Unique Combinations Of Packing Integer Squares,
2026
Fort Hays State University
Unique Combinations Of Packing Integer Squares, Keith M. Dreiling, Austin Leanna, William Mooney
SACAD: Scholarly Activities
This research investigates a function, informally named WAK(x), that describes the number of ways to divide an integer square into integer subsquares counting only the list of parts. Previous research has shown values up to 28, though finding these values is computationally complex and requires a long runtime using computer algorithms. We attempt to find patterns in the values and many aspects of the values, hoping to find a general solution. We are unsure if a solution exists, but we have ideas for how to move forward in finding a solution.
Counting Hamiltonian Cycles In Quartic Circulant Graphs,
2026
Pepperdine University
Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard
Seaver College Research And Scholarly Achievement Symposium
We consider the problem of counting Hamiltonian cycles in circulant graphs $C^K_n$ where $n$ is the number of vertices and $K$ is a set containing elements that correspond to the allowed edges in the circulant graphs. After sorting the cycles by a topological invariant called the winding number, we use a modified transfer matrix method to convert local data into global structures. The result is a generating function that counts the number of Hamiltonian cycles in a circulant graph with $n$ vertices. The results for $K=\{1,2\}$ and $K=\{1,3\}$ have been found by previous authors. We focus on the case where …
On Links Between A Theorem Of Schoenberg, Rohlin Decompositions Of Measures, The Bochner-Minlos Theorem And The Fock Space,
2026
Chapman University
On Links Between A Theorem Of Schoenberg, Rohlin Decompositions Of Measures, The Bochner-Minlos Theorem And The Fock Space, Daniel Alpay, Paula Cerejeiras, Palle Jorgensen, Uwe Kaehler
Mathematics, Physics, and Computer Science Faculty Articles and Research
The main goal of this paper is to gain new results in stochastics by drawing on, and combining, different areas that are normally not considered to be related. Thus, in this paper we extend the previous class of Gaussian-like functions ML which will allow for future generalized stochastic processes in infinite dimensional analysis. We show that an approach similar to the one by the classical Bochner-Minlos theorem for the white-noise case can be achieved by using Gaussian-like functions belonging to a large family -the MLr classes (0 < r ≤∞). We show how Schoenberg’s theorem for positive definite functions on a Hilbert space allows to go beyond the classical setting of Bochner-Milnos theorem. Furthermore, we show that the application of the Rohlin’s disintegration theorem allows for a decomposition of the associated probability measures , see Theorems 3.2 and 4.3. We end this paper with several important examples of functions in these classes MLr and provide some interesting counterexamples, e.g. Theorem 7.4, to get a …
Automating Cardiff Model Data Capture In Emergency Departments: Ambient Nlp Integration With Oracle-Cerner Fhir Systems,
2026
Southern Methodist University
Automating Cardiff Model Data Capture In Emergency Departments: Ambient Nlp Integration With Oracle-Cerner Fhir Systems, Simi Augustine, Marco A. Lopez, Jacquelyn Cheun, Chris Papesh
SMU Data Science Review
Violence and overdose events in Las Vegas occur at rates above the national average, with fewer than half of violent injuries reported to law enforcement [2,7]. The Cardiff Model offers a proven framework for standardized data collection and sharing between hospitals and public safety partners, yet many implementations still rely on manual entry. We propose an ambient triage pipeline integrated with Oracle-Cerner electronic health record systems to listen to nurse–patient dialogue, convert speech to text, extract Cardiff fields, and write standards-based FHIR Bundles for analytics. Using SMART on FHIR standards and Cerner Millennium APIs, the study evaluates whether ambient capture …
Numerals And Other Means Of Expressing Plurality In Language And Thought: A Developmental Perspective Across Cultures.,
2026
I.I.S. Fantini. Vergato (Bologna - Italy)
Numerals And Other Means Of Expressing Plurality In Language And Thought: A Developmental Perspective Across Cultures., Giovanni Giuseppe G.G. Nicosia Prof.
