(Si15-121) Analyzing Seitr Tuberculosis Transmission Model Using Caputo–Fabrizio Fractional Derivative With Diverse Contact Rates,
2025
Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology
(Si15-121) Analyzing Seitr Tuberculosis Transmission Model Using Caputo–Fabrizio Fractional Derivative With Diverse Contact Rates, S. S. Sumaiya Banu, T. Gunasekar, S. Manikandan, Kamalendra Kumar, M. Suba
Applications and Applied Mathematics: An International Journal (AAM)
In the modern age, tuberculosis remains a pressing global health concern. Our study introduces and evaluates the SEITR pandemic TB transmission model, dividing the population into five compartments to explore distinct characteristics relevant to our investigation. Additionally, we delve into the application of fractional calculus. Through the Laplace transform method, we derive series solutions for all compartments, ensuring their existence and uniqueness. We also investigate the reproduction number of the tuberculosis epidemic model, examining how varying contact rates impact disease spread. We apply the predictor-corrector method for the Caputo-Fabrizio fractional derivative to verify the accuracy of our approach. This accurately …
Investigating The Market Dynamics Of Aeroponically Cultivated Products With Delay,
2025
Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh
Investigating The Market Dynamics Of Aeroponically Cultivated Products With Delay, Pulak Kundu, Uzzwal Kumar Mallick
Mathematical Modelling and Numerical Simulation with Applications
Aeroponically grown potatoes offer higher yields and year-round production but often face delayed market entry due to high setup costs, technical barriers, and logistical challenges. A delay-based mathematical model has been newly proposed in this study to analyze the dynamics of demand, supply, and pricing for aeroponically grown products. The model’s existence, stability, and sensitivity have been investigated analytically, and numerical simulations have been carried out using the Runge-Kutta 4th order method with the dde23 solver. Findings reveal that market stability is maintained when delays are below seven years, but delays beyond this threshold lead to persistent fluctuations in price, …
Stabilized Weak-Gradient Discontinuous Finite Elements With Optimal Error Estimates For Second-Order Elliptic Pdes,
2025
Department of Mathematics, College of Computing and Mathematical Sciences, Khalifa University of Science and Technology, P.O. Box: 127788, Abu Dhabi, United Arab Emirates
Stabilized Weak-Gradient Discontinuous Finite Elements With Optimal Error Estimates For Second-Order Elliptic Pdes, Aymen Laadhari
Mathematical Modelling and Numerical Simulation with Applications
This work introduces an accurate finite element approach employing a new stabilized discrete weak gradient, designed for second-order elliptic problems on arbitrary conforming meshes. We formulate the approach within a discontinuous Galerkin framework and derive a consistent and coercive bilinear form. Appropriate error analysis on a model problem confirms optimal convergence. Building on the core analysis, we extend the method to more challenging settings, including time-dependent heterogeneous scenarios and a biophysically realistic optimal-control model of photobleaching in the budding yeast cell. We further illustrate the versatility of the weak-gradient construction by applying it to an unsteady level-set equation relevant to …
High-Order Adaptive Solutions For Coupled Fractional Riccati Equations Via Daubechies Redundant Frames,
2025
Department of Mathematics, Zayed University, Abu Dhabi, United Arab Emirates
High-Order Adaptive Solutions For Coupled Fractional Riccati Equations Via Daubechies Redundant Frames, Mutaz Mohammad, Alexander Trounev
Mathematical Modelling and Numerical Simulation with Applications
Coupled fractional Riccati equations play a fundamental role in modeling complex systems with memory effects and anomalous diffusion, frequently arising in engineering, control theory, finance, and quantum mechanics. Their analytical and numerical treatment remains highly challenging due to the nonlocal nature of fractional-order derivatives and the presence of nonlinear coupling terms. This study introduces an adaptive numerical framework that combines the Caputo fractional derivative with redundant Daubechies wavelet frames. The method leverages multi-resolution analysis, compact support, and controlled redundancy to achieve accurate approximation of both localized and global solution features, particularly in scenarios characterized by singular behavior and long-range memory …
The Consideration Of Two Scalarization Methods For The Multi-Objective Nurse-To-Patient Assignment Problem,
2025
Department of Industrial and Entrepreneurial Engineering and Engineering Management, Western Michigan University, Kalamazoo, 49008-5336, MI, USA
The Consideration Of Two Scalarization Methods For The Multi-Objective Nurse-To-Patient Assignment Problem, Ilgın Acar, Steven E. Butt, Aydın Sipahioğlu, İslam Altın
Mathematical Modelling and Numerical Simulation with Applications
