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Compilation Of A Nationwide River Image Dataset For Identifying River Channels And River Rapids Via Deep Learning, Nicholas Brimhall, Kelvyn K. Bladen, Thomas Kerby, Carl J. Legleiter, Cameron Swapp, Hannah Fluckiger, Julie Bahr, Makenna Roberts, Kaden Hart, Christina L. Stegman, Brennan L. Bean, Kevin R. Moon Jan 2026

Compilation Of A Nationwide River Image Dataset For Identifying River Channels And River Rapids Via Deep Learning, Nicholas Brimhall, Kelvyn K. Bladen, Thomas Kerby, Carl J. Legleiter, Cameron Swapp, Hannah Fluckiger, Julie Bahr, Makenna Roberts, Kaden Hart, Christina L. Stegman, Brennan L. Bean, Kevin R. Moon

Mathematics and Statistics Student Research and Class Projects

Remote sensing enables large-scale, image-based assessments of river dynamics, offering new opportunities for hydrological monitoring. We present a publicly available dataset consisting of 281,024 satellite and aerial images of U.S. rivers, constructed using an Application Programming Interface (API) and the U.S. Geological Survey’s National Hydrography Dataset. The dataset includes images, primary keys, and ancillary geospatial information. We use a manually labeled subset of the images to train models for detecting rapids, defined as areas where high velocity and turbulence lead to a wavy, rough, or even broken water surface visible in the imagery. To demonstrate the utility of this dataset, …

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Projective Corepresentations And Cohomology Of Compact Quantum Groups, Kiran Maity Jan 2026

Projective Corepresentations And Cohomology Of Compact Quantum Groups, Kiran Maity

Doctoral Theses

In this thesis, we briefly review various types of projective corepresentations of compact quantum groups and prove the existence of suitable envelopes for them. We also study the associated invariant (dual) 2-cohomology and calculate it in a few concrete examples

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High Frobenius Pushforwards Generate The Bounded Derived Category, Matthew R. Ballard, Srikanth B. Iyengar, Pat Lank, Alapan Mukhopadhyay, Josh Pollitz Jan 2026

High Frobenius Pushforwards Generate The Bounded Derived Category, Matthew R. Ballard, Srikanth B. Iyengar, Pat Lank, Alapan Mukhopadhyay, Josh Pollitz

Faculty Publications

This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme X of prime characteristic. The main result is that when the Frobenius map on X is finite, for any compact generator G of D(X) the Frobenius pushforward Fe*G generates the bounded derived category whenever pe is larger than the codepth of X, an invariant that is a measure of the singularity of X. The conclusion holds for all positive integers e when X is locally complete intersection. The question of when one can take G = …

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Does Sequence Matter? Impact Of Redesigning Sequential Calculus Course On Students’ Learning Outcomes, Chantal Levesque-Bristol Dr., Wonki Lee Dr., Emily M. Bonem, Benjamin C. Wiles, Jennifer D. Moss, Wilella D. Burgess, Weiling Li Jan 2026

Does Sequence Matter? Impact Of Redesigning Sequential Calculus Course On Students’ Learning Outcomes, Chantal Levesque-Bristol Dr., Wonki Lee Dr., Emily M. Bonem, Benjamin C. Wiles, Jennifer D. Moss, Wilella D. Burgess, Weiling Li

International Journal of Teaching and Learning in Higher Education

As colleges and universities increasingly transform their STEM courses through the adoption of more active, student-centered pedagogies, there is a growing need to understand the impact of these educational innovations on student outcomes. This study is conducted in the context of a university-wide faculty development and course redesign project, IMPACT (Instruction Matters, Purdue Academic Course Transformation). IMPACT supports faculty in implementing student-centered pedagogical practices and creating equitable and inclusive learning environments. This study focuses on a sequence of two introductory calculus courses (Calculus 1 and Calculus 2, hereafter CALC 1 and CALC 2) that were transformed as part of the …

