Applied Mathematics Commons^™

Design And Implementation Of A Low-Cost Educa-Tional Robot For Engineering Curriculums, Diana Refaat Henry Jacob, Ashraf Mohamed Hafez, Mohamed Tarek Elawa

Journal of Engineering Research

The role of educational robots is becoming increasingly important. Many commercial educational robots differ in their abilities and price. In general, the cost of these robots presents the main cause of their limited use in the teaching process, especially in countries with limited financial resources. This work attempts to solve this problem by designing and implementing an educational robot with a limited budget. The robot was initially intended to serve higher education students' needs, especially in engineering curriculums but can be extended to other application areas. This work presents robot hardware functional blocks, mechanical struc-ture design, and 3D printing implementation. …

A Greening The Diesel: Vegetable Oil Biodiesel Blends For Cleaner Emissions And Improved Direct Injection Diesel Engine Performance, Medhat Elkelawy Prof. Dr, Eng., Hagar Alm-Eldin Bastawissi, E. A. El Shenawy Prof. Dr., Mustafa Mohamed Ouda

Journal of Engineering Research

In this study, we conducted comprehensive experiments to assess and compare the performance of pure diesel fuel against biodiesel produced from corn oil in various blend ratios (15/85, 30/70, 45/55, and 60/40) in a conventional four-stroke, direct-injection diesel engine, fuel is injected directly into the combustion chamber at the end of the compression stroke, allowing for efficient combustion and power generation over four distinct phases: intake, compression, power, and exhaust. Each fuel blend was tested at an engine speed of 16,000 rpm across different load conditions (low, medium, and high). Key performance metrics, including volumetric fuel consumption, exhaust smoke, and …

Improved Minimum Variance Channel Estimation Techniques For Ofdm Systems, Kwame S. Ibwe

Tanzania Journal of Engineering and Technology (TJET)

Orthogonal frequency division multiplexing (OFDM) systems face challenges in channel estimation due to noise, variability, and the doubly dispersive nature of wireless channels, which degrade performance. To address these challenges, a multichannel minimum variance double dispersive channel estimator is proposed. The method employs a hybrid approach that combines subspace and minimum variance techniques, optimizing the filter bank output power under a signal-to-noise ratio (SNR) constraint. This design preserves the desired signal while effectively suppressing disturbances, achieving robust performance with reduced computational complexity compared to existing methods. Simulation results demonstrate that the proposed estimator outperforms subspace and asymptotic methods in terms …

Mathematics In Everyday Life: Exploring Practical Applications And Real-World Impact, Priyant Banerjee, Arshad Bhat

Himalayan Research Papers Archive

Mathematics is an essential part of daily life and influences decisions and problem-solving in various aspects of life. This study explores how mathematical concepts are embedded in daily activities such as financial management, cooking, travel planning, and technological interactions. We will show how arithmetic, algebra, geometry, and statistics are applied in real life to improve decision-making, efficiency, and productivity. Findings indicate that people with higher mathematical literacy solve problems more efficiently, especially in budgeting, as accurate calculations minimize financial mistakes and facilitate long-term financial planning. In cooking, proportional reasoning ensures the accuracy of recipes, thus providing consistent culinary results. Travel …

An Agent-Based Model Of Microglia And Neuron Interaction: Implications In Neurodegenerative Disease, Cheyenne Ty, Amanda Case, Emmanuel Mezzulo, Abigail Penland, Kamila Larripa

Spora: A Journal of Biomathematics

Whether immune cells protect or harm the brain is an open question depending on context, and their role is implicated in multiple diseases such as Alzheimer's disease, dementia, and other neurological disorders. Microglia, a specific type of immune cell in the central nervous system, play a key role in homeostasis, and genes associated with an elevated risk of Alzheimer's disease correspond with deficiencies in their behavior. We created an agent-based model that incorporates inflammatory signaling, chemotaxis, and phagocytosis of damaged neurons and allows the exploration of crucial pathways in the maintenance of brain health. We specifically investigated pathways related to …

On Solving Differential Equations Describing The Ecology Of Shallow Lakes: A Comparison Of Classical And Modern Computational Methods Through Python, Vruddhi Kapre, Jeffrey R. Anderson, Alessandro Maria Selvitella

Spora: A Journal of Biomathematics

In this exposition paper, we describe some computational methodologies to solve numerically differential equations modeling the shallow lake ecosystem, with particular focus on the dynamics of the phosphorus. We describe in detail Python implementations of classical algorithms, like Runge-Kutta, and more modern approaches, including physics-informed neural networks.

