Asian-European Journal of Mathematics

Loday introduced the notions of a dimonoid and a dialgebra, and constructed the free dimonoid and the free dialgebra. The $g$-dimonoids are a natural generalization of dimonoids and every $0$-dialgebra with associative operations is a linear analog of a $g$-dimonoid. This paper is devoted to the study of congruences on $g$-dimonoids. We characterize the least dimonoid congruence and the least semigroup congruence on the free (commutative, $n$-nilpotent) $g$-dimonoid. The obtained results can be applied to the theory of $0$-dialgebras with associative operations.

In this paper, we consider a Multi-Objective Stochastic Interval-Valued Linear Fractional Integer Programming problem (MOSIVLFIP). We especially deal with a multi-objective stochastic fractional problem involving an inequality type of constraints, where all quantities on the right side are log-normal random variables, and the objective functions coefficients are fractional intervals. The proposed solving procedure is divided in three steps. In the first one, the probabilistic constraints are converted into deterministic ones by using the chance constrained programming technique. Then, the second step consists of transforming the studied problem objectives on an optimization problem with an interval-valued objective functions. Finally, by introducing the concept of weighted sum method, the equivalent converted problem obtained from the two first steps is transformed into a single objective deterministic fractional problem. The effectiveness of the proposed procedure is illustrated through a numerical example.

In this paper, we introduce the class of split regular Hom-Leibniz–Poisson color algebras as the natural generalization of split regular Hom-Leibniz algebras, split regular Hom-Poisson algebras and split regular Hom-Leibniz–Poisson superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Leibniz–Poisson color algebra ${ℒ}$ is of the form ${ℒ}={𝒰}\oplus {\sum }_{[\alpha ]\in \mathrm{\Pi }/\sim }{I}_{[\alpha ]},$ with ${𝒰}$ a subspace of the abelian sub algebra ${\mathscr{H}}$ and any $I_{[\alpha ]},$ a well-described ideal of ${ℒ},$ satisfying $[I_{[\alpha ]},I_{[\beta ]}]+\mu (I_{[\alpha ]},I_{[\beta ]})=0$ if $[\alpha ]\ne [\beta ]$. Under certain conditions, in the case of ${ℒ}$ being of maximal length, the simplicity and the primeness of the algebra is characterized and it is shown that ${ℒ}$ is the direct sum of the family of its minimal ideals, each one being a simple split regular Hom-Leibniz–Poisson color algebra.

A semiring $(S,+,\cdot )$ is said to be a quasi-orthodox semiring if for any $e,f\in E^{+}(S)$, there exists some positive integer $n$ such that $n(e+f)=(n+1)(e+f)$. In this paper, we investigate the congruence generated by $\mathcal{𝒴}$ on quasi completely regular semirings with and without the special conditions like being quasi-orthodox. We further establish that the interval which ${\mathcal{𝒴}}^{\ast }$ belongs to is $[𝜖,\nu ]$.

The length of a longest $u-v$ path in a connected graph $G$ is called detour distance and denoted by $D(u,v)$, where the vertices $u$ and $v$ belong to the vertex set $V(G)$. In this paper, we find detour polynomial and detour index of $n$ connected vertex disjoint graphs, for $n\ge 3$ by the vertices identified and edges introducing with isolated vertex. Also, we find detour polynomial and detour index for some compound graphs from special graphs.

The power graph ${𝒢}(S)$ of a semigroup $S$ is a simple undirected graph whose vertex set is $S$ itself, and any two distinct vertices are adjacent if one of them is a power of the other. In this paper, we describe the power graph ${𝒢}({\mathbb{Z}}_p^r\times {\mathbb{Z}}_{p^2}^s)$ in terms of joins and disjoint unions of complete graphs, and use this to calculate the Laplacian polynomial of ${𝒢}({\mathbb{Z}}_p^r\times {\mathbb{Z}}_{p^2}^s)$. We finally calculate the Laplacian polynomial of the power graph ${𝒢}({\mathbb{Z}}_{p^m}^n)$.

A graph invariant is any function on a graph that does not depend on a labeling of its vertices. One of the best known graph invariants successfully applied in chemical graph theory over the last decade is the harmonic index. It is defined for a graph $G$ as the sum of the terms $\frac{2}{d_G(u)+d_G(v)}$ over all edges $uv$ of $G$, where $d_G(u)$ and $d_G(v)$ denote the degrees of the vertices $u$ and $v$ in $G$, respectively. The eccentric version of harmonic index has recently been proposed in an analogous way by replacing the vertex degrees with the vertex eccentricities. One of the main topics in chemical graph theory is to study how certain invariants of product graphs are related to the corresponding invariants of their components. Due to this, we investigate here the behavior of the eccentric version of harmonic index under various families of graph products and apply the derived results on some graphs of chemical and general interest.

In this study, we give another formula to all the generalized tribonacci ${(T_n(x,y,z))}_{n\in \mathbb{N}}$ and generalized tribonacci-Lucas ${(L_n(x,y,z))}_{n\in \mathbb{N}}$ polynomials by using the combinatorial calculus and their sum. Then, we give the explicit formula of partial derivative of such polynomials $\partial T_n(x,y,z)$, $\partial L_n(x,y,z)$ with respect to one of those variables and describe some properties.

In this paper, we investigate the periodic nature of the solutions of some systems of rational difference equations where the initial values are arbitrary real numbers such that the denominator is always nonzero. Furthermore, some numerical examples are presented to verify our theoretical results.

