Asian-European Journal of Mathematics

Many theorems and formulas of Lie superalgebras run quite parallel to Lie algebras, sometimes giving interesting results. So it is quite natural to extend the new concepts of Lie algebra immediately to Lie superalgebra case as the later type of algebras have wide applications in physics and related theories. Using the concept of isoclinism, Saeedi and Sheikh-Mohseni [A characterization of stem algebras in terms of central derivations, Algebr. Represent. Theory 20 (2017) 1143–1150; On ${\text{ID}}^{\ast }$-derivations of Filippov algebra, to appear in Asian-Eur. J. Math.; S. Sheikh-Mohseni, F. Saeedi and M. Badrkhani Asl, On special subalgebras of derivations of Lie algebras, Asian-Eur. J. Math. 8(2) (2015) 1550032] recently studied the central derivation of nilpotent Lie algebra with nilindex 2. The purpose of the present paper is to continue and extend the investigation to obtain some similar results for Lie superalgebras, as isoclinism in Lie superalgebra is being recently introduced.

For an element $a$ of a semigroup $S$, denote by $C(a)$ and $C^2(a)$, respectively, the first and second centralizers of $a$ in $S$. Let $X$ be an arbitrary set and let $\mathrm{\Gamma }(X)$ be the semigroup of all injective mappings from $X$ to $X$. For an arbitrary $\alpha \in \mathrm{\Gamma }(X)$, we characterize the elements of $C^2(\alpha )$, show that $C^2(\alpha )$ is a direct product of finite cyclic groups and the infinite cyclic monoid, and determine Green’s relations in $C^2(\alpha )$. We also describe those $\alpha \in \mathrm{\Gamma }(X)$ for which $C^2(\alpha )=C(\alpha )$, which will provide a class of maximal commutative subsemigroups of $\mathrm{\Gamma }(X)$.

We investigate the eigenvalue intervals of ${\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n$ for which the iterative system of four-point fractional-order boundary value problem has at least one positive solution by utilizing Guo–Krasnosel’skii fixed point theorem under suitable conditions. The obtained results in the paper are illustrated with an example for their feasibility.

Let $G=(V,E)$ be a graph and $u,v\in V.$ A dominating set $D$ is a set of vertices such that each vertex of $G$ is either in $D$ or has at least one neighbor in $D$. The minimum cardinality of such a set is called the domination number of $G$, $\gamma (G).$ $u$ strongly dominates $v$ and $v$ weakly dominates $u$ if (i) $uv\in E$ and (ii) $degu\ge degv.$ A set $D\subset V$ is a strong-dominating set, shortly sd-set, (weak-dominating set, shortly wd-set) of $G$ if every vertex in $V-D$ is strongly (weakly) dominated by at least one vertex in $D$. The strong (weak) domination number ${\gamma }_s({\gamma }_w)$ of $G$ is the minimum cardinality of an sd-set (wd-set). In this paper, we present weak and strong domination numbers of thorn graphs.

An edge irregular total $k$-labeling on simple and undirected graph $G(V,E)$ is a map $f:V\cup E\to \{1,2,\dots ,k\}$ such that for any different edge $xy$ and $x^{\prime }{y}^{\prime }$ their weights $f(x)+f(xy)+f(y)$ and $f(x^{\prime })+f(x^{\prime }{y}^{\prime })+f(y^{\prime })$ are distinct. The minimum $k$ for which the graph $G$ has an edge irregular total $k$-labeling is called the total edge irregularity strength of $G$ and is denoted by tes$(G)$. In this paper, we determine the exact value of the total edge irregularity strength of families of ladder-related graphs, namely triangular ladder graphs, diagonal ladder graphs and circular triangular ladder graphs.

In this paper, the classes of groups with given systems of $𝔉$-subnormal subgroups are studied. In particular, it is showed that if $ℌ$ and $𝔉$ are a saturated homomorph and a hereditary saturated formation, respectively, then the class of groups whose $ℌ$-subgroups are all $𝔉$-subnormal is a hereditary saturated formation. As corollaries, some known results about supersoluble groups, classes of groups with $𝔉$-subnormal cyclic primary and Sylow subgroups are obtained. Also the new characterization of the class of groups whose extreme subgroups all belong $𝔉$, where $𝔉$ is a hereditary saturated formation, is obtained.

In this paper, we study the existence of mild solutions of impulsive evolution fractional functional differential equation of order $0<\alpha <1$ involving a Lipschitz condition on term $I_k$. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators due to Burton and Kirk.

