GANIT
type: channel
description: 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.
language: en
publication name: GANIT
items: Slip Velocity Distribution on MHD Oscillatory Heat and Mass Transfer Flow of a Viscous Fluid in a Parallel Plate Channel
items: On R1 Space in l-Topological Spaces
items: Study on Eigen Values and Eigen Vectors of Matrices : An Iterative Approach
items: Numerical study of Unsteady Fluid Flow and Heat Transfer Through a Rotating Curved Rectangular Channel
items: Exact Traveling Wave Solutions to Benney- Luke Equation
items: Hawking Non-thermal and Purely Thermal Radiations of Rotating Black Hole in Anti-de Sitter Space Time by Hamilton-Jacobi Method
items: Mathematical Analysis of Epidemiological Model of Influenza a (H1N1) Virus Transmission Dynamics in Perspective of Bangladesh
items: Homogeneous and Inhomogeneous Maxwell’s Equations in Terms of Hodge Star Operator
items: A Study on Tidal Potential and Tide Generating Force
items: A Note on α-multipliers of Prime Rings
items: Modified Inverses of Centralizers of Semiprime Rings
items: Jordan Derivations on Lie Ideals of ?-Prime Rings
items: A Numerical Study to Find the Effect of Boundary Conditions on Natural Convection Flow in an Open Cavity
items: The Tower of Hanoi Problem and its Variants
items: Exact Traveling Wave Solutions of Modified Liouville Equation
items: Determination of the Homology and the Cohomology of a Few Groups of Isometries of the Hyperbolic Plane
items: An Impeccable Solution Procedure of Stochastic Programming Problems by Inserting Scenarios in Deterministic Case
items: Slip Velocity Distribution in a Parallel Plate Channel on Asymmetric Thermal Boundary Condition
items: Effects of Temperature Dependent Thermal Conductivity and Viscous Dissipation on Free Convective Flow along a Vertical Flat Plate with Asymptotic Solution
items: Explicit Exponential Finite Difference Scheme for 1D Navier-Stokes Equation with Time Dependent Pressure Gradient
items: Fuzzy Version of Secant Method to Solve Fuzzy Non-Linear Equations
items: Effect of Radiation and Heat Generation on Unsteady MHD Flow of Non-Newtonian Fluid Along a Stretching Vertical Surface
items: Critical Analysis of Magnetohydrodynamic Jeffery-Hamel Flow Using Cu-Water Nanofluid
items: Study of Inventory Model for Deteriorating Items With Exponential Demand Function
items: Numerical Simulation of a Second Order Traffic Flow Model
items: Numerical Relativity: Solving Geodesics equation for Massive Particle Around Black Holes Horizon
items: A Transformed Coordinate Model to Predict Tide and Surge Along the Head Bay of Bengal- Application to Cyclone of 1991 and 1970
items: Computation of Some Second Order Sturm-Liouville Bvps using Chebyshev-Legendre Collocation Method
items: Three Distinct Non-Hereditary Radicals Which Coincide with the Classical Radical for Rings with D.C.C.
items: An Evaluation of an Improper Integral Arises from an Analytic Solution of a Model Boltzmann Equation for Photon Transport

Slip Velocity Distribution on MHD Oscillatory Heat and Mass Transfer Flow of a Viscous Fluid in a Parallel Plate Channel
type: item
description: 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.
subject: Articles
  topic: section
subject: MHD fluid
  topic: keywords
subject: Navier slip
  topic: keywords
subject: porous medium
  topic: keywords
subject: thermal radiation
  topic: keywords
subject: heat transfer
  topic: keywords
creator: Venkateswarlu Malapati
creator: Venkata Lakshmi Dasari
rights: Copyright (c) 2017 Bangladesh Mathematical Society
date: 2017-06-03
publication date: 2017-06-03
doi: 10.3329/ganit.v36i0.32776

On R1 Space in l-Topological Spaces
type: item
description: 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.
subject: Articles
  topic: section
subject: L-fuzzy set
  topic: keywords
subject: L-topology
  topic: keywords
subject: Hereditary
  topic: keywords
subject: projective and productive
  topic: keywords
creator: Rafiqul Islam
creator: MS Hossain
rights: Copyright (c) 2018 Bangladesh Mathematical Society
date: 2018-02-20
publication date: 2018-02-20
doi: 10.3329/ganit.v37i0.35726

