Digital Commons Network^™

Sharing Four Biscuits Between Three People: An Illustrative Example Of How Mathematics Is Intertwined With Human Values, Lovisa Sumpter, David Sumpter

Journal of Humanistic Mathematics

Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread notion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how mathematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demonstrate that different solutions—hiding one biscuit, arbitrarily sharing the extra …

The Automathography: A Humanistic Autobiographical Writing Assignment For Mathematics Courses, Colton Sawyer, Ron Buckmire

Journal of Humanistic Mathematics

In this article, we discuss an autobiographical writing assignment that we call an “automathography” which can be used in different types of mathematics and mathematics education courses, and by extension, in other disciplines as well. This assignment can enhance student-instructor interactions, develop student communication skills, and provide outlets for student creativity by leveraging the lived experiences of students. We have deployed the assignment in different kinds of classes (general education [service] courses and major-only seminars) at different kinds of institutions (a private, open-admission, large university on the East Coast and a private, highly selective, small liberal arts college on the …

Finding Your Mathematical Roots: Inclusion And Identity Development In Mathematics, Linda Mcguire

Journal of Humanistic Mathematics

This paper details a semester-long course project that has been successfully adapted for use in mathematics courses ranging from introductory level, general-education classes to advanced courses in the mathematics major. Through creating aspirational mathematical family trees and writing mathematical autobiographies, this assignment is designed to help battle belonging uncertainty, to challenge students to self-situate in relation to the history of mathematical and scientific knowledge, and to make visible a student’s developing identity in mathematics and, more broadly, in STEM.

The construction and scaffolding of the project, assignments, examples of student work, foundational readings, assessment and outcomes, and adaptation strategies for …

Gödel's Theorem In The Continuing Education Of Mathematics Teachers, Ana J. Lemes

Journal of Humanistic Mathematics

The notion of dépaysement épistémologique (epistemological disorientation) aims to capture the sense of disorientation when a learner is led to question their prior assumptions and understandings, generating uncertainty in a context in which they thought they had certain knowledge. This article describes an activity used with a group of practicing mathematics teachers in Uruguay that integrates elements of the history of mathematics related to Gödel’s incompleteness theorem, with the aim of provoking in the participants the experience of dépaysement épistémologique. Results show that several of the teachers participating in the activity felt dépaysement épistémologique, and this feeling triggered …

Our Histories, Our Values, Our Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Total Variation Flow In R^N Dimensions With Examples Relating To Perimeters Of Level Sets, Luis Schneegans, Victoria Shumakovich

Undergraduate Research Symposium

In this project, we explore radial solutions to the Total Variation Flow (TVF) equation with the help of the Sign Fast Diffusion Equation (SFDE) and prior results in the 1-dimensional case. Specifically for radial solutions, we derive equations and explicit solutions relating to the n-dimensional case. Lastly, we look at how level sets and (time) profiles change.

Effect Of Methane Mitigation On Global Temperature Under A Permafrost Feedback, Hannah Bäck, Riley May, Divya Sree Naidu, Steffen Eikenberry

Mathematics and Statistics Student Research and Class Projects

Earth systems may fall into an undesirable system state if 1.5°C of warming is exceeded. Carbon release from substantial permafrost stocks vulnerable to near-term warming represents a positive climate feedback that may increase the risk of 1.5°C warming or greater. Methane (CH₄) is a short-lived but powerful greenhouse gas with a global warming potential 28.5 times that of carbon dioxide (CO₂) over a 100 year time span. Because permafrost thaw in the coming centuries is partly determined by the warming in the 21st century, rapid reductions in methane emissions early in the 21st century could have …

On The Qualitative Analysis Of Nonlinear Q-Fractional Delay Descriptor Systems, Abdullah Yi̇ği̇t

Turkish Journal of Mathematics

In this manuscript, we obtain some sufficient conditions for a nonlinear q fractional integro singular system with constant delays to be asymptotically admissible and a nonlinear q fractional non-singular system to be asymptotically stable. We use Lyapunov-Krasovskii functionals and some inequalities to obtain these conditions. At the same time, we present some numerical examples that confirm the sufficient conditions we obtained theoretically, with their annotated solutions and graphs.

On Lyapunov-Type Inequalities For Five Different Types Of Higher Order Boundary Value Problems, Mustafa Fahri̇ Aktaş, Bariş Berkay Erçikti

Turkish Journal of Mathematics

In this paper, we establish the uniqueness and existence of the classical solution to higher-order boundary value problems. Then, we give a new Lyapunov-type inequalities for higher order boundary value problems. Our study is based on Green’s functions corresponding to the five different types of two-point boundary value problems. In addition, some applications of the obtained inequalities are given.

Globally Generated Vector Bundles On The Del Pezzo Threefold Of Degree 6 With Picard Number 2, Takuya Nemoto

Turkish Journal of Mathematics

We classify globally generated vector bundles on a general hyperplane section of P2 × P2 embedded by the Segre embedding, considering small first Chern classes c1 = (1, 1) and c1 = (2, 1).

