Applied Mathematics Commons^™

(R2165) Two Different Stages With Two Distinct Harvesting Processes, S. Vijaya, Krishika M

Applications and Applied Mathematics: An International Journal (AAM)

This study extends the classical Lotka-Volterra prey-predator model by incorporating a stage structured prey population consisting of juvenile and adult stages, while considering a single predator species governed by a Holling type II functional response. The growth of the juvenile prey depends on the adult prey population and since the juvenile prey has no reproduction capability. Two distinct harvesting strategies are introduced in the model. Constant-yield harvesting is applied to the juvenile stage of the prey population and represents a fixed amount of harvest regardless of population size. Constant effort harvesting is applied to the adult stage of the prey …

Toward Mapping Multiphase Multicomponent Mixtures With Neural Networks, Kristen L. Hallas, Melissa De Jesus, Christine J. Wu, Jianzhi Li, Jason Bernstein, Philip C. Myint

School of Mathematical & Statistical Sciences Faculty Publications

Equation of state (EOS) tables are commonly used in hydrodynamic simulations of high-pressure, high-temperature phenomena in fields like planetary science, astrophysics, and high-energy-density science. However, generating and storing EOS tables for multiphase, multicomponent mixtures over a wide range of pressures and temperatures is computationally infeasible due to their memory-intensive nature. To address this issue, we have developed a neural network-based machine learning model to predict new EOS tables for binary mixtures. In particular, a deep feedforward neural network trained on a set of ten EOS tables at particular mixture compositions is able to predict nine new (hold-out) EOS tables at …

Progress Towards An Analog Of The Darboux-Griffiths Converse Of Abel's Theorem In Characteristic P, John B. Little

Mathematics and Computer Science Department Faculty Scholarship

In this working paper, we report our recent efforts concerning a possible characteristic p analog of the so-called converse of Abel's theorem discussed by Darboux and Griffiths.  The characteristic zero version is used in one proof of the Lie-Wirtinger theorem on double translation manifolds and also in related aspects of the geometry of webs.  In informal terms, our results indicate that, apart from some isolated counterexamples, formal power series Abel relations over an algebraically closed field of characteristic p essentially only arise in the (generalized) Jacobians of algebraic curves.  The ultimate goal is to complete thevwork started in the author's …

Integrating Gis With Interim Payment Valuation In Road Construction Projects: A Conceptual Framework, Abdulrahman I. Iro, Juma M. Matindana, Julian Ijumulana

Tanzania Journal of Engineering and Technology (TJET)

Abstract

Interim Payment Valuation is a critical process in road construction contract administration, yet conventional valuation practices remain heavily dependent on manual measurements, fragmented documentation, spreadsheets, and professional judgement. These limitations can affect measurement accuracy, transparency, traceability, and the timeliness of payment certification. Although Geographic Information Systems have increasingly been applied to construction planning, quantity measurement, progress monitoring, infrastructure management, and decision support, their integration with contractual and financial processes for interim payment valuation remains insufficiently explored. This study therefore develops a conceptual framework for integrating GIS with Interim Payment Valuation in road construction projects. A PRISMA-guided structured literature review …

Identifiability, Sequentiality And Infinity (--Remarks--), Jose L. Menaldi

Mathematics Faculty Research Publications

Two sections are added to my previous article with similar title, in relation to the so-called dynamic logic-error, other complications with modern mathematics and some details on the philosophy behind scene. These remarks could be seen as more details on the axioms of math-arguments and the actual basis-inspiration of the meta-math previously developed. In other words, this `continuation' gives the connection between (meta-)mathematics and the science of the creation-energy.

Voltage-Related Power Quality Issues And Impacts On Distribution Networks With Sensitive Loads - A Review, Godwin Elinazi Mnkeni, Jackson Justo, Aviti Thadei Mushi, Bakari M. M. Mwinyiwiwa

Tanzania Journal of Engineering and Technology (TJET)

Voltage disturbances are the most important power quality (PQ) complications that customers and power utilities face in this smart era. The growing adoption of sophisticated electronic equipment and integration of renewable energy sources (RES) into power grids has increased the susceptibility of power distribution networks (PDNs) to voltage sags, swells, interruptions, flicker, and voltage imbalance. These disturbances, mainly caused by upstream faults, switching operations, and RES integration, compromise voltage PQ and system reliability. Consequently, they accelerate equipment degradation, increase electronic waste (e-waste), raise reactive power demand and maintenance costs, increase power losses, and impose substantial economic losses on customers and …

