Small weak hyperfields in hadronic mechanics

Thomas Vougiouklis

Abstract


It was in mid 90es when Professor R. M. Santilli realized, for the first time, that his innovating theories can be appropriate expressed by multi-valued systems. At that time the largest class of hyper-structures, the Hv-structures, based on the weak properties, were introduced and studied deeply. The extremely large number of weak hyper-structures defined on the same set can be reduced by demanding a lot of properties. Therefore, whenever the Santilli’s Hadronic Mechanics need special elements satisfying a number of properties then the class of the Hv-structures is the appropriate one. The first Hv-structures in Hadronic Mechanics, introduced in 1996, are called e-hyper-structures. The main question in this theory proposed by Santilli is: What are the hyper-numbers? Hyper-numbers or Hv-numbers are called the elements of any Hv-field and they are important in representation theory, as well. In this presentation we give some constructions and properties on minimal Hv-fields.

Full Text:

PDF

References


R. Anderson, A.A. Bhalekar, B. Davvaz, P.S. Muktibodh, T.Vougiouklis, An intr. to Santilli’s …, NUMTA Bulletin, 6 (2012-13), 1-33.

P. Corsini, V. Leoreanu, Appl. of Hyperstructure Theory, Klower Ac. Publ., 2003.

P. Corsini, T. Vougiouklis, From groupoids to groups through hypergroups, Rend. Mat. VII, 9, 1989, 173-181.

B. Davvaz, On Hv-rings and Fuzzy Hv-ideals, J. Fuzzy Math.V.6,N.1, 1998, 33-42.

B. Davvaz, Fuzzy Hv-submodules, Fuzzy sets and Systems, 117, 2001, 477-484.

B. Davvaz, V. Leoreanu-Fotea, Hyperring Theory and Applications, Int. Acad. Press, USA, 2007.

B. Davvaz, R.M. Santilli, T. Vougiouklis, Studies of multi-valued hyperstructures for the characterization …, AGG 28(1), 2011, 105-116.

B. Davvaz, R.M. Santilli, T. Vougiouklis, Multi-valued Hypermathematics for characterization of matter and antimatter systems, JCMSE, 13, 2013, 37-50.

B. Davvaz, R.M. Santilli, T. Vougiouklis Algebra, Hyperalgebra and Lie-Santilli Theory, J. Generalized Lie Theory Appl., 2015, 9:2, 1-5.

B. Davvaz, S. Vougioukli, T. Vougiouklis, On the multiplicative Hv-rings derived from helix hyperoperations, Util. Math., 84, 2011, 53-63.

B. Davvaz, T. Vougiouklis, A Walk Through Weak Hyperstructures, Hv-Structures, World Scientific, 2018.

V. Leoreanu-Fotea, Ivo Rosenberg, B. Davvaz, T. Vougiouklis, A new class of n-ary hyperoperations, European J. Combinatorics, V.44, 2015, 265-273.

F. Marty, Sur un généralisation de la notion de groupe, 8éme Congr. Math. Scand., Stockholm, 1934, 45-49.

R.M. Santilli, Embedding of Lie-algebras into Lie-admissible algebras, Nuovo Cimento 51, 570, 1967.

R.M. Santilli, Dissipativity and Lie-admissible algebras, Mecc.1,3, l969.

R.M. Santilli, Hadronic Mathematics, Mechanics and Chemistry, Vol. I, II, III, IV and V, International Academic Press, USA, 2007.

R.M. Santilli, Studies on the classical determinism predicted by A. Einstein, B. Podolsky and N. Rosen, Ratio Mathematica, V.37, 2019, 5-23.

R.M. Santilli, Studies on A. Einstein, B. Podolsky and N. Rosen argument …, Ratio Mathematica V. 38, 2020, I: 5-69. II: 71-138, III: 139-222.

R.M. Santilli, T. Vougiouklis, Isotopies, Genotopies, Hyperstructures and their Appl., New frontiers Hyperstr., Hadronic, 1996, 1-48.

R.M. Santilli, T. Vougiouklis, Lie-admissible hyperalgebras, Italian J. Pure Appl. Math., N.31, 2013, 239-254.

S. Vougioukli, Helix-hyperoperations on Lie-Santilli admissibility, AGG, V.39, N.1, 2023, 77-936.

T. Vougiouklis, Cyclicity in a special class of hypergroups, Acta Un. Car.–Math. Et Ph., V.22, N1, 1981, 3-6.

T. Vougiouklis, Representations of hypergroups, Hypergroup algebra, Convegno: Ipergrouppi, altre strutture…, Udine, 1985, 59-73.