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Arbitrage-Free Pricing With Diffusion-Dependent Jumps, Hamza A. Virk, Yihren Wu, Majnu John Jan 2026

Arbitrage-Free Pricing With Diffusion-Dependent Jumps, Hamza A. Virk, Yihren Wu, Majnu John

Journal of Stochastic Analysis

Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous one-sided models that create arbitrage opportunities, our framework includes upward and downward jumps triggered by both large upward and large downward diffusion increments. We derive the explicit no-arbitrage condition linking the physical drift to model pa- rameters and market risk premia by constructing an Equivalent Martingale Measure using Girsanov’s theorem and a normalized Esscher transform. This condition provides a rigorous foundation for arbitrage-free pricing in models with diffusion-dependent jumps.

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Rogue Peakon, Posedness And Blow-Up Phenomenon For An Integrable Camassa–Holm Type Equation, Mingxuan Zhu, Zhenteng Zeng, Zaihong Jiang, Baoqiang Xia, Zhijun Qiao Jan 2026

Rogue Peakon, Posedness And Blow-Up Phenomenon For An Integrable Camassa–Holm Type Equation, Mingxuan Zhu, Zhenteng Zeng, Zaihong Jiang, Baoqiang Xia, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study an integrable Camassa–Holm (CH) type equation with quadratic nonlinearity. The CH type equation is shown integrable through a Lax pair, and particularly the equation is found to possess a new kind of peaked soliton (peakon) solution – called rogue peakon, that is given in a rational form with some logarithmic function, but not a regular traveling wave. We also provide multi-rogue peakon solutions. Furthermore, we discuss the local well-posedness of the solution in the Besov space 𝐵𝑠𝑝,𝑟 with 1 ≤ p, r ≤ ∞, 𝑠 >max⁡{1+1/𝑝,3/2} or 𝐵3/22,1 , and then prove the ill-posedness …

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Nonresonance For Problems Involving (P, Q)-Laplacian Equations With Nonlinear Perturbations, E. Lopera, Nsoki Mavinga, D. Sánchez Jan 2026

Nonresonance For Problems Involving (P, Q)-Laplacian Equations With Nonlinear Perturbations, E. Lopera, Nsoki Mavinga, D. Sánchez

Mathematics & Statistics Faculty Works

We are concerned with the existence of solutions of (p, q)-Laplacian problems that include nonlinear perturbation terms in both the differential equations and the boundary. Using variational methods and critical point theory, we prove the existence of weak solutions for the nonlinear problem when the nonlinearities involved remain asymptotically below the infimum of the set of eigenvalues of the (p, q)-Laplacian problem with weights and a spectral parameter present in both the differential equation and the boundary. Additionally, we establish an existence result for the nonlinear problem when the nonlinearities involved remain asymptotically below …

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Of Metaphors And Measurements: Cross-Disciplinary Learning In K-8 English Language Arts And Mathematics, Morgan Shiver, Janet Shiver Jan 2026

Of Metaphors And Measurements: Cross-Disciplinary Learning In K-8 English Language Arts And Mathematics, Morgan Shiver, Janet Shiver

New Jersey English Journal

English Language Arts and mathematics may seem like an unlikely pair, but together, literature and math can foster meaningful cross-disciplinary learning. This article presents strategies for using literature in K-8 classrooms to meet both ELA and math standards, enhancing student engagement and comprehension.

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ℤ3-Graded Cartan Calculus On 𝒪(ℂQ1|1|1), Sultan Çeli̇k, Sali̇h Çeli̇k Jan 2026

ℤ3-Graded Cartan Calculus On 𝒪(ℂQ1|1|1), Sultan Çeli̇k, Sali̇h Çeli̇k

Turkish Journal of Mathematics

After a brief introduction of the basic concepts of ℤ3-grading, the paper continues by introducing ℤ3-graded differential calculus and ℤ3-graded Cartan calculus. Then, using a matrix R which is a solution of the Yang-Baxter equation, a new ℤ3-graded quantum group and a ℤ3-graded quantum space are introduced. The scheme of the ℤ3-graded differential calculus developed on the algebra of functions on this quantum space is extended to the ℤ3-graded Cartan calculus and all the results obtained are formulated using the matrix R.