Study on Eigen Values and Eigen Vectors of Matrices : An Iterative Approach
type: item
description: 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.
subject: Articles
  topic: section
subject: Eigen value
  topic: keywords
subject: Eigen vector
  topic: keywords
subject: Power method
  topic: keywords
subject: Inverse Power method
  topic: keywords
subject: Iterative method
  topic: keywords
subject: Modified Hybrid Iterative Algorithm
  topic: keywords
creator: ARM Jalal Uddin Jamali
creator: Md Hasibul Haque
creator: Md Sah Alam
rights: Copyright (c) 2018 Bangladesh Mathematical Society
date: 2018-02-20
publication date: 2018-02-20
doi: 10.3329/ganit.v37i0.35725

Numerical study of Unsteady Fluid Flow and Heat Transfer Through a Rotating Curved Rectangular Channel
type: item
description: 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.
subject: Articles
  topic: section
subject: Rotating curved channel
  topic: keywords
subject: secondary vortex
  topic: keywords
subject: unsteady solutions
  topic: keywords
subject: Dean number
  topic: keywords
subject: Taylor number
  topic: keywords
subject: time evolution
  topic: keywords
creator: Md Zohurul Islam
creator: Md Arifuzzaman
creator: Rabindra Nath Mondal
rights: Copyright (c) 2018 Bangladesh Mathematical Society
date: 2018-02-20
publication date: 2018-02-20
doi: 10.3329/ganit.v37i0.35727

Exact Traveling Wave Solutions to Benney- Luke Equation
type: item
description: 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.
subject: Articles
  topic: section
subject: Traveling Wave
  topic: keywords
subject: Benney-Luke Equation
  topic: keywords
subject: Sobolev type PDEs
  topic: keywords
creator: Zahidul Islam
creator: Mohammad Mobarak Hossain
creator: Md Abu Naim Sheikh
rights: Copyright (c) 2018 Bangladesh Mathematical Society
date: 2018-02-20
publication date: 2018-02-20
doi: 10.3329/ganit.v37i0.35721

Hawking Non-thermal and Purely Thermal Radiations of Rotating Black Hole in Anti-de Sitter Space Time by Hamilton-Jacobi Method
type: item
description: 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.
subject: Articles
  topic: section
subject: Massive Particle Tunneling
  topic: keywords
subject: KAdS black hole
  topic: keywords
subject: Non-thermal and purely thermal radiations
  topic: keywords
creator: M Ilias Hossain
rights: Copyright (c) 2018 Bangladesh Mathematical Society
date: 2018-02-20
publication date: 2018-02-20
doi: 10.3329/ganit.v37i0.35729

Mathematical Analysis of Epidemiological Model of Influenza a (H1N1) Virus Transmission Dynamics in Perspective of Bangladesh
type: item
description: 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.
subject: Articles
  topic: section
subject: Basic Reproduction Number
  topic: keywords
subject: SEIR Model
  topic: keywords
subject: Herd Immunity Threshold
  topic: keywords
subject: Stability
  topic: keywords
subject: Next Generation Matrix
  topic: keywords
creator: Rafiqul Islam
creator: Md Haider Ali Biswas
creator: ARM Jalal Uddin Jamali
rights: Copyright (c) 2018 Bangladesh Mathematical Society
date: 2018-02-20
publication date: 2018-02-20
doi: 10.3329/ganit.v37i0.35724

Homogeneous and Inhomogeneous Maxwell’s Equations in Terms of Hodge Star Operator
type: item
description: 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.
subject: Articles
  topic: section
subject: Homogeneous
  topic: keywords
subject: Inhomogeneous
  topic: keywords
subject: Hodge Star operator
  topic: keywords
subject: differential forms
  topic: keywords
creator: Zakir Hossine
creator: Md Showkat Ali
rights: Copyright (c) 2018 Bangladesh Mathematical Society
date: 2018-02-20
publication date: 2018-02-20
doi: 10.3329/ganit.v37i0.35722