In this research, the application of two scalarization methods, namely the conic scalarization method and the $\varepsilon$-constraint method, is investigated within the context of a multi-objective optimization problem. These methods are used to address the challenge of assigning nurses to patients on a hospital unit during a shift. The two objective functions of this assignment problem are based on patient workload metrics and unit-related travel distance measures. The proposed solution approach demonstrates the ability to generate solutions that eluded the previous mathematical programming techniques that relied on simplistic weightings of conflicting objective functions. In addition, it is found that the …
Global Stability And Bifurcation Analysis Of A Predator-Prey Model Involving Allee Effect And Monod-Haldane Functional Response,
2025
Department of Mathematics, University of Brawijaya, Malang 65145, Indonesia
Global Stability And Bifurcation Analysis Of A Predator-Prey Model Involving Allee Effect And Monod-Haldane Functional Response, Resmawan Resmawan, Agus Suryanto, Isnani Darti, Hasan S. Panigoro
Mathematical Modelling and Numerical Simulation with Applications
In this paper, the complexity of the dynamic behavior of the interaction between prey and predator is studied. The predator-prey relationship involves Allee effects and Monod-Haldane functional response. The constructed model has been shown to have validity in several respects, including the existence and uniqueness of the solution, as well as its non-negativity and boundedness. Three equilibrium points, namely trivial, axial, and coexistence points, are found, including their global dynamics using the Lyapunov function together with the LaSalle's invariance principle. The effect of the predation conversion rate causes changes in the dynamic behavior of predators and prey, which is characterized …
Solution Of Fractional Order Diffusion Equations With Clique Neural Network,
2025
Distance Education Center, Agri Ibrahim Cecen University, Agri, Türkiye
Solution Of Fractional Order Diffusion Equations With Clique Neural Network, Merve Zeynep Kaya, Mesut Karabacak, Ercan Çelik
Mathematical Modelling and Numerical Simulation with Applications
In this paper, the clique artificial neural network method is used to solve the fractional diffusion equation, which is a subclass of partial differential equations. The clique neural network architecture is constructed using input, hidden, and output layers. Several degrees of clique polynomials were used as activation functions, and the output layer was obtained by multiplying them with weight coefficients. Subsequently, the optimization equation was derived, and the exact solution, numerical solution, and error function graphs were obtained using a specialized algorithm. Analysis of the results demonstrates that the clique artificial neural network method provides quicker and more accurate results …
Synergistic Modeling Of Hydrogel Gelation Via Time-Delay Dynamics And Machine Learning Algorithms,
2025
Department of Mathematics and Science Education, Faculty of Education, Kahramanmaraş Sütçü İmam University, Kahramanmaraş, Türkiye
Synergistic Modeling Of Hydrogel Gelation Via Time-Delay Dynamics And Machine Learning Algorithms, Mine Babaoglu, Dipesh ., Pankaj Kumar, Jagjit Singh Dhatterwal, Mansoor Alsulami
Mathematical Modelling and Numerical Simulation with Applications
This paper presents an integrated framework in which delay differential equation (DDE) modeling and machine learning (ML) approaches are coupled to study hydrogel formation kinetics, with emphasis on delayed crosslinker addition. Conventional mechanistic models disclose many physical and kinetic complexities of reacting mixtures; they seldom depict the nonlinear and time-evolving complexities inherent in developing polymer networks. To address this, a mathematical model is developed that examines how the insertion of crosslinkers affects system stability and equilibrium. Analytical and numerical results show that delays nearing critical levels cause bifurcation behavior with substantial implications on gelation kinetics. Sophisticated machine learning systems, including …
Dynamics And Optimal Intervention Strategies In A Shigellosis Transmission Model,
2025
Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Türkiye
Dynamics And Optimal Intervention Strategies In A Shigellosis Transmission Model, Mehmet Gümüs, Shewafera Wondimagegnhu Teklu, Kemal Türk
Mathematical Modelling and Numerical Simulation with Applications
This research explores how water treatment contributes to limiting the transmission of Shigellosis, an infection caused by bacteria from the Shigella genus. A mathematical framework is formulated to evaluate the influence of protective strategies and water purification on the spread of the disease. To confirm the model's biological relevance, its well-posedness is investigated. The basic reproduction number $(\mathfrak{R}_0)$, a critical indicator of disease behavior, is derived using the matrix operator method. Findings indicate that if $\mathfrak{R}_01$, the infection persists, with the endemic equilibrium exhibiting local asymptotic stability. A comprehensive cost-effectiveness analysis reveals that combining environmental protection with water treatment represents …
Some New Three-Term Conjugate Gradient Methods For Riemannian Optimization With Application To The Gough-Stewart Platform,