Extremal Functions For A Singular Super-Critical Trudinger-Moser Inequality, Juan Zhao

Turkish Journal of Mathematics

In this paper, we deal with a singular super-critical Trudinger-Moser inequality on a unit ball of Rn , n ≥ 3. For any p > 1, we set λp(B) = inf u∈W1,n 0 (B),u̸≡0 ∫ B |∇u|ndx ( ∫ B |u|pdx)n/p as an eigenvalue related to the n-Laplacian. Let S be a set of radially symmetric functions. Precisely, if β ≥ 0 and α < (1 + p nβ)n−1+n/pλp(B) , then there exists a positive constant ϵ0 such that when λ ≤ 1 + ϵ0 , sup u∈W1,n 0 (B)∩S, ∫ B |∇u|ndx−α( ∫ B |u|p|x|pβdx) np ≤1 ∫ B |x|pβ ( eαn(1+ p n β)|u| n n−1 − λ Σm k=0 |αn(1 + p nβ)u n n−1 |k k! ) dx is attained, where αn = nω1/(n−1) n−1 , ωn−1 is the surface area of the unit ball in Rn . The proof is based on the method of blow-up analysis. The case λ = 0 was studied by Yang-Zhu in [38]. de Figueiredo [11] considered the case p = 2, β ≥ 0, and α = 0 in two dimension. The case λ = 0, p = n,−1 < β < 0, and α = 0 was considered by Adimurthi-Sandeep [1]. Our results extend those of the above cases.

On Strong Solvability Of One Nonlocal Boundary Value Problem For Laplace Equation In Rectangle, Telman Gasymov, Baharchin Akhmadli, Ümi̇t Ildiz

Turkish Journal of Mathematics

One nonlocal boundary value problem for the Laplace equation in a bounded domain is considered in this work. The concept of a strong solution to this problem is introduced. The correct solvability of this problem in the Sobolev spaces generated by the weighted mixed norm is proved by the Fourier method. In a classic statement, this problem has been

Invariant Symplectic Forms On Number Fields, Ahmad Rafiqi, Ayberk Zeyti̇n

Turkish Journal of Mathematics

We show that a number field of the form Q(λ) admits a symplectic form which is invariant under multiplication by λ if and only if the minimal polynomial of λ is palindromic of even degree. In particular, if λ is an algebraic integer, it is forced to be a unit. In the case when the minimal polynomial of λ is palindromic of degree 2d, we show that there is a d-dimensional space of invariant symplectic forms on Q(λ) .

On The Invariance Of Hyperstoneanness Under Lattice Isomorphisms, Banu Güntürk

Turkish Journal of Mathematics

Let X and Y be compact Hausdorff spaces with Y hyperstonean. In this paper, we prove that if C(X,R) and C(Y,R) are lattice isomorphic then these Banach spaces are linearly isometric, and, consequently, X and Y are homeomorphic, which in turn implies that X is also hyperstonean. Actually, we prove more than what is announced in the headline above. This result, in some ways, is a generalization of the well-known Banach-Stone theorem.

Some Estimates On The Spin−Submanifolds, Serhan Eker

Turkish Journal of Mathematics

In this paper, an optimal lower bound is given for the Submanifold Dirac operator in terms of the trace of an Energy−Momentum tensor, scalar curvature and mean curvature. In the equality case, it is proven that the submanifold is Einstein if the normal bundle is flat. Key words: Spin geometry, eigenvalues,

Modelling Spatial Distributions Of Sediments Fingerprinting In The Ruvu Basin Of Tanzania Without Continuous Sediment Monitoring, Charles H. Kasanzu

Tanzania Journal of Science

This study investigates various hinterlands’ contribution of sediments into the sub-basin known as Ruvu that comprises Mindu, Kibungo, Mvuha and Mindu catchments of Morogoro, Eastern Tanzania. An integrated geochemical and isotopic data were used to constrain this. Strategic sampling of basement and silty-sized sediments was conducted and the data were modelled using mass-balance computations. This approach revealed that, more than 70% of suspended sediments in the Mgeta River originate from Kigalamila, Sezima, Kingule, Mafumbo and Kibuko areas. Thus, hills north of Kisaki are major contributors of sediments with less contribution from the southern terrain. After modelling of the data from …

Machine Learning For Wireless Network Throughput Prediction, Gustavo A. Fernandez

School of Mathematical & Statistical Sciences Faculty Publications

This paper analyzes a dataset containing radio frequency (RF) measurements and Key Performance Indicators (KPIs) captured at 1876.6MHz with a bandwidth of 10MHz from an operational 4G LTE network in Nigeria. The dataset includes metrics such as RSRP (Reference Signal Received Power), which measures the power level of reference signals; RSRQ (Reference Signal Received Quality), an indicator of signal quality that provides insight into the number of users sharing the same resources; RSSI (Received Signal Strength Indicator), which gauges the total received power in a bandwidth; SINR (Signal to Interference plus Noise Ratio), a measure of signal quality considering both …

The International Crisis In Numeracy Education, Nathan D. Grawe

Numeracy

The OECD recently released results from the 2022 administration of the Programme for International Student Assessment test. As other studies suggest, pandemic mitigation policies resulted in deep learning loss including in basic mathematics which forms the foundation of numeracy. Perhaps of greater concern, however, in many countries pandemic effects amplify declining performance that dates back a decade or more. Losses of two or more years' worth of mathematics education are not uncommon among developed countries. The editorial makes an urgent call for research that identifies practical steps to reverse these trends.