Study Of A Nonlinear Delayed Parabolic Model For Prion Disease Dynamics With The Unfolded Protein Response, Gangadhara Boregowda, Laurent Pujo-Menjouet, Zhaosheng Feng, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Prion diseases are neurodegenerative disorders characterized by the dynamic spread of misfolded toxic proteins in the brain. In this process, the normal cellular prion protein (PrPC) produced by neurons misfolds into a toxic form known as scrapie prion protein (PrPSc). These misfolded proteins propagate through the brain by converting healthy prions into their toxic form. This biological mechanism can be modeled by a system of nonlinear parabolic partial differential equations, accompanied by a nonlinear delayed integral boundary condition. Our primary objective is to establish the existence of nonnegative classical solutions to this system. Furthermore, we derive a priori estimates for …

Thermo-Entropic Analysis Of Unsteady Mhd Nanofluid Couette Flow: A Classical Spectral Approach With An Exploratory Quantum Linear-Solver Application, Serai Israel Mosala, Oluwole Daniel Makinde, Azwinndini Muronga

Mathematical Modelling and Numerical Simulation with Applications

This study presents a thermo-entropic analysis of unsteady MHD nanofluid Couette flow, combining a classical bivariate spectral quasilinearisation (BI-SQLM) and Crank--Nicolson solution with an exploratory application of quantum linear solvers. An incompressible, electrically conducting nanofluid flows between parallel plates under partial slip and convective heat exchange; the discretised linear systems are additionally solved via the Harrow--Hassidim--Lloyd (HHL) algorithm and the Variational Quantum Linear Solver (VQLS). Results are presented for Pure Water, Cu-Water, and Al₂O₃-Water across seven parameter variations. The Hartmann number dominates velocity suppression and entropy amplification, while velocity slip reduces upper-wall entropy generation more than …

Effects Of Co-Rotating Cylinders And Boundary Conditions On Heat And Mass Transfer In A Trapezoidal Enclosure, Olalekan Adebayo Olayemi, Olalekan Tajudeen Popoola, Leke Thaddeus Oladimeji, Isaac Kayode Adegun, Taofiq Omoniyi Amoloye, Oluwatayo Babatope Ojo, Benjamin Ohida Daniel, Michael Olabode Ibiwoye

Mathematical Modelling and Numerical Simulation with Applications

This study investigates the effects of rotational speed $(\Omega)$, Richardson number $\left(Ri\right)$, and Lewis number $\left(Le\right)$ on heat and mass transfer (HMT) around two co-rotating cylinders symmetrically situated in a trapezoidal enclosure. In the double-diffusive mechanism, the bottom wall of the trapezium is at a high temperature $\left(T_h\right)$ and concentration $\left(C_h\right)$, while the top wall is at a low temperature $\left(T_c\right)$ and concentration $\left(C_c\right)$. The side walls are perfectly insulated with zero mass flux, while the buoyancy ratio $\left(Br\right)$ is fixed at 1.0.  Two thermal-mass boundary scenarios are considered. Scenario 1: Cylinders are thermally insulated with zero mass flux, and …

Exact Solution Structure And Dynamic Preservation In A Nonstandard Finite-Difference Formulation Of The Sir Model, Ramsha Shafqat, Wutiphol Sintunavarat

Mathematical Modelling and Numerical Simulation with Applications

A new nonstandard finite difference method is developed for discretizing the classical Susceptible--Infected--Removed (SIR) epidemic model. In the proposed approach, the first derivatives in the continuous SIR system are replaced by two carefully constructed nonstandard denominator functions, yielding a dynamically consistent discrete model with improved numerical stability while preserving consistency with the original continuous system. It is proved that the proposed scheme preserves the fundamental dynamical properties and qualitative behavior of the continuous SIR model, including positivity and the long-term dynamics of the population classes. Moreover, the resulting discrete system admits explicit analytical solutions, providing further insight into the model …

Numerical Solution Of The Hjb Equation Using A Hybrid Bernstein–Fractional Chebyshev Spectral Collocation Method, Alvian Alif Hidayatullah, Subchan Subchan, Sena Safarina, Tahiyatul Asfihani, Dilshod Mashrabovich Akhmedov

