t. vougiouklis
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Journal of Algebraic Hyperstructures and Logical Algebras, Volume:6 Issue: 2, Spring 2025, PP 31 -40The helix-sum and helix-product overcome restrictions which ordinary sum and product of the classical non-square matrices have. They, in fact, are weak hyperstructures and can be used, among the other applications, in the representation theory of Hv-groups, as well. However, we focus on low dimensions and small cardinality of the underline sets. In the study of helix-products, new interesting Hv-groups, appeared.Keywords: Hv-Structures, Hv-Fields, Helix-Operation, Helix-Products
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Journal of Algebraic Hyperstructures and Logical Algebras, Volume:6 Issue: 2, Spring 2025, PP 41 -51The number of Hv-structures, defined on a set is extremely big and gives the chance to applied sciences to work in an opposite to usual direction. Thus one asks from applied sciences to give all restrictions they have, because they reduce the number of possible Hv-structures expressing their problem, by a mathematical model. Moreover, the way of treating Hv-structures gives some new proving methods which can be used in applications. This is the main reason that the Hv-structures have so many applications. Here we present an overview on applications of Hv-structures on other sciences as in Hadronic Mechanics, Lie-Santilli admissible, leptons, biology, teaching, education, and mathematics itself, as well.Keywords: Weak Hyper-Operation, Weak Axiom, Hv-Structure, Hv-Field. AMS Subject Classification: 20N20, 16Y99
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Journal of Algebraic Hyperstructures and Logical Algebras, Volume:6 Issue: 2, Spring 2025, PP 63 -75The Lie-Santilli admissible theory gives in physics applications mainly in producing energy. The mathematical models need to be multivalued and the class of Hv-structures is the most appropriate, since this is the largest class of hyper-structures. The Hv-numbers, weak hyper-numbers, used satisfy all needed axioms. We focus on small and very-thin Hv-fields with P-hyper-operations on the product.Keywords: Lie-Santilli Admissible, Iso-Theory, Weak Axioms, Hv-Fields
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Journal of Algebraic Hyperstructures and Logical Algebras, Volume:5 Issue: 2, Spring 2024, PP 33 -43The first use of the largest class of hyper-structures, the Hv-structures, and their fundamental relations was to define the general hyper-field. Moreover, the enormous number Hv-structures defined on the same set, admits a partial order and has a lot of applications in pure mathematics and other sciences. We present ways to obtain appropriate Hv-fields from given well-known classical rings.Keywords: Hyper-Structure, Hv-Group, Hv-Field
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Journal of Algebraic Hyperstructures and Logical Algebras, Volume:5 Issue: 2, Spring 2024, PP 63 -73The helix-hyperoperations, hyper-sum and hyperproduct, are defined on any type of ordinary matrices. Thus, they overcome restrictions which ordinary sum and product on matrices have. We focus on the representation theory of hyperstructures, where the helix-product on any type of matrices, can be used. In fact, the helixproduct gives a hyper- semi-hypergroup structure or its generalization the Hv-semigroup. We restrict on the case of two m × n, with m < n, matrices, cases. The crucial point is that all entries of the original matrices are used, so the helix-product do not lose any information. For the case of n × (n + 1) we present subsets closed under the helix-product. Finite or infinite fields and Hv- fields, are used, as well.Keywords: Hv-Structures, Hv-Fields, Helix-Hyperoperation
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In this paper, the notion of H-sets on Hv-groups is introduced and some related properties are investigated and some examples are given. In this regards, the concept of regular, strongly regular relations and homomorphism of H-sets are adopted. Also, the classical isomorphism theorems of groups are generalized to H-sets on Hv-groups. Finally, by using these concepts tensor product on Hv-groups is introduced andproved that the tensor product exists and is unique up to isomorphism.
Keywords: Hv -group, left(right)H-set, tensor product, regular relation, strongly regular relation -
Journal of Algebraic Hyperstructures and Logical Algebras, Volume:1 Issue: 3, Summer 2020, PP 91 -97
The study of cyclicity in hyperstructures was started very early, almost from the beginning of the introduction of a hypergroup by F. Marty in 1934. New concepts appeared in hyperstructures the main of which are the period of a generator and the single power cyclicity. These terms have no meaning in the classical structures as groups. We study the cyclicity in special large classes of Hv-groups.
Keywords: Hv-group, hope, cyclicity, single power cyclicity, generator -
Journal of Algebraic Hyperstructures and Logical Algebras, Volume:1 Issue: 3, Summer 2020, PP 51 -60
Hyperstructures have applications in mathematics and in other sciences. For this, the largest class of the hyperstructures, the Hv-structures, is used. They satisfy the weak axioms where the non-empty intersection replaces equality. The fundamental relations connect, by quotients, the Hv-structures with the classical ones. Since the number of Hv-structures defined on the same set is very big, it is important to study special elements. A lot of those special elements are not appeared in the classical theory therefore, one has to discover their properties from the beginning. We continuous our study on Hv-structures which have the so called strong inverse elements.
Keywords: Hyperstructure, hope, Hv-structure, strong inverse element -
The class of Hv-structures is the largest class of hyperstructures defined on the same set. For this reason, they have applications in mathematics and in other sciences, which range from biology, hadronic physics, leptons, linguistics, sociology, to mention but a few. They satisfy the weak axioms where the non-empty intersection replaces equality. The fundamental relations connect, by quotients, the Hv-structures with the classical ones. In order to specify the appropriate hyperstructure as a model for an application which fulfill a number of properties, the researcher can start from the basic ones. Thus, the researcher must know the minimal hyperstructures. Hv-numbers are elements of Hv-field, and they are used in representation theory. In this presentation we focus on minimal Hv-fields derived from rings.
Keywords: Hyperstructure, Hv -structure, hope, iso-numbers, hypernumbers
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