https://www.rgnpublications.com/journals/index.php/cma/issue/feedCommunications in Mathematics and Applications2020-01-18T10:03:14+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/1256On Ternary Monoid of All Hypersubstitutions of Type \(\tau=(2)\)2020-01-18T10:03:13+00:00Nagornchat Chansuriyanagornchat.c@sciee.kmutnb.ac.thSorasak Leeratanavaleesorasak.l@cmu.ac.th<p>The present paper gives the concept of a ternary monoid \(\mathit{Hyp}(2)\) and studies some algebraic-structural properties of this monoid. We consider some submonoids of \(\mathit{Hyp}(2)\) and study the relationship between these submonoids.</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/804Gaussian Pell-Lucas Polynomials2020-01-18T10:03:13+00:00Tülay Yağmurtulayyagmurr@gmail.com<p>In this paper, we first define the Gaussian Pell-Lucas polynomial sequence. We then obtain Binet formula, generating function and determinantal representation of this sequence. Also, some properties of the Gaussian Pell-Lucas polynomials are investigated.</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1129Numerical Solution of Singularly Perturbed Differential-Difference Equations using Multiple Fitting Factors2020-01-18T10:03:13+00:00M. Adilaxmimadireddyadilaxmi@gmail.comD. Bhargavibhargavi@nitw.ac.inK. Phaneendrakollojuphaneendra@yahoo.co.in<p>In this paper, a numerical scheme is proposed to solve singularly perturbed differentialdifference equations with boundary layer behaviour using two fitting factor inserted at convective and diffusion terms. The singularly perturbed differential difference equation is replaced by an equivalent two point singularly perturbation problem. Then to handle the boundary layer, a two parameter fitted scheme is derived and it is applied to get the accurate solution. Model examples are solved using this approach and numerical results along with graphical representation are shown to support the method.</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1210Generalization of Favard’s and Berwald’s Inequalities for Strongly Convex Functions2020-01-18T10:03:13+00:00Muhammad Adil Khanadilswati@gmail.comSyed Zaheer Ullahzaheerullah65@gmail.comYuming Chuchuyuming2005@126.com<p>In this paper, we give generalization of discrete weighted Favard’s and Berwald’s inequalities for strongly convex functions. The obtained results are the improvement and generalization of the earlier results.</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1266Digital Volume Pulse Analysis to Differentiate Diabetic From Non-Diabetic Subjects2020-01-18T10:03:13+00:00Yousef Qawqzehy.qawqzeh@mu.edu.saThis paper aims to examine the validity of digital volume pulse waveform index namely the <em>diastolic pulse peak</em> (Dpp) in the evaluation of type II diabetics. In total, 153 participants (115 healthy participants and 48 diabetics type II patients) are recruited during the study. A customized algorithm for DVP waveform analysis is developed in MATLAB to analyze and calculate Dpp and b/a indices. The b/a index is found to be negatively correlated with both age and HbA1C test (\(r=-83.8\) and \(r=-66.7\), respectively), while Dpp index is found to be positively correlated with age and HbA1C test (\(r=65.7\) and \(r= 63.3\), respectively). The DVP's Dpp index showed strong association with age and HbA1C test since it remains statistically significant based on the analysis of multi-linear regression. The model revealed that b/a, age, and Dpp contribute by 71.9\% of the variance in HbA1C test. The findings showed that age, b/a, and Dpp indices are promising factors in diabetes type II assessment. These findings expand the potential utility of DVP signal in clinical settings.2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1172Mathematical Modeling and Stability Analysis of a SIRV Epidemic Model with Non-linear Force of Infection and Treatment2020-01-18T10:03:13+00:00M. O. Okefemioke91@gmail.comO. M. Ogunmilorooluwatayo.ogunmiloro@eksu.edu.ngC. T. Akinwumicalebakinwumi@gmail.comR. A. Rajiadekunleraji2@gmail.comThis paper considers the <em>Susceptible-Infected-Vaccinated-Recovered</em> (<em>SIRV</em>) deterministic model with a non linear force of infection and treatment, where individual humans that are vaccinated losses their vaccination after some time and become vulnerable to infections. The basic reproduction number \(R_0\) obtained from the model system is an epidemic threshold that determines if a disease will continue to ravage the human population or not.