GANIT: Journal of Bangladesh Mathematical Society 2020-02-11T15:31:21+00:00 Associate Editor Open Journal Systems <p>The official journal of the Bangladesh Mathematical Society. Full text articles available.</p> On the Star Puzzle 2020-02-11T15:31:21+00:00 AAK Majumdar <p>In the <em>star puzzle</em>, there are four pegs, the usual three pegs, S, P and D, and a fourth one at 0. Starting with a tower of n discs on the peg P, the objective is to transfer it to the peg D, in minimum number of moves, under the conditions of the classical Tower of Hanoi problem and the additional condition that all disc movements are either to or from the fourth peg. Denoting by <em>MS(n)</em> the minimum number of moves required to solve this variant, <em>MS(n)</em> satisfies the recurrence relation . This paper studies rigorously and extensively the above recurrence relation, and gives a solution of it.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 1-14</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement## On Some Values of the Sandor-Smarandache Function 2020-02-11T15:30:56+00:00 AAK Majumdar <p>Sandor [1] posed a new function, denoted by <em>SS(n)</em>, and is defined as follows : being the binomial coefficients. This paper finds <em>SS(n)</em> for some particular cases of n.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 15-25</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement## Numerical Simulation on Heat Flow for Mixed Convection Within a Triangular Enclosure 2020-02-11T15:30:24+00:00 Muhammad Sajjad Hossain MM Billah MZI Bangalee MA Alim <p>Heat flow for laminar mixed convection in a triangular enclosure with uniformly heated bottom wall is solved using Galerkin weighted residual method of finite element formulation. A fluid with Prandtl number (<em>Pr</em> = 0.71) is also used to investigate the effects of heat flow for Reynolds number(40 ≤ <em>Re</em> ≤ 110) varying Rayleigh number (10<sup>3</sup>≤ <em>Ra</em> ≤ 10<sup>4</sup>) in that enclosure. In the enclosure, the left wall is considered cold; bottom wall is uniformly heated while the other inclined wall is insulated. The geometry of physical problems is represented mathematically by different sets of governing equations along with appropriate boundary conditions. Results are shown in terms of streamlines, isotherms, average Nusselt number and average temperature of the fluid in the cavity for uniform heating of bottom wall. It is seen that heat transfer rate from the heat source is higher for increasing value of <em>Re</em>. On the other hand, average bulk temperature declines significantly. It is also indicated that for fixed Prandtl number and various Ra, the buoyancy force and heat transfer rate inside the enclosure are increased for the greater value of <em>Re</em>.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 27-43</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement## Impact of Treatment on HIV-Malaria CoInfection Based on Mathematical Modeling 2020-02-11T15:30:15+00:00 Amit Kumar Saha Ashrafi Meher Niger Chandra Nath Podder <p>The distribution of HIV and malaria overlap globally. So there is always a chance of co-infection. In this paper the impact of medication on HIV-Malaria co-infection has been analyzed and we have developed a mathematical model using the idea of the models of Mukandavire, et al. [13] and Barley, et al. [3] where treatment classes are included. The disease-free equilibrium (DFE) of the HIV-only model is globally-asymptotically stable (GAS) when the reproduction number is less than one. But it is shown that in the malaria-only model, there is a coexistence of stable disease-free equilibrium and stable endemic equilibrium, for a certain interval of the reproduction number less than unity. This indicates the existence of backward bifurcation. Numerical simulations of the full model are performed to determine the impact of treatment strategies. It is shown that malaria-only treatment strategy reduces more new cases of the mixed infection than the HIV-only treatment strategy. Moreover, mixed treatment strategy reduces the least number of new cases compared to single treatment strategies.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 45-62</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement## On Orthogonal Generalized Derivations of Semiprime -Rings 2020-02-11T15:30:45+00:00 Kalyan Kumar Dey Sanjay Kumar Saha Akhil Chandra Paul <p>In this paper, we study the orthogonality of two generalized derivations in semiprime G-rings. Some results are obtained in connection with ideals of semiprime G-rings and using left annihilator which is taken to be zero.