Of Metaphors And Measurements: Cross-Disciplinary Learning In K-8 English Language Arts And Mathematics,
2026
Western Michigan University
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),
2026
TÜBİTAK
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,
2026
TÜBİTAK
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 Derivative Of Spectral Function Of The Problem With The Boundary Condition Dependent On Spectral Parameter,
2026
TÜBİTAK
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.
The Variation Of Eigenvalues Of The Two-Dimensional Magnetic Schrödinger Operator With Respect To The Angle Of A Flat Sector,
2026
TÜBİTAK
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,
2026
TÜBİTAK
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.
Cover And Contents,
2026
TÜBİTAK
Some Methods For Finding The Number Of Partitions Of N With M−Parts, P(N, M),
2026
Hakkari Üniversitesi
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 …
Representation Of Inverse Ordered Semigroups By Means Of Symmetric Inverse Semigroups On A Set,
2026
TÜBİTAK
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 …
Fubini Collocation Method For Numerical Solutions Of Differential Equations With Quadratic And Cubic Nonlinearities,
2026
Manisa Celal Bayar University
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 …
Cospectrality Results For Signed Graphs With Two Eigenvalues Unequal To ±1,
2026
Tilburg University
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,
2026
TÜBİTAK
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.
On Almost Kenmotsu Manifolds Admitting Nearly Vacuum Static Equations With Applications,
2026
TÜBİTAK
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 …
Power Domination Reconfiguration,
2026
Swarthmore College
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),
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 …
Optimal Quantization Of Finite Uniform Data On The Sphere,
2026
The University of Texas Rio Grande Valley
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 …
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 …
Distribution Of New Statistics Of Parking Functions And Their Generalizations,
2026
Uppsala Universitet
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,
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.
The Polymathematician,
2026
Williams College
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.
