A Unified Concept Of Periodicity On Any Time Scale And Applications,
2025
Missouri University of Science and Technology
A Unified Concept Of Periodicity On Any Time Scale And Applications, Martin Bohner, Jaqueline G. Mesquita, Sabrina H. Streipert
Mathematics and Statistics Faculty Research & Creative Works
We introduce a novel definition of periodicity on arbitrary time scales, dependent on a strictly increasing and differentiable function. This removes the commonly used and restrictive assumption of a periodic time scale to define periodic functions. Our new definition furthermore allows for a wider class of functions to be studied using the theory of periodic systems. After providing crucial properties of these periodic functions, such as the translation invariance of integrals of periodic functions, we apply the concept of this new periodicity to linear dynamic equations. We provide necessary and sufficient conditions for a linear dynamic equation to have such …
A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (El–Rk–Fv) Method For Scalar Nonlinear Conservation Laws,
2025
Swarthmore College
A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (El–Rk–Fv) Method For Scalar Nonlinear Conservation Laws, J. Chen, Joseph Nakao, J.-M. Qiu, Y. Yang
Mathematics & Statistics Faculty Works
We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for …
Line Graphs Of Directed Graphs I,
2025
Mississippi State University
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.
Localized Kernel Methods For Signal Processing,
2025
Claremont Graduate University
Localized Kernel Methods For Signal Processing, Sippanon Kitimoon
CGU Theses & Dissertations
This dissertation presents two signal processing methods using specially designed localized kernels for parameter recovery under noisy condition. The first method addresses the estimation of frequencies and amplitudes in multidimensional exponential models. It utilizes localized trigonometric polynomial kernels to detect the multivariate frequencies, followed by a more detailed parameter estimation. We compare our method with MUSIC and ESPRIT, which are classical subspace-based algorithms widely used for estimating the parameters of exponential signals. In the univariate case, the method outperforms MUSIC and ESPRIT under low signal-to-noise ratios. For the multivariate case, we develop a coordinate-wise projection and registration approach that achieves …
Enhanced Kneser-Type Oscillation Criteria For Second-Order Functional Quasilinear Dynamic Equations On Time Scales,
2025
Missouri University of Science and Technology
Enhanced Kneser-Type Oscillation Criteria For Second-Order Functional Quasilinear Dynamic Equations On Time Scales, Taher S. Hassan, Elvan Akın, Bassant M. El-Matary, Ioan Lucian Popa, Mouataz Billah Mesmouli, Ismoil Odinaev, Akbar Ali
Mathematics and Statistics Faculty Research & Creative Works
This work presents new Kneser-type oscillation criteria for second-order quasilinear functional dynamic equations defined on arbitrary unbounded above time scales. Our approach employs the Riccati transformation technique in conjunction with the integral averaging method. The results show a significant improvement over recent Kneser-type oscillation criteria. We provided several illustrative examples to highlight the importance of our findings.
How To Deal With High-Impact Low-Probability Events: Theoretical Explanation Of The Empirically Successful Fuzzy-Like Technique,
2025
The University of Texas at El Paso
How To Deal With High-Impact Low-Probability Events: Theoretical Explanation Of The Empirically Successful Fuzzy-Like Technique, Juan Ulloa, Aaron Velasco, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
When making decisions, it is important to take into account high-impact low-probability events. For such events, traditional probability-based approach -- which considers the product of the probability p that this event happens and the probability P that a randomly selected building will be destroyed -- often underestimates risks. Available data has lead to an empirical table that provides a more adequate risk estimate. Most of the entries in this table correspond to the fuzzy-like formula min(p,P). This paper explains this empirical result. Specifically, it explains both the effectiveness of the min formula -- and also explains deviations from this formula.