Numeracy
Several ancient languages use linguistic structures to differentiate between singular, dual, and plural forms that are used when one, two, or many objects are referenced. (Some languages go further, adding a trial form to differentiate two from three.) In many modern languages, numerals are used to convey precise number. After reviewing a range of ways languages express number (including the interesting case of Pirahã which does not express precise number), the paper concludes with a proposed developmental path for the expression of quantity in languages.
Minimal Supersolution Of Bsdes Driven By Continuous Martingales In A General Filtration,
2026
Cadi Ayyad University (UCA), National School of Applied Sciences of Marrakech (ENSA-M), BP 575, Avenue Abdelkrim Khattabi, 40000, Guéliz, Marrakech, Morocco
Minimal Supersolution Of Bsdes Driven By Continuous Martingales In A General Filtration, Badr Elmansouri, Mohamed El Otmani
Journal of Stochastic Analysis
In this paper, we study minimal supersolutions of backward stochastic differential equations (BSDEs) driven by a continuous local martingale in a general filtration. We establish existence, uniqueness, and stability results under various mild conditions on the terminal value and the generator. Additionally, we explore the connection between the concept of non-linear expectation and minimal supersolutions, emphasizing the specific properties that are relevant to our framework. We also prove a general monotonic limit theorem and apply this result to determine the smallest constrained supersolution of a BSDE with a possibly non-convex constraint.
A Virtual Community Math Circle,
2026
Santa Barbara Math Ellipse
A Virtual Community Math Circle, Skona Brittain, Sayonita Ghosh Hajra, Steve Heller, Daniel Hodgins, Peter Petto, Gabriella Pinter, Lauren Rose, A. Gwinn Royal, Asmita Sodhi
Journal of Math Circles
The Julia Robinson Mathematics Festival (JRMF) Community Math Circle is free, volunteer-run, and online. We collaborate with JRMF and use their activities in our events. Started during the pandemic, the Community Math Circle continues to thrive. We have about 40 participants attending every month, typically kids aged 6 to 13, teachers, facilitators, and other adults. This article describes how our event is organized, planned, and executed, and how we train facilitators. We will also offer reflections on our successes and challenges.
Effective Wordle Heuristics,
2026
Loyola University Chicago
Effective Wordle Heuristics, Ronald I. Greenberg
Computer Science: Faculty Publications and Other Works
While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions being gradually eliminated (with a new puzzle each day and no reuse), an improved strategy could be generated each day, but the computation time makes a daily exhaustive search impractical. This paper shows that simple heuristics allow for fast generation of effective strategies and that little is lost by guessing only words that are possible solution words rather than more obscure words.
Unitary Rational Functions: The Scaled Quaternion Case,
2026
Chapman University
Unitary Rational Functions: The Scaled Quaternion Case, Daniel Alpay, Ilwoo Choo, Mihaela Vajiac
Mathematics, Physics, and Computer Science Faculty Articles and Research
We develop the theory of minimal realizations and factorizations of rational functions where the coefficient space is a ring of the type introduced in our previous work, the scaled quaternions, which includes as special cases the quaternions and the split quaternions. The methods involved are not a direct generalization of the complex or quaternionic settings, and in particular, the adjoint is not the classical adjoint and we use properties of real Hilbert spaces. This adjoint allows to define the counterpart of unitarity for matrix-rational functions, and we develop the corresponding theories of realizations and unitary factorizations. We also begin a …
Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game,
2026
University of Luxembourg, Luxembourg
Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game, Thierry Meyrath, Clara-Ioana Mincu, Antonella Perucca
Journal of Humanistic Mathematics
We explore probability exercises based on the game UNO. Excluding the Wild cards, the deck contains precisely 100 cards, which makes it convenient to express probabilities as percentages. We discuss the mathematical relation between cards that can be played after other cards. We also propose an algebraic exercise that relates several quantities, such as the number of cards left in the losing player’s hand. Finally, we argue that UNO is a very inclusive game: it is logistically easy to play, allows for players of different skill levels, and can be adapted to meet special needs. Beyond being playful exercises, our …
Arbitrage-Free Pricing With Diffusion-Dependent Jumps,
2026
Dept of Math., Hofstra University, Hempstead, NY 11549, USA
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.