Let $X$ be a quasi-compact scheme and $x\in X$. By $cp(X)$ and $cl(x)$, we denote the set of closed points of $X$ and the closure of the subset $\{x\}$. Let $S$ be a nonempty subset of $cp(X)$. We define the $S$-Zariski topology graph on the scheme $X$, denoted by ${\mathrm{\Gamma }}_Z(X,S)$, as an undirected graph whose vertex set is the set $X$, for two distinct vertices $x$ and $y$, there is an arc from $x$ to $y$, denoted by $x\sim y$, whenever $cl(x)\cap cl(y)\cap S\ne \varnothing$. In this paper, we study the connectivity properties of the graph ${\mathrm{\Gamma }}_Z(X,S)$, we establish the relationship between the connectivity of the graph ${\mathrm{\Gamma }}_Z(X,S)$ and the structure of irreducible components of the scheme $X$. Also, we characterize when the complement graph of the Zariski topology graph ${\mathrm{\Gamma }}_Z(X,S)$ is a complete multipartite graph.

In this paper, by using the Faber polynomial expansions we can find the coefficient bounds for ${\mathrm{\Sigma }}_{{ℳ}}^{\ast }(\alpha ,\mu ,\lambda ,\gamma )$ subclass of meromorphic bi-univalent functions. The results presented in this paper would generalize and improve some recent works.

Cyclotomic classes of order 2 with respect to a product of two distinct odd primes $p$ and $q$ are represented in some specific forms and using these forms an alternate proof of Theorem 3 of [C. Ding and T. Helleseth, New generalized cyclotomy and its applications, Finite Fields Appl. 4 (1998) 140–166] is given, when $n=pq$. Further, it is observed that these classes are related to $l$-cyclotomic cosets, where $O_p(l)=\frac{\varphi (p)}{2}$ and $O_q(l)=\varphi (q)$ such that gcd($\frac{\varphi (p)}{2},\varphi (q))=1$. Finally, arithmetic properties of some families in $Z[x]/〈x^{pq}-1〉$ and hence in $F_l[x]/〈x^{pq}-1〉$ are studied.

We characterize connections between associative, Lie and Jordan structures of semiprime gamma rings.

In this paper, we prove that a class of fractional Burgers’ equations has a unique solution under some special conditions. Moreover, we show that an optimal control problem for a special class of fractional Burgers’ equations has at least one optimal solution.

Let $p$ and $q$ be integers such that $2\le p\le q,$ $p+q>4$ and let $H_{p,q}$ be generalized Hecke group associated to $p$ and $q.$ Generalized Hecke group $H_{p,q}$ is generated by $X(z)=-{(z-{\lambda }_p)}^{-1}$ and $Y(z)=-{(z+{\lambda }_q)}^{-1}$, where ${\lambda }_p=2cos\frac{\pi }{p}$ and ${\lambda }_q=2cos\frac{\pi }{q}.$ In this paper, for positive integer $m,$ we study the power subgroups $H_{p,q}^m$ of generalized Hecke groups $H_{p,q}$. Also, we give some results about free normal subgroups of generalized Hecke groups $H_{p,q}.$

In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. we propose a modified Fletcher–Reeves (abbreviated FR) [Function minimization by conjugate gradients, Comput. J. 7 (1964) 149–154] conjugate gradient algorithm satisfying a parametrized sufficient descent condition with a parameter ${\delta }_k$ is proposed. The parameter ${\delta }_k$ is computed by means of the conjugacy condition, thus an algorithm which is a positive multiplicative modification of the Hestenes and Stiefel (abbreviated HS) [Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards Sec. B 48 (1952) 409–436] algorithm is obtained, which produces a descent search direction at every iteration that the line search satisfies the Wolfe conditions. Under appropriate conditions, we show that the modified FR method with the strong Wolfe line search is globally convergent of uniformly convex functions. We also present extensive preliminary numerical experiments to show the efficiency of the proposed method.

In this paper, we give some characterizations for the boundedness of weighted fractional composition operator $D_{\phi ,u}^{\beta }$ from $\alpha$-Bloch spaces into weighted type spaces by deriving the bounds of its norm. Also, estimates for essential norm are obtained which gives necessary and sufficient conditions for the compactness of the operator $D_{\phi ,u}^{\beta }$.

The global determinism of a ternary semigroup $S$ is the set of all nonempty subsets of $S$, denoted by $P(S)$ equipped with the naturally defined multiplication. A class ${𝒦}$ of ternary semigroups is said to be globally determined if any two members $S_1$ and $S_2$ of ${𝒦}$ with isomorphic globals are themselves isomorphic i.e. $P(S_1)\cong P(S_2)$ implies that $S_1\cong S_2$ for any two ternary semigroups $S_1$ and $S_2$ in the class ${𝒦}$. In this paper, we mainly discuss that the class of all ternary semilattices are globally determined.

In this paper, we introduce some difference sequence spaces in bigeometric calculus. We determine the $\alpha$-duals of these sequence spaces and study their matrix transformations. We also develop an interpolating polynomial in bigeometric calculus which is analogous to the classical Hermite interpolating polynomial.

In this paper, we investigate some properties of sequences in a gradual normed space. We define some new notions such as gradual convergent sequences, gradual Cauchy sequences, etc., and then we state some theorems about these notions. Finally, in the last section, we bring some illustrative examples.