\ The model state equations considered in this paper possess two steady-state solutions such that if \(R_0<1\), the infection-absent steady-state solutions are locally and globally asymptotically stable. Also, if \(R_0>1\), a unique infection-persistent steady-state solutions are established, which is also locally and globally asymptotically stable. Thus, it leads to the persistence of infections in the human host population. Finally, numerical simulations were carried out to validate our theoretical results.2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1250The Analysis of Bifurcation Solutions by Angular Singularities2020-01-18T10:03:13+00:00Hussein K. Kadhimkhashanhussein@gmail.comMudhir A. Abdul Hussainmud_abd@yahoo.com<p>This paper studies a nonlinear wave equation’s bifurcation solutions of elastic beams situated on elastic bases with small perturbation by using the local method of Lyapunov-Schmidt. We have found the Key function corresponding to the functional related to this equation. The bifurcation analysis of this function has been investigated by the angular singularities. We have found the parametric equation of the bifurcation set (caustic) with the geometric description of this caustic. Also, the critical points’ bifurcation spreading has been found.</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1248The Domination Number of a Graph \(P_k ((k_1, k_2), (k_3, k_4))\)2020-01-18T10:03:13+00:00Monthiya Ruangnairuangnai.m@gmail.comSayan Panmapanmayan@yahoo.com<p>For each \(k, k_1, k_2, k_3, k_4 \in \mathbb{N}\), we will denote by \(P_k \big((k_1, k_2), (k_3, k_4)\big)\) a tree of \(k+k_1+k_2+k_3+k_4+1\) vertices with the degree sequence \((1,1,1,1,2,2,2,\dots,2,3,3)\). Let \(\alpha_{k_1}, \beta_{k_2}, \sigma_{k_3}\), and \(\delta_{k_4}\) be all four endpoints of the graph. Let the distance between both vertices of degree 3 be equal to \(k\). A subset \(S\) of vertices of a graph \(P_k \big((k_1, k_2), (k_3, k_4)\big)\) is a dominating set of \(P_k \big((k_1, k_2), (k_3, k_4)\big)\) if every vertex in \(V\big(P_k \big((k_1, k_2), (k_3, k_4)\big)\big)-S\) is adjacent to some vertex in \(S\). We investigate the dominating set of minimum cardinality of a graph \(P_k \big((k_1, k_2), (k_3, k_4)\big)\) to obtain the domination number of this graph. Finally, we determine an upper bound on the domination number of a graph \(P_k \big((k_1, k_2), (k_3, k_4)\big)\).</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1286Oscillation Theorems for Certain Forced Nonlinear Discrete Fractional Order Equations2020-01-18T10:03:13+00:00George E. Chatzarakisgeaxatz@otenet.grA. George Maria Selvamagmshc@gmail.comR. Janagarajjanagarajtk@gmail.comMaria Doukamaira_athens@hotmail.com<p>The main objective of this work is to obtain some new sufficient conditions that are essential for the oscillation of the solutions of forced nonlinear discrete fractional equations of the form <br />\begin{align*}<br />\Delta\left[\Delta^\mu(u(j))\right]+\eta(j)\Phi(u(j))=\psi(j), \ \ j\in N_0<br />\end{align*}<br />where \(\Delta^{\mu-1}u(0)=u_0\); \(\Delta u(j)=u(j+1)-u(j)\) and \(\Delta^\mu\) is defined as the difference operator of the Riemann-Liouville (R-L) derivative of order \(\mu\in(0,1]\) and \(N_0=\{0,1,2,\cdots\}\). Numerical examples are presented to show the validity of the theoretical results.</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1233New Inequalities for Nielsen’s Beta Function2020-01-18T10:03:13+00:00Kwara Nantomahknantomah@uds.edu.ghBy employing the classical mean value theorem, Hermite-Hadamard inequality and some other analytical techniques, we establish some new inequalities for Nielsen's beta function. Some of these inequalities provide bounds for certain ratios of the gamma function.2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1252Enumeration of Glued Graphs of Paths2020-01-18T10:03:13+00:00Monthiya Ruangnairuangnai.m@gmail.comSayan Panmapanmayan@yahoo.comLet \(G_1\) and \(G_2\) be two vertex-disjoint graphs with \(H_1\) a subgraph of \(G_1\) and \(H_2\) a subgraph of \(G_2\). Let \(f:H_1 \rightarrow H_2\) be an isomorphism between these subgraphs. The glued graph of \(G_1\) and \(G_2\) at \(H_1\) and \(H_2\) with respect to \(f\) is the graph that results from combining \(G_1 \cup G_2\) by identifying the subgraphs \(H_1\) and \(H_2\) according to the isomorphism \(f\) between \(H_1\) and \(H_2\). We refer \(G_1\) and \(G_2\) as its original graphs and refer \(H\) as its clone where \(H\) is a copy of \(H_1\) and \(H_2\). In this paper, we enumerate all non-isomorphic resulting glued graphs between two paths at connected clones. Moreover, we also give the characterization of the glued graph at a connected clone.2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1272Numerical Solution of Singularly Perturbed Boundary Value Problems with Twin Boundary Layers using Exponential Fitted Scheme2020-01-18T10:03:13+00:00S. Rakmaiahrakmajirao@gmail.comK. Phaneendrakollojuphaneendra@yahoo.co.in<p>This paper deals with a numerical method with fitted operator difference method for