Applied Mathematics Commons^™

A Categorical Framework For Modeling Genetic Drift, Taylor G. Mendes

Rose-Hulman Undergraduate Mathematics Journal

Genetic drift describes changes in allele frequencies that arise from chance sampling in finite populations. This paper develops a categorical framework for organizing the structural features of drift. Population states are modeled as objects, evolutionary transitions as morphisms, reversible transitions as groupoid morphisms, and structure-preserving comparisons between models as functors. Group actions are used to describe deterministic evolutionary operators such as mutation and selection, while orbits and fixed points identify reachable allele-frequency states and stable absorbing outcomes. Universal properties are then used to describe drift as a coherence condition connecting stochastic transitions with deterministic evolutionary maps. The resulting framework complements …

Multiplicity Of Laplacian Eigenvalues That Can Be Represented By Sum Of Two Squares Using Number Theory, Changfeng Zhou

Rose-Hulman Undergraduate Mathematics Journal

In this article, we use results of Number Theory to prove the conjecture on the eigenvalue problem of a 2D elliptic PDE proposed by P.Korman in his recent paper \cite{ref}: for any even integer $2k$, one can find an eigenvalue $N$ that can be represented as $N=a^{2}+b^{2}$, with integers $a\neq b$ with multiplicity $2k$, while for any odd integer $2k + 1$, one can find an integer $M$ that can be represented as $M=a^{2}+b^{2}$ with $a\neq b$ and multiplicity $2k+1$. In addition, the manuscript gives the formula to find those $N$'s.

A Differential Equation–Based Epidemiological Model Of Post-Operative Chronic Pain In Scoliosis Patients With Data-Driven Analysis, Paige Zhu, Padmanabhan Seshaiyer

CODEE Journal

Chronic post-surgical pain (CPSP) is a common and often overlooked complication following surgical correction of idiopathic scoliosis, impacting long-term patient wellbeing despite improvements in surgical outcomes. This project introduces a novel epidemiological framework to model the progression of CPSP using a compartmental structure. By applying a coupled system of nonlinear differential equations, we simulate pain trajectories over time and assess the effectiveness of surgical interventions. The model is implemented for a single-cohort population and extended to a two-cohort design to compare outcomes between Posterior Spinal Fusion (PSIF) and Vertebral Body Tethering (VBT) procedures. Further stratification by patient age enables us …

Numerical Range Of Rank-1 Partial Isometries And Elliptical Range Theorem, Lucas Saone

Theses

The Elliptical Range Theorem states that the numerical range of a 2x2 complex matrix A is an elliptical disc with foci at the eigenvalues of A and center at tr(A)/2. Many proofs have been offered for this theorem. In this paper, we provide another one. The strategy we will use is to decompose the matrix A into the sum of rank-1 operators of the form YxX*, where X and Y are in 2-D complex vectors. When analyzing the numerical range of a rank-1 operator of this form, three results can happen: i) the numerical range forms a disc at the …

What We Know About Accounting Ratios: Methodological Considerations, Wojciech Kuryłek, Oskar Kowalewski

Studia i Materiały Wydział Zarządzania Uniwersytet Warszawski

Purpose: This paper provides a comprehensive literature review of the methodological aspects of financial ratio analysis, consolidating dispersed knowledge on the computation, statistical properties, and appropriate usage of accounting ratios.

Design/Methodology/Approach: The study adopts a narrative literature review methodology, systematically surveying published research on financial ratio distributions, normality testing, data transformations, outlier handling, the proportionality assumption, dimensionality reduction techniques, compositional data analysis, and recommended ratio sets for corporate financial research.