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G-Topological Groupoids, Osman Mucuk Jan 2026

G-Topological Groupoids, Osman Mucuk

Turkish Journal of Mathematics

In the groupoid theory, it is unclear that a topological groupoid's quotient groupoid with the quotient topology is topological.  In this paper, we approach this problem considering  G-methods and G-convergence. We define  G-topological groupoid, which agrees with the sequential version of a topological groupoid in the particular case G=lim, and give some counterexamples. Then, we extend the usual properties of topological groupoids to the G-topological groupoids. We also prove that a G-topological groupoid's quotient groupoid is  G-topological groupoid when a normal subgroupoid is suitably chosen. This result enables us to obtain examples of topological quotient groupoids in a particular case.

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The Variation Of Eigenvalues Of The Two-Dimensional Magnetic Schrödinger Operator With Respect To The Angle Of A Flat Sector, Araz R. Aliev, Elshad H. Eyvazov Jan 2026

The Variation Of Eigenvalues Of The Two-Dimensional Magnetic Schrödinger Operator With Respect To The Angle Of A Flat Sector, Araz R. Aliev, Elshad H. Eyvazov

Turkish Journal of Mathematics

A two-dimensional Schrödinger operator with a spherically symmetric electric potential and an Aharonov Bohm magnetic field in a circular sector under Neumann boundary conditions is considered. The intervals of the angular variation of the flat region are found, where the eigenvalues of the Neumann problem for the Schrödinger operator with a spherically symmetric electric potential strictly decrease monotonically in the Aharonov-Bohm magnetic field.

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Further Geometric Properties Of The Generalized K-Bessel Functions, Merve Görgülü, İbrahi̇m Aktaş Jan 2026

Further Geometric Properties Of The Generalized K-Bessel Functions, Merve Görgülü, İbrahi̇m Aktaş

Turkish Journal of Mathematics

This study investigates certain geometric properties of the normalized k-Bessel function, which is a natural generalization of classical and modified Bessel functions of the first kind. These geometric properties include η-starlikeness, η-uniform convexity, starlikeness associated with exponential function and Bernoulli’s lemniscate, and convexity associated with exponential function and Bernoulli’s lemniscate. Moreover, certain corollaries related to classical and modified Bessel functions are presented by specialising parameters. In addition, some examples and their graphical representations are provided to support the findings of this study.

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Some Methods For Finding The Number Of Partitions Of N With M−Parts, P(N, M), Yusuf Soyvural, Ali̇ Bülent Eki̇n Jan 2026

Some Methods For Finding The Number Of Partitions Of N With M−Parts, P(N, M), Yusuf Soyvural, Ali̇ Bülent Eki̇n

Turkish Journal of Mathematics

P(n, m) denotes the number of partitions of n with m parts, while Pm(n) denotes the number of partitions of n with parts at most m. It is a well-known result that the number of partitions of n ≥ 0 into m or fewer parts is equal to Pm(n). In the literature, there are some results for P(n, m) and Pm(n) for some values of m. In this work, we give more compact results for P(n …

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On Almost Kenmotsu Manifolds Admitting Nearly Vacuum Static Equations With Applications, Uday Chand De, Krishnendu De, Sudhakar Kumar Chaubey Jan 2026

On Almost Kenmotsu Manifolds Admitting Nearly Vacuum Static Equations With Applications, Uday Chand De, Krishnendu De, Sudhakar Kumar Chaubey

Turkish Journal of Mathematics

In this article, we study certain characteristics of nearly vacuum static equations on almost Kenmotsu manifolds. It is established that an η-Einstein almost Kenmotsu manifold allowing nearly vacuum static equations is of constant scalar curvature and either the solution is trivial or, the manifold reduces to an Einstein manifold. Next,  nearly vacuum static equations on (κ,μ)-almost Kenmotsu manifolds and generalized (κ,μ)'-nullity distribution are considered and we obtain several interesting results. Moreover, we illustrate that if a 3-dimensional Kenmotsu manifold allows nearly vacuum static equations, then the manifold is locally isometric to the hyperbolic space Η3(-1). After that, we investigate a …

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Cover And Contents Jan 2026

Cover And Contents

Turkish Journal of Mathematics

No abstract provided.

