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Enhancement Of Security Of Diffie-Hellman Key Exchange Protocol Using Dual Rsa Cryptography
(Department of Mathematics, NITS, 2025) Hazra, Dipanwita
The field of cryptography focuses on securing sensitive information against unauthorized access and cyber threats. One of the most widely used techniques in secure communication is the Diffie-Hellman (DH) key exchange, which enables two parties to establish a shared secret key over a public network. However, DH is susceptible to Man-in-the-Middle (MitM) attacks, where an attacker can intercept or alter the exchanged messages. To mitigate this critical vulnerability, this thesis introduces a novel cryptographic protocol: the Dual RSA-Integrated Diffie Hellman Key Exchange Protocol. The proposed method enhances the standard DH protocol by incorporating two layers of RSA encryption, providing mutual authentication and stronger defense against interception and tampering. The performance and security of the proposed protocol are compared with traditional DH and standalone RSA schemes. Results demonstrate that the integrated approach significantly improves resistance to MitM attacks while maintaining the confidentiality of key exchanges. This makes the Dual RSA-Integrated protocol a more secure and reliable solution for modern encrypted communication systems.
A mathematical model on EMHD peristaltic flow of UO2 nanofluid with microbes through a porous conduit: Application to flows in esophagus
(Department of Mathematics, NITS, 2025) Mannan, Abdul
An analytical study is presented on the bioconvective peristaltic flow of a Newtonian nanofluid within a porous, symmetric channel featuring flexible walls. The nanofluid behavior is examined under the influence of externally applied electric and magnetic fields. The model incorporates effects from motile microorganisms. The electroosmotic flow is described using the Nernst–Planck and Poisson equations. To simplify the mathematical formulation, assumptions of long wavelength and low Reynolds number are employed. The Homotopy Perturbation Method (HPM), along with the lubrication approximation, is utilized to derive analytical solutions for the reduced, non-dimensional governing equations. Graphical analysis is used to explore the impacts of various physical parameters on axial velocity, temperature, nanoparticle concentration, and microorganism density. It is observed that increasing buoyancy forces promote increased axial velocity. The Hartmann number and Joule heating parameter contribute to temperature elevation by inhibiting convective heat loss and producing internal heat. Furthermore, higher thermophoresis effects lead to greater nanoparticle accumulation, an effect magnified by Brownian motion. Increased Peclet numbers and bioconvection parameters are found to diminish microorganism density due to restricted diffusion and intensified convective disturbances. we believe that the outcomes of this study have potential applications in several areas, including bioengineering, bioreactors, enzyme processing, solar thermal systems, and energy storage technologies.
A study on q-series and partitions
(Department of Mathematics, NITS, 2025) Shit, Sabuj Baran
This Thesis explores the rich field of the q-series, highlighting how it interacts with three important mathematical theorems: Euler’s identity, the Jacobi triple product and the Pentagonal number Theorem, Ramnujan’s Partition Congruences. A foundation for comprehending the structure of q-series and their generating functions is provided by Euler’s identity. The depth of q-series is further demonstrated by the Pentagonal Number Theorem, which relates to combinatorics and integer partitions. Together, these results illustrate the profound coherence of the q− series within mathematics.
A study on the Monkeypox virus disease using the Mathematical Modelling
(Department of Mathematics, NITS, 2025) Gupta, Abhishekh
In this study, we proposed a novel mathematical model to analyze the transmission dynamics of the Monkeypox virus. The model is formulated as a system of non-linear ordinary differential equations, incorporating key epidemiological classes for both hu man and rodent populations: susceptible, exposed, infected, and recovered humans (SEIR), and susceptible and infected rodents (SI). We conducted a thorough anal ysis of the model’s equilibrium points, identifying the Monkeypox-Free Equilibrium point (MFE), the Rodent-Free Endemic Equilibrium point (RDEE), and the Endemic Equilibrium point (EE). We rigorously established the local asymptotic stability of the model at the MFE and RDEE. Furthermore, the global asymptotic stability of the endemic equilibrium was demonstrated through the construction and analysis of a suitable Lyapunov function. A sensitivity analysis was performed on the parameters comprising the basic reproduction number to determine their relative influence on dis ease transmission. Finally, the theoretical findings were complemented and illustrated through specific numerical simulations.
Numerical Analysis For Singularly Perturbed Delay Differential Equations
(Department of Mathematics, NITS, 2025) Hazarika, Pradyut
This thesis investigates a singularly perturbed delay differential equation modeled as a parabolic partial differential equation (PDE). Such problems are characterized by the presence of a small perturbation parameter and a delay term, which together induce boundary and interior layers, making both analysis and numerical approximation challenging. We begin by decomposing the solution and the differential operator into regular and singular components, enabling precise characterization of the solution structure. Rigorous bounds are derived for both components, shedding light on their respective behaviors and interactions. To approximate the solution numerically, the domain is discretized, and a weak formulation of the model problem is developed. This formulation is further employed to construct a finite element method (FEM) tailored to handle the singular perturbation and delay effects efficiently. Stability and accuracy of the FEM are established through analytical and numerical validation. The methodology ensures robustness in capturing sharp gradients and delayed responses in the solution. Overall, the thesis provides a comprehensive framework for understanding and approximating singularly perturbed delay PDEs. The results lay the groundwork for future research in higher dimensions, nonlinear models, and applications in science and engineering involving time delays and rapid transitions.