On The Sharpness Of A Korn’S Inequality For Piecewise H1 Space And Its Applications, Qingguo Hong, Young Ju Lee, Jinchao Xu

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we investigate the sharpness of a Korn's inequality for piecewise H1 space and its applications. We first revisit a Korn's inequality for the piecewise H1 space based on general polygonal or polyhedral decompositions of the domain. We express the Korn's inequality with minimal jump terms. Then we prove that such minimal jump conditions are sharp for achieving the Korn's inequality. The sharpness of the Korn's inequality and explicitly given minimal conditions can be used to test whether any given finite element spaces satisfy Korn's inequality, immediately as well as to build or modify nonconforming finite elements for …

Long-Time Asymptotics For The Kadomtsev–Petviashvili I Equation With Small Initial Data, Samir Donmazov

Theses and Dissertations--Mathematics

We study the initial value problem for the Kadomtsev--Petviashvili I (KP I) equation (u_t + 6uu_x + u_xxx)_x = 3u_yy with small initial data belonging to a subspace of the energy space for the KP I equation. We establish the long-time asymptotics for solutions of the KP I equation using the inverse scattering transform formalism developed by Zhou. Within this framework, the inverse problem for the KP I equation is formulated as a nonlocal Riemann--Hilbert problem (RHP) in two spatial dimensions. As part of the asymptotic analysis, we determine the long-time behavior of the …

Collision Avoidance And Vegetation As Drivers Of Collective Motion In Australian Plague Locusts, Nathan S. Hasegawa

HMC Senior Theses

The Australian plague locust (Chortoicetes terminifera) is an agricultural and ecological pest that causes tens of millions of dollars in crop damage each year. In this thesis, we develop mathematical models of hopper bands, dense formations of juvenile locusts that move across a vegetated field and destroy plants in their path. We develop agent-based and PDE models of hopper bands moving through vegetation to examine how recently discovered behavior where locusts slow down to avoid collisions with other locusts may influence the shape, speed, and destructiveness of hopper bands. We find that collision avoidance may cause locusts to …

Multi-Valued Variational Inequalities For Variable Exponent Double Phase Problems: Comparison And Extremality Results, Siegfried Carl, Vy Khoi Le, Patrick Winkert

Mathematics and Statistics Faculty Research & Creative Works

We prove existence and comparison results for multi-valued variational inequalities in a bounded domain Ω of the form (Formula presented.) where A:W1,H(Ω)→W1,H(Ω)∗ given by (Formula presented.) for u∈W1,H(Ω), is the double phase operator with variable exponents and W1,H(Ω) is the associated Musielak–Orlicz Sobolev space. First, an existence result is proved under some weak coercivity condition. Our main focus aims at the treatment of the problem under consideration when coercivity fails. To this end we establish the method of sub–super-solution for the multi-valued variational inequality in the space W1, H(Ω) based on appropriately defined sub- and super-solutions, which yields the existence …

Caves, Calculus, And Climate Change: Measuring And Modeling The Discharge Of Biz Falls In Mammoth Cave National Park, Ava Lich

Mahurin Honors College Capstone Experience/Thesis Projects

Climate change poses a significant global challenge, with increasing levels of atmospheric carbon dioxide as a primary driver of rising temperatures and environmental disruptions. Karst systems, such as those in South-Central Kentucky, play a role in sequestering atmospheric CO₂ through the dissolution of limestone, a process that forms unique landscapes while mitigating climate impacts. This study investigates the discharge dynamics of Cascade River in Great Onyx Cave to enhance understanding of the relationship between hydrology and carbon sequestration in karst environments. A barrel weir equipped with pressure transducers was employed to collect and measure water flow, and Torricelli’s law was …

Line Graphs Of Directed Graphs I, Vaidy Sivaraman, Daniel Slilaty

Mathematics and Statistics Faculty Publications

We determine the forbidden induced subgraphs for the intersection of the classes of chordal bipartite graphs and line graphs of acyclic directed graphs. This is a first step towards finding the forbidden induced subgraphs for the class of line graphs of directed graphs.

Finite Hybrid- And Semi-Markov Chains, Jose L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The ergodic behaviour of finite Markov chains having also instantaneous transition are considered. Some estimates are obtained which complement our previous work [29]. Also, an optimal switching control model for semi-Markov chains is analysed, without any particular assumptions on the recurrent classes.

