Pseudodifferential Absorbing Boundary Conditions For Waves,
2026
University of Texas at Tyler
Pseudodifferential Absorbing Boundary Conditions For Waves, Lauren Taylor
Mechanical Engineering Theses
Absorbing boundary conditions (ABCs) are required to truncate the computational domain when performing Finite Element Analyses of exterior acoustic problems where physical domain is unbounded. ABC is applied on a fictitious boundary containing the scatterer and ideally allows outgoing waves to leave without non-physical reflections. Preventing artificial reflections is essential to benefit from the accuracy of the numerical method used. Otherwise, ABC acts as a reflective surface, and artificial reflections distort the solution in the entire domain which is not recoverable by any type of refinement. Pseudodifferential ABCs were used to describe the Dirichlet-to-Neumann map which maps known boundary values …
Analytic Solutions To Oceanographic Kinematic Property Equations,
2026
Rowan University
Analytic Solutions To Oceanographic Kinematic Property Equations, James Turbett
Theses and Dissertations
With the recent advent of large submesoscale drifter deployments, interpreting the timeseries of kinematic properties (KP) - divergence, vorticity, shear, and normal strain rates observed therein is a pressing issue. The evolution equations for the four KP are derived from the two-dimensional momentum conservation equations. The resulting equations, a nonlinear coupled system of ordinary differential equations, capture the submesoscale motion of drifters along fixed ocean surfaces, with time and space scales on the order of days and kilometers. This thesis builds theory around KP timeseries behavior by solving for the analytic solutions in the particular cases that one KP is …
Coupled-Pendulum Modeling In An Ode Class: An Assignment On Fourier-Initialized Gradient Descent In Machine Learning,
2026
Kansas State University
Coupled-Pendulum Modeling In An Ode Class: An Assignment On Fourier-Initialized Gradient Descent In Machine Learning, Huy Truong, Andrew Bennett
CODEE Journal
As data-driven methods are increasingly used in science and engineering, students benefit from learning to integrate machine learning techniques with traditional mathematical modeling. We present a hands-on extra-credit assignment for an undergraduate ordinary differential equations (ODE) course that enables students to compare classical analytical methods with data-driven approaches on the same physical system. Using a coupled-pendulum system---two pendulums connected by a spring---with real experimental data acquired via video tracking of a real physical setup, students work through three models in a guided Jupyter notebook with all code provided. First, they fit a neural network with Fourier features as a purely …
Differential Topology And The Poincaré-Hopf Theorem,
2026
Bellevue High School
Differential Topology And The Poincaré-Hopf Theorem, Tara Saini
Rose-Hulman Undergraduate Mathematics Journal
In this paper, we will develop the ideas needed to understand and prove the Poincaré–Hopf Theorem, which connects the local behavior of smooth vector fields to global topological properties. We will begin by introducing smooth manifolds and smooth maps, which are the basis of differential topology. We will then define derivatives of smooth maps through tangent spaces and use these to classify points. To build toward the theorem, we will introduce orientation, degree, and smooth vector fields. These concepts will culminate in a proof of the Poincaré–Hopf Theorem, aided by Brouwer’s Fixed Point Theorem. Finally, we will apply the result …
A Closed Form For The Pulsar Sequence,
2026
Del Norte High School
A Closed Form For The Pulsar Sequence, Ryan Z. Liu
Rose-Hulman Undergraduate Mathematics Journal
In this paper, we study the Pulsar Sequence, an integer sequence derived from Latin-square-based “Pulsar puzzles” introduced by the Cracking the Cryptic YouTube channel. A Pulsar puzzle consists of two interlocked spirals of circled and uncircled squares, generating the Dual and Pulsar sequences, respectively. We investigate the properties of the Pulsar puzzle and focus our work on constructing the Pulsar Sequence, allowing us to solve a Pulsar puzzle of any size. A general formula to calculate any term of the Pulsar Sequence is proposed at the end of the paper.