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 63-70</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement## Riemannian Geometry and Modern Developments 2020-02-11T15:31:12+00:00 AKM Nazimuddin Md Showkat Ali <p>In this paper, we compute the Christoffel Symbols of the first kind, Christoffel Symbols of the second kind, Geodesics, Riemann Christoffel tensor, Ricci tensor and Scalar curvature from a metric which plays a fundamental role in the Riemannian geometry and modern differential geometry, where we consider MATLAB as a software tool for this implementation method. Also we have shown that, locally, any Riemannian 3-dimensional metric can be deformed along a directioninto another metricthat is conformal to a metric of constant curvature</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 71-85</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement## Analytical Solution of Liénard Differential Equation using Homotopy Perturbation Method 2020-02-11T15:31:04+00:00 Md Mamun Ur Rashid Khan Goutam Saha <p>In this research work, the well-known Homotopy perturbation method (HPM) is used to find the approximate solutions of the nonlinear Liénard differential equation (LDE) using different types of boundary conditions. In order to find the accuracy of the approximate solution, one term, two terms and three terms HPM approximations are considered. This idea is actually based on the idea of Taylor’s series polynomials. It is found that solution converges to the actual solution with the increase of the terms in the guess solution. Moreover, in each of the new HPM solution, previously obtained solutions are added to it in order to find the exactness of HPM solutions. However, the nature of the solution seems to be complicated. In addition, comparisons are made with the previously published results and a good agreement is observed.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 87-100</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement## Inner Derivations on Semiprime Gamma Rings 2020-02-11T15:29:56+00:00 Sujoy Chakraborty Md Mahbubur Rashid Akhil Chandra Paul <p>We study inner derivations and generalized inner derivations in semiprime Γ-rings to develop some important results. If <em>f</em> and <em>g</em> are inner derivations of a semiprime Γ-ring <em>M</em> satisfying the equation &nbsp;for all , then we show that . This equation produces a number of results on generalized inner derivations as well.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 101-110</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement## Existence of Weak Solutions for Caputo’s Fractional Derivatives in Banach Spaces 2020-02-11T15:30:05+00:00 Samima Akhter <p>The objective of this project is to represent the existence of solutions for Caputo’s fractional derivatives in Banach spaces. The result is based on some well-known fixed point theorems. To show the efficiency of the stated result some examples will be demonstrated</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 111-118</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement## Symplectic and Contact Geometry with Complex Manifolds 2020-02-11T15:30:34+00:00 AKM Nazimuddin Md Showkat Ali <p>In this paper, we discuss about almost complex structures and complex structures on Riemannian manifolds, symplectic manifolds and contact manifolds. We have also shown a special comparison between complex symplectic geometry and complex contact geometry. Also, the existence of a complex submanifold of n-dimensional complex manifold which intersects a real submanifold</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 119-126</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement## A Comparative Analysis of the Black-Scholes- Merton Model and the Heston Stochastic Volatility Model 2020-02-11T15:29:47+00:00 Tahmid Tamrin Suki ABM Shahadat Hossain <p>This paper compares the performance of two different option pricing models, namely, the Black-Scholes-Merton (B-S-M) model and the Heston Stochastic Volatility (H-S-V) model. It is known that the most popular B-S-M Model makes the assumption that volatility of an asset is constant while the H-S-V model considers it to be random. We examine the behavior of both B-S-M and H-S-V formulae with the change of different affecting factors by graphical representations and hence assimilate them. We also compare the behavior of some of the Greeks computed by both of these models with changing stock prices and hence constitute 3D plots of these Greeks. All the numerical computations and graphical illustrations are generated by a powerful Computer Algebra System (CAS), MATLAB.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 39 (2019) 127-140</p> 2019-11-19T00:00:00+00:00 ##submission.copyrightStatement##