14th conference on algebraic hyperstructures and ...(a) school of mathematics, statistics and...
TRANSCRIPT
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14th Conference on Algebraic Hyperstructures and
Applications
Iasi, June 22-24, 2020
Abstract Book
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An Introduction on Topological Krasner Hypervector Spaces
R.AMERI1, M.HAMIDI2, AND A.SAMADIFAM3
1School of Mathematics,Statistics and Computer Sciences, University of
Tehran,Tehran,Iran, [email protected]
2,3Department of Mathematics, Faculty of Mathematics,Payame Noor University,
Tehran, Iran,[email protected],[email protected]
Abstract
Let F be a Krasner hyperfield and V be a hypervector spaces over F , in the sense
of Krasner. In this paper we introduce and study topological hypervector spaces. In
particular, we consider a classes of hypervector spaces such that each its open subsets
is a complete part. Also, we investigate quotient topological hypervector space
induced by a sub-hyperspace of a topological hypervector space over hyperfield and
obtain some basic properties of these spaces.
“Some results on graphs associated to a hypergroupoid”
R. Ameri(a), Z. Nazemashoora(b)
(a) School of Mathematics, Statistics and Computer Science, Collage of Sciences, University of
Tehran,
P.O. Box 14155-6455, Tehran, Iran. [email protected] (b) Department of Mathematics, Payamnour University
P.O. Box 19395-3697, Tehran, Iran. [email protected]
Abstract
In this paper, we introduce a graph associated to (hypergroupoid) hypergroup.
Precisely, let (H, ◦) be a hypergroup, we associated to H a graph ΓH = (H, E),
where x is adjacent to y if x and y belongs to a finite hyperproducts in H. In this
regard we investigate the relationship between graph properties of ΓH and algebraic
properties of H.
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Soft set theory and hypercompositional algebras
HASHEM BORDBAR
Center for Information Technology and Applied Mathematics,
University of Nova Gorica, Slovenia
Abstract
Some applications of soft set theory and fuzzy soft set theory (as a generalization of the soft set
theory) in decision making problem were investigated by Maji et al. in [1].
The aim of this manuscript is to apply the concept of (fuzzy) soft set theory in some
hypercompositional structure and specially hyper BCK-algebra. Some notations related to our
hyperstructure are introduced and some examples are provided
An overview of hyper logical algebras
R. A. Borzooei, M. Aaly Kologani
Department of Mathematics, Shahid Beheshti University, Tehran, Iran
[email protected], [email protected]
Abstract
Hyper logical algebras were first studied in 2000 by Borzooei et al. They applied the
concept of hyperstructures to one of the logical algebraic structures known as the BCK-
algebra, and intro- duced two generalizations of them called the hyper BCK-algebra and
hyper K-algebra. Then many researchers in this field continued their research and used
hyperstructures on other logical algebras and introduced the concepts of hyper residuated
lattices, hyper BL-algebras, hyper MV-algebras, hyper EQ-algebra, hyper BE-algebras,
hyper equality algebras, hyper hoops and etc. Moreover, they defined some new notions
such as different kinds of hyper ideals, hyper filters and hyper congruence relations on
these structures and studied some properties, the relation among them and the quotient
structure.
Now, in this talk, we will review the definitions of all those hyper logical algebras and
investigate relations among them. Then, we will study the filter and ideal theory on these
hyperstructures and introduce the related quotient structures that are made by them.
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"Defend yourself from Cybersecurity attacks with
Multi Factor Authentication"
Domenico Chillemi
IBM z Security Executive IT Specialist, Italy, [email protected]
Abstract
In a very globalized era like the current one we are often required to use
information technology to do a lot of personal activities, like working with our bank
account, booking services through internet, and many others, where we are requested
to provide a user and a password! You understand that this mechanism is subject to
possible frauds and intrusion detection, where hackers can steal your credentials and
considerably damage you!
This short session will show some risks that you might have and how it is often
possible to protect your identity much more strongly through a multi factor
authentication mechanism. You will also see a very quick and nice demo about
accessing a system using this innovative methodology!