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Fubini Collocation Method For Numerical Solutions Of Differential Equations With Quadratic And Cubic Nonlinearities, Kübra Erdem Bi̇çer, Havva Türkhan Jan 2026

Fubini Collocation Method For Numerical Solutions Of Differential Equations With Quadratic And Cubic Nonlinearities, Kübra Erdem Bi̇çer, Havva Türkhan

Turkish Journal of Mathematics

In this study, the Fubini collocation method is proposed for the approximate solution of nonlinear differential equations. The method utilizes fundamental relations involving Fubini polynomials and their derivatives, employing collocation points to enhance solution accuracy. Within this framework, the given differential equation is transformed into a system of nonlinear algebraic equations involving the unknown coefficients of the approximate solution. This resulting system is then solved using appropriate numerical techniques to obtain the approximate solution. The effectiveness of the proposed method is demonstrated through several test problems, with accuracy evaluated using absolute error functions. Furthermore, illustrative examples and residual-based error analysis …

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The Derivative Of Spectral Function Of The Problem With The Boundary Condition Dependent On Spectral Parameter, Eli̇f Başkaya, Haskiz Coşkun Jan 2026

The Derivative Of Spectral Function Of The Problem With The Boundary Condition Dependent On Spectral Parameter, Eli̇f Başkaya, Haskiz Coşkun

Turkish Journal of Mathematics

In this study, the computation of the derivative of the spectral function for Sturm-Liouville problem with eigenvalue dependent boundary condition at the finite left end is considered.

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Representation Of Inverse Ordered Semigroups By Means Of Symmetric Inverse Semigroups On A Set, Michael Tsingelis Jan 2026

Representation Of Inverse Ordered Semigroups By Means Of Symmetric Inverse Semigroups On A Set, Michael Tsingelis

Turkish Journal of Mathematics

A partial one-to-one mapping on a set X is a mapping whose domain is a subset of X. The set of partial one-one mappings on a set X is an inverse semigroup (the symmetric inverse semigroup on X). An element x of an ordered semigroup (S, ·, ≤) is called an inverse element of α ∈ S if α ≤ xαx and x ≤ xαx. An inverse ordered semigroup is an ordered semigroup S for which every element of S possesses an inverse element and the inverse elements of any element of S are in …

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Cospectrality Results For Signed Graphs With Two Eigenvalues Unequal To ±1, Willem H. Haemers, Hati̇ce Topcu Jan 2026

Cospectrality Results For Signed Graphs With Two Eigenvalues Unequal To ±1, Willem H. Haemers, Hati̇ce Topcu

Turkish Journal of Mathematics

Recently the collection G of all signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1 has been determined. Here we investigate G for cospectral pairs, and for signed graphs determined by their spectrum (up to switching). If the order is at most 20, the outcome is presented in a clear table. If the spectrum is symmetric we find all signed graphs in G determined by their spectrum, and we obtain all signed graphs cospectral with the bipartite double of the complete graph. In addition we determine all signed graphs cospectral with the …

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Codazzi Normalized Null Hypersurfaces, Théophile Kemajou Mbiakop, Cyriaque Atindogbe, Ferdinand Ngakeu Jan 2026

Codazzi Normalized Null Hypersurfaces, Théophile Kemajou Mbiakop, Cyriaque Atindogbe, Ferdinand Ngakeu

Turkish Journal of Mathematics

We introduce a class of null hypersurfaces of Lorentzian manifolds, namely Codazzi normalized null hyper surfaces, whose (screen) shape operator associated with the rigged vector field is a Codazzi tensor. Several examples are given to support our study. Moreover, we investigate conditions implying that the induced Riemannian screen structure on a Codazzi-type normalized null hypersurface of a Lorentzian space is locally a nontrivial warped product.

