Entropy generation due to unsteady hydromagnetic Couette flow and heat transfer with asymmetric convective cooling in a rotating system Sanatan Das Department of Mathematics, University of Gour Banga Malda 732 103, West Bengal, India author Rabindranath Jana Department of Applied Mathematics, Vidyasagar University Midnapore 721 102, West Bengal, India author Ali J. Chamkha Mechanical Engineering Department, Prince Mohammad Bin Fahd University (PMU), Al-Khobar 31952, Kingdom of Saudi Arabia author text article 2016 eng Entropy generation in an unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel plates in a rotating system have been analyzed. Both the lower and upper plates of the channel are subjected to asymmetric convective heat exchange with the ambient following the Newton's law of cooling. A numerical solution for governing equations is developed. The influences of the pertinent parameters on the fluid velocity components, temperature, entropy generation and Bejan number are discussed graphically. Journal of Mathematical Modeling University of Guilan 2345-394X 3 v. 2 no. 2016 111 128 https://jmm.guilan.ac.ir/article_1216_d75daac10f559e8edeab9b9c3b655a40.pdf An efficient algorithm for finding the semi-obnoxious $(k,l)$-core of a tree Samane Motevalli Faculty of Mathematics, Shahrood University, Shahrood, Iran author Jafar Fathali Faculty of Mathematics, Shahrood University, Shahrood, Iran author Mehdi Zaferanieh Department of Mathematics, Hakim Sabzevari University, Sabzevar, Iran author text article 2016 eng In this paper we study finding the $(k,l)$-core problem on a tree which the vertices have positive or negative weights. Let $T=(V,E)$ be a tree. The $(k,l)$-core of $T$ is a subtree with at most $k$ leaves and with a diameter of at most $l$ which the sum of the weighted distances from all vertices to this subtree is minimized. We show that, when the sum of the weights of vertices is negative, the $(k,l)$-core must be a single vertex. Then we propose an algorithm with time complexity of $O(n^2log n)$ for finding the $(k,l)$-core of a tree with pos/neg weight, which is in fact a modification of the one proposed by Becker et al. [Networks 40 (2002) 208]. Journal of Mathematical Modeling University of Guilan 2345-394X 3 v. 2 no. 2016 129 144 https://jmm.guilan.ac.ir/article_1217_decabc127c158c47e815e39eb31e5c64.pdf Effects of Hall current and ion-slip on unsteady hydromagnetic generalised Couette flow in a rotating Darcian channel Jitendra Kumar Singh Department of Mathematics, V. S. K. University, Bellary-583105, India author Shaik Ghousia Begum Department of Mathematics, V. S. K. University, Bellary-583105, India author Naveen Joshi Department of Mathematics, V. S. K. University, Bellary-583105, India author text article 2016 eng Unsteady hydromagnetic generalised Couette flow of a viscous, incompressible and electrically conducting fluid between two horizontal parallel porous plates Darcian channel in the presence of a uniform transverse magnetic field taking Hall current and ion-slip into account in a rotating system is investigated. An exact solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving porous plate due to primary and secondary flows is also derived. Asymptotic behavior of the solution is analyzed at the start-up and final stage of the motion to gain some physical insight into the flow pattern. Numerical values of primary and secondary velocities and that of shear stress at the moving porous plate of the channel due to primary and secondary flows are displayed graphically for various values of different flow parameters. Journal of Mathematical Modeling University of Guilan 2345-394X 3 v. 2 no. 2016 145 167 https://jmm.guilan.ac.ir/article_1249_055b19ea6a1deaa26e5e9403c504efea.pdf Simulation of particle diffusion and heat transfer in a two-phase turbulent boundary layer using the Eulerian-Eulerian approach Pradeep Kumar Tripathy Department of Mathematics and Science, U.C.P. Engg. School, Berhampur - 760 010, Dist. Ganjam, Odisha, India author Saroj Kumar Mishra Khallikote - 761030, Dist. Ganjam, Odisha, India author Ali Jawad Chamkha Prince Mohammad Bin Fahd University (PMU), P.O. Box 1664, Al-Khobar 31952, Kingdom of Saudi Arabia author text article 2016 eng This work investigates the response of two-dimensional, turbulent boundary layer characteristics over a flat plate to the presence of suspended particulate matter. Both phases are assumed to be interacting continua. That is, the carrier fluid equations are considered to be coupled with the particle-phase equations. A finite-difference technique with non-uniform grid has been employed for the solution of the governing equations and therefore, interpretation of the results and comparison of the present result with the results of other references. The results clearly demonstrate that the presence of particles damped the fluid turbulence and apparently affects the skin friction and heat transfer characteristics equally. Journal of Mathematical Modeling University of Guilan 2345-394X 3 v. 2 no. 2016 169 187 https://jmm.guilan.ac.ir/article_1316_109a3c89062bb60650a5a1e07a0ad303.pdf A model for the dynamical study of food-chain system considering interference of top predator in a polluted environment Om Prakash Misra School of Mathematics and Allied Sciences, Jiwaji University, Gwalior-474 011, India author Raveendra Babu Annavarapu School of Mathematics and Allied Sciences, Jiwaji University, Gwalior-474 011, India author text article 2016 eng The modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system. In the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. The stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the stress of toxicant are obtained. Further, it is also found that the predation rate of the intermediate predator is a bifurcating parameter and Hopf-bifurcation occurs at some critical value of this parameter. Finally, numerical simulation is carried out to support the analytical results. Journal of Mathematical Modeling University of Guilan 2345-394X 3 v. 2 no. 2016 189 218 https://jmm.guilan.ac.ir/article_1471_62c5a01d2ff91441d9018f8a6877e4a7.pdf Spline Collocation for system of Fredholm and Volterra integro-differential equations Nehzat Ebrahimi Department of Mathematics, Islamic Azad University, Central Tehran Branch, Iran author Jalil Rashidinia Department of Mathematics, Islamic Azad University, Central Tehran Branch, Iran author text article 2016 eng The spline collocation method  is employed to solve a system of linear and nonlinear Fredholm and Volterra integro-differential equations. The solutions are collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. We obtain the unique solution for linear and nonlinear system $(nN+3n)\times(nN+3n)$ of integro-differential equations. This approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. At the end, some examples are presented to illustrate the ability and simplicity of the method. Journal of Mathematical Modeling University of Guilan 2345-394X 3 v. 2 no. 2016 189 218 https://jmm.guilan.ac.ir/article_1502_5ff1cb86a8e40f42be09726a39ae2f0d.pdf