https://www.rgnpublications.com/journals/index.php/cma/issue/feedCommunications in Mathematics and Applications2019-10-06T17:22:15+00:00Head, Editorial Sectioneditorial@rgnpublications.comOpen Journal SystemsAuthors who publish with this journal agree to the following terms:<br /><ul><li>Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.</li><li>Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.</li><li>Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.</li></ul><p><span>The journal “<strong>Communications in Mathematics and Applications”</strong></span><span> (CMA) is being regularly published since 2010. </span><span>The “</span><strong>Communications in Mathematics and Applications</strong><span>” is an international journal devoted to the publication of original and high-quality research of pure mathematics.</span></p><p><strong>Subjects covered by <strong>Communications in Mathematics and Applications</strong>: </strong></p><ul><li><strong>Algebra <br /></strong></li><li><strong>Algebraic Geometry <br /></strong></li><li><strong>Analysis <br /></strong></li><li><strong>Category Theory <br /></strong></li><li><strong>Graph Theory <br /></strong></li><li><strong>Mathematical Logic & Foundations <br /></strong></li><li><strong>Number Theory <br /></strong></li><li><strong>Philosophy of Mathematics <br /></strong></li><li><strong>Topology</strong></li></ul><p>To ensure speedy publication, only articles which are sufficiently well presented, containing significant results and not required major revisions will be considered. The papers are accepted only after peer review.</p><p>Editorial decisions on acceptance or otherwise are taken within 4 to 8 weeks (two months) of receipt of the paper.</p><p>The journal will also publish survey articles giving details of research progress made during the last three decades in a particular area.</p><p><img src="/journals/icons/cma/icore.jpg" alt="" /></p>https://www.rgnpublications.com/journals/index.php/cma/article/view/1031The Dynamics and Analysis of Stage-Structured Predator-Prey Model With Prey Refuge and Harvesting Involving Disease in Prey Population2019-10-06T17:22:15+00:00Azhar Abbas Majeedazhar_abbas_m@scbaghdad.edu.iq<p>In this paper, a mathematical model consisting of the prey-predator model with SI infectious disease in prey is proposed and analyzed. The model includes harvesting on the infected prey population, it is assume that the disease is not transmitted from prey to predator. In addition, the disease spread by contact between susceptible individuals and infected individuals, the mature predator only can predate the susceptible and infected prey which are outside refuge according to Lotka-Volterra type of functional response. While, the immature predator depends completely in it’s feeding on the mature predator. The existence, uniqueness and boundedness of the solution are discussed. The stability analysis of all possible equilibrium points is studied. Also, Lyapunove function is used to study the global dynamics of the model. Further, the effect of the disease, refuge and harvest on the dynamical of the system is discussed using numerical simulation.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1275Weighted \((k,n)\)-arcs of Type \((n-q,n)\) and Maximum Size of \((h,m)\)-arcs in \(\mathrm{PG}(2,q)\)2019-10-06T17:22:15+00:00Mustafa T. Yaseenmustafataha89@yahoo.comAli Hasan Alialiaha1@yahoo.comIbrahim A. Shananibr1507him@gmail.comIn this paper, we introduce a generalized weighted \((k, n)\)-arc of two types in the projective plane of order \(q\), where \(q\) is an odd prime number. The sided result of this work is finding the largest size of a complete \((h, m)\)-arcs in \(\mathrm{PG}(2, q)\), where \(h\) represents a point of weight zero of a weighted \((k, n)\)-arc. Also, we prove that a \(\big(\frac{q(q-1)}{2}+1, \frac{q+1}{2}\big)\)-arc is a maximal arc in \(\mathrm{PG}(2, q)\).2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1199Existence and Convergence Theorems For Best Proximity Points of Proximal Multi-Valued Nonexpansive Mappings2019-10-06T17:22:15+00:00Panitarn Sarnmetapanitarn_s@cmu.ac.thSuthep Suantaisuthep.s@cmu.ac.th<p>The concepts of proximal contraction and proximal nonexpansive mapping have been investigated and extended in many direction. However, most of these works concern only single-valued mappings. So, in this paper, we introduce a concept of proximal nonexpansive for non-self set-valued mappings and prove the existence of best proximity point for such mappings under appropriate conditions. We also provide an algorithm to approximate a best proximity point of such mappings, and prove its convergence theorem. Moreover, a numerical example supporting our main results is also given.