GANIT is the official journal of Bangladesh Mathematical Society (BMS). It is dedicated to the publication of original and expository papers in pure & applied mathematics and mathematical sciences, and is reviewed and edited by an international group of scholars.
Slip Velocity Distribution on MHD Oscillatory Heat and Mass Transfer Flow of a Viscous Fluid in a Parallel Plate Channel
The present investigation deals with the effect of slip on the hydromagnetic pulsatile flow through a parallel plate channel filled with saturated porous medium. Based on the pulsatile flow nature, the transformed conservation equations are solved analytically subject to physically appropriate boundary conditions by using two term perturbation technique. Exact solutions are obtained for the velocity, temperature and concentration fields. In particular skin friction coefficient, Nusselt number and Sherwood number are found to evolve into their steady state case in the large time limit. The results obtained here may be further used to verify the validity of obtained numerical solutions for more complicated transient free convection fluid flow problems. Parametric study of the solutions are conducted and discussed.
Copyright (c) 2017 Bangladesh Mathematical Society
In this paper, R1 space in L-topological spaces are defined and studied. We give seven definitions of R1 space in L-topological spaces and discuss certain relationship among them. We show that all of these satisfy ‘good extension’ property. Moreover, some of their other properties are obtained.
Copyright (c) 2018 Bangladesh Mathematical Society
Study on Eigen Values and Eigen Vectors of Matrices : An Iterative Approach
Power method is frequently used for finding largest Eigen-pair. On the other hand, Inverse Power method is utilized to find smallest Eigen-pair. Using shifting property, Power method and/or Inverse Power method can be used to find out other desired Eigen pairs too. Several lemmas based on Power method with shifting property are presented here. Moreover, a Modified Hybrid Iterative Algorithm based upon both Power method and Inverse Power method is proposed to find both largest and smallest Eigen-pairs simultaneously with ease. Several experiments have been performed to investigate the robustness and effectiveness of the algorithm. The proposed algorithm is able to find both (largest and smallest) Eigen-pairs successfully and efficiently. Moreover, the proposed algorithm is able to find out the nature (positive and negative sign) of the Eigen values and in some cases the algorithm is also able to find out the second largest Eigen pair in consequence.
Numerical study of Unsteady Fluid Flow and Heat Transfer Through a Rotating Curved Rectangular Channel
Numerical study of unsteady fluid flow and heat transfer through a rotating curved rectangular channel with aspect ratio 2 and curvature ratio 0.05 has been performed by using a spectral-based numerical method, and covering a wide range of the rotational parameter, the Taylor number Ta, for both the positive and negative rotation of the channel. In this paper, unsteady flow characteristics are investigated under combined action of the centrifugal, Coriolis and buoyancy forces for the Dean number De = 1000. For positive rotation, we investigated unsteady solutions for 0 ≤Ta ≤500, and it is found that the chaotic flow turns into steady-state flow through periodic or multi-periodic flows. For negative rotation, on the other hand, unsteady solutions are investigated for –500 ≤Ta≤0, and it is found that the unsteady flow undergoes through various flow instabilities. Typical contours of secondary flow patterns and temperature profiles are obtained at several values of Ta, and it is found that the unsteady flow consists of asymmetric two- to eightvortex solutions. The present study shows that convective heat transfer is significantly enhanced as the secondary flow becomes stronger and the chaotic flow enhances heat transfer more effectively than the steady-state or periodic solutions.
Exact Traveling Wave Solutions to Benney- Luke Equation
By using the improved (G¢/G) -expansion method, we obtained some travelling wave solutions of well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation. We show that the improved (G¢/G) -expansion method is a useful, reliable, and concise method to solve these types of equations.
Hawking Non-thermal and Purely Thermal Radiations of Rotating Black Hole in Anti-de Sitter Space Time by Hamilton-Jacobi Method
We have explored Hawking non-thermal and purely thermal radiations of Kerr-anti-de Sitter (KAdS) black hole using massive particles tunneling method by taking into account the space time background as dynamical, energy and angular momentum as conserved incorporating the selfgravitation effect of the emitted particles. The results we have obtained for KAdS black hole have shown that the tunneling rates are related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum and also the obtaining results for KAdS black hole are accordant with Parikh and Wilczek’s opinion and gives a correction to the Hawking radiation of KAdS black hole.
