https://dspace.iiti.ac.in/handle/123456789/3645 2026-10-25T08:42:22Z https://dspace.iiti.ac.in/handle/123456789/19421 Title: Equivalent criteria for the Riemann hypothesis for a general class of L-functions Authors: Garg, Meghali (57456671600); Maji, Bibekananda (57007978500) Abstract: In 1916, Riesz gave an equivalent criterion for the Riemann hypothesis (RH). Inspired from Riesz’s criterion, Hardy and Littlewood showed that RH is equivalent to the following bound: (Formula presented.) Recently, the authors extended the above bound for the generalized Riemann hypothesis for Dirichlet L-functions and gave a conjecture for a class of “nice” L-functions. In this paper, we settle this conjecture. In particular, we give equivalent criteria for the Riemann hypothesis for L-functions associated to cusp forms. We also obtain an entirely novel form of equivalent criteria for the Riemann hypothesis of ζ(s). Furthermore, we generalize an identity of Ramanujan, Hardy and Littlewood for Chandrasekharan–Narasimhan class of L-functions. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2026. 2026-01-01T00:00:00Z https://dspace.iiti.ac.in/handle/123456789/19403 Title: Dynamics and parameter estimation of a monkeypox model via non-standard finite difference Authors: Ghosh, Bapan (55119344600) Abstract: In this paper, we propose a discrete-time monkeypox epidemic model with a saturated incidence rate using a non-standard finite difference (NSFD) scheme. The model consists of four human population compartments and three animal population compartments. We have investigated that the model has non-negative and bounded solutions. The model has three fixed points: disease-free, endemic in humans, and endemic in all populations. Each fixed point exists and is stable under certain conditions, which depend on the basic reproduction number and Jury’s conditions. We have performed a case study through parameter estimation using weekly monkeypox data in the United States. The metaheuristic methods GA and PSO are employed to estimate the model parameters and evaluate both performances. The fitted series show that both models offer good estimates, which is supported by (Formula presented.) values close to one. Based on RMSE, the model calibration with different step sizes shows that PSO generally offers better performance than GA. We have also performed numerical simulations that confirm the stability properties of each fixed point and show that the NSFD scheme preserves dynamical consistency compared with the fourth-order Runge–Kutta and the standard Euler scheme. Hence, the NSFD scheme captures biological phenomena more effectively than the standard scheme. © 2026 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain. 2026-01-01T00:00:00Z https://dspace.iiti.ac.in/handle/123456789/19395 Title: Lyapunov stable torsional wave in multi-permeable porous viscoelastic media with sliding contact interface Authors: Chakraborty, Manish (59943180300); Manna, Santanu (55667706200) Abstract: This study investigates torsional wave propagation in a complex geophysical configuration consisting of a homogeneous, isotropic, initially stressed, fluid-saturated multi-porous viscoelastic layer with multi-permeability overlying a transversely isotropic, heterogeneous viscoelastic half-space. The interface permits sliding contact, and the boundary surface is corrugated. Surface irregularity is represented using trigonometric functions, while binomial variations model heterogeneity in density and shear modulus. By employing separation of variables, the governing equations reduce to modified Bessel-type differential equations, enabling the derivation of a closed-form dispersion relation via asymptotic expansions. The formulation is validated by recovering the classical Love-wave dispersion relation as a limiting case. To assess numerical accuracy and corroborate the analytical results, linear and quadratic finite-element models are developed, and displacement fields and dispersion curves are compared.Furthermore, the stability of the resulting semi-discrete finite-element formulation is rigorously investigated through an energy-based Lyapunov framework, and the associated spectral characteristics of the assembled global damping and stiffness matrices are utilized to identify parameter-dependent stable and unstable regimes. Parametric analyses for a fractured triple-porous medium demonstrate that porous architecture, material properties, interface sliding, and boundary geometry significantly influence torsional wave characteristics. Convergence is quantified through L2 and energy norms, as well as relative L2 error norms under mesh refinement. In addition, frequency-domain measures, including energy flux, dissipated energy density, and quality factor, provide further physical insight into the attenuation mechanisms and energy transport within the proposed multi-porous viscoelastic medium. The results are pertinent to geophysical applications and structural engineering problems involving heterogeneous media and complex boundary conditions. © 2026 2027-01-01T00:00:00Z https://dspace.iiti.ac.in/handle/123456789/19363 Title: DEEP LEARNING ASSESSMENT OF NEUROLOGICAL IMAGING Authors: Tanveer, M. Abstract: Deep Learning Assessment of Neurological Imaging provides an introduction to deep learning structures and pre-processing methods for detecting MRI anomalies. The book also provides a comprehensive accounting of deep learning research on MRI images for Alzheimer's disease, Parkinson's disease, and schizophrenia, and includes a discussion on current research issues and future objectives. This book is a valuable resource to guide new entrants in the field, helping them make a meaningful impact in their development efforts. The book concludes with a brief overview of problems and potential future advancements in the field. Copyright © 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. 2026-01-01T00:00:00Z