Diophantine Avoidance, Number Fields, And Quadratic Forms, Sehun Jeong

CGU Theses & Dissertations

Diophantine avoidance has been studied by several authors in recent years. This term refers to effective results on existence of points of bounded size (where size is measured by norm or height, depending on the context) in a given algebraic set avoiding some specified subsets. The application of avoidance conditions allows to understand how ``well distributed" are points of bounded size in a given set. If it is possible to find them outside of some prescribed collection of subsets of the set in question, then it suggests that they are evenly distributed, in some appropriate sense. Our first result investigates …

Stability And Global Dynamics Of Autonomous And Nonautonomous Discrete Population Models With Stocking, Harvesting, And Cooperation, Sam Habach

Open Access Dissertations

This dissertation investigates the local and global behavior of several classes of discrete population models involving stocking, harvesting, and cooperation. The study is divided into three major manuscripts, each offering new theoretical in sights, bifurcation results, and applications to real-world data.

In Manuscript 1, we study the Beverton-Holt population models with constant and proportional stocking and harvesting, as well as sigmoid Beverton-Holt models under constant stocking and harvesting, both in autonomous and non-autonomous settings. We analyze stability and explore global dynamics using established local and global dynamics theorems, bifurcation theory, and explicit solutions when available. Special attention is given to …

Ergodic Switching Control For Markov-Feller Processes Ii, Jose L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

This is the continuation of Part I [14], where we considered control problems with long term average (or ergodic) cost for Markov switching processes (zt , nt ), nt being a discrete component with values in a finite set N . The control acts only on this discrete component and consists of immediate switching actions. We solve the ergodic problem in several situations extending previous works, mainly when zt is a reflected diffusion with or without jumps and when the set of control values is strictly smaller than N . In this Part II, we conclude our theoretical analysis with …

Ergodic Switching Control For Markov-Feller Processes I, Jose L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

We consider control problems with long term average (or ergodic) cost for Markov switching processes (zt, nt ), nt being a discrete component with values in a finite set N . The control acts only on this discrete component and consists of immediate switching actions. We solve the ergodic problem in several situations extending previous works, mainly when zt is a reflected diffusion with or without jumps and when the set of control values is strictly smaller than N .

Discrete Time Risk Processes With Stochastic Premiums And Dividends, Enoch J. Dangbe

Mathematics Dissertations - Archive

Risk processes typically emerge in insurance and finance and are concerned with stochastic representation of uncertainties of real-world events. Main objective amounts to quantifying the chances of both desirable and undesirable events and balancing their mutual impact for the purpose of developing models that in some sense optimize the outcome from the business perspective. Our research is concerned with studying the evolution of the surplus process in which time and assets are integer-valued. Initial capital, random premiums, random claims, dividend payments based on assets’ performance constitute the components of our model. Our findings established recursive formulas for the total expected …

A Time-Domain Boundary Integral Equation For Moving Acoustic Sources In Uniform Flow And Its Solution By An Advanced Time Propagation Approach, Fang Q. Hu, Douglas M. Nark

Mathematics & Statistics Faculty Publications

This paper presents a time-domain boundary integral equation (TDBIE) formulation for predicting acoustic scattering from moving sources in a uniform mean flow. This work is motivated by the increasing need for accurate aeroacoustic modeling of modern aircraft configurations, including VTOL and eVTOL systems with rotating components. A key challenge in time-domain scattering simulations with moving sources is the determination of retarded time for a given observer time, which involves solving an implicit equation at each time step. This can be computationally costly, particularly for numerical solution of the TDBIE where every surface element on the scattering body acts as an …

Covariate Selection For Rna-Seq Differential Expression Analysis With Hidden Factor Adjustment, Farzana Noorzahan, Hyeongseon Jeon, Yet Nguyen

Mathematics & Statistics Faculty Publications

In RNA-seq data analysis, a primary objective is the identification of differentially expressed genes, which are genes that exhibit varying expression levels across different conditions of interest. It is widely known that hidden factors, such as batch effects, can substantially influence the differential expression analysis. Furthermore, apart from the primary factor of interest and unforeseen artifacts, an RNA-seq experiment typically contains multiple measured covariates, some of which may significantly affect gene expression levels, while others may not. Existing methods either address the covariate selection or the unknown artifacts separately. In this study, we investigate two integrated strategies, FSR_sva and SVAall_FSR, …