Applied Mathematics Commons^™

Asymmetrical S-Curve For Residual Load Sways Suppression For Double-Pendulum Rotary Crane Using Bayesian Optimization, Haryson Johanes Nyobuya

Tanzania Journal of Science

In rotary crane operations, one of the main difficulties lies in suppressing the load sway during its movement. This can be achieved using only horizontal boom motion, offering a solution that is energy-saving, simple, and safe. However, this approach renders the system under actuated, making the suppression objective more difficult to achieve. In this study, a double-pendulum model is adopted to capture the coupled dynamics of the suspended load and hook, which shows a realistic basis for sway suppression. An asymmetric S-curve velocity trajectory is proposed to shape the horizontal boom motion, effectively minimizing residual vibrations without requiring direct sway …

Quantitative Analysis Of Cholera Dynamics And The Impact Of Integrated Control Measures., Kazeem Abidoye Odeyemi, Mutairu Kayode Kolawole

Tanzania Journal of Science

A comprehensive mathematical evaluation of cholera dynamics, emphasizing the crucial role of optimal control strategies which include vaccination, treatment in endemic region and environmental hygiene in controlling the disease spread in Western and Mid-Eastern regions of African setting. Through analysis of the local and global stability of the model and assessing the reproduction number (��0), this research highlights how targeted interventions can influence transmission rates of cholera disease. Sensitivity analysis identifies key parameters driving cholera dynamics, underlining the urgency of timely and adequate intervention. Utilizing the innovative Homotopy Perturbation Method for the numerical simulation, the study explores the interplay between …

Implementing A Clustering Framework On Distributional Bee Data, Roheel Nawaz

Research and Creativity Symposium

Understanding spatial patterns in biodiversity is important for identifying how ecological communities are structured across landscapes. Clustering methods provide a useful way to detect non-random species distributions and reveal potential environmental or geographic influences. In this study, we applied a clustering framework to a large long-term bee abundance dataset from the Mid-Atlantic United States to evaluate community structure across regions of Maryland, Delaware, and Washington, D.C.

The dataset included over 1,100 sites and more than 3,000 transects. Because sampling methods were not fully standardized, abundance data were converted to presence/absence and analyzed using the Jaccard index to measure site similarity. …

Low-Complexity Structured Neural Networks And Their Usage In Image And Signal Processing, Adam Kuzmicki

Doctoral Dissertations and Master's Theses

Conventional neural networks face significant challenges due to high computational costs, large parameter counts, and reliance on backpropagation, which restricts their application in resource-constrained and real-time settings. To address these challenges, this thesis proposes three structured neural network (NN) architectures grounded in the theories of sparse and self-contained factorizations of transforms, with applications to image compression, reconstruction, classification, encryption, and also adaptive wideband multi-beam beamforming. The first neural network architecture, named DCTrix-Net, replaces conventional spatial con- volution with highly sparse factorization of the discrete Cosine transform (DCT) complemented by Toeplitz-structured weight initialization, achieving at least 97% FLOP reduction over CNNs, …

Information Theory Analysis Of The Solar Wind Magnetic Structures For Space Weather Prediction, Katherine Holland

Doctoral Dissertations and Master's Theses

Forecasting space weather at Earth is highly complicated, because of the limited measurements of the dynamic processes in the Sun that span multiple temporal, spatial, and energy-scales. The solar wind is a highly structured, multi-scale, evolving plasma and consists of coronal mass ejections (CMEs), stream interaction regions (SIRs), expanding flux tubes (Borovsky, 2008), and interplanetary magnetic field (IMF) discontinuities and fluctuations. The aim of this research is to improve our understanding of the evolution and dissipation of different scale-size solar wind magnetic structures as they move from the Sun-Earth Lagrange point 1 (L1) to Earth's bow shock and, ultimately, to …