Mathematical Study on Wave Reflection in Graded Electro-elastic Waveguide
(Department of Mathematics, NITS, 2025) Parasar, Hemanga Jyoti
The incidence of quasi-P (qP) wave on a waveguide made of pre-stressed electro-elastic material with rigid boundary surface is studied in this work to determine how elastic waves are reflected. For reflected qP, quasi-SV (qSV) and electro-acoustic (EA) waves, closed form expressions for the reflection coefficients (RCs) are obtained by introducing suitable mechanical and electrical boundary conditions. Furthermore, functional grading and material rotation are taken into account as well. The dissertation consists of two chapters, outlined as follows: • In the introductory chapter, Chapter 1, important ideas related to wave reflection are defined and explained. It covers the fundamental ideas that are important to this in vestigation, such as the effects of pre-stress, electro-elastic materials, and elastic wave reflection. It also investigates how these waves behave at rigid boundary surfaces. Addi tionally, the chapter introduces the role of functionally graded materials and the influence of rotational motion on wave propagation. • Elastic wave reflection in a rotating graded electro-elastic waveguide is the primary focus of Chapter 2. It provides a thorough articulation of the problem, taking into account the complications brought out by rotational motion and functional grading. The chapter gives the analytical solution of the wave equations under the boundary conditions that correspond to a rigid surface. The RCs for the reflected waves, resulting from the inci dence of elastic waves on the rigid boundary, are derived and discussed. Furthermore, a number of particular instances are examined to establish the dependency of various physical parameters on RCs.
Unification, Dilation, and von Neumann’s Inequality
(Department of Mathematics, NITS, 2025) Roshan
In this project, we present elegant proofs of four fundamental theorems using Zabreiko’s Lemma. Subsequently, we delve into Dilation Theory and von Neumann’s Inequality, exploring their diverse applications. Inspired by [1, 2], our primary objective is to explicitly check the generalizations of Ando’s dilation for a Q-commutative setup, where Q is a unitary operator. Additionally, we would like to establish a concrete connection between von Neumann’s Inequality and distinguished varieties. We aim to investigate the Q-commutative extensions of both Dilation Theory and von Neumann’s Inequality.In a Q-commutative setup, we focus on an isometric dilation of a Q−commuting pairof contractions. The present attempt is inspired by the work done by Sibaprasad Barikand Bappa Bisai on the subject ”A Generalization of Ando’s Dilation, and Isometric Dilations for a Class of Tuples of q-Commuting Contractions” [3]. We are taking aQ−commuting pair of contractions to perform Ando’s dilation modulo some conditions.
Almost Periodic Functions and Their Applications
(Department of Mathematics, NITS, 2025) Samal, Jajati Keshari
Periodic functions are among the most frequently occurring classes of functions in both applied and analytical mathematics. Due to this wide range of applicability, we aim to extend this class of functions to enable broader analysis. The extended class we discuss is known as almost periodic functions. In this thesis, we begin by exploring the motivation for and development of almost periodic functions, which arise from the theory of periodic functions in Chapter 1. Chapter 2 presents the history of the development of almost periodic functions. In Chapter 3, we revisit some fundamental results from analysis that are useful for our proofs. Chapter 4 reviews key properties and characterizations of almost periodic functions, including Bochner’s criterion, and provides relevant counterexamples. In Chapter 5, we discuss important applications of these functions in the context of ordinary differential equations. Finally, Chapter 6 concludes the thesis with the future scope of almost periodic functions.
Quadratic Approximation based GA for Function Optimization
(Department of Mathematics, NITS, 2025) Kumar, Nitish
This thesis presents an enhanced Genetic Algorithm (GA) framework utilizing Quadratic Approximation (QA) to solve both constrained and unconstrained optimization problems more efficiently. The primary objective is to obtain better fitness values by accelerating convergence and improving solution accuracy. In the proposed approach, a local quadratic approximation is integrated into the GA to refine solutions, thus balancing global exploration and local exploitation. To evaluate the effectiveness of the proposed QA-based GA (QA-GA), extensive experiments were conducted on standard benchmark functions, including Sphere, Rastrigin, and Ackley functions, among others. The performance of the QA-GA was systematically compared with the classical GA in terms of convergence speed and optimal solution quality. Experimental results indicate that QA-GA consistently outperforms the traditional GA by converging faster and locating better global optima across various test cases. The findings confirm that the integration of quadratic approximation significantly enhances the search capability of GA, making QA-GA a robust approach for complex optimization tasks.
Mathematical modeling on particulate suspension couple stress fluid flow in a stenosed artery under electro-magnetic effects
(Department of Mathematics, NITS, 2025) Verma, Santosh Kumar
An analytical study is presented on the fluid dynamics of blood flow in stenosed arteries, with a focus on pulsatile flow, electric and magnetic fields, and the non-Newtonian nature of blood. The narrowing of arteries caused by stenosis induces significant alterations in blood flow, making it essential to explore these changes for improved disease evaluation and therapeutic strategies. A mathematical model is proposed to describe pulsatile, laminar, incompressible, and electrically conductive flow, represented by the Jeffrey fluid model with couple stress effects. This model accounts for the effects of electromagnetic forces and periodic body forces, under the assumptions of low Reynolds number, mild stenosis, and low wall zeta potential. To analyze key parameters, including axial velocity, wall shear stress, and flow resistance, the governing equations are solved using Laplace and Hankel transforms. Graphical representations of the flow characteristics are generated using MATLAB, providing insights into the complex flow dynamics in stenosed arteries. This research aims to contribute to the development of medical devices and enhance treatment methodologies for cardiovascular diseases.