Asian-European Journal of Mathematics

Our purpose in this paper is to investigate commutativity of a ring with involution $(R,\ast )$ which admits a generalized derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Moreover, we provide examples to show that the assumed restrictions cannot be relaxed.

We give a sufficient condition for sensitivity of continuous maps defined on a uniform space. We also study property $P$ for uniformly continuous maps defined on a uniform space and its relation with uniform entropy.

In this paper, we introduce the concept of Birkhoff center of a $c$-semiring and provide some characterizations of this center. Finally, we prove that the Birkhoff center of a $c$-semiring forms a distributive lattice.

The purpose of this paper is to introduce and study new notions of continuity, compactness and stability in ditopological texture spaces based on the notions of $\beta$-$g$-open and $\beta$-$g$-closed sets and some of their characterizations are obtained.

In the present paper, we classify varieties of algebraic systems of the type $((n),(m))$, for natural numbers $n$ and $m$, which are closed under particular derived algebraic systems. If we replace in an algebraic system the $n$-ary operation by an $n$-ary term operation and the $m$-ary relation by the $m$-ary relation generated by an $m$-ary formula, we obtain a new algebraic system of the same type, which we call derived algebraic system. We shall restrict the replacement to so-called “linear” terms and atomic “linear” formulas, respectively.

Let $X$ be a finite simple graph. The $2$-distance graph $D_2(X)$ of $X$ is the graph with the same vertex set as $X$ and two vertices are adjacent if and only if their distance in $X$ is exactly $2$. A graph $G$ is a $2$-distance graph if there exists a graph $X$ such that $D_2(X)\cong G$. In this paper, we give three characterizations of $2$-distance graphs, and find all graphs $X$ such that $D_2(X)\cong k{P}_2$ or $K_m\cup K_n$, where $k\ge 2$ is an integer, $P_2$ is the path of order $2$, and $K_m$ is the complete graph of order $m\ge 1$.

The aim of this paper is to study the existence and uniqueness of solutions for a boundary value problem associated with a fractional nonlinear differential equation with higher order posed on the half-line. An appropriate continuous embedding for suitable Banach spaces are proved and the Minty–Browder theorem for monotone operators is used in the proof of existence of solutions for a boundary value problem of fractional order posed on the half-line.

To tackle a linear Fredholm integral equation on great interval, two numerical processes are involved: discretization and iterative scheme. The conventional numerical process is discretize first then use an iterative scheme as Jacobi’s method to approach the solutions of the huge algebraic system. In this paper, we propose an alternative numerical process, we apply an iterative scheme based on construction of a generalization of the iterative scheme for Jacobi method which is adapted to the system of linear bounded operators, then we use Nyström method to discretize only the diagonal part of the system. The convergence analysis of this new method is proved and numerical tests developed show its effectiveness.

A discrete duality is a relationship between classes of algebras and classes of relational systems (frames). In this paper, discrete dualities are presented for De Morgan algebras with various kind of unary operators. To do this, we will extend the discrete duality given in [W. Dzik, E. Orłowska and C. van Alten, Relational representation theorems for general lattices with negations, in Relations and Kleene Algebra in Computer Science, Lecture Notes in Computer Science, Vol. 4136 (Springer, Berlin, 2006), pp. 162–176], for De Morgan algebras.

In this paper, we present a monotone domain decomposition iterative technique for boundary value problems of a nonlinear fractional differential equation. We construct two monotone domain decomposition sequences of upper and lower solutions which converge uniformly to the actual solution of the problem. The accuracy and efficiency of our new approach are demonstrated through two examples.

In this paper, we obtain a complete rewriting system for monoid presentation of Schützenberger product of $n$ groups, which is firstly defined in [G. M. S. Gomes, H. Sezinando and J. E. Pin, Presentations of the Schützenberger product of $n$ groups, Comm. Algebra 34(4) (2006) 1213–1235]. It gives an algorithm for getting normal form of elements and hence solving the word problem in this group.

The modules which are isomorphic to their non-zero submodules are known as iso-retractable. We characterize simple modules in terms of iso-retractable modules. We provide several sufficient conditions for iso-retractable modules to be simple. We show that if the endomorphism ring of an iso-retractable module is von-Neumann regular then $M$ is a simple module. In general, iso-retractable modules need not be projective (injective) and vice versa. We investigate some properties of iso-retractable modules with projectivity as well as injectivity. Finally, we provide some open problems.

The concepts of autonilpotent groups were introduced by Parvaneh and Moghaddam in 2010. In this paper, we introduce the generalized version of lower n-autocenteral and upper n-autocenteral series. Using these concepts, the notion of n-autonilpotent groups will be defined and some of the well-known theorems on autonilpotent groups will be proved in the generalized version.

In this paper, we establish Composition-Diamond lemma for multiple tensor products of commutative algebra $k[Y]$, free associative algebras $k〈X^{(i)}〉$, Grassman algebras $G_k(Z^{(j)})$ and path algebras ${\mathrm{\text{path}}}_k(\overrightarrow{P^{(l)}})$ over a field $k$.

In this work, we build a new numerical method to approximate the solution of Volterra’s nonlinear integro-differential equation. This method needs fewer conditions to converge, compared to the direct Nytröm method. Numerical tests show its efficiency. This new method is more practical and compatible with the Volterra nonlinear integro-differential equation.

In this paper, we showed that any clone of operations preserving a nontrivial $n$-equivalence on a finite set is categorically equivalent to the clone of operations preserving a nontrivial $n$-equivalence on a set having the cardinality of $3$.