Ideals And Lattices In Number Fields, Sarah Ali Alyammahi

Theses

This thesis investigates algebraic number fields and their rings of integers, which

generalize the ring of integers ℤ in ℚ. The study focuses on ideals, units, and ideal class

groups, which describe the arithmetic structure of number fields and the failure of unique factorization. Key invariants such as the norm, trace, and discriminant are developed and applied, with particular emphasis on quadratic number fields and classical examples such as the Gaussian and Eisenstein integers. Some explicit computations of ideal class groups are carried out. The thesis also explores connections with lattice theory by interpreting rings of integers as lattices and …

Employing Effective Solution Methods For Caputo-Based Sequential Fractional Models, Eman A. A. Ziada, Mohamed F. Abouelenein, Hijaz Ahmad, Monica Botros

Mathematical Modelling and Numerical Simulation with Applications

This paper investigates a class of nonlinear sequential singular fractional differential equations (FDEs) involving Caputo derivatives. This type of equation has several key advantages that enhance its value, such as capturing memory and hereditary effects. Viscoelastic materials and anomalous diffusion, as well as biological systems, can take advantage of this feature. In addition, fractional derivatives possess a sequential structure that enables the implementation of multiscale processes and hierarchical memory responses. Moreover, it provides an effective and flexible framework for solving differential equations compared to classical differential equations. It can therefore be used to model complex systems in physics, biology, and …

Optimal Control Strategies For Infectious Diseases: A Numerical Simulation Approach, M. Abu Salek, Jannatun Nayeem, Romana Yesmin, M. Haider Ali Biswas, M. Humayun Kabir

Mathematical Modelling and Numerical Simulation with Applications

Various infectious diseases, such as Tuberculosis and Hepatitis B virus (HBV), caused by Mycobacterium bacteria and hepatitis B virus, respectively, pose serious threats worldwide. This paper examines the spread of these diseases using a mathematical model that incorporates control measures, including vaccination and awareness programs. We use a system of differential equations with control variables and apply Pontryagin's principle to determine optimal control strategies. The stability of the Disease Free Equilibrium (DFE) has been analysed and demonstrated to be both locally and globally asymptotically stable when the basic reproduction number remains below unity, thereby ensuring disease elimination. Furthermore, the Endemic …

Exact Soliton Solutions Of The Nonlinear Time-Fractional Schrödinger Equation Via Atangana–Baleanu And M-Truncated Operators, Bahadır Kopçasiz, Fatma Nur Kaya Sağlam, Mehmet Şenol

Mathematical Modelling and Numerical Simulation with Applications

The main objective of this work is to obtain exact soliton solutions for a nonlinear time-fractional equation model describing wave profiles arising in various physical systems. To derive different wave structures associated with the considered model, two analytical techniques are employed: the extended G'\G^2-expansion method and the modified auxiliary equation (MAE) approach. A wave transformation is applied to reduce the nonlinear time-fractional equation to a nonlinear ordinary differential equation (NLODE) by means of the M-truncated and Atangana-Baleanu (AB) fractional operators. Several classes of solutions, including exponential, hyperbolic, and trigonometric wave forms, are obtained. Over and above the analytical results, graphical …

Dynamical Analysis And Optimal Control Of The Mpox Transmission Model With Stratified Susceptibility, Tuhfatul Janan, Fatmawati Fatmawati, Cicik Alfiniyah, Santi Martini, Dipo Aldila, Agus Hasan

Mathematical Modelling and Numerical Simulation with Applications

This study develops a mathematical model of Mpox transmission that combines stratified susceptibility (low-risk and high-risk groups) with vaccinated and asymptomatically infected compartments. The analysis of the model begins with examining the well-posedness, boundedness, and nonnegativity conditions for the solutions. The local stabilities of the equilibria are examined through the Jacobian matrix and phase plane analysis, while the global stabilities are provided through Lyapunov functions. The estimated parameters are verified using epidemiological data on Mpox cases in the United States, with an MAPE of 2.20% and R_0 > 1, indicating that Mpox remains endemic. Sensitivity analysis indicates that the contact rate …

