Asian-European Journal of Mathematics

Settlement and pore water pressure in soils during the consolidation process are of great concern for geotechnical and structural engineers. Therefore, different analytical and numerical methods have been proposed for its solution considering the complexity of soil behavior and geometry of soil layers. In this research study, consolidation equation has been solved using the matrix-based rationalized Haar wavelet transform method. Two typical and most commonly used cases are solved and compared with the classical solution method which is based on Taylor series expansion. The proposed method is fast, convenient and requires less computational effort due to its matrix calculation implementation and it yields accurate results when compared with the classical solution. Furthermore, this method may be used for implementing explicit functions rather than a constant value for the consolidation coefficient (c${}_v$).

Given a set of points in the complex plane, an incomplete polynomial is defined as one which has these points as zeros except one of them. Recently, the classical result known as Gauss–Lucas theorem on the location of zeros of polynomials and their derivatives was extended to the linear combinations of incomplete polynomials. In this paper, a simple proof of this result is given, and some results concerning the critical points of polynomials due to Jensen and others have extended the linear combinations of incomplete polynomials.

In this paper, we consider a vector optimization problem on Riemannian manifolds for which we define KT-B-invex and KT-B-pseudoinvex functions. Further, we prove that every vector Kuhn–Tucker point is a weak efficient solution for considered vector optimization problem under the suitable assumptions. Moreover, we also study the Mond–Weir dual problem for the aforesaid problem and establish its weak, strong and converse duality results.

The present paper deals with the approximation properties of generalization of Lupaş–Păltănea’s operators preserving exponential functions. We obtain moments using the concept of moment generating functions and establish a Voronovskaya type theorem, uniform convergence estimate and also an asymptotic formula in quantitative sense. In the end we present comparative study through graphical representation and propose an open problem.

In this paper, we first introduce a new class of $MT$-preinvex functions, which are called $(\xi ,m,MT)$-preinvex functions, then we give some new estimates of Hermite–Hadamard, Ostrowski and Simpson type inequalities using Riemann–Liouville fractional integral. The obtained results in this paper generalize the well-known results in recent years.

In this paper, we obtain equations of circular surfaces by using unit quaternions and express these surfaces in terms of homothetic motions. Furthermore, we introduce new roller coaster surfaces constructed by the spherical indicatrices of a spatial curve in Euclidean $3$-space. Then, we express parametric equations of roller coaster surfaces by means of unit quaternions and orthogonal matrices corresponding to these quaternions. Moreover, we present some illustrated examples.

In this paper, we present an interior-point algorithm for solving an optimization problem using the central path method. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear complementarity problem. For its numerical tests, some strategies are used and indicate that the algorithm is efficient.

In this paper, we give semiring version of some classical results in commutative algebra related to Euclidean rings, PIDs, UFDs, G-domains, and GCD and integrally closed domains.

The relative Cayley graph of a group $G$ with respect to its proper subgroup $H$ is a graph whose vertices are elements of $G$ and two vertices $h\in H$ and $g\in G$ are adjacent if $g=hc$ for some $c\in C$, where $C$ is an inverse-closed subset of $G$. We study the relative Cayley graphs and, among other results, we discuss on their connectivity and forbidden structures, and compute some of their important numerical invariants.

A 2-rainbow edge dominating function (2REDF) of a graph $G$ is a function $f$ from the edge set $E(G)$ to the set of all subsets of the set $\{1,2\}$ such that for any edge $e\in E(G)$ with $f(e)=\varnothing$ the condition ${\bigcup }_{e^{\prime }\in N(e)}f(e^{\prime })=\{1,2\}$ is fulfilled, where $N(e)$ is the open neighborhood of $e$. The weight of a 2REDF $f$ is the value ${\sum }_{e\in E(G)}|f(e)|$. The minimum weight of a 2REDF is the 2-rainbow edge domination number of $G$, denoted by ${\gamma }_{2r}^{\prime }(G)$. In this paper, we initiate the study of 2-rainbow edge domination in graphs. We present various sharp bounds, exact values and characterizations for the 2-rainbow edge domination number of a graph.

The set of linear terms, i.e. terms in which each variable occurs at most once, does not form a subsemigroup of the so-called diagonal semigroup. We consider the reduct of the diagonal semigroup to the linear terms, which is not a partial semigroup. We extend the set of linear terms by an expression “$\infty$”, that is formally a linear term, obtaining a semigroup. The algebraic structure of this semigroup will be studied in this paper. We characterize the Green’s relations and the regular elements as well as the idempotent elements. Moreover, we discuss the ideal structure.

In this paper, we have investigated Fekete–Szegö problems and coefficient estimates for some subclasses of bi-univalent functions defined in terms of quasi-subordination. These inequalities result in the bounds of the third coefficient in Maclaurin’s series expansion in the unit disc.

We present a number of fixed and common fixed point theorems for a class of nonlinear contractions in metric spaces and metric spaces endowed with graphs. Our results complement, extend and generalize a number of fixed point theorems including a recent fixed point theorem of Kim et al. [Suzuki-type of common fixed theorem in metric spaces, J. Nonlinear Convex Anal. 16 (2015) 1779–1786]. We also discuss an application to a system of integral equations.

In this paper, we study nonbinary quantum codes from cyclic codes over the ring $F_p[u]/〈u^3-u〉$ for odd prime $p$. We give the constructional properties of linear and cyclic codes over the ring $F_p[u]/〈u^3-u〉$. As an applications of these classes of codes, we obtain quantum codes over $F_p$ using self-orthogonal property. Moreover, we find some new nonbinary quantum codes with better parameters than the known quantum codes over $F_p$.

Merging the first and third classes in a connected graph is the operation of adding edges between all vertices at distance 3 in the original graph while keeping the original edges. We determine when merging the first and third classes in a bipartite distance-regular graph produces a distance-regular graph.

In this paper, we classify the modular group algebra $KG$ of a group $G$ over a field $K$ of characteristic $p>0$ having upper Lie nilpotency index $t^L(KG)=9p-7$. The group algebra $KG$ with $t^L(KG)<9p-7$ has already been described.

Mason introduced the notion of reflexive property for rings which play roles in noncommutative ring theory. In this paper, we extend this property to rings with involution and investigate their properties. We provide many examples of these rings and also consider some extensions such as trivial extension, Dorroh extension, etc.

An inversion of the weighted vector ray transform is performed jointly with the inversion of the scalar ray transform for the weighted function $𝜀(r)$. Initially, the ray transform of the basis vector functions for the vector field $𝜀(r)g(r)$ is evaluated in an analytical form and then the inversion problem is reduced by the method of the least squares to a linear system of equations.

This paper considers recovery of signals that are sparse or approximately sparse in terms of a general frame from undersampled data corrupted with additive noise. We show that the properly constrained $l_1$-analysis, called general-dual-based analysis Dantzig selector, stably recovers a signal which is nearly sparse in terms of a general dual frame provided that the measurement matrix satisfies a restricted isometry property adapted to the general frame. As a special case, we consider the Gaussian noise.