2025
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok, Thailand
Some New Three-Term Conjugate Gradient Methods For Riemannian Optimization With Application To The Gough-Stewart Platform, Nasiru Salihu, Poom Kumam, Lin Wang, Sani Salisu
Mathematical Modelling and Numerical Simulation with Applications
Three-term conjugate gradient (TTCG) methods have been extensively studied for optimization within Euclidean geometry, with some inherently satisfying the sufficient descent property, thus enhancing their theoretical superiority. However, other TTCG methods have been developed that incorporate restarting the search direction, simplify the steepest descent approach, or rely on the convexity assumptions of f to establish their convergence results. This paper introduces the Riemannian three-term conjugate gradient (RTTCG) methods. The search direction in these RTTCG methods consistently satisfies the sufficient descent condition, regardless of the line search employed, and does so without requiring a restart mechanism. By utilizing retraction and vector …
Memoir On A General Property Of A Very Extensive Class Of Transcendental Functions,
2025
College of the Holy Cross
Memoir On A General Property Of A Very Extensive Class Of Transcendental Functions, Niels Henrik Abel 1802--1829, John Little
Mathematics and Computer Science Department Faculty Scholarship
We present this new commentary and translation anticipating the 200th anniversary of the work, commonly known as Abel's ``Paris memoir.'' This is recognized today as one of Abel's most original and influential works. It is significant mostly because it marked the first appearance of a form of a result in the theory of algebraic curves and Riemann surfaces that has come to be known as ``Abel's theorem.'' However, Abel's original understanding of the meaning and context of his result was quite different from the typical modern formulation and the development of the modern understanding has been a long and tortuous …
Constructions Of Compact Dupin Hypersurfaces With Non-Constant Lie Curvatures,
2025
College of the Holy Cross
Constructions Of Compact Dupin Hypersurfaces With Non-Constant Lie Curvatures, Thomas E. Cecil
Mathematics and Computer Science Department Faculty Scholarship
A hypersurface M in the unit sphere Sn ⊂ Rn+1 is Dupin if along each curvature surface of M, the corresponding principal curvature is constant. If the number g of distinct principal curvatures is constant on M, then M is called proper Dupin. In this expository paper, we give a detailed description of two important types of constructions of compact proper Dupin hypersurfaces in Sn. One construction was published in 1989 by Pinkall and Thorbergsson [35], and the second was published in 1989 by Miyaoka and Ozawa [26]. Both types of examples have the …
Quantum General Relativity,
2025
State University of New York at Stony Brook
Quantum General Relativity, James Glimm
Department of Applied Mathematics & Statistics Faculty Publications
We construct a quantum general relativity model of spin 2 Yang-Mills fields, complete at the level of theoretical physics with complete mathematics not included. The construction includes a cosmological model. Existing Type Ia supernova data analysis used for this cosmology shows zero cosmological constant and zero dark energy.
Investigating Potential Alzheimer's Disease Therapies Through An Agent-Based Model Of Impaired Microglia Metabolismmodeling Impaired Microglia Metabolism,
2025
Cal Poly Humboldt
Investigating Potential Alzheimer's Disease Therapies Through An Agent-Based Model Of Impaired Microglia Metabolismmodeling Impaired Microglia Metabolism, Cheyenne Ty, Abigail Penland, John Gerving, Martin Mendoza-Ceja, Megan Pratt, Kamila Larripa
Spora: A Journal of Biomathematics
Alzheimer’s disease is the leading cause of dementia globally and is marked by amyloid-β plaque accumulation, decreased brain pH, disrupted metabolism, and increased permeability of the blood-brain barrier. Microglia, the resident immune cells of the central nervous system, are essential for maintaining brain homeostasis and are critically involved in the progression of AD. While microglia can initiate protective immune responses to injury and disease, dysregulated microglial metabolism may contribute to the exacerbation of Alzheimer's pathology. To investigate potential therapeutic strategies, we developed an agent-based model simulating the effects of exercise and metabolic enhancement on dysfunctional microglia. Our findings suggest that …
Imaging A Digital Stock Exchange,
2025
University of Alabama at Birmingham
Imaging A Digital Stock Exchange, Mrigank Mrigank
All ETDs from UAB
In 2021, Rama Cont and Marvin M¨uller proposed a stochastic partial differential equation (SPDE) that models the density of orders in the limit order book at a given distance from the mid-price. In this thesis, we begin with a generalized version of the Cont–M¨uller SPDE and formulate an associated inverse problem. We present two alternative approaches to framing this inverse problem and establish, under appropriate assumptions, that it is conditionally well-posed. To solve the inverse problem, specifically, to recover the coefficients in the generalized Cont–M¨uller model, we adapt a variational approach involving the minimization of convex functionals. The recovered coefficients …
