مقالات رزومه داریوش حیدری

Breakable semihypergroups, defined by a simple property: every non-empty subset of them is a subsemihypergroup. In this paper, we introduce a class of semihypergroups, in which every hyperproduct of $n$ elements is equal to a subset of the factors, called $\pi_n$-semihypergroups. Then, we prove that every semihypergroup of type $\pi_{2k}$, ($k\geq 2$) is breakable and every semihypergroup of type $\pi_{2k+1}$ is of type $\pi_3$. Furthermore, we obtain a decomposition of a semihypergroup of type $\pi_n$ into the cyclic group of order 2 and a breakable semihypergroup. Finally, we give a characterization of semi-symmetric semihypergroups of type $\pi_n$.

Breakable semihypergroups, defined by a simple property: every non-empty subset of them is a subsemihypergroup. In this paper, we introduce a class of semihypergroups, in which every hyperproduct of $n$ elements is equal to a subset of the factors, called $\pi_n$-semihypergroups. Then, we prove that every semihypergroup of type $\pi_{2k}$, ($k\geq 2$) is breakable and every semihypergroup of type $\pi_{2k+1}$ is of type $\pi_3$. Furthermore, we obtain a decomposition of a semihypergroup of type $\pi_n$ into the cyclic group of order 2 and a breakable semihypergroup. Finally, we give a characterization of semi-symmetric semihypergroups of type $\pi_n$.

In this paper, the notion of mp-residuated lattice, as a subclass of residuated lattices in which every prime filter contains a unique minimal prime filter, is introduced and investigated. For a residuated lattice A, the notion of ω-filter is introduced and it is shown that Ω(A), the set of ω-filters of A, is a bounded distributive lattice. Also, it is observed that γ(A), the set of coannulets of A, is a sublattice of Ω(A). Then for each prime filter P of A, the notion of the divisor filter D(P) as an important tool in investigating of minimal prime filters of A is introduced and it is proved that a prime filter P is minimal prime if and only if P=D(P). Finally, by the notion of ω-filters, as an extension of divisor filters, a fundamental characterization of mp-residuated lattices is given and it is shown that a residuated lattice is mp if and only if the set of its ω-filters is a sublattice of the lattice of its filters.

A salt metathesis reaction is a chemical process involving the exchange of bonds between two reacting chemical species, which results in the creation of products with similar or identical bonding affiliations. Hyperstructure theory is studied from the theoretical point of view and for its applications. In this paper, we provide some examples of hyperstructures associated with salt metathesis reactions, and we observe that these chemical reactions are examples of the phenomena when composition of two elements is a set of elements.

In this paper, we introduce a suitable generalization of Cayley graphs that is defined over polygroups (GCP-graph) and give some examples and properties. Then, we mention a generalization of NEPS that contains some known graph operations and apply to GCP-graphs. Finally, we prove that the product of GCP-graphs is again a GCP-graph.