Mathematical Modelling and Numerical Simulation with Applications

The Hamilton–Jacobi–Bellman (HJB) equation is fundamental in stochastic optimal control but is often difficult to solve accurately because of its nonlinear and multidimensional structure. This paper develops a hybrid tensor-product spectral collocation method based on shifted Bernstein polynomials in time and fractional-order Chebyshev polynomials in the state variables. The proposed shifted Bernstein–fractional Chebyshev (SBFC) framework allows the time and state directions to be approximated using different basis characteristics, while the fractional parameters provide adjustable resolution in the state domain. A weighted approximation framework is established, including density and convergence results for the mixed approximation space. The state collocation points are …

Neural Network-Based Analysis Of Heroin Epidemic Models With Modified Fractional Operators, M. A. El-Shorbagy, Sedat Pak, Mati Ur Rahman, Hossam A. Nabwey

Mathematical Modelling and Numerical Simulation with Applications

Heroin and synthetic narcotic abuse have become a major global concern, posing challenges to individuals, families, and communities. Their widespread availability and low cost have intensified the crisis. This study investigates a heroin transmission model using the modified Atangana--Baleanu--Caputo (mABC) fractional operator, with emphasis on non-zero solutions. Series solutions are derived by combining the Laplace transform with the Adomian decomposition method to address nonlinear components. Qualitative analysis is conducted through fixed-point theory, while stability is assessed using the T-Picard method. Numerical simulations explore the effects of different fractional orders and transmission parameters on the system. The study incorporates a deep …

Pattern Formation And Diffusion-Driven Instability Of A Modified Lengyel-Epstein Model, Müge Meyvacı, Hüseyin Merdan, Yafia Radouane

Mathematical Modelling and Numerical Simulation with Applications

We consider a modified Lengyel-Epstein model that is covered by a system of reaction-diffusion equations and investigate the sufficient conditions on parameters of the model at which the diffusion-driven instability occurs. We perform numerical simulations to support and extend the theoretical findings. Analytical results and numerical simulations show that the modified Lengyel-Epstein system with positive initial and non-flux boundary conditions presents Turing patterns under some conditions on its parameters.

Bifurcation Dynamics Of A Harvested Predator-Prey Model, Hala H. Emam, Mohamed F. Abouelenein, Mona Anis, M. Y. Hamada, F. A. Atia, H. El-Metwally

Mathematical Modelling and Numerical Simulation with Applications

In ecosystems, the harvesting effect is essential to preserving the relationships between prey and predator. This work examines a model of predator-prey in discrete time with harvesting. The Jacobian matrix's eigenvalues are calculated for the associated fixed points. We examine the dynamical and qualitative analysis of this model, look into the criteria for stability and bifurcation, and analyze analytical results that show the rich dynamics and complexity of this model. We give sufficient circumstances for the Period-doubling at the interior equilibrium point by employing the harvesting effect. The discrete system's chaos control is carried out, and the outcomes are supported …

Mathematical Modelling For Optimizing Predator–Prey Networks In A Resilient Wildlife Ecosystem: A Systematic Literature Review, Thadei Damas Sagamiko

Tanzania Journal of Science

The resilience of wildlife networks hinges on the adaptability and stability of complex predator-prey interactions. Mathematical modelling offers a crucial approach for examining and optimizing these dynamics under biological invasions and environmental pressures. This systematic literature review (SLR) employs a bibliometric analysis approach to synthesize global research on mathematical models applied to predator-prey network optimization, with an emphasis on their ecological implications, computational approaches, and modelling strategies. Using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA), 50 peer- reviewed studies (2000–2025) were analyzed using the Scopus and Google Scholar databases. The study identifies classical models, such as the …

Modelling Acute Haemorrhagic Conjunctivitis In East Africa: An Integrated Approach To Transmission Dynamics And Outbreak Response Strategies, Geofrey Wingi Sikazwe

Tanzania Journal of Science

Acute hemorrhagic conjunctivitis (AHC) poses a significant global health risk, with the potential for rapid spread during outbreaks. For instance, a localized outbreak in Yunnan Province, China, recorded infection rates of up to 48%, illustrating how transmission can intensify under favourable epidemiological and environmental conditions. Existing mathematical models of AHC transmission overlook seasonal variations, a critical factor in epidemic spread. This study combines species distribution models (SDMs) and epidemiological modelling to analyse key drivers of AHC in East Africa. We use the SEIR type (Susceptible-Exposed-Infected-Recovered - incorporating waning immunity) framework with temperature-dependent infectivity rate as the key driver of an …

When Three Points Aren't Enough: Parameter Estimation In Newton's Law Of Cooling, Alberto A. Condori, Cara D. Brooks, Madeline R. Goldberg