A Study on Tidal Potential and Tide Generating Force
type: item
description: 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.
subject: Articles
  topic: section
subject: Gravitational attraction
  topic: keywords
subject: Low water
  topic: keywords
subject: High water
  topic: keywords
subject: Tidal potential
  topic: keywords
subject: Tide generating forces
  topic: keywords
creator: M Mizanur Rahman
creator: Gour Chandra Paul
creator: Ashabul Hoque
rights: Copyright (c) 2018 Bangladesh Mathematical Society
date: 2018-02-20
publication date: 2018-02-20
doi: 10.3329/ganit.v37i0.35723

A Note on α-multipliers of Prime Rings
type: item
description: 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.
subject: Articles
  topic: section
subject: α-multiplier
  topic: keywords
subject: prime
  topic: keywords
subject: 2-torsion free
  topic: keywords
subject: commutative
  topic: keywords
subject: automorphism
  topic: keywords
creator: Kyung Ho Kim
rights: Copyright (c) 2018 Bangladesh Mathematical Society
date: 2018-02-20
publication date: 2018-02-20
doi: 10.3329/ganit.v37i0.35728

Modified Inverses of Centralizers of Semiprime Rings
type: item
description: 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.
subject: Articles
  topic: section
subject: Semiprime ring
  topic: keywords
subject: left (right) centralizer
  topic: keywords
subject: centralizer
  topic: keywords
subject: modified inverse
  topic: keywords
creator: Md Rezaul Islam
creator: Satrajit Kumar Saha
rights: Copyright (c) 2017 Bangladesh Mathematical Society
date: 2017-06-03
publication date: 2017-06-03
doi: 10.3329/ganit.v36i0.32773

Jordan Derivations on Lie Ideals of ?-Prime Rings
type: item
description: 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
subject: Articles
  topic: section
subject: Lie ideal
  topic: keywords
subject: ?-square closed Lie ideal
  topic: keywords
subject: ?-prime ring
  topic: keywords
subject: Jordan derivation
  topic: keywords
subject: derivation
  topic: keywords
creator: Akhil Chandra Paul
creator: Md Mizanor Rahman
rights: Copyright (c) 2017 Bangladesh Mathematical Society
date: 2017-06-03
publication date: 2017-06-03
doi: 10.3329/ganit.v36i0.32768

A Numerical Study to Find the Effect of Boundary Conditions on Natural Convection Flow in an Open Cavity
type: item
description: 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.
subject: Articles
  topic: section
subject: Natural convection flow
  topic: keywords
subject: CFD
  topic: keywords
subject: ?-? turbulence model
  topic: keywords
subject: Boundary condition
  topic: keywords
creator: Nishat Tasnim
creator: MZI Bangalee
rights: Copyright (c) 2017 Bangladesh Mathematical Society
date: 2017-06-03
publication date: 2017-06-03
doi: 10.3329/ganit.v36i0.32772

The Tower of Hanoi Problem and its Variants
type: item
description: 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
subject: Articles
  topic: section
subject: The Tower of Hanoi problem
  topic: keywords
subject: 3-peg variants
  topic: keywords
subject: 4-peg variants
  topic: keywords
subject: multi-peg generalization
  topic: keywords
subject: Mathematics
  topic: keywords
creator: AAK Majumdar
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v35i0.28578

Exact Traveling Wave Solutions of Modified Liouville Equation
type: item
description: 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.
subject: Articles
  topic: section
subject: Generalized Bernoulli Sub-ODE method
  topic: keywords
subject: Exp(-?(?))-expansion method
  topic: keywords
subject: Modified Liouville equation
  topic: keywords
subject: Traveling wave solutions
  topic: keywords
subject: Mathematics
  topic: keywords
creator: Md Abdus Salam
creator: Md Obayedullah
creator: Md Shajib Ali
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v35i0.28577