Recent Studies On The Super Edge-Magic Deficiency Of Graphs, Rikio Ichishima, Susana C. Lopez, Francesc Muntaner, Yukio Takahashi

Theory & Applications of Graphs

A graph $G$ is called edge-magic if there exists a bijective function $f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left(G\right) \right\vert \right\}$ such that $f\left(u\right) + f\left(v\right) + f\left(uv\right)$ is a constant for each $uv\in E\left( G\right) $. Also, $G$ is called super edge-magic if $f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}$. Furthermore, the super edge-magic deficiency $ \mu_{s}\left(G\right)$ of a graph $G$ is defined to be either the smallest nonnegative integer $n$ with the property that $G \cup nK_{1}$ is super edge-magic or $+ \infty$ if there exists no such …

A Survey Of Maximal K-Degenerate Graphs And K-Trees, Allan Bickle

Theory & Applications of Graphs

This article surveys results on maximal $k$-degenerate graphs, $k$-trees,

and related classes including simple $k$-trees, $k$-paths, maximal

outerplanar graphs, and Apollonian networks. These graphs are important

in many problems in graph theory and computer science. Types of results

surveyed include structural characterizations, enumeration, degree

sets and sequences, chromatic polynomials, algorithms, and related

extremal problems.

On Modeling Arterial Blood Flow With Or Without Solute Transport And In Presence Of Atherosclerosis, Daniel N. Riahi, Saulo Orizaga

School of Mathematical & Statistical Sciences Faculty Publications

In this article, we review previous studies of modeling problems for blood flow with or without transport of a solute in a section of arterial blood flow and in the presence of atherosclerosis. Moreover, we review problems of bio-fluid dynamics within the field of biophysics. In most modeling cases, the presence of red blood cells in the plasma is taken into account either by using a two-phase flow approach, where blood plasma is considered as one phase and red blood cells are counted as another phase, or by using a variable viscosity formula that accounts for the amount of hematocrit …

Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, Derek Brown

The Journal of Purdue Undergraduate Research

No abstract provided.

Generalized Splines On Graphs With Two Labels And Polynomial Splines On Cycles, Portia Anderson, Jacob P. Matherne, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

Generalized splines are an algebraic combinatorial framework that generalizes and unifies various established concepts across different fields, most notably the classical notion of splines and the topological notion of GKM theory. The for- mer consists of piecewise polynomials on a combinatorial geometric object like a polytope, whose polynomial pieces agree to a specified degree of differentiability. The latter is a graph-theoretic construction of torus-equivariant cohomology that Shareshian and Wachs used to reformulate the well-known Stanley–Stembridge con- jecture, a reformulation that was recently proven to hold by Brosnan and Chow and independently Guay-Paquet. This paper focuses on the theory of generalized …

Covariant Anyons Via Mackey Machinery, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.

Rad-⊕-Supplemented Semimodules Over Semirings, Ahmed H. Alwan

Al-Bahir

. In this paper, Rad-⊕-supplemented semimodules are defined as generalization of ⊕-supplemented semimodules. Let R be a semiring. An R-semimodule A is called a Rad-⊕-supplemented semimodule, if each subsemimodule of A has a Rad-supplement which is a direct summand of A. Here, we investigate some properties of these semimodules and generalize some results on Rad-⊕-supplemented modules to semimodules. We prove that any finite direct sum of Rad-⊕-supplemented semimodules is Rad-⊕-supplemented. Also, we prove that if A is a subtractive semimodule with (D₃) then A is Rad-⊕-supplemented if and only if every direct summand to A is …

Auslander-Reiten Triangles On A Bounded Derived Category Of Constructible Complexes, Vishnu Prasad Sivaprasad

LSU Doctoral Dissertations

In this dissertation, concepts from homological algebra are used to study the existence of Auslander-Reiten triangles.

Auslander-Reiten triangles are closely related to representable functors, and the main theorem characterizes the existence of representable functors in a specific bounded derived category of constructible complexes.

Under certain boundedness conditions, a specific bounded derived category is shown to have Auslander-Reiten triangles.

Special Issue On Public Policy: Front Matter

CODEE Journal

The Front Matter contains the Editor-in-Chief's Foreword, a Dedicatory by Associate Editor Douglas Meade, a Preface by the Special Editors Bev West and Samer Habre, and the Table of Contents.

Full Issue - Engaging The World: Differential Equations Can Influence Public Policies

CODEE Journal

This is the full issue (front matter and all papers) of the Third CODEE Special Issue, with the theme, "Engaging the World: Differential Equations can Influence Public Policies."

Nonlinear Filtering Of Classical And Quantum Spin Systems, Sivaguru S. Sritharan, Saba Mudaliar

Journal of Stochastic Analysis

No abstract provided.