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Power Domination Reconfiguration, B. Bjorkman, C. Bozeman, D. Ferraro, M. Flagg, Cheryl Grood, L. Hogben, B. Jacob, Carolyn Reinhart Jan 2026

Power Domination Reconfiguration, B. Bjorkman, C. Bozeman, D. Ferraro, M. Flagg, Cheryl Grood, L. Hogben, B. Jacob, Carolyn Reinhart

Mathematics & Statistics Faculty Works

Reconfiguration examines relationships among solutions to a problem. Power domination models placement of monitoring units that allow monitoring of an entire electrical power network, and information about modifying one monitoring solution to another has applications. The study of token addition and removal and token jumping reconfiguration graphs for power domination is initiated. Some results established here can be extended by applying the methods used for power domination to reconfiguration graphs for other parameters. A universal framework for the study of reconfiguration of parameters that are defined from sets of vertices of a graph and satisfy certain rules is introduced. This …

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Evaluating Lunch Plan Data In The St. Charles School District (Scsd), Maddy Alexander, Guillermo Bilbao Olarreaga, Duncan Krige, Alyssa Schreiber, Nick Wintz, Wojciech Golik Jan 2026

Evaluating Lunch Plan Data In The St. Charles School District (Scsd), Maddy Alexander, Guillermo Bilbao Olarreaga, Duncan Krige, Alyssa Schreiber, Nick Wintz, Wojciech Golik

The Confluence

The SCSD is a public school district in St. Charles, with, on average, 4500 students a year. The SCSD is subdivided into an early childhood center, six elementary schools, two intermediate (5-6,7-8) schools, and two high schools. Vocational schools are also within this district but were not included in this report. The SCSD is concerned with the impact of the Covid-19 pandemic on their district’s population and on the number of students that needed assistance with lunch. They have asked Lindenwood’s 2024-25 PIC Math group to analyze their data from the years 2020-25 and identify any trends. Identifying these trends …

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Optimal Quantization Of Finite Uniform Data On The Sphere, Mrinal Kanti Roychowdhury Jan 2026

Optimal Quantization Of Finite Uniform Data On The Sphere, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

This paper develops a systematic and geometric theory of optimal quantization on the unit sphere 𝕊2, focusing on finite uniform probability distributions supported on the spherical surface—rather than on lower-dimensional geodesic subsets such as circles or arcs. We first establish the existence of optimal sets of n-means and characterize them through centroidal spherical Voronoi tessellations. Three fundamental structural results are obtained. First, a cluster-purity theorem shows that when the support consists of well-separated components, each optimal Voronoi region remains confined to a single component. Second, a ring allocation (discrete water-filling) theorem provides an explicit rule describing how optimal representatives are …

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Existence Of Traveling Waves Of Lotka Volterra Type Models With Delayed Diffusion Term And Partial Quasimonotonicity, William Barker Jan 2026

Existence Of Traveling Waves Of Lotka Volterra Type Models With Delayed Diffusion Term And Partial Quasimonotonicity, William Barker

Faculty Scholarship

This paper investigates the existence of traveling wave solutions for diffusive two-species Lotka–Volterra systems with delays in both the reaction and diffusion terms under partial monotonicity assumptions. The model incorporates small-memory effects in the homo- geneous diffusion term, representing a modification of the random-walk interpretation underlying Fick’s law. We extend the partial (cross) monotone iteration method to systems satisfying a partial quasi-monotone condition through the construction of appropriate upper and lower solutions. Convergence of the iteration is established using Schauder’s fixed point theorem.

