Current Issue
Department of Mathematics, Lady Shri Ram College for Women presents Éclat, Volume XVI.
1. Rigour in Mathematics
a) Incorporating Uncertainity in Data Envelopment Analysis: A comparative Review of Stochastic and Fuzzy Extensions
Author: Jyoti Darbari and Alisha
Abstract Data Envelopment Analysis (DEA) is a non-parametric method used to evaluate the efficiency of Decision-Making Units (DMUs) by comparing multiple inputs and outputs without assuming a specific functional form. However, traditional DEA models operate under the assumption of deterministic data, which may not adequately capture the uncertainties inherent in real-world scenarios. To address this limitation, researchers have extended DEA methodologies to incorporate stochastic and fuzzy elements, leading to the development of Stochastic DEA (SDEA) and Fuzzy DEA (FDEA) models. This paper reviews advanced DEA models, focusing on SDEA and FDEA, and highlights their theoretical basis, key applications, and the role of uncertainty in efficiency analysis , while suggesting future research directions. & Download full PDF
b) Generalized Banach Contraction Principle
Author: Vidya Sagar, Anam Shaikh and Isha Yadav
Abstract This paper generalizes the Banach contraction principle to partial metric and b-metric spaces by relaxing classical contraction conditions and incorporating the coincidence property of mappings. These results unify existing fixed-point theorems and broaden their applications. & Download full PDF
c) Solution of the (2+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation using Generalized Kudryashov Method
Author: Shalini Yadav, Ayushi Singh, Chelsi Gurjar and Suhani Singh
Abstract This paper aims to obtain the exact solution of a non-linear partial differential equation, specifically the (2+1)-Dimensional Boiti-Leon-Manna-Pempinelli(BLMP) equation in shallow water which is extensively used in various fields of chemistry, mathematics, and physics, including fluid dynamics, mathematical physics, plasma physics, optics, and quantum mechanics. The study will utilize one recently developed efficient mathematical method, the Generalized Kudryashov (GK) method. This method provides useful tools for analyzing complex behaviors in various physical systems. The model is observed to have kink-type soliton wave solutions. The literature has never included any of the solutions obtained for this model. & Download full PDF
2. Extension of Course Content
a) Application of Bilinear Interpolation in Image Processing
Author: Sucheta Nayak, Dhriti Mahajan and Mansi Kandwal
Abstract This paper reviews a novel image zooming approach that employs Bilinear Interpolation to enlarge images. It provides a comparative study using Bicubic Interpolation using Python code. & Download full PDF
b) Dynamical Analysis and Exact Solutions of Drinfeld-Sokolov-Satsuma-Hirota Equation by
Generalized Exponential Rational Function Method.
Author: Setu Rani, Diya and Ishita Tayal
AbstractFor the Drinfeld-Sokolov-Satsuma-Hirota problem, we apply the Generalized Exponential Rational Function approach to obtain analytical solutions for Non-linear Partial Differential Equations. Combined with wave transformation, GERF yields exact solutions expressed in trigonometric, exponential, hyperbolic, and rational functions, with 2D, 3D, and contour plots showcasing dynamic behavior. These results offer insight and advance research in soliton theory and non-linear waves. & Download full PDF
3. Interdisciplinary Aspects of Mathematics
a) Mathematical Modeling to Analyze Price Stability Dynamics
Author: Sunil Kumar Yadav, Mehak Gupta and Ridhima Asija
AbstractFinancial markets have historically been subject to severe fluctuations driven by economic, political, and social factors. This paper analyses the price fluctuations and subsequent stabilization of gold during periods of extreme economic downturns and depicts the difference in price stability dynamics post-COVID-19. The study is divided into two broad categories, Monte Carlo Simulations for Long-term and Exponential Model for Short-term. Although prices typically stabilized within a five-year period during previous financial crises, it is hypothesized that the aftermath of the COVID-19 pandemic may unfold differently. & Download full PDF