Asian-European Journal of Mathematics

Evaluating the efficiency and the performance of decision making units (DMUs) at different time periods is one of the most critical and important issues of managers. Data envelopment analysis (DEA) is a powerful non-parametric technique to measure the relative efficiency of a set of DMUs where each DMU consumes multiple inputs to produce multiple outputs. In many DEA applications, DMUs are considered as systems with a two-stage structure. In these situations, two-stage DEA models are used to measure the efficiencies of these systems. In many of such systems, the simultaneous presence of two stages is not necessary for the final product and the shortcoming of one stage is compensated by another stage. Therefore, this paper will use compensatory property of the sum operator and will propose the additive model to measure the multi-period efficiency of these systems under the constant returns to scale (CRS) assumption. In addition, based on the obtained efficiencies, the new efficiency changes Indexes (ECIs) related to the whole system and the first and second stages between two periods will be proposed that have circularity property. Furthermore, ECI of the whole system (and stages) for two periods is defined as the difference between the efficiencies in these periods. Moreover, positive changes (or negative changes), or unchanged in the efficiency of stages will be concluded by the positive changes (or negative changes), or unchanged of the whole system. Finally, the data of 21 non-life insurance industry in Taiwan are used to describe our suggested model that extracted from the extant literature.

In this work, it is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non-constant coefficients in three dimensions. Also, a variety of Lamb–Bateman singular integral equation and a non-homogeneous time fractional Kd.V of order $2q+1$ are solved. Constructive examples are also provided.

In this paper, we gives lower and upper bounds on the covering radius of codes over ${\mathbb{Z}}_{2p}$, where $p$ is a prime integer with respect to Lee distance. We also determine the covering radius of various Repetition codes over ${\mathbb{Z}}_{2p}$, where $p$ is a prime integer.

We prove some characterizations of the incomparability graphs of some dismantlable lattices. We discuss the realizability of some standard graphs as a graph of a dismantlable lattice. We also find the minimum covering energy of the incomparability graph of some dismantlable lattices.

This paper secures chirped dark and bright solitons of the perturbed nonlinear Schrödinger equation with parabolic law nonlinearity and self-steepening effect in the nonlinear left-handed metamaterials (NLHMs). We use the ansatz method, sine-cosine, csch function method and the auxiliary equation method to fall out the various soliton solutions. In view of the results obtained, rational, hyperbolic and trigonometric solutions emerge and there are new in CRLH TL. The existence criteria of these solutions are also discussed. Finally, we observed that the use of the auxiliary equation method leads to the abundant and efficient solutions than the other methods.

This paper studies an exact soliton solutions for the perturbed nonlinear Schrödingers equation which describes the dynamics of ultrashort optical solitons in nonlinear left-handed metamaterials. To befall soliton solutions, the function transformation method is apply. Dark, bright and exact travelling wave solutions like Jacobi’s elliptic function solutions are reported.

It is known that a soft $\mathrm{\Gamma }$-hyperring is a generalization of soft ring. The concept of soft $\mathrm{\Gamma }$-hyperring was first introduced by Zhan et al. In fact, Zhan et al. also established three isomorphism theorems of soft rings in 2012. Science then, the study of soft $\mathrm{\Gamma }$-hyperrings has been rapidly grown. The aim of this paper is to consider the equivalence relation on a $\mathrm{\Gamma }$-hyperring previously defined by Zhan et al. It is proved that the above relation is strongly regular and hyperaddition on all quotient soft $\mathrm{\Gamma }$-hyperrings. Also, by using the fundamental relations on $\mathrm{\Gamma }$-hyperrings and hypergroups, we define covariant functor between the category soft $\mathrm{\Gamma }$-hyperrings and soft rings.

In this paper, a weighted short-step primal-dual path-following interior-point algorithm for solving linear optimization (LO) is presented. The algorithm uses at each interior-point iteration a full-Newton step, thus no need to use line search, and the strategy of the central-path to obtain an $𝜖$-approximated solution of LO. We show that the algorithm yields the iteration bound, namely, ${𝒪}(\sqrt{n}log\frac{n}{𝜖})$. This bound is currently the best iteration bound for LO. Finally, some numerical results are reported in order to analyze the efficiency of the proposed algorithm.