Analytical And Numerical Approaches To Parameter Estimation In Damped Oscillatory Systems,
2025
University of Tennessee at Chattanooga
Analytical And Numerical Approaches To Parameter Estimation In Damped Oscillatory Systems, Gracie Crooks, F. Ayça Çetinkaya
CODEE Journal
We investigate the inverse problem of identifying damping and stiffness parameters in one-dimensional damped oscillatory systems governed by second-order differential equations. Focusing on mass–spring–damper models, we analyze the qualitative behavior of solutions across underdamped, critically damped, and overdamped regimes, and derive explicit conditions for parameter recovery based on time-domain observations such as equilibrium crossings and turnaround points. Two numerical estimation methods are developed and compared: a finite-difference least-squares approach based on central difference approximations, and a finite element formulation derived from a variational framework using piecewise linear basis functions. Computational experiments using synthetic data assess the accuracy, stability, and noise …
Greedy Algorithm For Neural Networks For Indefinite Elliptic Problems,
2025
Missouri University of Science and Technology
Greedy Algorithm For Neural Networks For Indefinite Elliptic Problems, Qingguo Hong, Jiwei Jia, Young Ju Lee, Ziqian Li
Mathematics and Statistics Faculty Research & Creative Works
The paper presents a priori error analysis of the shallow neural network approximation to the solution to the indefinite elliptic equation and a cutting-edge implementation of the Orthogonal Greedy Algorithm (OGA) tailored to overcome the challenges of indefinite elliptic problems, which is a domain where conventional approaches often struggle due to the lack of coerciveness. A rigorous priori error analysis that shows the neural network's ability to approximate the solution of indefinite problems is confirmed numerically by OGA. We also present the error analysis of the relevant numerical quadrature. In particular, massive numerical implementations are conducted to justify the theory, …
(Si15-068) Advanced Numerical Methods For The Solution Of Nonlinear Fisher Equation,
2025
National Institute of Technology
(Si15-068) Advanced Numerical Methods For The Solution Of Nonlinear Fisher Equation, Vikash Vimal, Richa Kumari, Ashish Awasthi
Applications and Applied Mathematics: An International Journal (AAM)
This paper examines the use of advanced numerical techniques to approximate solutions of the Fisher equation with higher-order accuracy. This technique integrates the method of lines with a strong stability-preserving Runge–Kutta scheme of orders four and five stages (SSPRK-54) for the numerical formulation. This scheme is then tested on two examples and the results show that it is more efficient than existing methods and requires less computing power. These equations are widely used across scientific and engineering disciplines, with particular relevance in biomedical studies, such as estimating the boundary size of tumors. The difficulties arising from their nonlinear nature are …
The Pure Yang-Mills Field,
2025
State University of New York at Stony Brook
The Pure Yang-Mills Field, James Glimm
Department of Applied Mathematics & Statistics Faculty Publications
We construct a pure Yang-Mills quantum gauge field theory. The construction is based on the axial gauge, ghost states, the BRST framework and the entropy production maximizing Gribov extension of the Hamiltonian, with a loop expansion to all finite orders for the dynamics. The construction is established by renormalized perturbation theory to finite order. Reflection positivity and the reconstruction theorem are established. Hilbert space convergence of renormalized perturbation theory is a consequence of the reconstruction theorem. All Osterwalder-Schrader axioms are verified. A two-sided mass gap exists in the energy spectrum for the weak coupling limit of low temperature. The conditions …
A Dual-Model Machine Learning Framework For Predictive Maintenance Of Industrial Digital Press Components,
2025
Ghana Institute of Management and Public Administration
A Dual-Model Machine Learning Framework For Predictive Maintenance Of Industrial Digital Press Components, Richmond Darko, Emmanuel Adabor
African Conference on Information Systems and Technology
This study presents a novel dual-model predictive maintenance framework designed to improve maintenance scheduling for components in industrial digital presses. The framework integrates two complementary approaches: a Threshold-Based Maintenance Approach (TBMA) for components operating within acceptable usage limits, and an Overdue Severity-Based Maintenance Approach (OSBMA) for those that have exceeded their expected lifespans or show signs of critical degradation. This study uses real-world operational data from a Konica Minolta C6000 press. It applies advanced machine learning models, including Gradient Boosting Machines and Random Forest for classification, and Generalized Additive Models (GAM) for Remaining Useful Life (RUL) prediction. The goal is …