A Categorical Framework For Modeling Genetic Drift,
2026
Spelman College
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,
2026
University of Cincinnati
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.
Symmetries In Apollonian Circle Packings,
2026
University of Colorado, Boulder
Symmetries In Apollonian Circle Packings, Clyde Kertzer
Rose-Hulman Undergraduate Mathematics Journal
An Apollonian circle packing is generated from a Descartes quadruple (a set of four mutually tangent circles) by repeatedly filling the spaces between mutually tangent circles with further tangent circles. By studying the circles' curvatures $a,b,c,d$, two distinct types of symmetric packings appear: one where $a+b+c=d$ and one where $c=d$. We give complete parameterizations of these symmetric packings and count how many packings of each type are contained by a given enclosing circle.
A Differential Equation–Based Epidemiological Model Of Post-Operative Chronic Pain In Scoliosis Patients With Data-Driven Analysis,
2026
Phillips Academy
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 …
Fixed-Parameter Extrapolation And Aperiodic Order,
2026
University of South Carolina
Fixed-Parameter Extrapolation And Aperiodic Order, Stephen Fenner, Frederic Green, Steven Homer
Mathematics
Fix any λ∈C. We say that a set S⊆C is λ-convex if, whenever a and b are in S, the point (1-λ)a+λb is also in S. We investigate the properties of λ-convex sets and their (topological) closures, and we prove a number of facts about them. Let Qλ⊆C be the least λ-convex superset of {0,1}. Generalizing results of R. G. E. Pinch, we give a sufficient condition on λ for Qλ and some other related λ-convex sets to be discrete by introducing the notion of a strong PV number. These conditions give rise to a number of periodic and aperiodic …
Trattato Dell’Alcibra Amuchabile (Anonimo): A Guided Translation,
2026
SUNY Geneseo
Trattato Dell’Alcibra Amuchabile (Anonimo): A Guided Translation, Gary Towsley, Olympia Nicodemi
Geneseo Authors
The Trattato dell’Alcibra Amuchabile is a pre-modern algebra text from c. 1365. It is written in a Tuscan dialect of Italian and is situated in the abbacus school tradition, schools that taught the mathematics needed for a mercantile society. Like all the algebra written in Italy at the time, it was inherited from al-Khwarizmi and, like his, written with no symbols—no x’s, y’s, plus signs, etc. It was what is sometimes called “rhetorical algebra.” There is very little source material available in English from this important era in the history of algebra. This book helps fill that gap. …
Math 119: Math For Elementary School Teachers Instructor Guide,
2026
CUNY Queens College
Math 119: Math For Elementary School Teachers Instructor Guide, Seth Lehman
Open Educational Resources
OER instructor guide for Math 119: Math for Elementary School Teachers at Queens College
Cdt-1d Cnn Integration With Simpson-Sobolev Regularization For High-Frequency Options Trading: With Fem-Based Heston Option Pricing,
2026
Southern Methodist University
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 …
Math 119: Math For Elementary School Teachers Syllabus,
2026
CUNY Queens College
Math 119: Math For Elementary School Teachers Syllabus, Seth Lehman
Open Educational Resources
OER course syllabus for Math 119, Math for Elementary School Teachers, at Queens College
Matching The Stars To A Game Of Aggression,
2026
Berea College
Matching The Stars To A Game Of Aggression, E. Chambers, Kristen Barnard
Electronic Proceedings of Undergraduate Mathematics Day
Region against region and army against army, we chart and battle among the stars! This paper studies the combinatorial game Aggression using graph-theoretic models. We focus on how winning strategies depend on the structure of the game graph, with particular attention to star graphs, matchings, and their disjoint union. The results presented here come from research conducted under the guidance of Dr. Kristen Barnard during the summer of 2025. We begin by introducing the game, describing the rule set used, and explaining how maps can be represented as graphs. From there, we examine how adjacency, placement order, and tie-breaking rules …
Strict Steiner Symmetrization For Polygons,
2026
Princeton University
Strict Steiner Symmetrization For Polygons, Joseph Chai, Sun-Yung Alice Chang
