Construction of Ternary H v -groups and Ternary P-hyperoperations

In this paper, we study the concept of ternary H _v -groups and some their properties. We give some examples of ternary H _v -groups. Also, we consider the fundamental relation β* on a ternary H _v -group and prove that β* is a compatible relation on a ternary H _v -group. In addition, we define the P-hyperoperation, and then, we construct a new ternary H _v -group.     

Hypergraphs and Hypergroups Based on a Special Relation

The purpose of this paper is the study of hypergroups associated with hypergraphs. In this regards, we construct a ρ-hypergroup by means a given hypergraph by defining a special relation ρ, and then we investigate some related properties. Further, we introduce a special product of ρ-hypergroups. Also, we bridge between subhypergraphs and subhypergroups. Finally, the fundamental relation of a ρ-hypergroup is studied.     

Some Properties of the Idempotent Graph of a Ring

The idempotent graph of a ring R, denoted by I(R), is a graph whose vertices are all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = yx = 0. In this paper, we show that diam\({(I(M_n(D))) = 4}\), for all natural number \({n \geq 4}\) and diam\({(I(M_3(D))) = 5}\), where D is a division ring. We also provide some classes of rings whose idempotent graphs are connected. Moreover, the regularity, clique number and chromatic number of idempotent graphs are studied.     

θ*-Relation on Hypermodules and Fundamental Modules Over Commutative Fundamental Rings

The main tools in the theory of hyperstructues are the fundamental relations. The fundamental relation on a hypermodule over a hyperring was already introduced by Vougiouklis. The fundamental relation on a hypermodule over a hyperring is defined as the smallest equivalence relation so that the quotient would be the module over a ring. Note that generally the commutativity with respect to both sum in the (fundemental) module and product in the (fundamental) ring are not assumed. In this article we introduce a new strongly regular equivalence relation on hypermodules so that the quotient is module (with abelin group) over a commutative ring. Also we state the conditions that is equivalent with the transitivity of this relation and finally we characterize the complete hypermodules over hyperrings.     

On α-Relation and Transitivity Conditions of α

The main tools in the theory of hyperstructurs are the fundamental relations. The fundamental relation on hyperring was introduced by Vougiouklis at the fourth AHA congress (1990). The fundamental relation on a hyperring is defined as the smallest equivalence relation so that the quotient would be the ring. Note that, generally, the commutativity in the ring are not assumed. In this article, we introduce a new strongly regular equivalence relation on hyperring so that the quotient is a commutative ring. Also we state the condition that is equivalent with the transitivity of this relation and finally we characterize the complete hyperring (with the fundamental relation as commutative).     

Flow characteristics in a model of a left ventricle in the presence of a dysfunctional mitral mechanical heart valve

Journal of Visualization -     

The effects induced by proton irradiation on structural characteristics of nuclear graphite

A grade TSX graphite was irradiated by a 2.5 MeV proton and a dose of 1.47 × 10¹⁸ ion cm⁻² at 330 K. The displacement per atom under this irradiation condition was about 0.02. The lattice parameter, crystallite size and the vacancies density in the graphite was measured before and after irradiation. It was found that the proton irradiation led to an increase in the volume of the sample. The volume change in the irradiated sample was confirmed by atomic force and scanning electron microscopes observations as increased roughness and pore size. Also, FTIR results showed that graphite is slightly oxidized by irradiation.

     

Relationship between Rings and Hyperrings by Using the Notion of Fundamental Relations

In the theory of hyperrings, fundamental relations make a connection between hyperrings and ordinary rings. The fundamental relation α on hyperrings is studied by Davvaz and Vougiouklis in Communications in Algebra [8 Davvaz , B. , Vougiouklis , T. ( 2007 ). Commutative rings obtained from hyperrings (H _v -rings) with α*-relations . Comm. Algebra 35 ( 11 ): 3307 – 3320 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. Now, in this article, we obtain more results about this relation. In particular, we determine necessary and sufficient conditions such that the relation α is transitive.