On the g-hypergroupoids associated with g-hypergraphs

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4819-4831 ◽  
Author(s):  
Mehdi Farshi ◽  
Bijan Davvaz ◽  
Saeed Mirvakili
Keyword(s):  
Direct Product ◽  
Fundamental Relation ◽  
Join Space ◽  
Commutative Hypergroup ◽  
Regular Relation

In this paper, we associate a partial g-hypergroupoid with a given g-hypergraph and analyze the properties of this hyperstructure. We prove that a g-hypergroupoid may be a commutative hypergroup without being a join space. Next, we define diagonal direct product of g-hypergroupoids. Further, we construct a sequence of g-hypergroupoids and investigate some relationships between it?s terms. Also, we study the quotient of a g-hypergroupoid by defining a regular relation. Finally, we describe fundamental relation of an Hv-semigroup as a g-hypergroupoid.

Fundamental relations on hyper bi-modules and characterizations of complete hyper bi-modules

2021 ◽  
pp. 2250040
Author(s):  
M. Nooranian ◽  
B. Davvaz
Keyword(s):  
Fundamental Relation ◽  
The Right ◽  
Commutative Hypergroup

A hyper bi-module is a commutative hypergroup that is both a left and a right hypermodule, such that the left and the right multiplications are compatible. We define the fundamental relation on an [Formula: see text]-hyper bi-module, where [Formula: see text] and [Formula: see text] are hyperrings and the left and the right multiplications are compatible. Also, we state some conditions that are equivalent to the transitivity of this relation and finally we characterize the complete [Formula: see text]-hyper bi-modules.

scholarly journals Fundamental relation on m-idempotent hyperrings

2017 ◽  
Vol 15 (1) ◽  
pp. 1558-1567 ◽  
Author(s):  
Morteza Norouzi ◽  
Irina Cristea
Keyword(s):  
Fundamental Relation ◽  
Strongly Regular Relation ◽  
Strongly Regular ◽  
Regular Relation

Abstract The γ*-relation defined on a general hyperring R is the smallest strongly regular relation such that the quotient R/γ* is a ring. In this note we consider a particular class of hyperrings, where we define a new equivalence, called $\varepsilon^{*}_{m} $, smaller than γ* and we prove it is the smallest strongly regular relation on such hyperrings such that the quotient R/ $\varepsilon^{*}_{m} $ is a ring. Moreover, we introduce the concept of m-idempotent hyperrings, show that they are a characterization for Krasner hyperfields, and that $\varepsilon^{*}_{m} $ is a new exhibition for γ* on the above mentioned subclass of m-idempotent hyperrings.

scholarly journals The commutative quotient structure of m-idempotent hyperrings

2020 ◽  
Vol 28 (1) ◽  
pp. 219-236
Author(s):  
Azam Adineh Zadeh ◽  
Morteza Norouzi ◽  
Irina Cristea
Keyword(s):  
Commutative Ring ◽  
Quotient Ring ◽  
Fundamental Relation ◽  
Strongly Regular Relation ◽  
Strongly Regular ◽  
Regular Relation

AbstractThe α* -relation is a fundamental relation on hyperrings, being the smallest strongly regular relation on hyperrings such that the quotient structure R/α* is a commutative ring. In this paper we introduce on hyperrings the relation ζm, which is smaller than α*, and show that, on a particular class of m-idempotent hyperrings R, it is the smallest strongly regular relation such that the quotient ring R/ζ*m is commutative. Some properties of this new relation and its differences from the α* -relation are illustrated and discussed. Finally, we show that ζm is a new representation for α* on this particular class of m-idempotent hyperrings.

Structural studies of small amorphous volumes by electron diffraction

1990 ◽  
Vol 48 (4) ◽  
pp. 122-123
Author(s):  
Pierre Moine
Keyword(s):  
Electron Diffraction ◽  
Born Approximation ◽  
Structural Information ◽  
Fundamental Relation ◽  
X Rays ◽  
Structural Studies ◽  
Diffraction Experiment ◽  
Transmission Electron ◽  
Amorphous Structures ◽  
Diffraction Patterns

Qualitatively, amorphous structures can be easily revealed and differentiated from crystalline phases by their Transmission Electron Microscopy (TEM) images and their diffraction patterns (fig.1 and 2) but, for quantitative structural information, electron diffraction pattern intensity analyses are necessary. The parameters describing the structure of an amorphous specimen have been introduced in the context of scattering experiments which have been, so far, the most used techniques to obtain structural information in the form of statistical averages. When only small amorphous volumes (< 1/μm in size or thickness) are available, the much higher scattering of electrons (compared to neutrons or x rays) makes, despite its drawbacks, electron diffraction extremely valuable and often the only feasible technique.In a diffraction experiment, the intensity IN (Q) of a radiation, elastically scattered by N atoms of a sample, is measured and related to the atomic structure, using the fundamental relation (Born approximation) : IN(Q) = |FT[U(r)]|.

Equitable Total Coloring of Direct Product of Path and Cycle

2019 ◽  
Vol 10 (7) ◽  
pp. 1476-1481
Author(s):  
S. Moidheen Aliyar ◽  
S. Manimaran ◽  
K. Manikandan
Keyword(s):  
Direct Product ◽  
Total Coloring

Sport and nationalism in the Republic of North Macedonia

Focaal ◽  
2019 ◽  
pp. 1-13
Author(s):  
Vasiliki P. Neofotistos
Keyword(s):  
Direct Product ◽  
Nation Building ◽  
National History ◽  
Sports Teams ◽  
The Balkans ◽  
The North ◽  
Political Forces ◽  
The Republic

Using the Republic of North Macedonia as a case study, this article analyzes the processes through which national sports teams’ losing performance acquires a broad social and political significance. I explore claims to sporting victory as a direct product of political forces in countries located at the bottom of the global hierarchy that participate in a wider system of coercive rule, frequently referred to as empire. I also analyze how public celebrations of claimed sporting victories are intertwined with nation-building efforts, especially toward the global legitimization of a particular version of national history and heritage. The North Macedonia case provides a fruitful lens through which we can better understand unfolding sociopolitical developments, whereby imaginings of the global interlock with local interests and needs, in the Balkans and beyond.

The relation between philosophy of creativity and education in the knowledge society

2020 ◽  
pp. 49-57
Author(s):  
Ernesta Molotokienė
Keyword(s):  
Social Space ◽  
Knowledge Society ◽  
Research Work ◽  
Knowledge Worker ◽  
Modern Society ◽  
Educational Goals ◽  
Fundamental Relation ◽  
Educational Organizations ◽  
Technological Environment ◽  
Changing Knowledge

The aim of the article is to reveal a fundamental relation between the philosophy of creativity and education in the knowledge society. Knowledge society as a special social space of modern society is formed in the middle of the 20th century with a new system of educational organizations, therefore training a knowledge worker who is able to be productive in a rapidly changing knowledge and technological environment is one of the main challenges of modern education. The contemporary philosophy of creativity has an important impact on education in knowledge society. The creative nature of learning determines the knowledge worker’s ability to achieve social, technical and technological innovations, while research work forms a dynamic competence and socio-economic performance. The article stresses that creativity remains one of the most important educational goals of knowledge society.

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