Let $G$ be a finite group and ${\mathrm{\text{cd}}}^{\ast }(G)$ be the set of nonlinear irreducible character degrees of $G$. Suppose that $\rho (G)$ is the set of primes dividing some elements of ${\mathrm{\text{cd}}}^{\ast }(G)$. The bipartite divisor graph for ${\mathrm{\text{cd}}}^{\ast }(G)$, $B(G)$, is a graph whose vertices are the disjoint union of $\rho (G)$ and ${\mathrm{\text{cd}}}^{\ast }(G)$, and a vertex $p\in \rho (G)$ is connected to a vertex $a\in {\mathrm{\text{cd}}}^{\ast }(G)$ if and only if $p|a$. In this paper, we consider groups whose graph has four or fewer vertices. We show that all these groups are solvable and determine the structure of these groups. We also provide examples of any possible graph.

The paper deals with the study of Casorati curvature of submanifolds of generalized $(k,\mu )$-space-form with respect to Levi-Civita connection as well as semisymmetric metric connection and derived two optimal inequalities between scalar curvature and Casorati curvature of such space forms. The equality cases are also considered.

In this paper, we present all types of 3-point quadrature rules on continuous function on interval $[a,b]$ with constant weight function and compare there with the composite type also. All 3-point (open and closed) rules are taken from available papers and some new results like non-polynomial fitting and derivative type are introduced. Also, differences, comparisons, and errors between method procedures have been shown.

In this paper, we use the variational iteration method (VIM) to construct approximate solutions for the general $n$th-order integro-differential equations. We show that his method can be effectively and easily used to solve some classes of linear and nonlinear Volterra integro-differential equations. Finally, some numerical examples with exact solutions are given.

In this paper, we apply two powerful methods, namely, the new extended auxiliary equation method and the generalized Kudryashov method for constructing many exact solutions and other solutions for the higher order dispersive nonlinear Schrödinger’s equation to secure soliton solutions in quadratic-cubic medium. Various solutions of the resulting nonlinear ODE are obtained by using the above two methods.

In this paper, we introduce the definition of $(G,{\alpha }_f)$-bonvex/$(G,{\alpha }_f)$-pseudobonvex functions and to show the existence of such functions, we construct nontrivial numerical examples. In the next section, we formulate a pair of second-order symmetric dual model in optimization problem and proved the duality results under $(G,{\alpha }_f)$-bonvexity/$(G,{\alpha }_f)$-pseudobonvexity assumptions. Further, we also construct nontrivial concrete examples which justifying definitions as well as the weak duality theorem presented in the paper.

The distance signless Laplacian matrix of a simple connected graph $G$ is defined as $D^Q(G)=\mathrm{\text{Tr}}(G)+D(G)$, where $D(G)$ is the distance matrix of $G$ and $\mathrm{\text{Tr}}(G)$ is the diagonal matrix whose main diagonal entries are the vertex transmissions in $G$. In this paper, we first determine the distance signless Laplacian spectrum of the graphs obtained by generalization of the join and lexicographic product graph operations (namely joined union) in terms of their adjacency spectrum and the eigenvalues of an auxiliary matrix, determined by the graph $G$. As an application, we show that new pairs of auxiliary equienergetic graphs can be constructed by joined union of regular graphs.

Let $(R,𝔪)$ be a Noetherian local ring, $I,J$ two ideals of $R$, and $M,N$ two finitely generated $R$-modules. It is first shown that ${\mathrm{\text{Ass}}}_R({𝔉}_I^{\mathrm{\text{dim}}M-1}(M))$ is a finite set. We also prove that except the maximal ideal $𝔪$, the set ${\mathrm{\text{Ass}}}_R({𝔉}_I^{d-1}(N_n))$ is stable for large $n$, where we use $N_n$ to denote $R$-module $J^{n}M/J^{n+1}M$ or $M/J^{n}M$ and $d$ is the eventual value of $\mathrm{\text{dim}}{N}_n$.

In this paper, we propose the generalized solutions of a certain $n$th order Cauchy–Euler equation of the form $t^n{y}^{(n)}(t)+t^{n-1}{y}^{(n-1)}(t)+\cdots +t{y}^{\prime }(t)+my(t)=0$, where $m$ and $n$ are any integers with $n\ge 2$, and $t\in ℝ$ using Laplace transform technique. We find that the types of solutions either distributional solutions or weak solutions, depend on the values of $m$. At the end of the paper, we give some examples showing the types of solutions.

We present a local convergence analysis of an optimal eighth-order family of Ostrowski like methods for approximating a locally unique solution of a nonlinear equation. Earlier studies [T. Lotfi, S. Sharifi, M. Salimi and S. Siegmund, A new class of three-point methods with optimal convergence and its dynamics, Numer. Algorithms 68 (2015) 261–288.] have shown convergence of these methods under hypotheses up to the eighth derivative of the function although only the first derivative appears in the method. In this study, we expand the applicability of these methods using only hypotheses up to the first derivative of the function. By this way the applicability of these methods is extended under weaker hypotheses. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.