MATHEMATICAL SCIENCES
Year:2018 | Volume:12 | Issue:3|Papers Count:10

We consider signed graphs, i. e., graphs with positive or negative signs on their edges. The notion of signed strongly regular graph is recently defined by the author (Signed strongly regular graphs, Proceeding of 48th Annual Iranian Mathematical Conference, 2017). We construct some families of signed strongly regular graphs with only two distinct eigenvalues. The construction is based on the well-known method known as star complement technique.

In this paper, we have proposed an estimator of finite population mean in stratified random sampling. The expressions for the bias and mean square error of the proposed estimator are obtained up to the first order of approximation. It is found that the proposed estimator is more efficient than the traditional mean, ratio, exponential, regression, Shabbir and Gupta (in Commun Stat Theory Method 40: 199– 212, 2011) and Khan et al. (in Pak J Stat 31: 353– 362, 2015) estimators. We have utilized four natural and four artificial data sets under stratified random sampling scheme for assessing the performance of all the estimators considered here.

This paper aims to study vector optimization through improvement sets in locally convex spaces. This investigation could be viewed as an extension of the work of Lalitha and Chatterjee (J Optim Theory Appl 166: 825– 843, 2015) who studied an open problem on stability posed by Chicco et al., in normed linear spaces. This paper also establishes some existence results for this kind of vector optimization using the celebrated KKM theorem (or Fan’ s Lemma, which is more common in the literature). Some examples illustrating the advantage of this work than that of Lalitha and Chatterjee (2015) are included too.

The aim of this work is to introduce an efficient algorithm for the numerical solution of nonlinear integral equation arising from chemical phenomenon which is a famous equation in chemistry engineering. A procedure is described for transforming the nonlinear integral equation by using Chebyshev polynomials to nonlinear system of algebraic equations. Also, we present a convergence analysis and error bound for presented method. In addition, some numerical results are reported to evaluate the validity and applicability of the method and also comparison has been done with existing results.

A numerical scheme has been developed for solving the system of linear Fredholm integro-differential equations subject to the mixed conditions using Laguerre polynomials. Using collocation method, the system of Fredholm integro-differential equations has been transformed to the system of linear equations in unknown Laguerre coefficients, which leads to the solution in terms of Laguerre polynomials. Moreover, the accuracy and applicability of the scheme have been compared with Tau method and Adomian decomposition method that reveals the proposed scheme to be more efficient.

The conventional data envelopment analysis suggests each decision-making unit selecting its most desirable weight. Applying these weights lets the units achieve their maximum performance. But, the performance of different units is achieved with different sets of weights. So, comparison and ranking of units on a common basis seems such an impossible challenge. However, the flexibility in choosing weights will make more than one efficient unit to be claimed as an efficient unit. In order to resolve these shortcomings, this paper proposes a method that only one common set of weights is obtained through this method. Toward this end, firstly, the efficiency of each unit is calculated, and then, the units are ranked by the efficiency scores earned from common weights. The weight restriction approach here not only generates positive weights but also prevents weights dissimilarity. The production of strictly positive weights through the proposed model makes it possible that no input and output variables are ignored.

In image processing, edge detection and image enhancement can make use of fractional differentiation operators, especially the Gru¨ nwald– Letnikov derivative. In this paper, we present a modified Gru¨ nwald– Letnikov derivative to enhance more and detect better the edges of an image. Our proposed fractional derivative is very flexible and can be easily performed. We present some examples to justify our suggested approach.

The susceptible– infected– recovered model of computer viruses is investigated as a nonlinear system of ordinary differential equations by using the homotopy analysis method (HAM). The HAM is a flexible method which contains the auxiliary parameters and functions. This method has an important tool to adjust and control the convergence region of obtained solution. The numerical solutions are presented for various iterations, and the residual error functions are applied to show the accuracy of presented method. Several  h-curves are plotted to demonstrate the regions of convergence, and the residual errors are obtained for different values of theses regions.

In this paper, we introduce the concept of the rectangular M-metric spaces, along with its topology and we prove some fixed-point theorems under different contraction principles with various techniques. The obtained results generalize some classical fixed-point results such as the Banach’ s contraction principle, the Kannan’ s fixed-point theorem and the Chatterjea’ s fixed-point theorem. Also we give an application to the fixed-circle problem.

In this paper, we continue to study properties of skew polynomial ring R½ x; a; d , where R is an associative ring equipped with an endomorphism a and an a-derivation d. We first introduce weak (a; d)-skew Armendariz ideals, a generalization of (a; d)-compatible ideals have the insertion of factors property (or simply, IFP). We also prove that if J is a weak (a; d)-skew Armendariz ideal of R, then J[x] is a weak (a; d)-skew Armendariz ideal of R[x].