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/650On Asymptotically \(f\)-statistical Equivalent Set Sequences in the Sense of Wijsman2019-10-06T17:22:15+00:00Şükran Koncaskonca@beu.edu.trMehmet Küçükaslanmkucukaslan@mersin.edu.tr<p>The aim of this paper is to introduce a generalization of statistical convergence of asymptotically equivalent set sequences and examine some inclusion relations related to a new concept of Wijsman asymptotically equivalent statistical convergence of sequences of sets with respect to a modulus function \(f\).</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1157Degree-Magic Labelings on the Join and Composition of Complete Tripartite Graphs2019-10-06T17:22:15+00:00Phaisatcha Inpoonjaiphaisatcha_in@outlook.com<p>A graph is called supermagic if there is a labeling of edges, where all edges are differently labeled with consecutive positive integers such that the sum of the labels of all edges, which are incident to each vertex of this graph, is a constant. <br />A graph \(G\) is called degree-magic if all edges can be labeled by integers \(1,2,\ldots ,|E(G)|\) so that the sum of the labels of the edges which are incident to any vertex \(v\) is equal to \((1+|E(G)|)\deg(v)/2\). Degree-magic graphs extend supermagic regular graphs. In this paper, the necessary and sufficient conditions for the existence of degree-magic labelings of graphs obtained by taking the join and composition of complete tripartite graphs are found.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/717Generalized Szász-Kantorovich Type Operators2019-10-06T17:22:15+00:00Arun Kajlarachitkajla47@gmail.comSerkan Araciserkan.araci@hku.edu.trMeenu Goyalmeenu.goyal700@gmail.comMehmet Acikgozacikgoz@gantep.edu.tr<p>In this note, we present Kantorovich modification of the operators introduced by V. Mihe<span>ş</span>an [<em>Creative Math. Inf.</em> <strong>17</strong> (2008), 466 – 472]. First, we derive some indispensable auxiliary results in the second section. We present a quantitative Voronovskaja type theorem, local approximation theorem by means of second order modulus of continuity and weighted approximation for these operators. Furthermore, we show the rate of convergence of these operators to certain functions with the help of the illustrations using Maple algorithms.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1299On Zagreb Indices of Two New Operations of Graphs2019-10-06T17:22:15+00:00A. Bharalia.bharali@dibru.ac.inJ. Buragohainj.bgohain75@yahoo.comA. Mahantaam02dib@gmail.com<p>Recently, Wang et al. (2017) introduced two new operations of graphs. In this paper we establish explicit expressions of some Zagreb indices viz. first Zagreb index, second Zagreb index and forgotten topological index of these two newly proposed operations of graphs. Then as an application we further establish explicit formulae of some other topological indices of the two operations of graphs.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/902Split Jacobsthal and Jacobsthal-Lucas Quaternions2019-10-06T17:22:15+00:00Tülay Yağmurtulayyagmur@aksaray.edu.tr<p>In this paper, we introduce split Jacobsthal and split Jacobsthal-Lucas quaternions. We obtain generating functions and Binet’s formulas for these quaternions. We also investigate some properties of them.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/603On Generalized Absolute Matrix Summability of Infinite Series2019-10-06T17:22:15+00:00Hikmet S. Özarslanseyhan@erciyes.edu.trAhmet Karakaşahmetkarakas1985@hotmail.comIn this paper, we have generalized a known theorem on \(|\bar{N},p_n|_{k}\) summability factors of infinite series with a new summability method by using almost increasing sequences. This new theorem also includes several new and known results.2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1100Gaussian Quadrature for Two-Point Singularly Perturbed Boundary Value Problems with Exponential Fitting2019-10-06T17:22:15+00:00K. Phaneendrakollojuphaneendra@yahoo.co.inM. Lalulalunaikmudavathou@gmail.com<p>In this paper, the Gaussian quadrature method with exponential fitting is proposed for the solution of two-point singularly perturbed boundary value problems with layer at one endpoint, dual boundary layers and internal boundary layers. The given boundary value problem is reduced into an equivalent first order differential equation with the perturbation parameter as deviating argument. Then, Gaussian two-point quadrature technique with exponential fitting is implemented to solve the first order equation with deviating parameter. The analysis of the convergence of the method is discussed. Several numerical examples are illustrated with a layer at one end, a layer at two ends and internal layers. Comparison of maximum errors in the solution of the examples with other methods is shown to justify the method.