twin (dual) boundary layers singularly perturbed boundary value problems. In this method, Numerov method is extended to the given second order problem having derivative of first order. Using the non standard differences and modified upwind difference for the first order derivatives, the discrete scheme is deduced. A fitting parameter is utilized in the difference scheme, which handles the rapid changes that occur in the boundary layers due to the small perturbation parameter. Tridiagonal solver is implemented to solve the system of the method. Convergence analysis of the deduced method is discussed. Maximum errors in the solution of the model numerical examples are tabulated and comparison is made, to illustrate and support the method. Solutions are depicted graphically to show the layer behaviour.</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1273Some Algebraic Properties of Regular Tree Transformations2020-01-18T10:03:13+00:00Sarawut Phuapongphuapong.sa@gmail.comNuthawud SungtongNuthawud@gmail.com<p>A regular generalized hypersubstitutions is a mapping from \(\{f_{i} \mid i \in I \}\) to \(W_{\tau}(X)\) such that for every \(i \in I\), each of the variables \(x_{1},x_{2}, \ldots , x_{n_{i}}\) occur in \(\hat{\sigma}[f_{i}(x_{1}, x_{2},\ldots ,x_{n_{i}})]\). We use the extension of regular generalized hypersubstitutions to define tree transformations which is useful for abstract data type specifications in Theoretical Computer Science. In this paper, we study some algebraic properties of tree transformations.</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1249Hyers-Ulam-Rassias Stability of the \(C^*\)-ternary Bi-homomorphisms and \(C^*\)-ternary Bi-derivations in \(C^*\)-ternary Algebras2020-01-18T10:03:13+00:00Prondanai Kaskasemprondanaik@nu.ac.thChakkrid Klin-eamchakkridk@nu.ac.thIn this paper, we prove Hyers-Ulam-Rassias stability of \(C^*\)-ternary bi-homomorphisms and \(C^*\)-ternary bi-derivations in \(C^*\)-ternary algebras by using alternative fixed point theorem.2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1263Facilitating Strategic Operations by Making Use of a Model Incorporating a Stochastic Integral2020-01-18T10:03:13+00:00Constantinos T. Artikisctartikis@gmail.comPanagiotis T. Artikisptartikis@gmail.com<p>Formulation, investigation, and practical interpretation of stochastic models are generally recognized as extremely useful research activities for a wide class of scientific disciplines. The paper makes use of a stochastic integral and a product of two positive random variables for formulating a stochastic model. A characterization and an interpretation in strategic operations arising in financial economics of the formulated stochastic model are also established by the paper.</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1309Numerical Approach for Differential-Difference Equations with Layer Behaviour2020-01-18T10:03:13+00:00G. Sangeethasangeethadantam@gmail.comG. Maheshgattumahesh790@gmail.comK. Phaneendrakollojuphaneendra@yahoo.co.in<p>A numerical scheme is proposed using a non polynomial spline to solve the differential-difference equations having layer behaviour, with delay as well advanced terms. The retarded terms are handled by using Taylor’s series, subsequently the given problem is substituted by an equivalent second order singular perturbation problem. A finite difference scheme using non polynomial spline is derived and it is applied to the singular perturbation problem using non standard differences of the first derivatives. Tridiagonal algorithm is used to solve the resulting system. The method is exemplified on numerical examples with various values of perturbation, delay and advance parameters. Maximum absolute errors are computed and tabulated to support the method. Numerical solutions are pictured in graphs and the effects of small shifts on the boundary layer region has been investigated. Also, the convergence of the proposed method has also been established.</p>2019-12-31T00:00:00+00:00https://www.rgnpublications.com/journals/index.php/cma/article/view/1290The Analytic Solution of Time-Space Fractional Diffusion Equation via New Inner Product with Weighted Function2020-01-18T10:03:14+00:00Süleyman Çetinkayasuleyman.cetinkaya@kocaeli.edu.trAli Demirademir@kocaeli.edu.tr<p>In this research, we determine the analytic solution of initial boundary value problem including time-space fractional differential equation with Dirichlet boundary conditions in one dimension. By using separation of variables the solution is constructed in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem including fractional derivative in Caputo sense. A new inner product with weighted function is defined to obtain coefficients in the Fourier series.</p>2019-12-31T00:00:00+00:00