Bifurcation Exploration Of Ion Acoustic Solitons Formation Of A Nonlinear Beta Fractional Kadomtsev-Petviashvili Burger Model In Plasma State, Mst. Razia Pervin, Alrazi Abdeljabbar, Fahad Sameer Alshammari, Mst. Shekha Khatun, Harun Or-Roshid

Mathematical Modelling and Numerical Simulation with Applications

This research presents an extensive investigation of Ion acoustic soliton dynamics governed by a Beta-fractional Kadomtsev-Petviashvili-Burgurs (KPB) model. By engaging the planar dynamical system scheme in aggregation with the extended $(\phi, \psi)$ expansion, Kudryashov expansion, and the NMKM analytic schemes, we create a broad class of exact nonlinear pattern wave solutions. The local stability edifice of the fractional plasma model is explored through bifurcation theory, enabling the far-reaching classification of all admissible phase diagrams. Conforming Ion acoustic wave structures allied with every detour alignment are systematically assembled. Owing to the fractional and dissipative appearances of the model, an all-embracing assortment …

Numerical Simulations And Hyers-Ulam Stability Of A Novel Nonlocal Anthropogenic Cutaneous Leishmaniasis Mathematical Model, Khalid Fanoukh Al Oweidi, Zakirullah -, Kamal Shah, Thabet Abdeljawad

Mathematical Modelling and Numerical Simulation with Applications

In this work, the fractal-fractional Atangana-Baleanu derivative with the Mittag-Leffler kernel is employed to capture the memory and hereditary effects inherent to anthropogenic cutaneous leishmaniasis transmission dynamics. The Banach fixed-point theorem and contraction mapping principle are used to prove the existence and uniqueness of solutions, while Hyers-Ulam stability of the system is analyzed to demonstrate the robustness of solutions with respect to small perturbations. Using a nonlinear least-squares approach, model parameters and fractional order are estimated using epidemiological data from the World Health Organization. The basic reproduction number $R_0 = 0.53$ indicates that the disease is under control after adding …

Markov-Modulated Queueing Network For Mobile Traffic Aggregation With Threshold-Controlled Buffers, Anton A. Esin, Elmira Yu. Kalimulina

Mathematical Modelling and Numerical Simulation with Applications

We study the problem of data transmission from mobile platforms operating in high-speed transit between cellular base stations, under conditions of unstable and intermittent connectivity. Conventional queueing and connectivity models often fail to capture the combined effects of rapidly changing signal conditions, finite buffer capacity, and dynamic topology. We aim to develop a tractable yet expressive model that integrates stochastic link availability, queue dynamics, and buffer control. We propose a mathematical framework based on queues whose service intensities are modulated by a continuous-time Markov chain (CTMC) representing signal conditions along a high-speed trajectory. The core subsystem is a two-stage (aggregation …

Optimal Control And Bifurcation Analysis Of A Predator–Prey Model With Self-Limiting Growth And Predator Disease, Dipo Aldila, Muhammad Akmal Fasya, Bevina D. Handari, Chidozie Williams Chukwu, Olumuyiwa James Peter

Mathematical Modelling and Numerical Simulation with Applications

We propose and analyze an eco-epidemiological predator–prey model that incorporates self-limitation and disease transmission within the predator population. The model is formulated as a system of ordinary differential equations describing logistic prey growth under the interspecific interaction with the predator. On the other hand, the predator population is divided into susceptible and infected classes, whose growth is constrained by prey availability. Three biologically relevant equilibria are identified: predator extinction, disease-free coexistence, and coexistence with endemic disease. The existence and stability of these equilibria are determined by key ecological and epidemiological thresholds, including the basic reproduction number. Using numerical continuation methods, …

Measuring Market Risk Through Entropic Var, Dragomir Nedeltchev, Tsvetelin Zaevski

