Digital Commons Network^™

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.

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.

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.

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.

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.

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 P_m(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 P_m(n). In the literature, there are some results for P(n, m) and P_m(n) for some values of m. In this work, we give more compact results for P(n …

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 …

Cover And Contents

Turkish Journal of Mathematics

No abstract provided.

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 …

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.

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 …

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 …

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.

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 …

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 …

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 …

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.

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 …

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 …

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.

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.

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.

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 L^p-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.

A New Functional Setting For Term Structure Modeling Using The Health-Jarrow-Morton Framework, Michael Pokojovy, Ebenezer Nkum, Thomas M. Fullerton Jr.

Mathematics & Statistics Faculty Publications

The well-known Heath–Jarrow–Morton (HJM) framework provides a universal and efficacious instrument for modeling the stochastic evolution of an entire yield curve by explaining the interest rate dynamics in continuous time under no-arbitrage conditions. Existing implementations involve exponentially weighted function spaces as theoretical settings for the former stochastic evolution. While the choice of weight can have a drastic effect on model calibration and subsequent forecasting, it cannot be estimated from market data and does not allow for any objective interpretation. The proposed approach does not have this shortcoming as it adopts a suitably designed unweighted function space. The HJM equation is …

Toward Completeness Theorem For Guarded Kleene Algebra With Tests, Hung Pham

Honors Theses

Code refactoring is a fundamental practice in software engineering, in which a program is restructured without changing the actions it performs and the results it produces. To carry out refactoring with confidence, one requires a formal method for verifying that two programs are equivalent. Guarded Kleene Algebra with Tests (GKAT) provides such a framework, an algebraic system designed to reason about a natural class of programs, namely those in which every branch and loop is governed by a Boolean condition, such as if–else and while statements. Central to GKAT is a finite set of algebraic axioms for deriving program equivalences. …

Meshless Collocation Methods For Time-Dependent Nonlocal Problems Based On Radial Basis Functions, Qiao Zhuang, Yanzhi Zhang, Zhongqiang Zhang

Mathematics and Statistics Faculty Research & Creative Works

We present radial basis function (RBF) collocation methods for time-dependent space fractional problems on general bounded domains. Building on a recently developed approach for accurately computing the integral fractional Laplacian of any RBF, we design collocation schemes for fractional heat and Stokes equations using extended-domain techniques. In particular, we propose a numerical Leray projection method for fractional Stokes problems, where both the discrete projection operator and the collocation scheme are formulated on extended domains to handle complex domains. Numerical results demonstrate the effectiveness of the proposed methods in solving time-dependent nonlocal problems on complex domains.

Identifying Relevant Covariates In Rna-Seq Analysis By Pseudo-Variable Augmentation, Yet Nguyen, Dan Nettleton

Mathematics & Statistics Faculty Publications

RNA-sequencing (RNA-seq) technology allows for the identification of differentially expressed genes, which are genes whose mean transcript abundance levels vary across conditions. In practice, RNA-seq datasets often include covariates that are of primary interest in addition to a set of covariates that are subject to selection. Some of these covariates may be relevant to gene expression levels, while others may be irrelevant. Ignoring relevant covariates or attempting to adjust for the effect of irrelevant covariates can compromise the identification of differentially expressed genes. To address this issue, we propose a variable selection method that uses pseudo-variables to control the expected …

Prime Numbers And Rsa Encryption In Cryptology, Burak Safaker

A with Honors Projects

This project centers on developing an encryption and decryption system using the RSA (Rivest-Shamir-Adleman) cryptographic algorithm, which is based on the mathematical properties of prime numbers.

From Wikipedia Tables To Public Data Visualizations, Tanvir Prince

Open Educational Resources

This open educational resource presents a practical mathematics lesson in which students turn numerical data from Wikipedia into a clear data visualization. Students select a Wikipedia page with a data table but little or no visual representation. They examine the original source, date, units, definitions, and possible data limits. They then organize the data in Microsoft Excel or another spreadsheet, choose an appropriate chart, and explain what the visualization helps readers understand. A complete worked example uses the 2017 population growth rates of South American countries.

The resource package includes an instructor lesson plan, a student project guide, a Wikimedia …

Fourier Pseudospectral Methods For The Variable-Order Space Fractional Wave Equations, Yanzhi Zhang, Xiaofei Zhao, Shiping Zhou

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we propose Fourier pseudospectral methods to solve the variable-order space fractional wave equation and develop an accelerated matrix-free approach for its effective implementation. In constant-order cases, fast algorithms can be designed via the fast Fourier transforms (FFTs), and the computational cost at each time step is O(Nlog⁡N) with N the total number of spatial points. In variable-order cases, however, the spatial dependence in the power s(x) leads to the failure of inverse FFTs. While the direct matrix-vector multiplication approach becomes impractical due to excessive memory requirements. Hence, we propose an accelerated matrix-free approach for effective implementation in …