Applied Mathematics Commons^™

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 …

(Si17-07) Application Of Triple Laplace Transform To Solve Poisson Equation, Ranjana Gothankar, Bhawna Agrawal

Applications and Applied Mathematics: An International Journal (AAM)

The well-known Laplace equation, having an elliptical character, is popularly known as the Poisson partial differential equation. It occupies a central place in mathematical physics and engineering due to its ability to describe steady-state diffusion, electrostatics, gravitational potential, and heat conduction problems. The Poisson partial differential equation in three variables is solved by employing the triple Laplace transform in Laplace domain. In original domain, the solutions are obtained numerically using the Brancik technique. The numerous illustrative examples are presented to demonstrate the behavior and sensitivity of the solutions. This dual approach analytical simplification via the triple Laplace transform and accurate …

(Si17-06) Green-Naghdi Theory Of Two-Temperature Fractional Thermoelasticity Under Thermal Shock And Ramp-Type Heating, Sagar Sankeshwari, Vinayak Kulkarni

Applications and Applied Mathematics: An International Journal (AAM)

The linear thermoelasticity theory without energy dissipation developed by Green-Naghdi has been reconstructed by using two temperature theory in the context of a time fractional derivative. In half-space, the mathematical model is discussed for one-dimensional wave propagation subject to two different problems, viz., thermal shock and ramp-type heating at the bounding surface. Assume the bounding surface is traction-free. The analytical solutions are obtained in the Laplace domain. The Gaver-Stehfest technique is numerically used to perform time domain inversion of the Laplace transform, satisfying Kuznetsov’s convergence condition. The impact of fractional order parameters on the variations of various fields inside the …

(Si17-13) A Study Of Generalized (𝜶,𝜷)-Nonexpansive Type 1 Mapping In 𝒃-Metric Space, M. J. Ali, G. Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

In this research article, we generalized KF-iteration process in 𝑏-metric space for the generalised (𝛼,𝛽)−nonexpansive type 1 mappings. We present some convergence theorems for KF-iteration process with respect to generalised mappings in 𝑏-metric space. We discussed some numerical examples of generalised (𝛼,𝛽)-nonexpansive type 1 mappings and we proved that KF-iteration process is stronger than the other iterations. The results obtained in this research generalize and improve several related results of fixed-point convergence in the literature.

(Si17-02) Integrated Mathematical Modeling And Optimization Approaches In Contemporary Engineering And Economic Applications, D. Christo Stalin, Ilakkia S., A. Parameshwari, Sahaya Brainy J., Aman Jolly, Vikas Pandey

Applications and Applied Mathematics: An International Journal (AAM)

This paper offers a calibrated synthesis of integrated modeling and optimization methods central to modern engineering and economic problems.We scrutinize the convergence of numerical methods, operations research, fuzzy-logical systems, and mathematical economics, demonstrating how these components conjointly illuminate complicated, real-world phenomena. Through an exhaustive review of prevailing frameworks, the investigation emphasizes the strategic role of stochastic modeling, queuing architecture, and optimization curricula within the twin arenas of system engineering design and economic construction. Empirical confrontation reveals that the synergistic coupling of distinct mathematical branches exponentially enhances our ability to resolve tightly-knit, largescale systems. Application re-routing is systematically demonstrated first on …

(Si17-16) Approximate Solution Of Fredholm Integral Equations Using Szász-Mirakyan Polynomials, Ruchi S. Rajawat, Shikha Pandey

Applications and Applied Mathematics: An International Journal (AAM)

This manuscript examines a family of Szász-Mirakyan operators that approximate functions on the unbounded interval [0,∞). Furthermore, we examine the discretization method for Fredholm integral equations of the first and second kind based on Szász-Mirakyan operators.We offer numerical techniques and estimate the error bound of the solution in this direction. Finally, we demonstrate numerical analysis showing the effectiveness of the newly developed algorithm constructions in the domain of one-dimensional approximation.

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 …

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 …

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.