Findings: Financial ratios predominantly deviate from normal distributions, exhibiting skewness, excess kurtosis, and sensitivity to outliers. Transformation techniques such as logarithmic, square root, and Box‑Cox methods yield mixed results in …

Mengukur Capaian Dan Identifikasi Konvergensi Pembangunan Infrastruktur Antarprovinsi Di Indonesia, Ressa Isnaini Arumnisaa', Aisyah Fitri Yuniasih

Jurnal Ekonomi dan Pembangunan Indonesia

Indonesia’s economic challenges are characterized by stagnant economic growth and regional development disparities. This study analyzes the achievement and convergence of infrastructure development across provinces in Indonesia during 2011–2021 through the construction of an Infrastructure Development Index (IPI). The study employs panel data from 33 provinces, using factor analysis to construct the IPI and the First Difference Generalized Method of Moments (FD-GMM) to examine convergence and its determinants. The results show that many provinces still have IDI scores below the national average. Furthermore, the FD-GMM model shows that σ-convergence and β-convergence occur in Indonesia. In addition, GRDP per capita, inflation, …

Cdt-1d Cnn Integration With Simpson-Sobolev Regularization For High-Frequency Options Trading: With Fem-Based Heston Option Pricing, Daniel M. Margolis, Johannes Tausch, Arthur K. Selender

Mathematics Theses and Dissertations

This dissertation presents a computational framework for high-frequency options trading that combines Cross-Data-Type 1-D Convolutional Neural Networks (CDT-1D CNN) with Simpson-Sobolev regularization for directional prediction, and finite element methods (FEM) for realistic option pricing during backtesting. The core innovation lies in developing a mathematically rigorous regularization approach that maintains the adaptability of modern deep learning while enabling accurate evaluation through stochastic volatility models. The primary contribution is the Simpson-Sobolev regularization scheme, which extends traditional Sobolev regularization by incorporating Simpson’s rule for numerical integration. This approach achieves higher-order accuracy in approximating the Sobolev norms that control function smoothness. Simpson’s rule attains …

Linear Programming Model For Optimal Crop Allocation Under Varying Land Sizes In Pawaga, Tanzania, Mustapha Abbas Kiswanya, Seleman Ismail, Saul Mpeshe

Tanzania Journal of Science

Farmers often rely on intuition when selecting crops, which can lead to suboptimal profits. In this study, we examine the optimal annual crop allocation under varying land sizes for farmers in Pawaga, Iringa District, Tanzania. A parametric linear programming (LP) model is developed to determine crop allocation combinations that maximise profit subject to land, labour, and capital constraints. Unlike conventional approaches that require separate models for different farm sizes, the proposed model accommodates land holdings ranging from 1 to 9 acres and integrates nine crop types within a single framework. Data were collected over three (3) agricultural seasons from extension …

A Mathematical Model For Managing Diphtheria Outbreaks In Nigeria Via Vaccination, Enhanced Surveillance, Effective Quarantine, And Social Distancing Measures, Hycienth Ortser Orapine, Nyiutya Cephas Ine, Dekera Jacob Washachi, Ali Audu Baidu, Lubem Matthew Kwaghkor

Mathematical Modelling and Numerical Simulation with Applications

Diphtheria is a highly infectious respiratory and skin disease that poses a significant threat to global public health. In Nigeria, children and adults with low immunity remain at high risk due to recurring annual outbreaks in the last decade, with a death rate of as high as 68.8\%. This paper presents a deterministic compartmental model to evaluate the effectiveness of interventions implemented by the Nigerian government. The model's mathematical and epidemiological validity is established through proofs of non-negativity and boundedness. The basic reproduction number ($R_0$) is derived, and stability analysis confirms that the diphtheria-free equilibrium is locally and globally asymptotically …

Stochastic Analysis Of Epidemic Size And Peak Infection In An Svir Model With Imperfect Vaccine And External Source Of Infection, María Gamboa Pérez

Mathematical Modelling and Numerical Simulation with Applications

The dynamics of an infectious disease outbreak are studied under a stochastic framework in a closed population where individuals are homogeneously mixed. A vaccination program is implemented in the community prior to the start of the epidemic. The administered vaccine is imperfect, meaning that vaccinated individuals may still become infected upon contact with infected individuals. The mathematical Susceptible-Vaccinated-Infected-Recovered (SVIR) model describing the evolution of the epidemic is formulated as an absorbing, continuous-time, three-dimensional Markov chain with compartments for vaccinated, susceptible, infected and recovered individuals. The aim of this study is to characterize two fundamental epidemiological quantities: the maximum number of …

