Asian-European Journal of Mathematics

Let S be a monoid and $X$ a class of $S$-acts which is closed under coproducts. The object of this paper is to find conditions under which all $S$-acts have $X$-precovering, especially when $X$ is the class of injective (C-injective) acts. We have shown that the existence of injective precovering over Noetherian monoids implies the existence of injective covering. This work is an attempt to further facilitate the study of the conjecture that all $S$-acts have flat cover.

In this paper, we study various annihilator properties in a ring $R$ with an endomorphism $\sigma$ and some subrings of the skew triangular matrix rings $T_n(R,\sigma )$. They allow the construction of rings with a nonzero nilpotent ideal of arbitrary index of nilpotency which have various zero-divisor properties.

In this paper, we improve the infeasible full-Newton interior-point algorithm presented by Mansouri et al. [A full-Newton step $O(n)$ infeasible interior-point algorithm for linear complementarity problems, Nonlinear Anal. Real World Appl. 12 (2011) 545–561] for monotone linear complementarity problems (MLCPs). In each iteration of Mansouri’s algorithm two types of full-Newton steps are used, one feasibility step and some ordinary (centering) steps. In this paper, we use a new search direction, and reduce the number of the centering steps, so that only one centering step is needed. We prove that the complexity of the algorithm is as good as the best-known complexity for infeasible interior-point methods for MLCPs.

We introduce a family of extensions of bounded distributive lattices. These extensions are obtained by adding two operations: an internal unary operation, and a function (called generalized implication) that maps pair of elements to ideals of the lattice. A bounded distributive lattice with a generalized implication is called gi-lattice in [J. E. Castro and S. A. Celani, Quasi-modal lattices, Order 21 (2004) 107–129]. The main goal of this paper is to introduce and study the category of frontal gi-lattices (and some subcategories of it). This category can be seen as a generalization of the category of frontal weak Heyting algebras (see [S. A. Celani and H. J. San Martín, Frontal operators in weak Heyting algebras, Studia Logica 100(1–2) (2012) 91–114]). In particular, we study the case of frontal gi-lattices where the generalized implication is defined as the annihilator (see [B. A. Davey, Some annihilator conditions on distributive lattices, Algebra Universalis 4(1) (1974) 316–322; M. Mandelker, Relative annihilators in lattices, Duke Math. J. 37 (1970) 377–386]). We give a Priestley’s style duality for each one of the new classes of structures considered.

The classical logic was axiomatized algebraically by means of Boolean algebras in 19th century by George Boole. Similar attempts went on 20th century for algebraic axiomatization of non-classical logics, e.g. intuitionistic logics (Brouwer and Heyting algebras), many-valued logics (Łukasiewicz, Chang’s MV-algebras, Post algebras), the logic of quantum mechanics (orthomodular lattices and posets) and fuzzy logics (residuated lattices). In this paper, we are focused in a common generalization of MV-algebras and orthomodular lattices. The resulting algebras, called basic algebras, have surprisingly strong and interesting properties and they can be investigated in their own. The aim of the paper is to get an overview of results reached during the last decade.

Necessary and sufficient conditions for an Almost Distributive Lattice (ADL) to become a BL-ADL are derived. Different characterization of a BL-ADL are obtained. Relation between the operators on BL-ADL are derived. Wide choice of fundamental operations for a BL-ADL are derived.

The properties of right ample semigroups have been extensively considered and studied by many authors. In this paper, we concentrate on the matrix representations of right ample semigroups. The (left; right) uniform matrix representation is initially defined. After some properties of left uniform matrix representations of a right ample semigroup are given, we prove that any irreducible left uniform representations of a right ample semigroup can be obtained by using an irreducible left uniform representation of some primitive right ample semigroup. In particular, a construction theorem of prime left uniform representation of right ample semigroups is established.

We investigate how the evolutionary network is associated among Human, Chimpanzee and Mouse with regards to their genomic information. We provide a quantitative description of genomic evolution through indexes based on fractals and mathematical morphology. These indexes are carefully chosen and reveal quantitatively the similarity or differences among the structure of the concerned sequences. They also reveal how the sequences have evolved over the course of time. We have considered olfactory receptors (ORs) as our case study. These ORs do function in different species with the subtle differences in between the structures of DNA sequences. Such differences are quantified in this paper.

We prove the existence of infinitely many singular radial positive solutions for a quasilinear elliptic system with no variational structure

It is shown that, how spectral sequence arguments can contribute to a solution in a concrete setting. For one-dimensional extensions of a Heisenberg algebra, we determine the Betti numbers exactly and then show that some families in this class have a M-shaped Betti number distribution, and construct the first examples with an even more exotic complete bipartite graph which are independent of choice of field. Finally, we discuss the Betti numbers for the star graph with $n$ vertices.

In this paper, we consider two generalized binary sequences and then give a generalization of a matrix equality proposed as an advanced problem. Then, we derive new certain finite sums including the generalized binary sequences as applications.

The incomplete Beta function $B(a,b;x)$ is defined for $a,b>0$ and $0<x<1$. This definition was extended to negative integer values of $a$ and $b$ by Özçaḡ et al. using neutrix limits. Partial derivatives of the incomplete Beta function $B(a,b;x)$ for negative integer values of $a$ and $b$ were then evaluated. In the following, a number of results are obtained for the incomplete Beta function $B(a,b;x)$ and then the corresponding results for the Beta function $B(a,b)$ are deduced.