Determination of the Homology and the Cohomology of a Few Groups of Isometries of the Hyperbolic Plane
type: item
description: 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.
subject: Articles
  topic: section
subject: Group presentation
  topic: keywords
subject: Metacyclic group
  topic: keywords
subject: Heisenberg group
  topic: keywords
subject: Free resolution Huebschmann perturbation method
  topic: keywords
subject: Homology
  topic: keywords
subject: Cohomology
  topic: keywords
creator: Nasima Akhter
creator: Subrata Majumdar
rights: Copyright (c) 2017 Bangladesh Mathematical Society
date: 2017-06-03
publication date: 2017-06-03
doi: 10.3329/ganit.v36i0.32774

An Impeccable Solution Procedure of Stochastic Programming Problems by Inserting Scenarios in Deterministic Case
type: item
description: 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.
subject: Articles
  topic: section
subject: SP
  topic: keywords
subject: DBP
  topic: keywords
subject: AMPL
  topic: keywords
subject: Scenarios
  topic: keywords
creator: Sajal Chakroborty
creator: M Babul Hasan
rights: Copyright (c) 2017 Bangladesh Mathematical Society
date: 2017-06-03
publication date: 2017-06-03
doi: 10.3329/ganit.v36i0.32770

Slip Velocity Distribution in a Parallel Plate Channel on Asymmetric Thermal Boundary Condition
type: item
description: 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.
subject: Articles
  topic: section
subject: Slip
  topic: keywords
subject: Knudsen number
  topic: keywords
subject: Compressible
  topic: keywords
subject: Reynolds number
  topic: keywords
subject: Incompressible
  topic: keywords
subject: Mathematics
  topic: keywords
creator: Md Tajul Islam
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v35i0.28575

Effects of Temperature Dependent Thermal Conductivity and Viscous Dissipation on Free Convective Flow along a Vertical Flat Plate with Asymptotic Solution
type: item
description: 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).
subject: Articles
  topic: section
subject: Surface temperature
  topic: keywords
subject: Small and large values x
  topic: keywords
subject: Flat plate
  topic: keywords
subject: Velocity
  topic: keywords
subject: Prandtl number
  topic: keywords
creator: AKM Safiqul Islam
creator: MA Alim
creator: Md Rezaul Karim
creator: ATM M Rahman
rights: Copyright (c) 2017 Bangladesh Mathematical Society
date: 2017-06-03
publication date: 2017-06-03
doi: 10.3329/ganit.v36i0.32771

Explicit Exponential Finite Difference Scheme for 1D Navier-Stokes Equation with Time Dependent Pressure Gradient
type: item
description: 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.
subject: Articles
  topic: section
subject: Navier-Stokes equation
  topic: keywords
subject: Burgers equation
  topic: keywords
subject: Explicit exponential finite difference scheme
  topic: keywords
creator: MAK Azad
creator: LS Andallah
rights: Copyright (c) 2017 Bangladesh Mathematical Society
date: 2017-06-03
publication date: 2017-06-03
doi: 10.3329/ganit.v36i0.32775

Fuzzy Version of Secant Method to Solve Fuzzy Non-Linear Equations
type: item
description: 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.
subject: Articles
  topic: section
subject: Fuzzy version of Secant method
  topic: keywords
subject: Fuzzy non-linear equation (FNLE)
  topic: keywords
subject: Linear fuzzy real number (LFRN)
  topic: keywords
subject: Mathematics
  topic: keywords
creator: Goutam Kumar Saha
creator: Shapla Shirin
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v35i0.28576

Effect of Radiation and Heat Generation on Unsteady MHD Flow of Non-Newtonian Fluid Along a Stretching Vertical Surface
type: item
description: 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.
subject: Articles
  topic: section
subject: Unsteady MHD flow
  topic: keywords
subject: Non-Newtonian fluid
  topic: keywords
subject: Heat generation/absorption
  topic: keywords
subject: Radiation
  topic: keywords
creator: Shirin Provat
creator: MR Hossain
creator: MA Samad
rights: Copyright (c) 2017 Bangladesh Mathematical Society
date: 2017-06-03
publication date: 2017-06-03
doi: 10.3329/ganit.v36i0.32769

