Abstract: This paper investigates an SIS epidemic model with variable population size including a vaccination program. Dynamics of the endemic equilibrium of the model are obtained, and it will be shown that this equilibrium exists and is locally asymptotically stable when \({\mathcal {R}}_0 > 1\) . In this case, the disease uniformly persists, and moreover, using a geometric approach we conclude that the model is globally asymptotically stable under some conditions. Also, a numerical discussion is given to verify the theoretical results. PubDate: 2018-11-08

Abstract: The problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis. In this context, this paper proposes a mixed ridge regression model via shrinkage methods to analyze such data. Furthermore, in view of obtaining more efficient estimators, we propose preliminary and Stein-type estimators using prior information for fixed-effects parameters. The model parameters are estimated via the EM algorithm. A simulation study is also presented to assess the performance of the estimators under different estimation methods. An application to the HIV data is also illustrated. PubDate: 2018-11-01

Abstract: We introduce a new wrapped exponential distribution named transmuted wrapped exponential (TWE) distribution, for the modeling of circular datasets by using the Transmutation Rank-Map method. This method is employed for the first time for a wrapped distribution with this study. The introduced distribution is more flexible than traditional wrapped exponential distribution. The paper provides the explicit form of important distributional properties of the introduced distribution such as expectation, median, moments, characteristic function, quantile function, hazard rate function and stress-strength reliability. Rényi and Shannon entropies are also obtained. The statistical inference problem for the TWE distribution is investigated using maximum likelihood, least squares and weighted least squares and comparative numerical study results are presented. Furthermore, we present a real dataset analysis. PubDate: 2018-10-25

Abstract: In this paper, a numerical technique is developed to discretize variable-order fractional Heston differential equation. The proposed strategy is followed by an optimization technology, genetic algorithm, for tuning the unknown parameters in the proposed model. The performance of the model is analyzed to profit and loss 500 close index from the US stock markets. Simulations illustrate the application of the proposed technique. PubDate: 2018-10-22

Abstract: The key objective of the proposed work in this paper is to introduce a new version of picture linguistic fuzzy set, so-called spherical linguistic fuzzy sets. The novel concept of spherical linguistic fuzzy set consists of linguistic term, positive, neutral and negative membership degrees which satisfies the conditions that the square sum of its membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of spherical linguistic fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose spherical linguistic fuzzy Choquet integral weighted averaging (SLFCIWA) operator based on spherical fuzzy numbers. Further, the proposed SLFCIWA operator of spherical fuzzy number is applied to multi-attribute group decision-making problems. Also, we propose the GRA method to aggregate the spherical fuzzy information. To implement the proposed models, we provide some numerical applications of group decision-making problems. Also compared with the previous model, we conclude that the proposed technique is more effective and reliable. PubDate: 2018-10-16

Abstract: In Riemannian manifolds, there exists a canonical Riemannian metric on the product of them (Lee in Riemannian geometry an introduction to curvature, Springer, New York, 1997). But at the product of Finsler manifolds, the canonical Finsler metric has not been defined. In this paper, we are going to study the product of Finsler manifolds and give a canonical Finsler metric on it. PubDate: 2018-10-13

Abstract: This paper aims to modify Shewhart, the weighted variance and skewness correction methods in industrial statistical process control. The robust and asymmetric control limits of range chart are constructed to use in contaminated and skewed distributed process. The way of construction of control limits is simple and corresponds to three methods in which sample range estimator is replaced with the robust interquartile range. These three modified methods are evaluated in terms of their type I risks and average run length by using simulation study. The performance of the proposed range charts is assessed when the Phases I and II data are uncontaminated and contaminated. The Weibull, gamma and lognormal distributions are chosen since they can represent a wide variety of shapes from nearly symmetric to highly skewed. PubDate: 2018-10-04

Abstract: 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. PubDate: 2018-09-01

Abstract: 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. PubDate: 2018-09-01

Abstract: 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. PubDate: 2018-09-01

Abstract: In image processing, edge detection and image enhancement can make use of fractional differentiation operators, especially the Grünwald–Letnikov derivative. In this paper, we present a modified Grünwald–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. PubDate: 2018-09-01

Abstract: In this paper, we continue to study properties of skew polynomial ring \(R[x;\alpha ,\delta ]\) , where R is an associative ring equipped with an endomorphism \(\alpha\) and an \(\alpha\) -derivation \(\delta\) . We first introduce weak ( \(\alpha ,\delta\) )-skew Armendariz ideals, a generalization of ( \(\alpha ,\delta\) )-compatible ideals have the insertion of factors property (or simply, IFP). We also prove that if J is a weak ( \(\alpha ,\delta\) )-skew Armendariz ideal of R, then J[x] is a weak ( \(\alpha ,\delta\) )-skew Armendariz ideal of R[x]. PubDate: 2018-09-01

Abstract: 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 \(\hbar\) -curves are plotted to demonstrate the regions of convergence, and the residual errors are obtained for different values of theses regions. PubDate: 2018-09-01

Abstract: 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. PubDate: 2018-09-01

Abstract: 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. PubDate: 2018-09-01

Abstract: 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. PubDate: 2018-09-01

Abstract: 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. PubDate: 2018-09-01

Abstract: In this work, we applied a new method for solving the linear weakly singular mixed Volterra–Fredholm integral equations. We now begin the theoretical study with acquirement of the variational form; in addition, we are using Bernstein spectral Galerkin method to be approximate to my problems. We estimate the error of the method by proved some theorems. Moreover, in the final section, we solved some numerical examples. PubDate: 2018-06-01

Abstract: This paper introduces an approach based on hybrid operational matrix to obtain a numerical scheme to solve fractional differential equations. The idea is to convert the given equations into a system of equations, based on the block-pulse and Legendre polynomials. Also, we employ the Banach fixed-point theorem to analyze the problem on the Banach algebra C[0, b] for some fractional differential equations, which include many key functional differential equations that arise in linear and nonlinear analysis. PubDate: 2018-06-01

Abstract: Fourth-order B-spline collocation method has been applied for numerical study of Fisher’s equation which represents several important phenomena such as biological invasions, reaction diffusion in chemical processes and neutron multiplication in nuclear reactions, etc. Results are found to be better than second-order B-spline collocation method. It is observed that when time becomes sufficiently large, local initial disturbance propagates with constant limiting speed. Proposed method is satisfactorily efficient in terms of accuracy and stability. PubDate: 2018-06-01