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1106A New Generalization of Pell-Lucas Numbers (Bi-Periodic Pell-Lucas Sequence)2019-10-06T17:22:15+00:00Sukran Uygunsuygun@gantep.edu.trHasan Karatashasan_karatas@dicle.edu.tr<p>In this study, we bring into light, a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as<br />\begin{align*}<br />Q_{n}=<br />\begin{cases}<br />2bQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is even} \\<br />2aQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is odd}%<br />\end{cases} \text{\ \ }n\geq 2,<br />\end{align*}<br />with initial conditions \(Q_{0}=2\), \(Q_{1}=a\). The Binet formula as well as the generating function for this sequence are given. The convergence<br />properties of the consecutive terms of this sequence are also examined after which the well known Cassini, Catalans and the D'Ocagne's identities as well as some related summation formulas are also given.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1068A New Approach to Operations on Neutrosophic Soft Sets and to Neutrosophic Soft Topological Spaces2019-10-06T17:22:15+00:00Taha Yasin Ozturktaha36100@kafkas.edu.trCigdem Gunduz Arascaras@kocaeli.edu.trSadi Bayramovbaysadi@gmail.com<p>In this study, we re-define some operations on neutrosophic soft sets differently from the studies [3, 9]. On this operations are given interesting examples and them basic properties. In the direction of these newly defined operations, we construct the neutrosophic soft topological spaces differently from the study [3]. Finally, we introduce basic definitions and theorems on neutrosophic soft topological spaces.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1116A New Combination of Lagrangean Relaxation, Dantzig-Wolfe Decomposition and Benders Decomposition Methods for Exact Solution of the Mixed Integer Programming Problems2019-10-06T17:22:15+00:00Hadi Mohammadih_mohammadi_z@aut.ac.irEsmaile Khorramesmaile.khorram@iran.ir<p>The combinational technique of cross decomposition is a suitable one for exact solution of the mixed integer programming problems which uses simultaneously the advantages of Lagrangean relaxation, Dantzig-Wolfe decomposition and Benders decomposition methods for Minimization problem that each reinforces one another. The basic idea for this technique is the generation of suitable upper and lower bounds for the optimal value of the original problem at each iteration. In this paper, new cross decomposition algorithm, with the combination of Lagrangean relaxation method (the combination of three concepts of cutting-plane, sub-gradient and trust region), Dantzig-Wolfe decomposition and Benders decomposition methods are used in order to reinforce bounds and to speed up convergence. By increasing the problem scale and regarding the use of the Lagrangean relaxation method in this technique, the lower bound with more strength and efficacy, and by the aid of Dantzig-Wolfe decomposition method more suitable upper bound (if exists) and furthermore less number of iterations for achieving optimal solution is obtained. The convergence of this technique regarding the convergence of Benders decomposition method in finite iteration numbers is guaranteed.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1220Morphisms Between Grassmannian Complex and Higher Order Tangent Complex2019-10-06T17:22:15+00:00Sadaqat Hussainsadaqatku@gmail.comRaziuddin Siddiquirsiddiqui@iba.edu.pk<p>In this article we extend the notion of tangent complex to higher order and propose morphisms between Grassmannian subcomplex and the tangent dialogarithmic complex for a general order. Moreover, we connect both these complexes and prove the commutativity of resulting diagram. The interesting point is the reappearance of classical Newton’s Identities here in a completely different context to the one he had.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1203Semi Unit Graphs of Commutative Semi Rings2019-10-06T17:22:15+00:00Yaqoub Ahmedyaqoubahmedkhan@gmail.comM. Aslamaslam298@gcu.edu.pkIn this article, we introduce semi unit graph of semiring \(S\) denoted by \(\xi(S)\). The set of all elements of $S$ are vertices of this graph where distinct vertices \(x\) and \(y\) are adjacent if and only if \(x+y\) is a semiunit of \(S\). We investigate some of the properties and characterization results on connectedness, distance, diameter, girth, completeness and connectivity of \(\xi(S)\).2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1227Hölder Type Inequalities Involving Tracy-Singh Products and Khatri-Rao Products of Hilbert Space Operators2019-10-06T17:22:15+00:00Arnon Ploymukdaarnon.p.math@gmail.comPattrawut Chansangiampattrawut.ch@kmitl.ac.th<p>This paper generalizes the famous Hölder type inequalities for positive real numbers to positive operators on an arbitrary complex Hilbert space. We use appropriate integral representations of certain operator-monotone functions to deduce the concavity and convexity of certain maps involving Tracy-Singh products of operators. These results lead to Hölder type inequalities for operators concerning Tracy-Singh products, Khatri-Rao products, Tracy-Singh sums, and Khatri-Rao sums. In particular, we obtain Cauchy-Schwarz type inequalities for operators involving Tracy-Singh products and Khatri-Rao products.