Electronic Proceedings of Undergraduate Mathematics Day
In this note, we introduce a method called Strict Steiner Symmetrization (see Section 2.2) that is an altered form of Steiner Symmetrization that fixes the number of vertices. The context of this paper will be to prove the Isoperimetric Inequality in R2 via approximation by polygons. Specifically, to establish that among all n-gon domains in the plane, the regular m-gon, m ≥ n, uniquely minimizes the isoperimetric ratio and that the limit of this regular polygon (that is the circle) achieves equality in the isoperimetric inequality. This note is an extracted portion of my junior thesis (A Polygonal Proof of …
Predator-Prey Dynamics: Exploration And Logistic Extension Of The Lotka-Volterra System,
2026
University of Dayton
Predator-Prey Dynamics: Exploration And Logistic Extension Of The Lotka-Volterra System, Amanda Maylath, Samuel Brensinger
Electronic Proceedings of Undergraduate Mathematics Day
The Lotka-Volterra system is a classic model of predator–prey interactions, capturing the interdependent growth and decline of two species. Using a dynamical systems approach, we identify fixed points, linearize the system via the Jacobian, and analyze phase space trajectories to determine stability and long-term behavior. This analysis provides insight into predator-prey dynamics without requiring explicit solutions. We further extend the model by incorporating a carrying capacity for the prey, reflecting more realistic population dynamics.
Huffman Tree Uniqueness,
2026
University of Notre Dame
Huffman Tree Uniqueness, Elijah Diller, Adam Volk
Electronic Proceedings of Undergraduate Mathematics Day
The Huffman algorithm is a standard algorithm used to generate an optimized binary encoding of a string. Using this algorithm, it may be possible to come up with more than one possible optimized binary encoding for a given string, so the following question arises: what strings have a unique optimized binary encoding? By unique encoding, we mean a unique vertex-labeled binary tree resulting from the Huffman algorithm. We do not worry about edge labels as every binary tree corresponding to a string with n distinct characters has 2n−1 ways of assigning the edge labels and determining the code. This investigation …
Conditionals And Modalities In Constructive Quantum Logics,
2026
TU Wien
Conditionals And Modalities In Constructive Quantum Logics, Juan P. Aguilera, Guillaume Massas
Mathematics, Physics, and Computer Science Faculty Articles and Research
We investigate logics that generalize both intuitionistic logic and quantum logic. In earlier work, we introduced Ex-logic, an extension of Holliday's fundamental logic that coincides with the intersection of orthologic and the implication-free fragment of intuitionistic logic. In this paper, we add an implication connective to Ex-logic and axiomatize iEx-logic, the intersection of full intuitionistic logic and orthomodular logic with the implication connective interpreted as the Sasaki hook. As a consequence, we obtain a characterization of the lattice of logics extending iEx-logic as the product of the lattice of intermediate logics and the lattice of orthomodular logics. We also explore …
Principal Leadership As A Predictor Of Teacher Performance: Evidence From An Indonesian Elementary School,
2026
Universitas Katolik Santo Thomas
Principal Leadership As A Predictor Of Teacher Performance: Evidence From An Indonesian Elementary School, Irminapinem Pinem, Antonius Remigius Abi, Hamela Sari Sitompul
Jurnal Pendidikan Sains
Teacher performance is a critical determinant of educational quality and student achievement, making the identification of factors that influence teacher effectiveness an important area of educational research. Among these factors, principal leadership has been recognized as a key organizational variable that shapes teachers’ professional practices and instructional performance. This study aimed to examine the relationship between principal leadership and teacher performance at State Elementary School Raya Kahean, Simalungun Regency, Indonesia. The study employed a quantitative correlational research design involving 52 teachers selected through total sampling. Data were collected using two structured questionnaires measuring principal leadership and teacher performance. The principal …
