http://www.rgnpublications.com/journals/index.php/cma/issue/feedCommunications in Mathematics and Applications2019-02-20T12:15:36+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. Papers are accepted only after peer review.</p><p>Editorial decisions on acceptance or otherwise are taken within 4 to 12 weeks (three 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>http://www.rgnpublications.com/journals/index.php/cma/article/view/547Geometric Means and Tracy-Singh Products for Positive Operators2019-02-20T12:04:00+00:00Arnon Ploymukdaarnon.p.math@gmail.comPattrawut Chansangiampattrawut.ch@kmitl.ac.thWe investigate relationship between metric/spectral/Sagae-Tanabe geometric means for several positive operators and Tracy-Singh products in terms of identities and inequalities. In particular, we obtain various generalizations of arithmetic-geometric-harmonic means inequality and its reverse. Moreover, we introduce the weighted Sagae-Tanabe spectral geometric mean for several positive operators and deduce its properties related to Tracy-Singh products.2018-09-26T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/591Properties of Some Dynamic Partial Integrodifferential Equations on Time Scales2019-02-20T12:04:00+00:00Deepak B. Pachpattepachpatte@gmail.com<p>The main objective of this paper is to study some properties of new dynamic equations partial integrodifferential equations in two independent variables on time scales. The tools used in obtaining our results are application of Banach Fixed point theorem. We also used dynamic inequality with explicit estimates to study the properties of solution of dynamic partial integrodifferential equation.</p>2018-09-26T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/835A Subdivision Approach to the Approximate Solution of 3rd Order Boundary Value Problem2019-02-20T12:04:00+00:00S. A. Manansakinakakar@rocketmail.comA. Ghaffarabdulghaffar.jaffar@gmail.comM. Rizwanrizwanbsm@gmail.comG. Rahmangauhar55uom@gmail.comG. Kanwalvirgostar086@gmail.comAn algorithm to solve 3rd order boundary value problem is focused in this paper which is 8-point approximating scheme. It concludes the results with stability and convergence that is evaluated with the illustration of numerical example. This paper also contains the analysis of approximation properties for the mentioned collocation algorithm.2018-09-26T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/882Solutions of Integral Nonclassical Ordinary Differential Equations Via Contractor Maps2019-02-20T12:04:00+00:00S. A. Bishopsheila.bishop@covenantuniversity.edu.ngK. S. Ekestella.eke@covenantuniversity.edu.ngH. Akewehudson.akewe@covenantuniversity.edu.ngG. Okekega.okeke@mouau.edu.ng<p>Existence of a unique and bounded stochastic solution of integral nonclassical ordinary differential equation is studied using the method of integral contractor operators.</p>2018-09-26T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/918On the Solution of Stochastic Generalized Burgers Equation2019-02-20T12:04:00+00:00Nidal Dailinourdaili_dz@yahoo.frAmar Guesmiaguesmiasaid@yahoo.frNoureddine Dibdib_nidal@yahoo.comWe are interested in one dimensional nonlinear stochastic partial differential equation: the generalized Burgers equation with homogeneous Dirichlet boundary conditions, perturbed by additive space-time white noise. We propose a result of existence and uniqueness of the local solution to the viscous equation using fixed point argument, then if we impose a condition to the viscosity coefficient we can prove that this solution is global.2018-09-26T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/1096Refinements and Reverses of Operator Callebaut Inequality Involving Tracy-Singh Products and Khatri-Rao Products2019-02-20T12:04:00+00:00Arnon Ploymukdaarnon.p.math@gmail.comPattrawut Chansangiampattrawut.ch@kmitl.ac.thIn this paper, we establish certain refinements and reverses of Callebaut-type inequality for bounded continuous fields of Hilbert space operators, parametrized by a locally compact Hausdorff space equipped with a finite Radon measure. These inequalities involve Tracy-Singh products, Khatri-Rao products and weighted geometric means. In addition, we obtain integral Callebauttype inequalities for tensor products and Hadamard products. Our results extend Callebaut-type inequalities for real numbers, matrices and operators.