GANIT: Journal of Bangladesh Mathematical Society

Lyapunov Functions and Qualitative Analysis of an Epidemic Model with Vaccination

Thu, 14 Mar 2024 00:00:00 +0000

The spatial-temporal diffusion dynamics of infectious disease with vaccination therapy are studied through a mathematical model. We have investigated the well-posedness, disease-free equilibrium, disease equilibrium, the existence and the uniqueness of solutions, and the calculation of basic reproduction numbers by Jacobian matrix. After that, the positivity, as well as boundedness of solutions, are also established. The global stability of diseasefree and steady-state disease results is established by utilizing compatible Lyapunov functions and LaSalle’s invariance principle. Illustration of the numerical examples to show the dynamics of different population groups over time. The effects of different parameters on the compartments are shown in detail.

GANIT J. Bangladesh Math. Soc. 44.1 (2024) 01- 22

Intuitionistic Fuzzy R₀ Bitopological Space: An In-depth Exploration

Saikh Shahjahan Miah, Badrun Naher Jumur — Thu, 14 Mar 2024 00:00:00 +0000

We popose intuitionistic fuzzy bitopological R0-spaces (abbreviated IFB-R0) in this study. On intuitionistic fuzzy bitopological space, we introduce several new ideas of R0-space. Our notions are maintained under one-one, onto, fuzzy open, and fuzzy continious mappings, and we demonstrate that R0-spaces satisfy the "good extention" property.

GANIT J. Bangladesh Math. Soc. 44.1 (2024) 23- 28

A Comparative Study of ARIMA, Artificial Neural Networks, and Kalman Filter Models for Dhaka Stock Exchange Forecasting

Anika Tahsin Biva, Md Shafiul Alom Khan, A B M Shahadat Hossain — Tue, 25 Jun 2024 00:00:00 +0000

Abstract not available

GANITJ. Bangladesh Math. Soc. 44.1 (2024) 29-58

On the Soliton Structures of the (2+1)-Dimensional Long Wave-Short Wave Resonance Interaction Equation with Two Analytical Techniques and its Bifurcation Analysis

S M Rayhanul Islam — Tue, 25 Jun 2024 00:00:00 +0000

The (2+1)-dimensional long-wave-short-wave resonance interaction (LWSWRI) equation has extensive applications in various fields of science and engineering. The (2+1)-dimensional LWSWRI equation and two analytical techniques have been considered in this manuscript. These schemes, via the advanced auxiliary equation, improve F-expansion techniques applied to the considered model and obtain soliton solutions with a lot of parameters. These derived soliton solutions manifest as trigonometric, hyperbolic, rational, and exponential function solutions, highlighting their utility as mathematical tools. The study offers visual representations, including both three-dimensional (3D) and two-dimensional (2D) combined charts, to illustrate selected solutions and demonstrate the influence of parameters. Furthermore, the bifurcation analysis (BA) of the model is studied through the planar dynamical systems. The stability of the equilibrium points (EPs) and a graphical representation of the phase chart of the system are investigated. The Hamiltonian function is also derived in this manuscript. These methodologies function as dependable, straightforward, and powerful instruments for examining diverse nonlinear evolution equations encountered in physics, applied mathematics, engineering, and other disciplines.

GANITJ. Bangladesh Math. Soc. 44.1 (2024) 59–76

Analytic Mapping Associated with Generalized Modular Equation

Md Shafiul Alam — Tue, 25 Jun 2024 00:00:00 +0000

Abstract available in PDF

GANIT J. Bangladesh Math. Soc. 44.1 (2024) 77–91

A Characterization of Jordan Automorphisms on Jordan Ideals of Prime Gamma Rings

Sujoy Chakraborty, Akhil Chandra Paul — Tue, 25 Jun 2024 00:00:00 +0000

We study and develop the concepts of homomorphism and anti-homomorphism to derive some important results in the theory of gamma rings. This article attempts to analyze some of the results of Ali et al. [1] in case of classical rings for extending those in the context of gamma rings. We establish a number of results related to automorphism, antiautomorphism and Jordan automorphism on Jordan ideal of prime gamma rings to obtain a new characterizing result. If M is a 2-torsion free prime gamma ring fulfilling a suitable condition, J is a non-zero Jordan ideal as well as a subring of M and Φ:M → M is a Jordan automorphism, then we prove that Φ is an automorphism or Φ is an anti-automorphism.

GANIT J. Bangladesh Math. Soc. 44.1 (2024) 92–98

A New Method for Solving Fully Generalized Quadratic Fuzzy Transportation Problem under Fuzzy Environment

A S M Mohiul Islama, Md Habibur Rahmana, Usama Ibn Aziza, Yeasin Rezaa — Tue, 25 Jun 2024 00:00:00 +0000

This paper presents a solution approach for the transportation problem (TP) in an uncertain environment using trapezoidal intuitionistic fuzzy numbers (TrIFNs). We introduces a new approach to solving Transportation Problems (TP) in uncertain environments, focusing on the Trapezoidal Fermatean Fuzzy Number (TrFFN). The Fermatean Fuzzy TP (FFTP) treats transportation cost, supply, and demand as TrFFN, offering superior performance and feasibility compared to existing methods. It also highlights its advantages in uncertain environments. Using standard LP algorithms, the IFTP is converted into a deterministic linear programming (LP) problem. The quadratic fuzzy transportation problem is a significant problem in operations research and optimization, involving finding the best feasible solution for a transportation problem with quadratic function cost coefficients. The paper presents a new method for solving the fully generalized quadratic fuzzy transportation problem under an ambiguous environment, considering uncertainties and fuzziness inherent in real-world transportation scenarios. The paper also addresses the minimum spanning tree (MST) problem, which involves a graph with either trapezoidal or triangular fuzzy numbers assigned to each arc length. The graded mean integration representation of fuzzy numbers is used to solve these problems. The paper proposes an alternative undefined outranking method by extending the Elimination Et Choix Traduisant La Realite (ELECTRE 1) Method method to consider uncertain, imprecise, and linguistic assessments a group of decision-makers provides. The report addresses the gap in the Electre 1 literature for problems involving conflicting systems of criteria, uncertainty, and imprecise information.

GANITJ. Bangladesh Math. Soc. 44.1 (2024) 99–106