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 …
Enhancing Deep Learning Image Reconstruction In Breast Ct With Task-Driven Training And Physics-Informed Models,
2026
Marquette University
Enhancing Deep Learning Image Reconstruction In Breast Ct With Task-Driven Training And Physics-Informed Models, Megan Ariel Murphy
Dissertations (1934 -)
Dedicated breast X-ray computed tomography (breast CT) is a developing imaging modality that has potential as an alternative to mammography. Unlike traditional mammography, breast CT offers high-resolution, fully 3D anatomical detail, which aids in the detection of microcalfications and subtle lesions that are potential indicators of cancer. To be effective for screening, breast CT must limit radiation exposure by reducing CT view angles. However, traditional image reconstruction methods yield noisy, artifacted images in this sparse-view CT setting. This dissertation develops image restoration and reconstruction methods that address these limitations by integrating physics-informed iterative methods with machine learning tools, and a …
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
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
Existence And Uniqueness Of Positive Solutions For Hilfer–Hadamard-Type Fractional Differential Equations With Γ-Concave And Sub-Homogeneous Operators,
2026
Missouri University of Science and Technology
Existence And Uniqueness Of Positive Solutions For Hilfer–Hadamard-Type Fractional Differential Equations With Γ-Concave And Sub-Homogeneous Operators, Hasan Rasouli, Hojjat Afshari, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
In this research, we present necessary and sufficient conditions for the existence and uniqueness of positive solutions for a class of Hilfer–Hadamard-type fractional differential equations with boundary value problems, including those with integral boundary conditions. The obtained results are conditional on a specific set of strong assumptions, which substantially narrow the class of admissible nonlinearities, coefficients, and boundary data. Thus, the present work extends the Hadamard-type framework to the Hilfer–Hadamard setting only within this restrictive regime, rather than providing a full extension to all Hilfer–Hadamard systems. We utilize the properties of (Formula presented.) -concave and sub-homogeneous operators along with two …
Toward A Didactical Phenomenology For The Completeness Axiom,
2026
The University of Texas Rio Grande Valley
Toward A Didactical Phenomenology For The Completeness Axiom, Sean Larsen, Tenchita Alzaga Elizondo, Kristen Vroom, Stephen Strand Ii
School of Mathematical & Statistical Sciences Faculty Publications
The study is part of an instructional design project focused on introductory real analysis. The goal of the project is to develop a theoretically grounded and empirically supported instructional approach that builds on students’ experiences in the calculus sequence to engage them in the reinvention of the rigorous foundations of the calculus. An essential aspect of this foundation is the completeness of the real numbers. Drawing on the didactical phenomenology heuristic from the theory of Realistic Mathematics Education (RME), we conducted an iterative instructional design study focused on the completeness axiom. The work proceeded in two phases. First, we conducted …
Quantization Dimension For A Generalized Inhomogeneous Bi-Lipschitz Iterated Function System,
2026
Indian Institute of Information Technology, Allahabad
Quantization Dimension For A Generalized Inhomogeneous Bi-Lipschitz Iterated Function System, Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma
School of Mathematical & Statistical Sciences Faculty Publications
For a given r∈(0,+∞), the quantization dimension of order r, if it exists, denoted by Dr(μ), of a Borel probability measure μ on Rd represents the speed how fast the nth quantization error of order r approaches to zero as the number of elements n in an optimal set of n-means for μ tends to infinity. If Dr(μ) does not exists, we call D̲r(μ) and D¯r(μ), the lower and upper quantization dimensions of μ of order r. In this paper, we estimate the quantization dimension of condensation measures associated with condensation systems ({fi}i=1N,(pi)i=0N,ν), where the …
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 …
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 …
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.
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 …
Comparing The Effects Of Project-Based Learning, Inquiry Learning, And Conventional Instruction On Students' Learning Motivation In Biology,
2026
Universitas Muhammadiyah Bengkulu
Comparing The Effects Of Project-Based Learning, Inquiry Learning, And Conventional Instruction On Students' Learning Motivation In Biology, Yeyen Angraini, Irwandi Irwandi, Jayanti Syahfitri
Jurnal Pendidikan Sains
Learning motivation is an important factor influencing students’ engagement, persistence, and success in Biology learning. However, classroom instruction at the senior high school level is often dominated by teacher-centered approaches, which may limit students’ active participation and motivational development. This study aimed to compare students’ learning motivation across Project-Based Learning (PjBL), Inquiry Learning, and conventional instructional approaches in Biology learning. The study employed a quantitative quasi-experimental design with a pretest–posttest approach involving three groups. Participants consisted of 85 Grade XI students from SMA Negeri 1 Talang Padang, South Sumatra, distributed across three classes: PjBL (n = 28), Inquiry (n = …