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/1105The Dynamical System for System of Variational Inequality Problem in Hilbert Spaces2019-02-20T12:04:00+00:00Jittiporn Tangkhawiwetkulj_suwannawit@psru.ac.thNarin Petrotnarinp@nu.ac.thIn this paper, we will present a dynamical system which relates to the system of variational inequality problem by starting with introducing a Wiener-Hopf equation for the system of variational inequality problem and using a such Wiener-Hopf equation for proposing a dynamical system for the system of variational inequality problem. Moreover, the existence solution of such dynamical system is considered and the stability, globally asymptotically stable and also globally exponential convergence, of the solution for the system of a such dynamical system are proved. The results in this paper improve and extend the variational inequality problems which have been appeared in literature.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/1108Logarithmically Complete Monotonicity of Certain Ratios Involving the \(k\)-Gamma Function2019-02-20T12:04:00+00:00Kwara Nantomahknantomah@uds.edu.ghLi Yinyinli_79@163.com<p>In this paper, we prove logarithmically complete monotonicity properties of certain ratios of the \(k\)-gamma function. As a consequence, we deduce some inequalities involving the \(k\)-gamma function and the \(k\)-trigamma function.</p>2019-02-16T11:40:39+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/460A Study on The Quadratic Jaco Graph2019-02-20T12:04:00+00:00R. Jayasreesree.ramachandran14@gmail.comA. Kulandai Thereseinfanta1960@gmail.comU. Marymarycbe@gmail.comJohan Kokkokkiek2@tshwane.gov.zaIn this paper we introduce the quadratic Jaco graph. The characteristics, properties and some graph invariants of quadratic Jaco graphs are also discussed. The observation that quadratic Jaco graphs are well-structured in respect of complete graphs and bridges led to the notion of braided complete graphs.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/1036Some Fixed Point Theorems in C-complete Complex Valued Metric Spaces2019-02-20T12:04:00+00:00Anil Kumar Duneyanilkumardby70@GMAIL.COMShweta Bibayshweta.bibay90@gmail.comRavi Prakash Dubeyravidubey_1963@yahoo.co.inMithilesh Deo Pandeymithileshpandey1978@gmail.comIn this paper, we prove common fixed point theorems for a pair of mappings satisfying rational inequality in C-complete complex valued metric spaces. The results of this paper generalize and extend the known results in C-complete complex valued metric spaces.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/655Trend of Rainfall Indices at Kg. Kedaik Station, Pahang2019-02-20T12:04:00+00:00A.H. Syafrinasyafrinahalim@gmail.comK. Badronkhairayu@iium.edu.myA. Norzaidazaida.kl@utm.myMalaysia has been constantly facing massive floods caused by excessive weather events during monsoon and inter-monsoon seasons. Major concerns on the consequences of flood include structural and erosional damage, loss of life and property and disruption of socio-economic activities. Mitigation efforts require proper planning, relying on credible quantification of such changes. The eastern part of Peninsular Malaysia is frequently affected by severe floods especially during north east monsoon season. Affected area includes Pahang state which is located in the middle and more towards the eastern part of Peninsular Malaysia. As such, this study examine the trend of rainfall indices to have a better understanding on rainfall distribution within the area. In particular, the performance of Gamma and Weibull distributions incorporated in Neyman Scott Rectangular Pulse model in reproducing rainfall indices was assessed at Kg. Kedaik station in Pahang. The trends of indices based on thirty years data were calculated and analysed using non-parametric, Mann Kendall test. Performance of both probability distributions was compared using Root Mean Square Error criteria. Results suggest that Gamma is the better distribution in reproducing the hourly rainfall series for Kg. Kedaik station. Further analysis indicate Gamma able to replicate the key rainfall characteristics such as the total amount of rainfall, mean rainfall amount on wet days or rainfall intensity, including the extreme indices; frequency of wet days exceeding the 95th percentile and rainfall intensity exceeding the 95th percentile. Meanwhile, the calculated trend in this study is consistent with previous studies, indicating the presence of positive trend at Kg. Kedaik station.