CODEE Journal

We begin with a paradoxical three-point problem where the standard parameter estimation formula fails because temperature data must satisfy a concavity condition reflecting Newton's Law of Cooling's exponential structure. Although a closed-form solution for A exists for equally-spaced measurements, high sensitivity to error motivates the use of overdetermined systems with many measurements. The "profiling over A" technique transforms this three-parameter nonlinear problem into a sequence of simple linear regressions, providing computational efficiency and conceptual transparency. This approach can be generalized to many parameter estimation problems in science and engineering, making it a valuable tool for undergraduates interested in applied mathematics. …

Knowledge-Enhanced Feature Store For Operational Ml And Llm Workflows, Saurabh Suman

Master's Theses

Modern machine learning (ML) organizations rely on feature stores to manage training and production data, yet as catalogs grow to thousands of features, semantic management becomes the bottleneck: discovery, governance, and metric selection remain largely manual. This thesis proposes and evaluates a knowledge-enhanced feature store that augments a dual-plane store with a hybrid knowledge layer—relational provenance, a lineage graph, semantic vector retrieval, and an online cache—and an LLM-driven multi-agent layer for profiling, matching, grounded metric recommendation, and pipeline generation. A working prototype was evaluated across three task families—semantic profiling, feature-matching retrieval, and discovery—using classification, ranking, and operational metrics computed by …

Differential Equation Modeling For Sustainable Resource Management: A Steady-State Optimal Harvesting Approach, Iordanka N. Panayotova, Aleksei Talonov

CODEE Journal

Mathematical models based on differential equations provide a powerful framework for connecting real-world data to informed decision-making. In this work, we present a student-accessible project that uses an optimal-control framework to study the sustainable management of biological resources.

Motivated by fisheries management, we examine a predator--prey system in which harvesting decisions must balance ecological and economic considerations. The model is formulated as an optimal control problem that seeks to maximize the total discounted net revenue from harvesting. Rather than solving for the complete time-dependent harvesting trajectory, we restrict the analysis to positive controlled coexistence equilibria and characterize an interior stationary …

Taut And Dupin Submanifolds (Updated Version), Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

This is an updated version of the paper [29] by the author which originally appeared in 1997. The original paper was a survey of the closely related fields of taut and Dupin submanifolds of Euclidean space, and this updated version includes many results in the field that have appeared since the publication of the original version. The emphasis is on stating results in their proper context and noting areas for future research, and relatively few proofs are given. The important class of isoparametric hypersurfaces is surveyed in detail, as is the relationship between the two concepts of taut and Dupin. …

Fast Computation And Model Order Reduction Of The Friction Stir Welding Process With Pod-Deim, Joshua Kay, Zilong Song

Mathematics and Statistics Student Research and Class Projects

Friction stir welding (FSW) is a solid-state manufacturing process widely used in joining aluminum and other metal workpieces. The FSW process can be modeled by a coupled system of non-Newtonian Navier–Stokes and heat-transfer equations. However, solving this non-linear system with high accuracy requires significant computational power. This work refines the system by introducing corrected coefficients and new treatments for boundary conditions near the tool. Then, model order reduction, including the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), is applied to efficiently solve the FSW system in a low-dimensional space. To enhance accuracy and effectiveness, two novel treatments …

Using Graphic Novels In The Teaching And Learning Of Mathematics And Physics, Jason Ho, David Klanderman, Sarah Klanderman, James Turner

University Faculty Publications and Creative Works

Are you looking for innovative teaching strategies for geometry or other mathematics and physics courses? In this article, we o!er a discussion of several graphic novels and their potential for successful teaching and learning at the high school and university levels. We describe how engaging stories, combined with mathematical and scientific meaning found in both text and image, can help to excite students, enrich learning, and explain mathematical concepts. We report on recent data collected from multiple mathematics and physics classes that extend prior research on the use of graphic novels to teach English Language Arts (Boerman-Cornell and Kim, 2020) …

The Inverse Elasto-Acoustic Problem, Patrick Grice

Dissertations

A stable and numerically efficient boundary integral method formulation of the elasto-acoustic problem is presented, based on Fourier analysis. The method generalizes well to multiple scattering. The Frechet derivative of the elasto-acoustic problem with respect to shape perturbations is derived, and geometric flow theory is used to design stable numerical methods for the simulation of moving boundaries. The shape derivative is used to define a regularized Gauss-Newton algorithm for shape fitting of elasto-acoustic scatterers.