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Teaching Numeracy For Social Justice: Educational Equity, Esther Isabelle Wilder, Crystal C. Rodriguez, Caterina Shost, Eduardo Vianna, Frank Wang Jan 2026

Teaching Numeracy For Social Justice: Educational Equity, Esther Isabelle Wilder, Crystal C. Rodriguez, Caterina Shost, Eduardo Vianna, Frank Wang

Numeracy

The special collection, “Teaching Numeracy for Social Justice: Educational Equity,” focuses on how quantitative reasoning (QR) can function as a vehicle for equity, empowerment, and democratic participation. Building on a longstanding tradition that treats numeracy as inseparable from social justice, these contributions highlight how progressive pedagogies (e.g., active learning, authentic research, and equity-oriented assessment) have the potential to broaden access for students historically excluded from quantitative fields. The studies span a variety of conceptual frameworks, introductory and advanced quantitative instruction, and interdisciplinary applications, showcasing how inclusive QR practices can build confidence, agency, and real-world understanding. These articles demonstrate that when …

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Distribution Of New Statistics Of Parking Functions And Their Generalizations, Stephan Wagner, Catherine H. Yan, Mei Yin Jan 2026

Distribution Of New Statistics Of Parking Functions And Their Generalizations, Stephan Wagner, Catherine H. Yan, Mei Yin

Mathematics: Faculty Scholarship

In this paper we present new results on the enumeration of parking functions and labeled forests. We introduce new statistics on parking functions, which are then extended to labeled forests via bijective correspondences. We determine the joint distribution of two statistics on parking functions and their counterparts on labeled forests. Our results on labeled forests also serve to explain the mysterious equidistribution between two seemingly unrelated statistics in parking functions recently identified by Stanley and Yin and give an explicit bijection between the two statistics. Extensions of our techniques are discussed, including joint distribution on further refinement of these new …

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The Sunday Math Circle, Nathan Pflueger Jan 2026

The Sunday Math Circle, Nathan Pflueger

Journal of Math Circles

Bob and Ellen Kaplan envisioned and organized a style of math circle centered on the idea that children of all ages can work like mathematicians do: creatively, collaboratively, and ecstatically. This article surveys four sample topics covered during a Sunday morning math circle in the Boston area, based on Bob and Ellen's invaluable guidance. I also offer some reflections on what I learned from Bob and Ellen, and how it is reflected in these math circles.

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The Polymathematician, Leo Goldmakher Jan 2026

The Polymathematician, Leo Goldmakher

Journal of Math Circles

In loving memory of Bob Kaplan, the wisest and most inspiring seven-year-old I’ve ever met.

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Infinite Line, Infinite Knowledge: The 'Spera' And Organized Chaos In Lambert's Encyclopedia, The 'Liber Floridus', Ava Romano Jan 2026

Infinite Line, Infinite Knowledge: The 'Spera' And Organized Chaos In Lambert's Encyclopedia, The 'Liber Floridus', Ava Romano

Theses and Dissertations

The Liber Floridus is a medieval encyclopedia renowned for its program of circular diagrams, or sperae. Inside this manuscript of 190 chapters, these diagrams frame and embody written knowledge, revealing a connection between encyclopedism and life in the Benedictine monastery by creating a coherent visual organization of chapters.

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Sharp Polynomial Decay For Polynomially Singular Damping On The Torus, Perry Kleinhenz, Ruoyu P.T. Wang Jan 2026

Sharp Polynomial Decay For Polynomially Singular Damping On The Torus, Perry Kleinhenz, Ruoyu P.T. Wang

Faculty Publications – Mathematics

We study energy decay rates for the damped wave equation with unbounded damping, without the geometric control condition. Our main decay result is sharp polynomial energy decay for polynomially controlled singular damping on the torus. We also prove that for normally Lp-damping on compact manifolds, the Schrödinger observability gives p-dependent polynomial decay, and finite time extinction cannot occur. We show that polynomially controlled singular damping on the circle gives exponential decay.

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