Non-thermal and purely thermal radiations
Mathematical Analysis of Epidemiological Model of Influenza a (H1N1) Virus Transmission Dynamics in Perspective of Bangladesh
This study deals with transmission dynamics of novel influenza A (H1N1) virus to understand the evolution of its epidemic in Bangladesh. For this purpose an SEIR model has been employed to study the dynamics of A (H1N1) virus relating to data of Bangladesh. To find threshold conditions, the equilibria and stability of the equilibria of the model have been determined and also analyzed. Basic Reproductive Number (R0) is determined relating to data of Bangladesh by which Herd Immunity Threshold has been estimated. Our numerical result suggests that vaccinating 12.69% population of Bangladesh can control spread of the pandemic novel A (H1N1) virus when outbreak occurs.
Homogeneous and Inhomogeneous Maxwell’s Equations in Terms of Hodge Star Operator
The main purpose of this work is to provide application of differential forms in physics. For this purpose, we describe differential forms, exterior algebra in details and then we express Maxwell’s equations by using differential forms. In the theory of pseudo-Riemannian manifolds there will be an important operator, called Hodge Star Operator. Hodge Star Operator arises in the coordinate free formulation of Maxwell’s equation in flat space-time. This operator is an important ingredient in the formulation of Stoke’stheorem.
A Study on Tidal Potential and Tide Generating Force
This study deals with the derivation of tidal potential and tide generating forces. Tidal potential is derived from the gravitational attraction of masses of the moon and the sun and from this potential tide generating forces are derived taking its horizontal gradients.
In this paper, we investigate the commutativity of prime rings admitting α-multipliers of R satisfying certain identities and some related results have also been discussed.
Modified Inverses of Centralizers of Semiprime Rings
The main purpose of this paper is to investigate the properties of centralizers of semiprime ring R as well as to establish necessary and sufficient conditions for a centralizer T of a semiprime ring R to have a commuting modified inverse.
Jordan Derivations on Lie Ideals of ?-Prime Rings
In this paper we prove that, if U is a s-square closed Lie ideal of a 2-torsion free s-prime ring R and d: R(R is an additive mapping satisfying d(u2)=d(u)u+ud(u) for all u?U then d(uv)=d(u)v+ud(v) holds for all u,v?UGANIT J. Bangladesh Math. Soc.Vol. 36 (2016) 1-5
A Numerical Study to Find the Effect of Boundary Conditions on Natural Convection Flow in an Open Cavity
In this study, effect of boundary conditions on natural convection flow in an open cavity has been studied numerically. The computational fluid dynamics (CFD) simulations are performed to investigate the natural convection flow phenomena within the cavity. The ?-? turbulence model is chosen to capture the turbulence phenomena of the flow. A numerical case is chosen from literature to validate the method used in this study. For accurate prediction of the flow phenomenon a sufficiently large surrounding domain around the cavity is considered. The effects of boundary conditions applied in the apertures of the open cavity are observed.
The Tower of Hanoi Problem and its Variants
The Tower of Hanoi is a popular mathematical puzzle, which appeared in 1885. During the past years, the problem has seen many variations. This paper reviews the Tower of Hanoi and its different variants. Some 3-peg variants are given in §2, §3 treats some 4-peg variants, §4 deals with the multi-peg generalization, and §5 gives some open problemsGANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 145-163
Copyright (c) 2016 Bangladesh Mathematical Society
Exact Traveling Wave Solutions of Modified Liouville Equation
In this paper fuzzy version of secant method has been introduced to obtain approximate solutions of a fuzzy non-linear equation. Graphical representations of the approximate solutions have also been shown. The idea of converging to the root to the desired degree of accuracy, which is the optimum solution, of a fuzzy non-linear equation has been focused.
Determination of the Homology and the Cohomology of a Few Groups of Isometries of the Hyperbolic Plane
In this paper we determine the homology and the cohomology groups of two properly discontinuous groups of isometries of the hyperbolic plane having non-compact orbit spaces and the fundamental group of a graph of groups with a finite vertex groups and no trivial edges by extending Lyndons partial free resolution for finitely presented groups. For the first two groups, we obtain partial extensions and the corresponding homology. We also compute the corresponding cohomology groups for one of these groups. Finally we obtain homology and cohomology in all dimensions for the last of the above mentioned groups by constructing a full resolution for this group.
Free resolution Huebschmann perturbation method
An Impeccable Solution Procedure of Stochastic Programming Problems by Inserting Scenarios in Deterministic Case
In this paper, a new technique has been developed for solving stochastic programming problems by using the idea of decomposition based pricing method. A computer code has also been developed by using a mathematical programming language AMPL and a real life oriented model has been developed. The technique has been demonstrated by analyzing the model for different data sets which has been collected for different scenarios. To our knowledge, this is the first work for solution procedure of stochastic programming problems by using decomposition based pricing method.