Modelling Of Dust Devil Flow Dynamics: Effects Of The Sharpness Parameter On Velocity And Pressure, Deepanshu Kumar, Hossein Jafari

Mathematical Modelling and Numerical Simulation with Applications

This work discusses the development of a straightforward model of dust devils, demonstrating a method for estimating wind speed and pressure. The current model incorporates momentum equations and the mass conservation equation for steady, axisymmetric, inviscid, and incompressible flow. In this model, the radial velocity is first considered, which is restricted in both the radial and axial directions. The sharpness parameter is also incorporated into the radial velocity formulation, as described by Vatistas model. Using the radial velocity as a foundation, we derive the azimuthal and axial velocities. The study further evaluates the pressure. Notably, for large values of the …

Dynamical Behavior, Extinction And Persistence In A Stochastic Delayed Two-Strain Epidemic Model With A Generalized Crowley-Martin Incidence Rate, Amina Allali, Dounia Bentaleb, Saida Amine

Mathematical Modelling and Numerical Simulation with Applications

This paper develops and analyzes a novel delayed stochastic SIR epidemic model with two interacting strains and general incidence functions. By establishing the existence and uniqueness of a positive global solution, the well-posedness of the model under stochastic perturbations is ensured. Extinction occurs when the stochastic reproduction number falls below unity, as demonstrated through Itô calculus and martingale convergence theorems, while persistence is guaranteed under the Crowley–Martin incidence when it exceeds one. Numerical experiments based on the Positive Preserving Truncated Euler–Maruyama (PPTEM) scheme confirm the analytical predictions and highlight the influence of time delay and noise intensity on the long-term …

Tumor–Immune Dynamics With Memory And Time Delay: A Fractional-Order Model With Ctla-4 Regulation, Mutaz Mohammad, Mohyeedden Sweidan, Alexander Trounev, Fathalla Rihan

Mathematical Modelling and Numerical Simulation with Applications

This study develops a fractional-order tumor-immune interaction model incorporating Caputo memory effects, delayed immune activation, and CTLA-4 checkpoint regulation. The model describes the coupled dynamics of tumor cells, CD4$^{+}$ T cells, IFN-$\gamma$, and CTLA-4, and extends classical integer-order tumor-immune models by accounting for hereditary immune responses and biologically motivated latency effects. Theoretical properties, including positivity, boundedness, equilibrium structure, and fractional-order stability, are examined to establish the biological and mathematical consistency of the model. The delayed fractional system is then investigated computationally by comparing several numerical methods, including finite difference discretization, Daubechies wavelet collocation, Euler wavelet collocation, and a predictor-corrector scheme. …

Numerical Method For Strongly Variable-Density Flows At Low Mach Number: Flame-Sheet Regularisation And A Mass-Flux Immersed Boundary Method, Matheus P. Severino, Fernando F. Fachini, Elmer M. Gennaro, Daniel Rodríguez, Leandro F. Souza

Mathematical Modelling and Numerical Simulation with Applications

A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the disparity between the flow and acoustic speed. Therefore, low-Mach-number flows impose mathematical and computational challenges in their description. Standard numerical methods for compressible flows, which are typically designed for problems with a single dominant spatial and temporal scale, require alternative approaches, such as preconditioning techniques or solvers tailored for low-Mach-number equations. The present work introduces a simplified fluid dynamics model for flows …

Physicochemical Properties And Chemical Compositions Of Cashew Nut Shell Liquid Extracted With Carbon Dioxide–Expanded Hexane, Neema Msuya, Joseph Yn Philip, Frank Jacob, Kando K. Janga

Tanzania Journal of Engineering and Technology (TJET)