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/844Approximate Solution of Multi-Pantograph Equations With Variable Coefficients via Collocation Method Based on Hermite Polynomials2019-02-20T12:04:00+00:00Dianchen Ludclu@ujs.edu.cnChen Yuanchenyuanjs@163.comRabia Mehdisyedxamehdi@gmail.comShamoona Jabeenshamoonaafzal@yahoo.comAbdur Rashidprof.rashid@yahoo.comThis research article presents an approximate solution of the non-homogenous Multi-Pantograph equation comprising of variable coefficients by utilizing a collocation method based on Hermite polynomials. These orthogonal polynomials along with its collocation points transform the equation and the initial conditions into matrix equation comprising of a system of linear algebraic equations. Subsequently, by solving this system, the unknown Hermite coefficients are calculated. To reveal the accuracy and efficiency of the method applied, the approximate results obtained by this technique have been compared with exact solutions. Moreover, some numerical illustrations in the form of examples are given to exhibit the applicability of the proposed technique.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/968On the Oscillation Criteria and Computation of Third Order Oscillatory Differential Equations2019-02-20T12:04:00+00:00J. Sundaysunday578@adsu.edu.ng<p>One of the sets of differential equations that find applications in real life is the oscillatory problems. In this paper, the oscillation criteria and computation of third order oscillatory differential equations are studied. The conditions for a third order differential equation to have oscillatory solutions on the interval \(I=[t_0,\infty)\) shall be analyzed. Further, a highly efficient and reliable one-step computational method (with three partitions) is formulated for the approximation of third order differential equations. The paper also analyzed the basic properties of the method so formulated. The results obtained on the application of the method on some sampled modeled third order oscillatory problems show that the method is computationally reliable and the method performed better than the ones with which we compared our results.</p>2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/669On F-\(\alpha\)-Geraghty Contractions2019-02-20T12:04:00+00:00Jiraporn Janwisedaejunwised@gmail.comDuangkamon Kitkuanor_duangkamon@hotmail.comPheerachate Bunpatcharacharoenor_duangkamon@hotmail.comIn this paper, we introduce the notion of F-\(\alpha\)-Geraghty contraction type mappings and establish some common fixed point theorems for an admissible pair mappings under the notion of F-\(\alpha\)-Geraghty contractive type in the setting of metric spaces. We give example for support results.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/942Solving Nonlinear Integro-Differential Equations Using the Combined Homotopy Analysis Transform Method With Adomian Polynomials2019-02-20T12:04:00+00:00Nahid Khanlarinahid_1351_kh@yahoo.comMahmoud Paripourmahmoud.paripour@iran.irIn this paper, we propose a reliable combination of the homotopy analysis method (HAM) and laplace transform-Adomian method to find the analytic approximate solution for nonlinear integro-differential equations. In this technique, the nonlinear term is replaced by its Adomian polynomials for the index \(k\), and hence the dependent variable components are replaced in the recurrence relation by their corresponding homotopy analysis transforms components of the same index. Thus, the nonlinear integro-differential equation can be easily solved with less computational work for any analytic nonlinearity due to the properties and available algorithms of the Adomian polynomials. The results show that the method is very simple and effective.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/838Some Infinite Sums Related to the \(k\)-Fibonacci Numbers2019-02-20T12:04:00+00:00Onur Karaoğluokaraoglu@selcuk.edu.trKemal Uslukuslu@selcuk.edu.tr<p>In this study, some infinite sums related to the \(k\)-Fibonacci numbers have been obtained by using in nite sums related to classic Fibonacci numbers in literature.</p>2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/879A Note on the Generalized Solutions of the Third-order Cauchy-Euler Equations2019-02-20T12:04:00+00:00Nutgamol Sacornnutgamolsacorn@outlook.comKamsing Nonlaoponnkamsi@kku.ac.thHwajoon Kimcellmath@gmail.comIn this paper, we propose the generalized solutions of the third order Cauchy-Euler equations $$at^3y'''(t) + bt^2y''(t) + cty'(t) + dy(t)=0,$$ where \(a, b, c\) and \(d\) are real constants with \(a \neq 0\) and \(t\in\mathbb{R}\) using Laplace transform technique. We find that the types of solutions depend on the conditions of the values of \(a, b, c\) and \(d\). Precisely, we obtain a distributional solution if \((k^3 + 3k^2 + 2k)a - (k^2 + k)b + kc - d = 0\), for all \(k \in \mathbb{N}\) and a weak solution if \((k^3 - 3k^2 + 2k)a + (k^2 - k)b + kc + d = 0\), for all \(k \in \mathbb{N}\cup\{0\}\). Our work improves the result of \(A\). Kananthai [Distribution solutions of the third order Euler equation, <em>Southeast Asian Bull. Math.