Slip Velocity Distribution in a Parallel Plate Channel on Asymmetric Thermal Boundary Condition
Steady, laminar and fully developed flows in parallel plate microchannel with asymmetric thermal wall conditions are solved by control volume technique. In order to examine the influence of Reynolds number and Knudsen number on the velocity distributions, a series of simulations are performed for different Reynolds and Knudsen numbers. Nitrogen gas is used as working fluid and we assume the fluid as continuum but employ the slip boundary conditions on the walls. The Navier-Stokes and energy equations are solved simultaneously. The results are found in good agreement with those predicted by analytical solutions in 2D continuous flow model employing first order slip boundary conditions. It is concluded that the rarefaction flattens the velocity distribution. If the product of Reynolds numbers and Knudsen numbers is fixed, the cross sectional average velocity is fixed for incompressible flow.
Effects of Temperature Dependent Thermal Conductivity and Viscous Dissipation on Free Convective Flow along a Vertical Flat Plate with Asymptotic Solution
This paper reports us the surface temperature distribution effects of free convective flow along a vertical flat plate with temperature dependent thermal conductivity and viscous dissipation with asymptotic solution. The governing equations with associated boundary conditions reduce to local non-similarity boundary layer equations for this phenomenon are converted to dimensionless forms using a suitable transformation. The transformed non-linear equations are then solved using the implicit finite difference method together with Keller-box technique. Numerical results of the velocity and temperature profiles, skin friction and surface temperature profiles for different values of the thermal conductivity variation parameter, the Prandtl number and the viscous dissipation parameters are presented graphically. Also we considered the asymptotic solution for the effect of the thermal conductivity variation parameter, the Prandtl number and the viscous dissipation parameters in skin friction and surface temperature profiles. Detailed discussion is given for the aforementioned parameters. A good similarity is found in small and large value solution with all value solution for the thermal conductivity variation parameter, the Prandtl number and the viscous dissipation parameter for skin friction and surface temperature. Divergence is found near one (1).
Explicit Exponential Finite Difference Scheme for 1D Navier-Stokes Equation with Time Dependent Pressure Gradient
In this paper, numerical technique for solving the one-dimensional (1D) unsteady, incompressible Navier-Stokes equation (NSE) is presented. The governing time dependent non-linear partial equation is reduced to non-linear partial differential equation named as viscous Burgers equation by introducing Orlowski and Sobczyk transformation (OST). An explicit exponential finite difference scheme (Expo FDS) has been used for solving reduced 1D NSE. The accuracy of the method has been illustrated by taking two numerical examples. Results are compared with the analytical solutions and those obtained based on the numerical results of reduced 1D NSE as Burgers equation. The accuracy and numerical feature of convergence of the Expo FDS is presented by estimating their error norms. Excellent numerical results indicate that the proposed numerical technique is efficient admissible with efficient accuracy for the numerical solutions of the NSE.
Explicit exponential finite difference scheme
Fuzzy Version of Secant Method to Solve Fuzzy Non-Linear Equations
Effect of Radiation and Heat Generation on Unsteady MHD Flow of Non-Newtonian Fluid Along a Stretching Vertical Surface
In this paper, the unsteady forced convection boundary-layer flow of a non-Newtonian fluid along a continuously moving stretching sheet with thermal radiation and heat generation or absorption in the presence of magnetic field has been studied. First, the governing equations have been nondimensionalized by usual transformations to obtain the similar solutions. Then, the obtained equations have been solved by an implicit finite difference method. The convergency of explicit and implicit finite difference method has also been discussed. The results are presented for the effect of various parameters such as magnetic parameter (M), radiation parameter (N), heat source parameter (Q), Prandtl number (Pr) and power-law fluid index (n). The effects of these parameters on skin-friction coefficient (Cf) and the local Nusselt number (NuL) which are of physical and engineering interest have also been studied and presented graphically.
Critical Analysis of Magnetohydrodynamic Jeffery-Hamel Flow Using Cu-Water Nanofluid
The effects of nanoparticles and magnetic field on the nonlinear Jeffery-Hamel flow using Cuwater nanofluid are analysed in the present study. The basic dimensionless governing equations are solved using power series, which is then analysed by applying a semi-numerical analytical technique called Hermite- Padé approximation. The velocity profiles are presented in convergentdivergent channels for various values of nanoparticles solid volume fraction, Hartmann number, Reynolds number and channel angle. The dominating singularity behavior of the problem is analysed numerically and graphically for nanofluid. The critical relationships among the parameters are also performed qualitatively with the effect of Cu-nanoparticles.