Mathematical Modelling and Numerical Simulation with Applications

The article aims to measure the market risk beyond the basic risk measures like the Value-at-Risk (VaR) and the Expected Shortfall (ES). The Entropic Value-at-Risk is selected among the available measures based on its advantages -- it is the coherent upper bound of the VaR and ES. This risk measure is applied to the classical Black-Scholes model as well as to some more realistic ones, such as the exponential tempered stable model (the log-returns are presented by a tempered stable L\'evy process), the stochastic volatility model of Heston, its jump extension of Bates, and another stochastic volatility model but with …

Patterns Of Multimorbidity Among Low-Income Adults Who Smoke With Implications For Tailored Interventions: A Cluster Analysis Using A Mixture Of Bernoulli Model, Monique T. Cano, Michael R. Lindstrom, Oscar F. Rojas Perez, Ricardo F. Muñoz

School of Mathematical & Statistical Sciences Faculty Publications

Introduction: Smoking cigarettes remains a leading modifiable risk factor for preventable health conditions. In the United States, the health burden of smoking disproportionately impacts low-income individuals. Multimorbidity is common in this group, complicating treatment and worsening outcomes. Identifying multimorbidity clusters can support targeted, individualized interventions. This study aimed to identify multimorbidity clusters among individuals who smoke and experience economic hardship and provide clinical recommendations to enhance health outcomes.

Method: Individuals who smoke and experience economic hardship (N = 60) were recruited from the San Francisco Health Network (SFHN) and were assessed for physical and mental conditions. Cluster analysis was …

(Si16-04) Some Fixed Point Theorems On Chatterjea Type Contractions, Irom Shashikanta Singh, Y. Mahendra Singh

Applications and Applied Mathematics: An International Journal (AAM)

This paper establishes the existence of fixed points related to strict Chatterjee contractive mappings by relaxing the compactness of the underlying spaces and the continuity of the mapping involved, using altering distance functions and comparison functions in the general setting of metric spaces. Several non-trivial and illustrative examples are provided to demonstrate, support, and validate the obtained theoretical results. In addition, a theorem that can characterize the completeness of metric spaces through the existence of fixed points is rigorously proven and discussed. Furthermore, a theorem on strict Chatterjea-type modulus contractive mappings without continuity assumptions and with relaxed compactness conditions is …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission With Inter- And Intra-Group Structural And Behavioural Heterogeneous Syringe-Sharing Networks (5), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model incorporates structural heterogeneity through a three-group interaction framework and behavioural heterogeneity through group-specific syringe-sharing rates with additional intra-group variability. The syringe-sharing population in the model is divided into core, inner, and outer circle groups representing individuals with high, moderate, and low levels of syringe-sharing interaction intensity, respectively. In addition to differences in the number of daily interaction opportunities across groups, agents in each group are assigned syringe-sharing probabilities that vary at the individual level around their …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission In A Two-Group Structural Heterogeneous Syringe-Sharing Network (M2), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model extended a baseline homogeneous model by incorporating structural heterogeneity via a two-group interaction framework. The syringe-sharing population in the model is divided into inner and outer circle groups representing individuals with differing levels of syringe-sharing interaction intensity. While all agents share the same syringe-sharing probability and epidemiological processes remain identical across agents, the number of daily interaction opportunities differs between the two groups. Interactions in the model are generated dynamically using proximity-based sampling at each timestep …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission In A Three-Group Structural Heterogeneous Syringe-Sharing Network (M3), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model incorporates structural heterogeneity through a three-group interaction framework. The syringe-sharing population in the model is divided into core, inner, and outer circle groups representing individuals with high, moderate, and low levels of syringe-sharing interaction intensity, respectively. While the syringe-sharing rate and all epidemiological processes remain identical across agents, the number of daily interaction opportunities differs by agent grouping, capturing variation in structural position within the syringe-sharing network. Interactions are generated dynamically using proximity-based sampling at each …