Critical Analysis of Magnetohydrodynamic Jeffery-Hamel Flow Using Cu-Water Nanofluid
type: item
description: 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.
subject: Articles
  topic: section
subject: Jeffery-Hamel flow
  topic: keywords
subject: Magnetohydrodynamic
  topic: keywords
subject: Nanofluid
  topic: keywords
subject: Dominating singularity
  topic: keywords
subject: Critical relationship
  topic: keywords
subject: Hermite- Padé approximation
  topic: keywords
subject: Mathematics
  topic: keywords
creator: Md S Alam
creator: MAH Khan
creator: MA Alim
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v34i0.28559

Study of Inventory Model for Deteriorating Items With Exponential Demand Function
type: item
description: 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.
subject: Articles
  topic: section
subject: Inventory
  topic: keywords
subject: Deterioration
  topic: keywords
subject: Non-linear demand
  topic: keywords
subject: Inflation
  topic: keywords
subject: Trade-credit policy
  topic: keywords
subject: Mathematics
  topic: keywords
creator: Manik Mondal
creator: Mohammed Forhad Uddin
creator: Kazi Anowar Hussain
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v34i0.28557

Numerical Simulation of a Second Order Traffic Flow Model
type: item
description: 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.
subject: Articles
  topic: section
subject: Fluid dynamical traffic flow model
  topic: keywords
subject: Finite difference method
  topic: keywords
subject: Numerical Simulation
  topic: keywords
subject: Mathematics
  topic: keywords
creator: Tauhedul Azam
creator: MK Pandit
creator: LS Andallah
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v34i0.28558

Numerical Relativity: Solving Geodesics equation for Massive Particle Around Black Holes Horizon
type: item
description: 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.
subject: Articles
  topic: section
subject: Static and rotating black holes
  topic: keywords
subject: Geodesics equation
  topic: keywords
subject: Schwarzschild solution
  topic: keywords
subject: Kerr solution
  topic: keywords
subject: Mathematics
  topic: keywords
creator: Shohel Ahmed
creator: Md Showkat Ali
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v35i0.28571

A Transformed Coordinate Model to Predict Tide and Surge Along the Head Bay of Bengal- Application to Cyclone of 1991 and 1970
type: item
description: 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.
subject: Articles
  topic: section
subject: 1970 Bhola Cyclone
  topic: keywords
subject: 1991 Cyclone
  topic: keywords
subject: Tropical Storms
  topic: keywords
subject: Surge
  topic: keywords
subject: Shallow water equations
  topic: keywords
subject: Transformation of Coordinates
  topic: keywords
subject: Bay of Bengal
  topic: keywords
subject: Mathematics
  topic: keywords
creator: Farzana Hussain
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v35i0.28561

Computation of Some Second Order Sturm-Liouville Bvps using Chebyshev-Legendre Collocation Method
type: item
description: 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.
subject: Articles
  topic: section
subject: Sturm-Liouville problems
  topic: keywords
subject: Eigenvalue
  topic: keywords
subject: Chebyshev nodes
  topic: keywords
subject: Legendre polynomials
  topic: keywords
subject: Spectral collocation method
  topic: keywords
subject: Mathematics
  topic: keywords
creator: Humaira Farzana
creator: Md Shafiqul Islam
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v35i0.28574

Three Distinct Non-Hereditary Radicals Which Coincide with the Classical Radical for Rings with D.C.C.
type: item
description: 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?.
subject: Articles
  topic: section
subject: Mathematics
  topic: keywords
creator: Subrata Majumdar
creator: Kalyan Kumar Dey
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v35i0.28560

An Evaluation of an Improper Integral Arises from an Analytic Solution of a Model Boltzmann Equation for Photon Transport
type: item
description: 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.
subject: Articles
  topic: section
subject: Boltzmann Transport equation
  topic: keywords
subject: Support
  topic: keywords
subject: Radiotherapy
  topic: keywords
subject: Minimum rectangle
  topic: keywords
subject: Scattering cross section
  topic: keywords
subject: Compton scattering
  topic: keywords
subject: Arts and Sciences
  topic: keywords
creator: Taposh Kumar Das
rights: Copyright (c) 2016 Bangladesh Mathematical Society
date: 2016-06-28
publication date: 2016-06-28
doi: 10.3329/ganit.v35i0.28572