Geometric Convergence And State-Space Decompositions For Stochastic Gradient Descent Markov Chains, Philip Zaleski

Dissertations

No abstract provided.

Simulated Versus Non-Simulated Imputed Data: A Comparison Of Handling Missing Data Techniques For Numerical Covariates, Rahibu A. Abassi, Rocky R.J. Akarro

Tanzania Journal of Science

Missing data poses a great challenge in much research, and if not appropriately handled, can negatively impact the analysis and bias the results and study conclusions. This article assesses the performance of numerous methods used to impute missing data by using Root Mean Squared Error (RMSE) under various missing data proportions and two common missingness mechanisms, namely Missing at Random (MAR) and Missing Completely at Random (MCAR). RMSE values were used to judge the accuracy of imputation techniques using real data and across different simulation settings. The results showed magnitude of RMSE increased with increased proportions of missing data, regardless …

Evaluating A Dual-Beacon Hartmann Turbulence Profiling Technique Using Wave Optics Simulations, Benjamin C. Wilson, Matthew Kalensky, Santasri Bose-Pillai, Jack E. Mccrae

Faculty Publications

Resolving how optical turbulence varies along a propagation path remains a key challenge for designers of free-space optical propagation systems. Instruments such as scintillometers and differential image motion monitors are commonly used, but only provide path-integrated turbulence estimates. Point sensors provide localized estimates of turbulence strength and can be used to generate path-resolved profiles when an array of point sensors are distributed along the optical path. However, this approach can be costly and complex to deploy in certain environments. Alternatively, a single point sensor can be mounted on a mobile platform that collects data while traversing the optical path, although …

Electronic Structure Discretization And Compression Using Diagonal Basis Sets, Casey Lee Dowdle

Dartmouth College Ph.D Dissertations

Numerically solving the electronic structure problem is a fundamentally difficult problem due to the exponential growth in the dimension of the Hilbert space as the system size increases. In order to solve problems at a chemically relevant accuracy, both the choice of basis set and numerical method are important factors that are intrinsically connected.

In this thesis, we study the discretization and resulting compression of electronic Hamiltonians using diagonal basis sets. A diagonal basis set approximately diagonalizes the matrix and tensor representations of the one- and two-body potentials. This can reduce storage, simplify matrix-vector products, and lower the complexity of …

Modeling The Clonal Rosette Composition Of A Bromeliaceae Genet: A Combinatorial Approach, Layla K. Lammers, Erin N. Bodine

Spora: A Journal of Biomathematics

Bromeliaceae, a neo-tropical plant family encompassing over 3,000 species, exhibit two modes of reproduction: sexual reproduction via flowers and seeds, and asexual reproduction via genetically identical clonal rosettes. The vegetative bodies of bromeliads form rosettes with new leaves emerging from the center and clonal rosettes emerging above a single leaf in the rosette, resulting in a genetic individual consisting of a seed-grown rosette and multiple iterations of clonal rosettes. This research develops a combinatorial model of probability that a single genetic individual will include at least n clonal rosettes when a single rosette can produce at most 1 or 2 …

Human-Centered Modeling Of Traffic As A Complex System, Poorendra P. Ramlall

Discovery Day - Daytona Beach

Traffic systems are driven not only by motion, but by interaction: vehicles influence one another, drivers continuously adapt to surrounding behaviour, and cognitive processes shape decisions that can propagate through the flow of traffic. Understanding these layered interactions is essential for improving traffic safety and for designing the next generation of intelligent, connected, and automated transportation systems. This PhD research develops a multiscale, data-driven framework for identifying, modelling, and ultimately interpreting interaction structure in traffic systems. The work first established an information-theoretic basis for this problem, demonstrating how information flow can uncover directional relationships in traffic dynamics and help infer …

Low-Rank Spectral Analysis For The Reddening Of The Seven Sisters Star Cluster, Eric Rodarte, Angelina Scalice, Madison Warner, Kevin Numbe

Discovery Day - Daytona Beach

The Pleiades, also known as the Seven Sisters, is a stunning star cluster located approximately 440 light-years from Earth. This vibrant assemblage of hot blue stars in the Taurus constellation can be admired with the naked eye or through binoculars during early autumn. In this presentation, we utilize spectral theory to measure the reddening in the Pleiades star cluster. To evaluate the impact of interstellar dust on reddening, we employ principal component analysis (PCA) on a matrix representing color indices from various photometric bands linked to the cluster’s photometric data. This dataset was obtained from VIZIER. Our PCA analysis of …