Möbius Transformations And Hyperbolic Geometry In The Upper Half-Plane,
2025
Western Kentucky University
Möbius Transformations And Hyperbolic Geometry In The Upper Half-Plane, Emma Bunch
Mahurin Honors College Capstone Experience/Thesis Projects
In this thesis, we discuss several properties of Möbius transformations and hyperbolic geometry, a type of non-Euclidean geometry, in the upper half-plane using tools of complex analysis. We begin with preliminaries for our work, comprising the stereographic projection, the representation of circles and lines in the complex plane, conformal maps, and a result on cross-products, which we include for further development. We proceed to Möbius transformations and discuss their properties, cross-ratios, and various mappings. We additionally provide useful calculations. Lastly, we conclude with the hyperbolic metric in the upper half-plane and explore hyperbolic distance, including its invariance under Möbius transformations. …
Gaps In Knowledge: Topological Insights Into The Structure Of Science,
2025
Macalester College
Gaps In Knowledge: Topological Insights Into The Structure Of Science, Gavin Engelstad
Mathematics, Statistics, and Computer Science Honors Projects
Understanding scientific development is essential to ascertaining the mechanisms leading us into the future. Building this understanding requires both methodological developments and empirical research. This thesis contributes in both aspects using a topological approach to examine scientific knowledge. The first section presents a new algorithm to find optimal cycle representatives for homological features in complex networks, a context for which we demonstrate existing algorithms can be inadequate. The second section applies a number of topological methods, including our cycle optimization algorithm, to data on individual scientific fields, demonstrating the value of topological approaches and highlighting new insights about how science …
Existence And Uniqueness Of The Solution Of A Traffic Flow Partial Differential Equation On Multi-Lane Freeways,
2025
Claremont Graduate University
Existence And Uniqueness Of The Solution Of A Traffic Flow Partial Differential Equation On Multi-Lane Freeways, Sina Zareian
CGU Theses & Dissertations
In this dissertation, we shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential equation which forms when we apply the operator splitting method to the traffic flow stochastic partial differential equation.
Diophantine Avoidance, Number Fields, And Quadratic Forms,
2025
Claremont Graduate University
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 …
Classical And Quantum Computational Methods For Predicting Fluid Transport In Fracture Networks,
2025
Claremont Graduate University
Classical And Quantum Computational Methods For Predicting Fluid Transport In Fracture Networks, John Kath
CGU Theses & Dissertations
This dissertation addresses the challenge of modeling complex geophysical systems by developing efficient surrogate models and scalable quantum algorithms. Our approaches provide uncertainty quantification, assessing confidence in estimates while accounting for subsurface heterogeneity. These innovations are designed to replace costly solvers with parsimonious emulators. In combination with multi-fidelity and quantum techniques, they make physics-informed modeling computationally feasible. One of our studies involves the use of Gaussian process regression to generate Bayesian predictions for gas transport in 3D discrete fracture networks. This provides accurate estimates while offering substantial savings over computationally intensive high-fidelity simulations. Additionally, we study multi-fidelity modeling through the …
Optimization Of Free-Time Controlled Constrained Sweeping Processes And Applications,
2025
Wayne State University
Optimization Of Free-Time Controlled Constrained Sweeping Processes And Applications, Thi Dai Trang Nguyen
Wayne State University Dissertations
Optimization and optimal control have a wide range of applications across fields like engineering, biology, data science, and economics. This dissertation is devoted to advanced optimal control problems discontinuous constrained differential inclusions of the sweeping type involving the duration of the dynamic process into optimization, which are truly challenging and underinvestigated in control theory while being highly important for various applications. To attack such problems, we use the method of discrete approximation while establishing its well-posedness and strong convergence to optimal solutions of the controlled sweeping process. This approach, married to advanced tools of variational analysis, enables this research to …
Examining Student Understanding Of Series Convergence Using Script Writing,
2025
University of Texas at Arlington
Examining Student Understanding Of Series Convergence Using Script Writing, Eduardo Torres Manzanarez
Mathematics Dissertations - Archive
This exploratory study investigates second-semester calculus students’ understanding of series convergence using both nonscripting and scripting-based tasks. Researchers recognize that students encounter difficulties with learning series, including series convergence, and that there is a need for more meaningful tasks that aid students’ learning of series. Script writing, used mainly with prospective mathematics teachers, can be used to explore mathematical understandings. Thus, this study examines how script writing, in the form of a scripting task, elicits students’ understanding of series convergence in contrast to nonscripting-based tasks to determine the potential of script writing in assessing this student understanding. We examine students’ …
A New Formulation Of Hardy-Type Dynamic Inequalities On Time Scales,
2025
Missouri University of Science and Technology
A New Formulation Of Hardy-Type Dynamic Inequalities On Time Scales, Martin Bohner, Irena Jadlovská, Ahmed I. Saied