Evaluating Lunch Plan Data In The St. Charles School District (Scsd),
2026
Lindenwood University
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 …
Teaching Numeracy For Social Justice: Educational Equity,
2026
Lehman College and the Graduate Center of the City University of New York (CUNY)
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 …
The Sunday Math Circle,
2026
Amherst College
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.
Mathematics And Political Ideology: A Historical Argument Against The Cultural Understanding Of Mathematics As An Apolitical Field, And A Journalistic Report On The Impact Of The Trump Administration On American Mathematics In 2026, Philo Judson
Pitzer Senior Theses
The interplay between political ideology and mathematics is a recurring theme throughout the history of the academic field. Mathematics has been used as a tool of empire, while mathematicians have been elevated by states as symbols of national genius for political prestige. Political ideologies have also shaped the field from within, both through the suppression of mathematical thought and the enforcement of mathematical authority. Since 2025, the Trump administration has launched large-scale political attacks on American institutions of higher education, which include lawsuits, discrimination investigations, and the removal of federal funding from certain institutions that don’t adhere to the administration’s …
Fostering A Growth Mindset In Mathematics: Faculty And Student Experiences,
2026
Illinois State University
Fostering A Growth Mindset In Mathematics: Faculty And Student Experiences, Yolanda G. Rush
Theses and Dissertations
According to the Center for Community College Student Engagement (2019), many students attending two-year institutions need productive persistence strategies, including the development of a growth mindset. Although some growth mindset interventions have been effective in improving academic achievement among students (Boaler, 2016; Canning et al., 2024) and persistence (Lewis, 2019) among students, especially those with developmental needs (Suh et al., 2019) and those in mathematics, little is known about the experiences of students and teachers (i.e., students’ perceptions of teachers’ intentions and implementation) as teachers work to foster a growth mindset culture (Murphy et al., 2021). In this dissertation, I …
Balanced Multi-Party Tournament Designs,
2026
Wayne State University
Balanced Multi-Party Tournament Designs, Parsa Nematollahe
Honors College Theses
This paper introduces Multi-Party Tournament (MPT) designs that generalize established combinatorial structures, including Whist, Pitch, and Generalized Whist tournament designs. This work will formally define MPTs, establish the fundamental properties of resolvability, fullness, and balance, and formulate a mathematical and algorithmic foundation for multi-party tournament scheduling. The primary contributions of this research are the presentation of necessary and sufficient existence conditions for MPTs across various properties and parameters, the identification of connections between MPTs and other fields of mathematics such as combinatorial design theory, graph theory, and probability theory, and the investigation of MPT construction algorithms, including tree-search, finite-field constructions, …
Understanding Möbius Inversion As Composite Of Dual Pairs,
2026
University of Kentucky
Understanding Möbius Inversion As Composite Of Dual Pairs, Isaac B. Kochmaan
Theses and Dissertations--Mathematics
Möbius inversion is a well-studied computational tool in number theory and combinatorics, but it exhibits a pattern which may be familiar to those who study categorical traces. In 2016, Kate Ponto and Michael Shulman characterized duality and traces in the bicategory of profunctors for a particularly nice class of one-cells. We extend these results. Consequently, we construct, for a given poset, a profunctor whose Euler characteristic is the Möbius function of said poset. In light of this, we propose a categorical notion of Möbius inversion.
Mat 1500 Calculus I Syllabus,
2026
CUNY Kingsborough Community College
Mat 1500 Calculus I Syllabus, Tian Cai
Open Educational Resources
No abstract provided.
Mat 1600 Syllabus Ii Syllabus,
2026
CUNY Kingsborough Community College
Mat 1600 Syllabus Ii Syllabus, Tian Cai
Open Educational Resources
No abstract provided.
