we generalize concepts of left hyperfilters, right hyperfilters and an ordered semihypergroup by introducing left-m-hyperfilters, right-n-hyperfilters (m,n)-hyperfilters semihypergroup. Then, some properties these generalized have been studied. Finally, left-m-hyperfilters (resp. right-n-hyperfilters, (m,n)-hyperfilters) (m, 0)-regular (0,n)-regular, (m,n)-regular) semihypergroups characterize in terms...

Given a permutation σ $$ \sigma , its corresponding binary search tree is obtained by recursively inserting the values ( 1 ) … n (1),\dots, (n) into so that label of each node larger than labels left subtree and smaller right subtree. In this article, we study height trees drawn from record-biased model permutations whose probability measure on set proportional to θ record {\theta}^{\mathrm{rec...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

In this article, we present $GPW$-flatness property of acts over monoids, which is a generalization of principal weak flatness. We say that a right $S$-act $A_{S}$ is $GPW$-flat if for every $s in S$, there exists a natural number $n = n_ {(s, A_{S})} in mathbb{N}$ such that the functor $A_{S} otimes {}_{S}- $ preserves the embedding of the principal left ideal ${}_{S}(Ss^n)$ into ${}_{S}S$. We...

In this study, some 4-(1,5-diarylimidazol-2-yl)thioacetyl-1-phenyl-2,3-dimethyl-3-pyrazoline-5-one derivatives were prepared by reacting 4-(2-chloroacetyl)-1-phenyl-2,3-dimethyl-3-pyrazoline-5-one and 2-mercapto-1, 5-diarylimidazole derivatives. The antinociceptive and anticancer activities of the compounds obtained were investigated. It was observed that some of the compounds, 2a, 2d, 2g, and ...

The aim of this paper is to investigate harmonic Stieltjes constants occurring in the Laurent expansions function \[ \zeta_{H}\left( s,a\right) =\sum_{n=0}^{\infty}\frac{1}{\left( n+a\right) ^{s}}\sum_{k=0}^{n}\frac{1}{k+a},\text{ }\operatorname{Re}\left( s\right) >1, \] which we call Hurwitz zeta function. In particular evaluation formulas for $\gamma_{H}\left( m,1/2\right) $ and m,1\right) ar...

It is well-known that the antipode $S$ of a commutative or cocommutative Hopf algebra satisfies $S^{2}=\operatorname*{id}$ (where $S^{2}=S\circ S$). Recently, similar results have been obtained by Aguiar, Lauve and Mahajan for connected graded algebras: Namely, if $H$ with grading $H=\bigoplus_{n\geq0}H_n$, then each positive integer $n$ $\left( \operatorname*{id}-S^2\right)^n \left( H_n\right)...