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we introduce a novel formulation of dynamic Hardy-type inequalities on a time scale, motivated by a recently established convexity approach in the Haar measure. The classical Hardy inequality is refined so that the classical Lebesgue-measure constant is replaced by the sharp constant 1. We obtain time-scale analogues on finite intervals with best constants, and, for nonincreasing and nondecreasing functions, reversed inequalities with explicit weights described by incomplete β-functions. To establish our results, we employ two distinct time scales and apply the chain rule, together with the substitution rule, the derivative of inverse functions, and Fubini's theorem for …
Self-Tor Persistence Of Modules Over Determinantal Rings,
2025
University of Texas at Arlington
Self-Tor Persistence Of Modules Over Determinantal Rings, Tatheer F. Ajani
Mathematics Dissertations - Archive
Tor-persistence is the claim that Tor of a module with itself is only zero if the module has finite projective dimension. Work done by Avramov, Iyengar, Nasseh, Sather-Wagstaff, and various other authors have proved Tor-persistence of modules over certain rings. In this work, we will prove Tor-persistence for certain modules over determinantal rings, specifically for the hypersurface defined by the determinant of a generic matrix. We will then give an explicit proof that Tor^R_2(M,M) is never zero, that Tor^R_1(M,M)=0, and due to the periodicity of the given free resolution, our result can be extended to the entire complex, showing that …
Adding Libraries To The Equation: Mathematical Sciences’ Underutilization Of Academic Librarians,
2025
Butler University
Adding Libraries To The Equation: Mathematical Sciences’ Underutilization Of Academic Librarians, Jennifer Lc Burke, Elizabeth C. Novosel, Daniel G. Kipnis, Rasitha Jayesekere
Scholarship and Professional Work
Academic librarians do not engage with all disciplinary departments equally. Despite equal or even greater efforts, some departments are less responsive to librarian outreach. One such department is mathematics. To understand mathematics departments’ relationships with their academic librarians, three mathematics librarians created a 20-question survey that was disseminated to mathematics faculty, instructors, and instructional staff in the United States and Canada. Of the 188 survey participants, more than a third reported that they never engage with their librarians, approximately half only do so occasionally, and a mere eight percent of participants collaborated with librarians to provide information literacy instruction (IL) …
Modeling Deductive Inference: A Historico-Philosophical Introduction To First-Order Logic,
2025
Northern Illinois University
Modeling Deductive Inference: A Historico-Philosophical Introduction To First-Order Logic, David J. Buller
Faculty Books & Book Chapters
This book is a companion text for lectures on first-order logic and its elementary metatheory (used in Intermediate Logic at Northern Illinois University). It covers the basic concepts of set theory necessary for a mathematical development of first-order logic; develops a formal language of first-order logic; presents a classical Tarskian semantics for the language and the “semantic” conception of logical consequence; presents a Gentzenian proof system and the “syntactic” conception of logical consequence; develops a partial decision procedure for logical consequence in the language; demonstrates applications of the formal system to modeling deductive inference expressed in natural language; and extends …
Designing An Affordable Motion Capture System For Multi-Robot Research And Education,
2025
Swarthmore College
Designing An Affordable Motion Capture System For Multi-Robot Research And Education, Hojune Kim , '25
Senior Theses, Projects, and Awards
In this work, we propose a low-cost motion capture system for real-time tracking of multiple robots’ positions and orientations in indoor environments, specifically tailored for research and educational applications. Precise localization is essential for evaluating robotics algorithms such as decentralized multi-agent control, cooperative path planning, and collision avoidance. [1-3] However, commercial motion capture systems like Vicon and OptiTrack cost between $50,000 and $150,000, making them inaccessible for many smaller institutions, student clubs, and low-resource labs. To address this challenge, we developed an affordable alternative based on three ceiling-mounted 1080p USB cameras and AprilTags. Our system operates at 30 Hz and …
Runner Locating With Multiple Probes,
2025
Northern Kentucky University
Runner Locating With Multiple Probes, Kola Akinrele, Axel Brandt, Elizabeth Breen, Catherine Erbes, Matthew Lee, Patrick O’Doherty, Weston Rainer
2025 Faculty Bibliography
In the runner locating variation of cops and robbers on a graph, a chaser attempts to locate an invisible runner by probing a single vertex v each turn, from which the chaser learns the runner’s distance. The runner is then permitted to stay at his current vertex or move to an adjacent vertex other than v. A graph is locatable if the chaser is able to locate the runner in a finite number of turns, and the location number of a graph is the minimum number of turns necessary to determine the runner’s location regardless of the runner’s evasion strategy. …
Vanishing Of Local Cohomology With Applications To Hodge Theory,
2025
DePauw University
Vanishing Of Local Cohomology With Applications To Hodge Theory, Scott Hiatt
Mathematics Faculty Publications
Let H = ((H, F •), L) be a polarized variation of Hodge structure on a smooth quasi-projective variety U . By M. Saito’s theory of mixed Hodge modules, the variation of Hodge structure H can be viewed as a polarized Hodge module M ∈ HM (U ). Let X be a compactification of U , and j : U ↪→ X is the natural map. In this paper, we use local cohomology with mixed Hodge module theory to study j+M ∈ DbM HM (X). In particular, we study the graded pieces of the de Rham complex GrF p DR(j+M) …