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1269A Deep One-Pass Learning based on Pre-Training Weights for Smartphone-Based Recognition of Human Activities and Postural Transitions2019-10-06T17:22:15+00:00Setthanun Thongsuwantsetthanun@gmail.comPraveen Agarwalgoyal.praveen2011@gmail.comSaichon Jaiyensaichon.ja@kmitl.ac.th<p>We describe a new deep learning model – <em>Deep One-Pass Learning</em> (DOPL) for Smartphone-Based Recognition of Human Activities and Postural Transitions based on the Pre-Trained Weights, DOPL consists of several stacked convolutional layers to learn the features of the input and is able to learn features automatically, followed by the Extreme gradient boosting (XGBoost) as the last layer for predicting the class labels. DOPL is much faster in the training phase, because the input weights are optimal weights from the Pre-Trained weights module and it does not have to re-adjust weights repeatedly. Further, we replaced the final fully connected layer with XGBoost to increase predictive efficiency. In the worst case, our model with demonstrated an accuracy of 99.2% for the smartphone sensors database data, which was significantly better than CNN or XGBoost alone as well as several other models assessed.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1200Bounds for Toader Mean in Terms of Arithmetic and Second Seiffert Means2019-10-06T17:22:15+00:00Zai-Yin Hehzy830430@hnu.edu.comYue-Ping Jiangypjiang@hnu.edu.cnYu-Ming Chuchuyuming2005@126.com<p>In the article, we prove that the double inequalities<br />\begin{align*}<br />&\alpha_{1}T(a,b)+(1-\alpha_{1})A(a,b)<TD(a,b)<\beta_{1}T(a,b)+(1-\beta_{1})A(a,b),\\<br />&T^{\alpha_{2}}(a,b)A^{1-\alpha_{2}}(a,b)<TD(a,b)<T^{\beta_{2}}(a,b)A^{1-\beta_{2}}(a,b)<br />\end{align*}<br />hold for all \(a,b>0\) with \(a\neq b\) if and only if \(\alpha_{1}\leq<br />3/4\), \(\beta_{1}\geq1\), \(\alpha_{2}\leq 3/4\) and \(\beta_{2}\geq 1\),<br />where \(A(a,b)\), \(TD(a,b)\) and \(T(a,b)\) are the arithmetic, Toader and second Seiffert means of \(a\) and \(b\), respectively.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1154A Mathematical Analysis and Modelling of Hepatitis B Model with Non-Integer Time Fractional Derivative2019-10-06T17:22:15+00:00Muhammad Farmanfarmanlink@gmail.comAqeel Ahmadaqeelahmad.740@gmail.comM. Umer Saleemumerlinks@ue.edu.pkAmina Hafeezaminahafeez82@gmail.com<p>In this paper, we develop time fractional Hepatitis B model and analyze qualitatively. The Caputo fractional derivative operator of order \(\alpha\in (0,1]\) is employed to obtain the system of fractional differential equations. The stability and sensitivity analysis of fractional order model has been made and verify the non-negative unique solution. LADM was successfully used for solving different problems. Laplace transform method is a useful technique in different field of biological science, engineering and applied mathematics. The latest technique (LADM) is employed on the developed fractional order model for numerical solutions. Finally, numerical simulations are also established to investigate the influence of the system parameter on the spread of the disease and which show the effect of fractional parameter \(\alpha\) on our obtained solutions.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/626A New Approach for the Solution of Space-Time Fractional Order Heat-Like Partial Differential Equations by Residual Power Series Method2019-10-06T17:22:15+00:00Ali Demirademir@kocaeli.edu.trMine Aylin Bayrakaylin@kocaeli.edu.tr<p>The main concern of this article has been to apply the <em>Residual Power Series Method</em> (RPSM) effectively to find the exact solutions of fractional-order space-time dependent nonhomogeneous partial differential equations in the Caputo sense. Our first step is to reduce fractional-order space-time dependent non-homogeneous partial differential equations to fractional-order space-time dependent homogeneous partial differential equations before applying the proposed method. Obtaining fractional power series solutions of the problem and reproducing the exact solution is the main step. The illustrative examples reveal that RPSM is a very significant and powerful method for obtaining the solution of any-order time-space fractional non-homogeneous partial differential equations in the form of fractional power series.