HYPERSTRUCTURES: A BRIEF HYSTORY AND SOME NEW
RESEARCH TOPICS
Piergiulio Corsini University of Udine, Italy
Abstract
One gives the most important definitions: Hypergroupoid, Semihypergroup, Hypergroup, Join Space,Chinese Hypergroupoid,Fuzzy Set. One does a brief Hystory, from the beginning (Marty, Dresher and Ore, Prenowitz, Krasner), to the last fifty years (for instance Corsini, Fotea, Cristea), and of the places in Europe, Asia, America, Australia, where hyperstructures flourished. Finally one illustrates some new topics of Applications of hyperstuctures to Fuzzy Sets (some results by Corsini)
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"Some open problems in Hypercompositional Algebra"
Irina Cristea
University of Nova Gorica, Slovenia
[email protected] [email protected]
Abstract
In this note I will focus on some topics in Hypercompositional Algebra that I have studied in
the last two years, in collaboration with colleagues from Czech Republic, Slovenia,
Montenegro, and Iran. They are related to: dependence relations, fuzzy reducibility, m-
idempotent hyperrings, breakable and factorizable semihypergroups, curves on Krasner
hyperrings, the support of a hypermodule. After a brief presentation of each of the above
mentioned topics, I will state some open problems related to them, both from a theoretical and
practical point of view.
Twenty Five Years With Algebraic Hyperstructures
Bijan Davvaz
Department of Mathematics,
Yazd,University, Yazd,Iran
Dedicated to Professors Piergiulio Corsini and Thomas Vougiouklis
Abstract
I am working in algebraic hyperstructures from 1995. During the last twenty five years, I
studied and developed the theory of algebraic hyperstructures in many direc- tions. In
particular, I tried to find real examples of hyperstructures in nature. The following is a list of
subjects that I worked till the present time
(1) Fundamental relations on hyperstructures, specially Hv-structures.
(2) Fuzzy sets and hyperstructures.
(3) Rough sets and hyperstructures.
(4) Topology and hyperstructures.
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(5) Number theory and hyperstructures.
(6) Γ-hyperstructures.
(7) Ordered hyperstructures.
(8) n-ary hypergroups and there extension to hyperrings and hypermodules.
(9) Combinatorial aspects of hyperstructures.
(10) Graph and hypergraph connected to hyperstructures.
(11) Development of polygroup theory.
(12) Hyperlattices.
(13) Hyperdynamical systems.
(14) Soft sets and hyperstructures.
(15) Applications of hyperstructures in physics, chemistry and biology.
(16) Meet plus hyperalgebra.
In this paper, we shall review some items of the above subjects
New Type Of Neutrosophic topological Group
Riad K. Al-Hamido
Department of Mathematics, College of Science, Al-Furat University, Deir-ez-
Zor, Syria. [email protected]
Abstract
Neutrosophic topological groups are neutrosophic groups in algebraic sense together with
neutrosophic continuous group operations. In this article, we presented new type of
neutrosophic topological groups with illustrative examples. Finally, Some basic properties of
neutrosophic groups are investigated.
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HX–POLYGROUPS
MORTEZA JAFARPOUR 1∗AND HOSSIEN AGHABOZORGI 2
1 Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
2 Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
Abstract
We have studied a characterization of HX-groups in torsion groups. The notion of HX-
polygroup has been defined for the class of polygroups and proposed some conditions that char-
acterize an HX-polygroup as a polygroup of cosets. Moreover a characterization of HX-
polygroups which are double coset algebra according to Dresher and Ore’s definition is
investigated.
ABSTRACT
In this paper, we study the concept of projectivity and injectivity in the categories of
Krasner (m, n)- hypermodules over a Krasner (m, n)-hyperring to generalize the projective
and injective modules over a ring. As the main result, we introduce the concepts of normal
Bearian injectivity and Bearian injectivity as the versions of Bear's critesion in the
categories of Krasner (m, n)-hypermodules.
Finally we find the relation between fundamental functor and normal injective Krasner (m,
n)- hypermodules.
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Fixing a Krasner hyperring R, one of the most important and well-behaved class of
Cyclicity in some classes of Hv-groups Paraskevi A. Kamporoudi
Panagathou 44B, Alexandroupolis, 68131, Greece, [email protected]
Thomas Vougiouklis
Democritus University of Thrace
Neapoli 14-6, Xanthi 67100, Greece, [email protected]
Abstract
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.
REDUCIBILITY IN CORSINI HYPERGROUPS
Milica Kankaras
University of Montenegro, Podgorica
Abstract
This paper is an overview of the concept of reducibility introduced first by James Jantosciak
for hypergroups, noticing that the elements can play interchangeable roles with respect to the
hyperoperation. The concept has been studied later by Cristea for hypergroups associated
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with binary and n-ary relations. In 2019, Cristea and Kankaras investigated the fuzzy
reducibility in hypergroups, extended to the fuzzy case the fundamental relations introduced
by Jantosciak, that are at the basis of the definition of reducibility. The fuzzy reducibility is
considered for the specific types of hypergroups, as complete hypergroups, i.p.s. hypergroups
and non-complete 1-hypergroups, with respect to the grade fuzzy set, defined by Corsini for
studying the fuzzy grades of hypergroups. New results have been recently obtained by
Kankaras and they are related to reducibility and fuzzy reducibility of Corsini hypergroups
and productional hypergroups
On strong-inverse elements Theodora Kaplani
Fotada, 42100 Trikala, Greece, [email protected]
Thomas Vougiouklis
Democritus University of Thrace
Neapoli 14-6, Xanthi 67100, Greece, [email protected]
Abstract
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.