The purpose of this paper is to establish the uniqueness and existence of the common fixed point under generalized contractive conditions in $b$-metric spaces with supportive examples. We also approximate the common fixed point by Jungck–Picard and Picard iteration procedures along with the $P$ property of the mappings. Further, $(T,f)$-stability of Jungck–Picard iterative and $T$-stability of Picard iterative schemes are proved.

Let $G$ be a connected graph. For a configuration of pebbles on the vertices of $G$, a pebbling move on $G$ is the process of taking two pebbles from a vertex and adding one of them on an adjacent vertex. The pebbling number of $G$, denoted by $\pi (G)$, is the least number of pebbles to guarantee that for any configuration of pebbles on $G$ and arbitrary vertex $v$, there is a sequence of pebbling movement that places at least one pebble on $v$. The graph $G$ is said to be of Class 0 if its pebbling number equals its order. For a Class $0$ connected graph $G$, we improve a recent upper bound for $\pi (G^n)$ in terms of $\left|G\right|$.

In this paper, we provide a simple generalization of results of Sullivan for ${{𝒯}}_{{ℳ}}(X)$ the full transformation monotone pomonoid and for ${{𝒫}}_{{ℳ}}(X)$ the partial transformation monotone pomonoid by showing that every automorphism of ${{𝒯}}_M(X)$ and ${{𝒫}}_{{ℳ}}(X)$ is inner induced by the elements of ${{𝒮}}_{{ℳ}}(X),$ the pogroup of all ordered bijections on $X$. We also show that ${\text{Aut}}_{{ℳ}}({{𝒯}}_{{ℳ}}(X))$ is isomorphic to ${{𝒮}}_{{ℳ}}(X)$. Finally, we apply these results to get some more results in this direction.

In the present paper, we estimate the rate of convergence of Fourier series of functions by Deferred Nörlund mean in Besov space which is a generalization of $H(\alpha ,p)$ space.

A module $M$ is called ${𝒜}$-separable if every proper finitely generated submodule of $M$ is contained in a proper finitely generated direct summand of $M$. Indecomposable ${𝒜}$-separable modules are shown to be exactly the simple modules. While direct summands of an ${𝒜}$-separable module do not inherit the property, in general, the question of the stability under direct sums is unanswered. But we obtain some partial answers. It is shown that any infinite direct sum of ${𝒜}$-separable modules is ${𝒜}$-separable. Also, we prove that if $M_1$ and $M_2$ are ${𝒜}$-separable modules such that $M_1$ is $M_2$-projective, then $M_1\oplus M_2$ is ${𝒜}$-separable. We conclude the paper by providing some characterizations of several classes of rings in terms of ${𝒜}$-separable modules. Among others, we prove that the class of rings $R$ for which every (injective) $R$-module is ${𝒜}$-separable is exactly that of semisimple rings.

In this paper, we study ∗-Conformal $\eta$-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting ∗-Conformal $\eta$-Ricci soliton. We obtain some significant results on ∗-Conformal $\eta$-Ricci soliton in Sasakian manifolds satisfying $R(\xi ,X)\cdot S=0$, $S(\xi ,X)\cdot R=0$, $\overline{P}(\xi ,X)\cdot S$ $=0$, where $\overline{P}$ is Pseudo-projective curvature tensor. The conditions for ∗-Conformal $\eta$-Ricci soliton on $\varphi$-conharmonically flat and $\varphi$-projectively flat Sasakian manifolds have been obtained in this paper. Lastly we give an example of five-dimensional Sasakian manifolds satisfying ∗-Conformal $\eta$-Ricci soliton.

In this paper, we present a refinement of the well-known arithmetic-geometric mean inequality. As application of our result, we obtain an operator inequality. We give an improvement of the inequality presented by Kittaneh for the numerical radius.

In this paper, we present a new encryption scheme using generalization k-Fibonacci-like sequence, we code the points of an elliptic curve with the terms of a sequence of k-Fibonacci-like using of Fibonacci sequence and we call it as k-Fibonacci like sequence $\{V_{k,n}\}$ defined by the recurrence relation:

The set of all $n$-ary terms of type $\tau$ together with a binary operation derived from a superposition $S^n$ forms various forms of semigroups. One may generalize such binary operation by deriving it from an inductive composition of terms and call it an inductive product. However, this operation is not associative on the same base set but it becomes associative when all elements of subterms of a fixed term used in an inductive product except itself are excluded from the base set. Hence, a semigroup is formed. In this paper, we mainly focus on the algebraic structures of this semigroup such as idempotent elements, elements associating with each type of regularity condition, and Green’s relations. The formulae of complexity of inducted terms are also under investigation.

The distance Laplacian matrix of a simple connected graph $G$ is defined as $D^L(G)=Tr(G)-D(G)$, where $D(G)$ is the distance matrix of $G$ and $Tr(G)$ is the diagonal matrix whose main diagonal entries are the vertex transmissions in $G.$ In this paper, we determine the distance Laplacian spectra of the graphs obtained by generalization of the join and lexicographic product of graphs (namely joined union). It is shown that the distance Laplacian spectra of these graphs not only depend on the distance Laplacian spectra of the participating graphs but also depend on the spectrum of another matrix of vertex-weighted Laplacian kind (analogous to the definition given by Chung and Langlands [A combinatorial Laplacian with vertex weights, J. Combin. Theory Ser. A 75 (1996) 316–327]).

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 $(R,S)$-hyper bi-module, where $R$ and $S$ 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 $(R,S)$-hyper bi-modules.