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1190Two Classes of Integrals Involving Extended Wright Type Generalized Hypergeometric Function2019-10-06T17:22:15+00:00A. Ghaffarabdulghaffar.jaffar@gmail.comA. Saifayesha.saif@buitms.edu.pkM. Iqbalimudassar03@gmail.comM. Rizwanrizwanbsm@gmail.com<p>In this article, our main purpose is to investigate generalized integral formulas containing the extended Wright type generalized hypergeometric function. Moreover, certain special cases of the main results given here have also been pointed out for the Wright type hypergeometric function.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1219Homogeneous Sagbi Bases Under Polynomial Composition2019-10-06T17:22:15+00:00Nazish Kanwalnkanwal@iba.edu.pk<p>The process of replacing indeterminates in a Polynomial with other polynomials is the polynomial composition. Homogeneous Sagbi bases are the Sagbi bases generated by the subset of homogeneous polynomials. In this article we present adequate and essential criterion on a set of polynomials to guarantee that the composed set \(S\circ \ominus\) is Homogeneous Sagbi basis whenever \(S\) is a Homogeneous Sagbi basis.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/916Embankment Surfaces in Euclidean 3-Space and Their Visualizations2019-10-06T17:22:15+00:00Ahmet Kazanahmet.kazan@inonu.edu.trH. Bayram Karadağbayram.karadag@inonu.edu.tr<p>In the present paper, we obtain the parametric representation of an embankment surface and give an example for it. We define the notions of embankmentlike surfaces and tubembankmentlike surfaces. Furthermore, we create some embankmentlike and tubembankmentlike surface examples with the aid of different directrix and draw these directrix and surfaces. Also, we find the Gaussian, mean and second Gaussian curvatures of these surfaces and draw the Gaussian, mean and second Gaussian curvature functions’ graphics and the variations of Gaussian, mean and second Gaussian curvatures on related surfaces with the aid of Mathematica.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1218Lower Bounds for Gas Turbines Aircraft Engines2019-10-06T17:22:15+00:00Mahdi Jemmalimah_jem_2004@yahoo.frLoai Kayed Bani Melhiml.banimelhim@mu.edu.saSayer Obaid B. Alharbil.banimelhim@mu.edu.saAbdullah Saeed Bajahzarl.banimelhim@mu.edu.sa<p>Turbine maintenance process is performed periodically at predefined time slots to replace certain turbine parts by new or refurbished parts. The developed heuristics will address the scheduling of turbine maintenance problem to maximize crafts operation time. Scheduling is based on the life span of the replaced parts. Mathematical modeling for the lower bounds of the aircraft turbine maintenance problem will be presented to achieve the desired goal. this study is based on three heuristic categories, the randomized lower bounds, the utilization of the iterative methods solving the subset sum problems and the repeating of the resolution of the knapsack problems.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1221Binomial Transform of the Generalized \(k\)-Fibonacci Numbers2019-10-06T17:22:15+00:00Sergio Falcónsergio.falcon@ulpgc.es<p>We recall the concept and some properties of the generalized \(k\)-Fibonacci numbers and then apply the binomial transform to these sequences. As consequence, we obtain new integer sequences related to the generalized \(k\)-Fibonacci numbers. Finally, we find the recurrence relation of these new sequences and the formulas for their sums.</p>2019-09-30T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1238Approximate Solutions for the Projects Revenues Assignment Problem2019-10-06T17:22:15+00:00Mahdi Jemmalim.jemmali@mu.edu.sa<p>The aim of this research work is to find algorithms solving an NP-hard problem by elaborating several heuristics. This problem is to find an appropriate schedule to assign different projects, which will be expected to generate fixed revenues, to several cities. For this work, we assume that all cities have the same socio-economic and strategic characteristics. The problem is as follow. Given a set of projects which represented by its expected revenues. The objective is to distribute on several cities all projects with a minimum expected revenues gap between cities. Thus, our objective is to minimize the expected revenue gap. The suitable assignment is searching equity between cities. In this paper, we formulate mathematically the studied problem to find an approximate solutions and apply some methods to search resolution of the studied problem.</p>2019-09-30T00:00:00+00:00