Study of Inventory Model for Deteriorating Items With Exponential Demand Function
This paper develops an inventory model for deteriorating items consisting the ordering cost, unit cost, opportunity cost, deterioration cost and shortage cost. In this inventory model instead of linear demand function nonlinear exponential function of time for deteriorating items with deterioration rate has been considered. The formulated model has numerically solved by bisection method. The effects of inflation and cash flow are also taken into account under a trade-credit policy of discount with time. In order to validate the model, numerical examples have been solved by bisection method using Matlab. Further, the sensitivity of different parameters is considered in order to estimate the cash flow.
Numerical Simulation of a Second Order Traffic Flow Model
A second order fluid dynamical traffic flow model is considered which is a parabolic type second order partial differential equation appended with initial and boundary conditions reads as an initial boundary value problem (IBVP). For a linear velocity-density relation the paper presents the analytical solution of the model by using Cole-Hopf transformation. For the numerical solution of the IBVP, we investigate explicit central difference scheme and implement the numerical scheme by developing computer programming code. Error estimation is produced which shows the numerical solution is accurate up to eight decimal places and this result is much better than the work presented in [6]. The numerical feature of rate of convergence observed by graphical presentation is also found better than the previous work. The computed numerical simulation results are seen in a good qualitative agreement with the well known traffic flow behavior for various parameters.
Numerical Relativity: Solving Geodesics equation for Massive Particle Around Black Holes Horizon
General relativity is the most beautiful physical theory ever invented. It describes one of the most pervasive features of the world we experience - gravitation. The gravitational field acts on nearby matter defines by the curvature of space-time. The black holes of nature are the most perfect macroscopic objects there are in the universe that constructed our concept of space-time. In this paper we use Einsteins general relativity to model the motions of massive particles around the two black holes: static and rotating. These equations of motion around black holes will be studied with special focus towards the variation of symmetry by the change of gravitational effect.
A Transformed Coordinate Model to Predict Tide and Surge Along the Head Bay of Bengal- Application to Cyclone of 1991 and 1970
The head Bay of Bengal region is one of the most vulnerable regions for extreme water levels associated with severe tropical cyclones. The shallow nature of the head Bay, presence of a large number of deltas formed by major rivers and high tidal range are responsible for storm surge flooding in the region. Specifically, the rise and fall of tidal phases influence the height, duration, and arrival time of peak surge along the coast. The objective of the present study is to evaluate the tide-surge interaction during the super cyclone of 1991 and 1970. A transformed coordinate model is developed to estimate the possible water levels along the coast of Bangladesh.
Computation of Some Second Order Sturm-Liouville Bvps using Chebyshev-Legendre Collocation Method
We propose Chebyshev-Legendre spectral collocation method for solving second order linear and nonlinear eigenvalue problems exploiting Legendre derivative matrix. The Sturm-Liouville (SLP) problems are formulated utilizing Chebyshev-Gauss-Lobatto (CGL) nodes instead of Legendre Gauss-Lobatto (LGL) nodes and Legendre polynomials are taken as basis function. We discuss, in details, the formulations of the present method for the Sturm-Liouville problems (SLP) with Dirichlet and mixed type boundary conditions. The accuracy of this method is demonstrated by computing eigenvalues of three regular and two singular SLP's. Nonlinear Bratu type problem is also tested in this article. The numerical results are in good agreement with the other available relevant studies.
Three Distinct Non-Hereditary Radicals Which Coincide with the Classical Radical for Rings with D.C.C.
Majumdar and Paul [3] introduced and studied a new radical E defined as the upper radical determined by the class of all rings each of whose ideals is idempotent. In this paper the authors continue the study further and also study the join radical and the intersection radical (due to Leavitt) obtained from E and the Jacobson radical J. These have been denoted by E + J and EJ respectively. The radical and the semisimple rings corresponding to E + J and EJ have been obtained. Both of these radicals coincide with the classical nil radical for Artinian rings. Important properties of these radicals and their position among the well-known special radicals have been investigated. It has been proved that E, EJ and E + J are non-hereditary. It has also been proved as an independent result that the nil radical N is not dual, i.e., N ? N?.
An Evaluation of an Improper Integral Arises from an Analytic Solution of a Model Boltzmann Equation for Photon Transport
In this article we adopted the Mathematical model of solution of an improper integral which is created from the solution of the Boltzmann Transport equation (BTE) for photons. For the dose calculation of radiotherapy for cancer treatment, we need to solve the Boltzmann Transport equation. This improper integral is the important part of the BTE. Also the calculating time of the dose calculation is mostly dependent on the calculating time of this improper integral. For reducing the calculating time we need the minimum integrating area which is explained in this paper.