T. Vougiouklis, Representations of hypergroups by hypermatrices, Rivista Mat. Pura ed Appl., N 2, 1987, 7-19.

T. Vougiouklis, Generalization of P-hypergroups, Rend. Circolo Mat. Palermo, Ser.II, 36, 1987, 114-121.

T. Vougiouklis, The very thin hypergroups and the S-construction, Combinatorics ’88, Incidence Geom. Comb. Str., 2, 1991, 471-477.

T. Vougiouklis, The fundamental relation in hyperrings. The general hyperfield, 4thAHA, Xanthi 1990, World Scientific, 1991, 203-211.

T. Vougiouklis, Representations of hypergroups by generalized permutations, Algebra Universalis, 29, 1992, 172-183.

T. Vougiouklis, Representations of Hv-structures, Proc. Int. Conf. Group Theory 1992, Timisoara, 1993, 159-184.

T. Vougiouklis, Hyperstructures and their Representations, Monographs in Math., Hadronic, 1994.

T. Vougiouklis, Some remarks on hyperstructures, Contemporary Math., Amer. Math. Society, 184, 1995, 427-431.

T. Vougiouklis, Hv-groups defined on the same set, Discrete Math., 155, 1996, 259-265.

T. Vougiouklis, Consructions of Hv-structures with desired fundamental structures, New frontiers in Hyperstructures, Hadronic, 1996, 177-188.

T. Vougiouklis, Convolutions on WASS hyperstructures, Discrete Math., 174, 1997, 347-355.

T. Vougiouklis, Enlarging Hv-structures, Algebras Comb., ICAC’ 97, Hong Kong, Springer, 1999, 455-463.

T. Vougiouklis, On Hv-rings and Hv-representations, Discrete Math., Elsevier, 208/209, 1999, 615-620.

T. Vougiouklis, Hyperstructures in isotopies and genotopies, Advances in equations and Inequalities, Hadronic Press, 1999, 275-291.

T. Vougiouklis, Finite Hv-structures and their representations, Rend. Seminario Mat. Messina, S II, V9, 2003, 245-265.

T. Vougiouklis, The h/v-structures, J. Discrete Math. Sciences Cryptography, V.6, 2003, N.2-3, 235-243.

T. Vougiouklis, The Santilli’s theory ‘invasion’ in hyperstructures, AGG 28(1), 2011, 83-103.

T. Vougiouklis, The e-hyperstructures, J. Mahani Math.R.C.,V.1,N.1, 2012, 13-28.

T. Vougiouklis, The Lie-hyperalgebras and their fundamental relations, Southeast Asian Bull. Math., V.37(4), 2013, 601-614.

T. Vougiouklis, Lie-Santilli Admissibility using P-hyperoperations on matrices, Hadronic J., Dec.7, 2014, 1-14.

T. Vougiouklis, From Hv-rings to Hv-fields, IJAHA, V.1, N.1, 2014, 1-13.

T. Vougiouklis, On the isoHv-numbers, Hadronic J., Dec.5, 2014, 1-18.

T. Vougiouklis, Hypermathematics, Hv-structures, hypernumbers, hypermatrices and Lie-Santilli admissibility, American J. Modern Physics,4(5), 2015, 34-46.

T. Vougiouklis, Hypermatrix representations of finite Hv-groups, European J. Comb., V.44 B, 2015, 307-315.

T. Vougiouklis, Iso-Hv-numbers, CACAA, V. 4, N. 4, 2015, 345-352.

T. Vougiouklis, On the Hyperstructure Theory, SABM, V. 40(4), 2016, 603-620.

T. Vougiouklis, Hv-fields, h/v-fields, Ratio Mathematica, V33, 2017, 181-201.

T. Vougiouklis, Minimal Hv-fields, Ratio Mathematica V38, 2020, 313-328.

T. Vougiouklis, Fundamental Relations in Hv-structures. The ‘Judging from the Results’ proof, JAHLA, V.1, N.1, 2020, 21-36.

T. Vougiouklis, P. Kambakis-Vougiouklis, Bar in Questionnaires, Chinese Business Review, V.12, N.10, 2013, 691-697.

T. Vougiouklis, S. Vougiouklis, The helix hyperoperations, Italian J. Pure Appl. Math., N.18, 2005, 197-206.

T. Vougiouklis, S. Vougiouklis, Hyper-representations by non square matrices. Helix-hopes, American J. Modern Physics, 4(5), 2015, 52-58.

T. Vougiouklis, S. Vougioukli, Hyper Lie-Santilli Admissibility, AGG, V.33, N.4, 2016, 427-442.




DOI: http://dx.doi.org/10.23755/rm.v52i0.1621

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Thomas Vougiouklis

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.