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Prof. Sudip Kumar Acharyya
Professor (Retd.)
Department of Pure Mathematics
University of Calcutta
Title: u-topology and m-topology on the ring of measurable functions
Abstract: Let M(X,A, μ) stand for the ring of real-valued measurable functions defined over a measure space (X,A, μ). As in the case of rings of realvalued continuous functions over Tychonoff spaces, the u-topology and the m-topology on the ring M(X,A, μ) are introduced appropriately via the measure μ. It turns out that these two topologies coincide when and only when each function in M(X,A, μ) is essentially bounded on X. The component of 0 in the m-topology on M(X,A, μ) is found out to be the set Lψ(X,A, μ) = {f ∈ M(X,A, μ) | for each g ∈M(X,A, μ), f · g is essentially bounded on X}. It is also proved that the measure μ on (X,A) is atomic if and only if Lψ(X,A, μ) contains at least one function which takes non-zero value on a set of positive μ-measure.
Professor
Department of Mathematics
Cooch Behar Panchanan Barma University
Title: Mass transport process of solute in hydrodynamics and magneto-hydrodynamics flow
Abstract: The transport phenomena of solute in hydrodynamics and magneto-hydrodynamics flow have a wide range of applications in the diversified fields such as environmental fluid dynamics, biomedical engineering, chemical engineering and physiological fluid dynamics. Wetlands play a vital role in sustaining ecosystems, supporting biodiversity and controlling environmental degradation. Despite its importance, the combined effects of wind shear and bed absorption on sediment transport remain underexplored. This study investigates sediment removal efficiency in wetland flow influenced by wind shear, absorbent beds, and particle settling. The time-dependent convection-diffusion equation is solved using a hybrid approach, combining Aris’s method of integral moments with a finite difference implicit scheme. Analytical expressions for two-dimensional spatial concentration distributions are derived via Gill’s series expansion. Key parameters, including wind direction (W), relative wind strength (Er), bed absorption coefficient (β), vegetation parameter (α), and settling velocity (ω), are analyzed to determine their impact on dispersion characteristics like the dispersion coefficient, concentration distribution, skewness, and kurtosis. Results show that wind shear enhances sediment dispersion when aligned with the flow (W = +1) but induces backflow and reduces dispersion within a certain wind strength range when opposing it (W = −1). On the other hand, researchers have extensively studied solute transport in magneto-hydrodynamics (MHD) channel flow, focusing on the applied magnetic field. However, the impact of the induced magnetic field on solute dispersion between two parallel plates remains poorly understood. This article presents an analytical investigation using Mei’s multi-scale homogenization approach to examine the effects of the Hartmann number, Grashof number and absorption parameter on the multi-dimensional concentration distribution and removal efficiency of a reactive solute in MHD laminar channel flow. The findings provide insights into concentration behaviour, such as the decrease in the Taylor transport coefficient with an increase in the induced magnetic field. These insights have practical implications for improving sewage and wastewater treatment by effectively separating desired particles from contaminants, contributing to advancements in environmental purification techniques.
Professor
Department of Mathematics
University of Kalyani
Title: A survey on the existence and forms of solutions of q-shift Fermat type functional equations in different dimensional complex plane
Abstract: The progression of work on functional equations, particularly those derived from classical Fermat’s equation, is both remarkable and historically significant. Notable advancements have been made in solving functional equations using various forms of c-shift equations, as evidenced by recent developments in the literature. However, despite these achievements, the study of solutions to q-shift differential equations in higher-dimensional complex spaces remains largely unexplored.
This represents a significant gap in the current body of research, as no substantial results have yet been reported in this specific domain. In this survey, we aim to address this gap by investigating the solutions and structural forms of a range of Fermat-type generalized q-shift, difference, and differential equations in Cn.
To demonstrate the existence and feasibility of such forms, we provide several illustrative examples.
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