Cashew nut shell liquid (CNSL) is a mixture of phenolic compounds that can effectively replace commercially available phenols in various applications. This study investigated the physicochemical properties and chemical composition of CNSL extracted using CO₂–expanded hexane (CXH) and compared to the traditional Soxhlet extraction method. Steamed cashew nut shells (sCNS) were used in both cases.  The CXH was carried under varying CO₂-mole fractions (0.468-0.892) and temperatures (20-36 °C) whereas Soxhlet extraction was performed at atmospheric pressure and hexane boiling point. Response Surface Methodology (RSM) with Central Composite Face-Centred Design (CCFD) was employed to evaluate the effect …

Enhancing Community Engagement Through ‘Nitunze Kilombero’ Mobile App: Case Of Climate Land Use And Cover Management For Kilombero Basin, Ghanima Chanzi, Subira Munishi

Tanzania Journal of Engineering and Technology (TJET)

The Kilombero Basin in southeastern Tanzania faces significant challenges due to rapid land use and land cover (LULC) changes driven by climate change, population growth, and unsustainable farming practices. This study assessed the role of community engagement and digital reporting through the 'NITUNZE KILOMBERO', mobile application in supporting water resources management in the basin. The App facilitates real-time reporting of environmental issues, provides educational resources, and enables collaboration between local communities and authorities. A mixed-methods approach, including household surveys and key informant interviews, was employed to assess the app's effectiveness. Results indicate high community awareness of LULC impacts, with 85% …

Hybrid Solar - Coal Thermal Energy System For Industrial Process Heat At Sayona Drinks Limited In Tanzania, Santos Kihwele, Elisha D. Bitesigirwe

Tanzania Journal of Engineering and Technology (TJET)

Over the past two decades, global efforts to mitigate pollution from conventional energy sources have intensified, with coal remaining a major contributor to carbon emissions. While fossil fuels cannot be eliminated from thermal generation in manufacturing industries, particularly in middle‑income countries such as Tanzania, they continue to dominate as the primary energy source. Industries including food and beverage, paper, textile, paints, chemicals, and pharmaceuticals require substantial thermal energy for heating and drying, and typically rely on coal and natural gas.This study introduces a unique application of a parabolic trough solar thermal system with integrated thermal energy storage, specifically tailored to …

(R2077) Enhancing Queue Management: Dynamic Server Allocation And Optional Services In Stochastic Modeling, G. Ayyappan, S. Sankeetha

Applications and Applied Mathematics: An International Journal (AAM)

Consider a queueing system with a single server, where customer arrivals follow a Markovian arrival process and service times follow a phase-type distribution. The main server has the capability to recruit an additional server when the number of customers in the system exceeds a certain threshold, denoted as L. Both servers provide normal service to customers, and optional service is provided upon request. The main server takes multiple vacations, with the durations following an exponential distribution with rate parameter η, until there is at least one customer in the system. This system can be represented as a Markov chain process, …

(R2072) A Method To Sample From Transition Densities Of Diffusion Processes With Unknown Densities, Yasin Kikabi, Juma Kasozi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a reliable method that can be used to sample paths of a diffusion process described by a system of stochastic differential equations. These are types of processes whose transition density is not known in closed form. This reliable method involves solving a partial differential equation of the Fokker-Planck type by rejection sampling techniques applied to the associated densities. We then use the novel method to sample from the Ornstein-Uhlenbeck (OU) process whose transition density is known and has unbounded drift. The results obtained compare excellently with the analytical results, thus rendering the method reliable and …

(R2147) Effect Of Mass Variation With Log-Logistic Distribution In Perturbed Interacting Cr3bp, Abdullah Abdullah, Majhar Ali, S. K. Sahdev

Applications and Applied Mathematics: An International Journal (AAM)

This paper investigates the motion of the infinitesimal body in the perturbed restricted three-body problem where the primary is heterogeneous in shape and secondary is with modified Newtonian potential. With the use of log-logistic distribution, space-time transformation and the above-said perturbations, we determine the equations of motion and quasi-Jacobian integral. Further, we numerically perform the locations of equilibrium points, their stability, regions of motion, periodic orbits and Poincaré surfaces of section.