Asian-European Journal of Mathematics

We show that the posemigroup dominion of a commutative posemigroup is again a commutative posemigroup and all varieties of commutative posemigroups are epimorphically closed. Next, we show that certain subvarieties of the variety of all commutative posemigroups are saturated. Finally, we show that a commutative posemigroup $S$ is saturated if $S^k$ is saturated for some positive integer $k$.

A set $D_k\subseteq V$ is said to be a $k$-hop dominating set ($k$-HDS) of a graph $G=(V,E)$ if every vertex $x\in V$ is within $k$-distances from at least one vertex $t\in D_k$, i.e. $d(x,t)\le k$, where $k$ is a fixed positive integer. A dominating set $D_k$ is said to be minimum $k$-hop connected dominating set of a graph $G$, if it is minimal as well as it is $k$-HDS and the subgraph of G made by $D_k$ is connected. In this paper, we present an $O(n)$-time algorithm for computing a minimum $k$-hop connected dominating set of permutation graphs with $n$ vertices.

Using an $(n+1)$-ary superposition operation $S^n$ on the set $W_{{\tau }_n}^C(X_n)$ of all $n$-ary term of ${\tau }_n$, one obtains a unitary Menger algebra $(W_{{\tau }_n}^C(X_n);S^n,x_1,\dots ,x_n)$ of rank $n$. In this paper, we define the set ${{𝒞}{ℱ}}_{({\tau }_n,(2))}(X_n)$ of all $n$-ary C-quantifier free formulas of type $({\tau }_n,(2))$ on the set $W_{{\tau }_n}^C(X_n)$ and define the operation $R^n$ on the set ${{𝒞}{ℱ}}_{({\tau }_n,(2))}(X_n)$. After this definition, we have a unitary Mengar algebra $({{𝒞}{ℱ}}_{({\tau }_n,(2))}(X_n);R^n,x_1,\dots ,x_n)$.

We consider the skew Laplacian matrix of a digraph $\overrightarrow{G^{}}$ obtained by giving an arbitrary direction to the edges of a graph $G$ having $n$ vertices and $m$ edges. With ${\nu }_1,{\nu }_2,\dots ,{\nu }_n$ to be the skew Laplacian eigenvalues of $\overrightarrow{G^{}}$, the skew Laplacian energy $\mathrm{\text{SLE}}(\overrightarrow{G^{}})$ of $\overrightarrow{G^{}}$ is defined as $\mathrm{\text{SLE}}(\overrightarrow{G^{}})={\sum }_{i=1}^n\left|{\nu }_i\right|$. In this paper, we analyze the effect of changing the orientation of an induced subdigraph on the skew Laplacian spectrum. We obtain bounds for the skew Laplacian energy $\mathrm{\text{SLE}}(\overrightarrow{G^{}})$ in terms of various parameters associated with the digraph $\overrightarrow{G^{}}$ and the underlying graph $G$ and we characterize the extremal digraphs attaining these bounds. We also show these bounds improve some known bounds for some families of digraphs. Further, we show the existence of some families of skew Laplacian equienergetic digraphs.

In the present work, classical Lie symmetry method is adopted to obtain the Lie symmetries and similarity reductions of the $(2+1)$-dimensional dispersive long wave equation. We also demonstrate that the symmetry algebra of this equation is an infinte dimensional, together with Kac–Moody–Virasoro type subalgebras.

In this paper, we give an explicit description of the action of the super Lie group $\mathrm{\text{GL}}(m|n)$ on supergrassmannian $G_{k|l}(m|n)$ in the functor of points language. In particular, we give a concrete proof of the transitively of this action, and the gluing of the local charts of the supergrassmannian.

In this paper, the following composite analytic functions $F(z)=f(\mathrm{\Phi }(z))$ and $H(z)=G(\mathrm{\Phi }(z),\dots ,\mathrm{\Phi }(z))$ are considered, where $f:ℂ\to ℂ,$ $\mathrm{\Phi }:{𝔹}^n\to ℂ,$ $G:{ℂ}^m\to ℂ.$ We established conditions which provide equivalence of boundedness of the $l$-index of the function $f$ and boundedness of the $L$-index in joint variables of the function $F,$ where $l:ℂ\to {ℝ}_{+}$ is a continuous function, $L(z)=(l(\mathrm{\Phi }(z))|\frac{\partial \mathrm{\Phi }(z)}{\partial z_1}|,\dots ,$ $l(\mathrm{\Phi }(z))\left|\frac{\partial \mathrm{\Phi }(z)}{\partial z_n}\right|).$ For the function $H$ with additional restrictions, the function $L$ is constructed such that $H$ has bounded $L$-index in joint variables in the case when the function $G$ has bounded $L$-index in the direction $1=(1,\dots ,1)$, where $L:{ℂ}^n\to {ℝ}_{+}^n$ is a positive continuous function. Our proofs are based on the application of analog of Hayman’s theorem for these classes of functions.

Let $M$ be a lattice module over a $C$-lattice $L$. In this paper, we introduce the concept of the Zariski second radical of elements of $M$ and investigate some properties of Zariski second radical of elements of $M$. We also investigate when the Zariski second radical is equal to the second radical of elements of $M$. We give a characterization of Noetherian space by using Zariski second radical of elements of $M$.

Inspired by the recent work by Abd-Elmageed et al., who established recursion formulas satisfied by the first Appell matrix function, namely $F_1$, Sahai et al. presented various recursion formulas for the Gauss hypergeometric matrix function and all four Appell matrix functions. In this paper, we obtain recursion formulas and infinte summation formulas for Srivastava’s triple hypergeometric matrix functions $H_{{𝒜}}$, $H_{{ℬ}}$ and $H_{{𝒞}}$.