We study existence of mild solution to a $n$-dimensional generalized incompressible magneto-hydrodynamic (GMHD) system with initial value $(u_0,b_0)$ in a new critical space ${(Q_{\alpha ,\infty }^{\beta ,-1}({ℝ}^n))}^{2n}:={(\nabla \cdot {(Q_{\alpha }^{\beta }({ℝ}^n))}^n)}^{2n}$, and $Q_{\alpha }^{\beta }({ℝ}^n)$ is the space of all measurable functions $f$ on ${ℝ}^n$ satisfying

Let $f:A\to B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we study the transfer of fqp-property in the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A{\bowtie }^{f}J),$ introduced and studied by D’Anna, Finocchiaro and Fontana in 2009. Our aim is to provide new classes of commutative rings satisfying this property.

Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and to study a new class of modules over $R$ called quasi-primaryful $R$-modules. This class contains the family of finitely generated modules properly, on the other hand it is contained in the family of primeful $R$-modules properly, and three concepts coincide if they are multiplication modules. We show that free modules, projective modules over domains and faithful projective modules over Noetherian rings are quasi-primaryful modules. In particular, if $R$ is an Artinian ring, then all $R$-modules are quasi-primaryful and the converse is also true when $R$ is a Noetherian ring.

For a non-empty ground set $X$, finite or infinite, the set-valuation or set-labeling of a given graph $G$ is an injective function $f:V(G)\to {𝒫}(X)$, where ${𝒫}(X)$ is the power set of the set $X$. A set-valuation or a set-labeling of a graph $G$ is an injective set-valued function $f:V(G)\to {𝒫}(X)$ such that the induced function $f^{\ast }:E(G)\to {𝒫}(X)-\{\varnothing \}$ is defined by $f^{\ast }(uv)=f(u)\ast f(v)$ for every $uv\in E(G)$, where $\ast$ is a binary operation on sets. Let ${\mathbb{N}}_0$ be the set of all non-negative integers and ${𝒫}({\mathbb{N}}_0)$ be its power set. An integer additive set-labeling (IASL) is defined as an injective function $f:V(G)\to {𝒫}({\mathbb{N}}_0)$ such that the induced function $f^{+}:E(G)\to {𝒫}({\mathbb{N}}_0)$ is defined by $f^{+}(uv)=f(u)+f(v)$. An IASL $f$ is said to be an integer additive set-indexer if $f^{+}$ is also injective. A weak IASL is an IASL $f$ such that $|f^{+}(uv)|=max(f(u),f(v))$. In this paper, critical and creative review of certain studies made on the concepts and properties of weak integer additive set-valued graphs is intended.

Given a positive integer $n$, how many zero rings exist of order $n$? Inspired from this question, in this paper, author is mainly concerned to determine the structure of zero rings of a given order; in particular, we tempted to try out the structure of each zero ring of order $\le 50$. In the course of the investigation, basic properties of zero rings are obtained and the results relevant to the counting of subrings, and ideals for a given zero ring have established.

In this paper, the continuous fractional wavelet transform is defined and boundedness results of this transform on generalized weighted Sobolev spaces are obtained. Characterization of the range of continuous fractional wavelet transform is also discussed.

We prove that for any Boolean space $X$ and a dense Almost Distributive Lattice (ADL) $D$ with a maximal element, the set ${𝒞}(X,D)$ of all continuous functions of $X$ into the discrete $D$ is a Stone ADL. Conversely, it is proved that any Stone ADL is a homomorphic image of ${𝒞}(X,D)$ for a suitable Boolean space $X$ and a dense ADL $D$ with a maximal element.

In this paper, some new unbounded operators are introduced and characterizations, properties of these operators are also obtained.

In this paper, we indicate some inequalities for double integrals of functions whose partial derivatives in absolute value are convex on the coordinates on rectangle from the plane. Our established results generalize some recent results for functions whose partial derivatives in absolute value are convex on the coordinates on the rectangle from the plane.

In this paper, the concepts of ${\Omega }^{\ast }$-closed and ${\Omega }^{\ast }$-continuous maps are introduced and several properties of them are investigated. These concepts are used to obtain several results concerning the preservation of $\Omega$-closed sets. Moreover, we use ${\Omega }^{\ast }$-closed and ${\Omega }^{\ast }$-continuous maps to obtain a characterization of semi-$T_{\frac{1}{2}}$ spaces.

In this paper, we study an iterative approximation of common fixed points of two nonself asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in a uniformly convex Banach space.

In this paper, we investigate the problem of robust exponential stability analysis for uncertain linear systems with discrete interval time-varying delay, distributed time-varying delay and nonlinear perturbations. Based on constructing an augmented Lyapunov–Krasovskii functional with some parameter, decomposition technique of coefficient matrix, mixed model transformation with Leibniz–Newton formula and utilization of zero equations, new delay-range-dependent robust exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the superiority of our results to those in the literature.

Using a generalized form of Weber’s theorem we construct a family of quaternary quartic forms representing infinitely many prime squares.