</em> <strong>23</strong> (1999), 627-631].2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/874SO\((3,\mathbb{C})\) Representation and Action on a Homogeneous Space in \(\mathbb{C}^3\)2019-02-20T12:04:00+00:00Emilija Celakoskaemilija.celakoska@mf.edu.mkVesna Celakoska-Jordanovavesnacj@pmf.ukim.mkDushan Chakmakovdushan.chakmakov@mf.edu.mkWe consider a homogeneous manifold \(\mathcal{H}\) embedded in \(\mathbb{C}^3\) composed of complex vectors with constraints, potentially representing space of complex velocities. The imposed constraints include orthogonality between the real and the imaginary parts of vectors which together with the non-conjugate scalar product provide real vector magnitudes. The corresponding representation of the group SO\((3,\mathbb{C})\) acting on \(\mathcal{H}\) which is in agreement to the polar decomposition of complex orthogonal matrices is also discussed.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/972Strongly Solid Varieties in Many-Sorted Algebras2019-02-20T12:04:00+00:00Sorasak Leeratanavaleesorasak.l@cmu.ac.thDawan Chumpungamdawan_c@cmu.ac.thIn this paper, we apply the general theory of conjugate pairs of additive closure operators to characterized the strongly solid variety which is extended from one-sorted algebras to many-sorted algebras. Moreover, we give the concept of V-normal form which is useful for testing the strongly solid variety in many-sorted algebra.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/901Commutativity and Commutative Pairs of Some Differential Equations2019-02-20T12:04:00+00:00Mehmet Emir Koksalemirkoksal@gmail.comIn this study, explicit differential equations representing commutative pairs of some well-known second-order linear time-varying systems have been derived. The commutativity of these systems are investigated by considering 30 second-order linear differential equations with variable coefficients. It is shown that the system modeled by each one of these equations has a commutative pair with(or without) some conditions or not. There appear special cases such that both, only one or neither of the original system and its commutative pair has explicit analytic solution. Some benefits of commutativity have already been mentioned in the literature but a new application in cryptology for obscuring transmitted signals in telecommunication is illustrated in this paper.2018-12-28T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/1044Properties of a Composition of Exponential and Ordinary Generating Functions2019-02-20T12:04:00+00:00Dmitry V. Kruchininkruchinindm@gmail.comYuriy V. Shablyashablya-yv@mail.ruVladimir V. Kruchininkru@2i.tusur.ruAlexander A. Shelupanovsaa@keva.tusur.ruIn this paper, we consider the composition of ordinary and exponential generating functions. The obtained property of the composition of ordinary and exponential generating functions can be used for distinguishing prime numbers from composite numbers. For example, it can be applied for constructing new probabilistic primality criteria. Using the obtain property, we get several congruence relations for the Uppuluri-Carpenter, Euler, and Fubini numbers.2018-12-25T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/975A Study on Soft S-Metric Spaces2019-02-20T12:04:00+00:00Cigdem Gunduz Arascarasgunduz@gmail.comSadi Bayramovbaysadi@gmail.comVefa Cafarliceferli_vefa@mail.ru<p>The first aim of this paper is to define soft S-metric space and examine some of its properties. Later we define the concepts of soft continuous mapping, soft sequential continuous and investigate the relationship between them.</p>2018-12-28T00:00:00+00:00http://www.rgnpublications.com/journals/index.php/cma/article/view/1047Fixed Point Theorems on Soft \(S\)-Metric Spaces2019-02-20T12:15:36+00:00Cigdem Gunduz Arascarasgunduz@gmail.comSadi Bayramovbaysadi@gmail.comVefa Cafarliceferli_vefa@mail.ru<p>The first aim to this paper is to define soft \(S\)-metric spaces and to investigate some important properties. In addition to, we prove some fixed point theorems of soft contractive mappings on soft \(S\)-metric spaces.</p>2018-12-28T00:00:00+00:00