In this paper, we establish some properties concerning the condition pseudospectrum of the linear operator pencils $\lambda S-T$ when, $S$ is not necessarily invertible. Also, we give some results related to the generalized condition pseudospectra and the generalized essential condition pseudospectra of linear operators. We start by studying the stability of these condition pseudospectra and some characterization.

In this paper, we introduce a viscosity-type proximal point algorithm comprising of a finite composition of resolvents of monotone bifunctions and a generalized asymptotically nonspreading mapping recently introduced by Phuengrattana [Appl. Gen. Topol. 18 (2017) 117–129]. We establish a strong convergence result of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a generalized asymptotically nonspreading and nonexpansive mappings, which is also a unique solution of some variational inequality problems in an Hadamard space. We apply our result to solve convex feasibility problem and to approximate a common solution of a finite family of minimization problems in an Hadamard space.

(i) Every complex $F$-algebra with an identity and with an orthonormal basis is functionally continuous; (ii) Every complex complete LMC algebra with an orthogonal basis is functionally continuous; (iii) Every complex sequentially complete locally convex algebra with an unconditional orthonormal basis and with an element $x$ for which $n$th coefficient functional value tends to infinity as $n$ tends to infinity is functionally continuous. These results are proved and an example is provided for non-extendability of these results. A representation for positive linear functionals on a sequentially complete locally convex algebra with an unconditional orthonormal basis, with an identity, and with an element $x$ mentioned in (iii) is obtained. All results are obtained only for commutative algebras.

The purpose of this paper is to study the notion of quasi-compact linear operators acting in a Banach space. This class of operators contains the set of compact, polynomially compact, quasi-nilpotent and that of all Riesz operators. We show the equivalence between different definitions of quasi-compactness known in the mathematical literature and we present several general theorems about quasi-compact endomorphisms: stability under algebraic operations, extension of Schauder theorem and the Fredholm alternative. We also study the question of existence of invariant subspaces and we examine the class of semigroups for quasi-compact operators. The obtained results are used to describe Markov chains.

In this paper, we prove a uniqueness theorem for meromorphic mappings of a complete Kähler manifold $M$ into ${\mathbb{P}}^n(ℂ)$ sharing hyperplanes in general position under a general condition that the codimension of the intersection of inverse images of any $k+1$ hyperplanes is at least two.

The aim of this study is to compute the edge metric dimension of some subdivision of the wheel graphs. In particular, we determine and compare the metric and edge metric dimensions of the graphs obtained after the cycle, spoke and barycentric subdivisions of the wheel graph. Furthermore, some families of graphs have been constructed through subdivision process for which $\mathrm{\text{dim}}({{𝒲}{𝒞}{𝒫}}_{n,1})<{\mathrm{\text{dim}}}_e({{𝒲}{𝒞}{𝒫}}_{n,1})$, and also $\mathrm{\text{dim}}({{𝒲}{𝒞}{𝒴}}_{n,1})={\mathrm{\text{dim}}}_e({{𝒲}{𝒞}{𝒴}}_{n,1})$ which partially answer a question in [A. Kelenc, N. Tratnik and I. G. Yero, Uniquely identifying the edges of a graph: The edge metric dimension, Discrete Appl. Math. 251 (2018) 204–220].

In this paper, we introduce a new mixed type iterative process, which approximates the common fixed points of single-valued nonexpansive mappings and two multi-valued nonexpansive mappings in a uniformly convex Banach space. We establish strong and weak convergence theorems for the new iterative process in Banach space and give their corresponding applications.

In this paper, the authors prove some inequalities and completely monotonic properties of polygamma functions. As an application, we give lower bound for the zeta function on natural numbers. Partially, we answer the fifth and sixth open problems listed in [F. Qi and R. P. Agarwal, On complete monotonicity for several classes of functions related to ratios of gamma functions, J. Inequalities Appl. 2019(36) (2019) 42]. We propose two open problems on completely monotonic functions related to polygamma functions.

Let $𝔽$ be a field. Set $J:=\left[\right.\begin{array}{cc}\hfill 0\hfill & \hfill I_n\hfill \\ \hfill -I_n\hfill & \hfill 0\hfill \end{array}\left]\right.$. A matrix $X\in {𝔽}^{2n\times 2n}$ is symplectic if ${XJ}^{-1}{X}^{T}J=I$. We say that a matrix $P\in {𝔽}^{2n-1\times 2n-1}$ has a symplectic completion of order $2n$ if there exist $x,y\in {𝔽}^{2n-1\times 1}$ and a scalar $\alpha \in 𝔽$ such that $\left[\right.\begin{array}{cc}\hfill P\hfill & \hfill x\hfill \\ \hfill y^T\hfill & \hfill \alpha \hfill \end{array}\left]\right.$ is symplectic. If $P$ is nonsingular, we give necessary and sufficient conditions such that $P$ has a symplectic completion of order $2n$. We give an implicit characterization of all matrices of order 3 which have symplectic completions of order 4.

Since orthomodular posets serve as an algebraic axiomatization of the logic of quantum mechanics, it is a natural question how the connective of implication can be defined in this logic. It should be introduced in such a way that it is related with conjunction, i.e. with the partial operation meet, by means of some kind of adjointness. We present here such an implication for which a so-called unsharp residuated poset can be constructed. Then this implication is connected with the operation meet by the so-called unsharp adjointness. We prove that also conversely, under some additional assumptions, such an unsharp residuated poset can be converted into an orthomodular poset and that this assignment is nearly one-to-one.

We found conditions under which additive mappings defined on additively inverse semirings and satisfying the $n$th power property are derivations.