersection. This extremely large class can used to define several objects that they are not possible to be defined in the classical hypergroup theory. It is convenient, in applications, to use more axioms and conditions to restrict the research in smaller classes. In this direction, in the present paper we continue our study on H v -structures which have strong-inverse elements. More precisely we study the small finite cases

Studies on A. Einstein. B. Podolsky and N. Rosen argument that “quantum mechanics is not a complete theory,” III: Illustrative examples and applications

In the preceding Papers I and II of this series, we have presented a review and upgrade of basic mathematical, physical and chemical methods, and provided a confirmation of the apparent proof of the EPR argument [1] that extended particles within physical media (interior dynamical problems) admit classical counterparts [9], while Einstein’s determinism appears to be progressively verified with the increase of the density of the medium [10]. In this third and final paper of the series, we shown that the EPT argument in general, and Einstein’s determinism in particular, appear to be progressively verified in the structure of mesons, baryon, nuclei, and molecular bonds while being fully verified at the limit of gravitational collapse. We additionally show, apparently for the first time, the validity of the EPR final statement to the effect that the wavefunction [of quantum mechanics] does not provide a complete description of the physical reality” since the covering isowavefunctions of hadronic mechanics provide an otherwise impossible representation of all characteristics of various physical and chemical interior systems existing in nature.