The second minimum/maximum value of the number of cyclic subgroups of
finite p-groups
Mihai-Silviu Lazorec
University Alexandru Ioan Cuza, Iasi, Romania,
Abstract
Let C(G) be the poset of cyclic subgroups of a finite group G and let P be the class of p-groups
of order 𝑝𝑛 (n≥ 3). Consider the function α:P → (0, 1] given by α(G)=|C(G)|/|G|. Our aim is
to determine the second minimum value of α, as well as the corresponding minimum points.
Further, since the problem of finding the second maximum value of α was completely solved
for p=2, we focus on the case of odd primes and we outline a result in this regard.
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“Hyperstructures on bar of V&V in pieces” Pipina Nikolaidou
Democritus University of Thrace,
Orestiada, 68200, Greece [email protected]
Abstract
An application of hyperstructure theory on social science is presented. In social sciences when
questionnaires are used, there is a new tool, the bar instead of Likert scale. The bar has been
suggested by Vougiouklis & Vougiouklis in 2008, who have proposed the replacement of Likert
scales, usually used in questionnaires, with bar. This new tool, gives the opportunity to
researchers to elaborate the questionnaires in different ways, depending on the filled
questionnaires and of course on the problem. We study these filled questionnaires using
hyperstructure theory. Moreover, the filled questionnaire procedure has been improved using
computers. The hyperstructure theory is being related with questionnaires and we study the
obtained hyperstructures which are used as an organized device of the problem and we focus
on special problems.
SOME NEW CLASSES OF HYPERNEAR-
RINGS
Sanja Jančić Rašović 1
, Irina Cristea 2
, Jelena Dakić 3
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Faculty of Science and Mathematicis,University of Montenegro, Podgorica,
Montenegro, [email protected], [email protected]
2 Centre for Systems and Information Tecnologies, University of Nova Gorica,
Slovenia, [email protected]
Abstract
In this note themain properties of three classes of hypernear-rings are summarized. The first
part of this paper contains the main results about the hypernear-rings with a defect of
distributivity. The second part is devoted to the class of division hypernear-rings . The third
part contains our results about the general hypernear-rings associated with a hypergroup.
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“The class equation in reversible regular hypergroup theory”
Andromeda Sonea and Violeta Fotea
University Alexandru Ioan Cuza, Iaşi, Romania,
[email protected], [email protected]
Abstract
We analyze the center and the centralizer of an element in reversible regular hypergroups,
using the complete parts. All these notions are useful to obtain the class equation in this
theory. Also, we establish the form of the class equation for complete hypergroups, i.e. hypergroups for which C(xoy)=xoy for all x,y from H, where C(xoy) represents the complete closure of xoy.
Hyperoperations defined on sets of S-Helix Matrices Souzana Vougiouklis
17 Oikonomou str, Exarheia, Athens 10683, Greece, [email protected]
Abstract
A hyperproduct on non-square ordinary matrices can be defined by using the, so called, helix-
hyperoperation. Therefore, the helix-hyperoperation (abbreviated hope) is based on a classical
operation and was introduced in order to overcome the non-existing cases. We study the helix-
hyperstructures on the special type of matrices, the S-helix matrices, used in on the small
dimension representations. In this paper, we introduce and focus our study on the class of S-
helix matrices called k-overlap helix matrices. The reason is that their hyper-vector spaces can
represent n-dimensional spaces which have independent both, single valued dimensions and
multivalued dimensions.
From rings to minimal Hv-fields Thomas Vougiouklis
Emeritus Professor
Democritus University of Thrace
Neapoli 14-6, Xanthi 67100, Greece, [email protected]
Abstract
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
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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.
Hyperstructures in mobile robot path
reconstruction
J. Vyroubalova 1 and M. Novak2
Abstract
In mobile robotics, path reconstruction is an essential part of the process of robot localization
and mapping. In our presentation we briefly describe already known robotic approach to path
reconstruction, where the key part of this method we investigated from mathematical point of
view and discover the involvement of algebraic hyperstructure in it.
“Some Categorical Aspects of Algebraic hyperstructures”
Reza Ameri
School of Mathematics, Statistic and Computer Science, College of Science,
University of Tehran, P.O. Box 14155-6455, Tehran, Iran
"Some Results on hyperideals of a general hyperring"
Hoda Mohamadi