Digital Commons Network^™

Emergence Of Purely Elastoplastic Turbulence In Shear Flows, Muhammad Abdullah, Shravan Pradeep, Doug J. Jerolmack, Becca Thomases, Paulo E. Arratia

Mathematics Sciences: Faculty Publications

Yield-stress fluids only flow above a critical stress. Here, we observe the emergence of a distinct, elasticity-driven flow state in a yield-stress fluid in the absence of inertia. Numerical simulations show that this elastoplastic turbulent state is characterized by non-Gaussian bimodal velocity distribution and a broad spectrum of velocity and stress fluctuations. Results show a nonmonotonic relationship between the volume fraction of the unyielded flow and plasticity. Surprisingly, the system can fluidize near the emergence of the elastoplastic turbulent state. Our results reveal the complex interplay between elasticity and plasticity in simple shear flows, indicating that plasticity can mobilize the …

Modelling Acute Haemorrhagic Conjunctivitis In East Africa: An Integrated Approach To Transmission Dynamics And Outbreak Response Strategies, Geofrey Wingi Sikazwe

Tanzania Journal of Science

Acute hemorrhagic conjunctivitis (AHC) poses a significant global health risk, with the potential for rapid spread during outbreaks. For instance, a localized outbreak in Yunnan Province, China, recorded infection rates of up to 48%, illustrating how transmission can intensify under favourable epidemiological and environmental conditions. Existing mathematical models of AHC transmission overlook seasonal variations, a critical factor in epidemic spread. This study combines species distribution models (SDMs) and epidemiological modelling to analyse key drivers of AHC in East Africa. We use the SEIR type (Susceptible-Exposed-Infected-Recovered - incorporating waning immunity) framework with temperature-dependent infectivity rate as the key driver of an …

The Use Of Gadgets And Learning Motivation Among Grade Xi Students In Biology Learning At Sma Negeri 5 Palu, Yulia Citra, Mohammad Jamhari, Masrianih Masrianih, Lestari M.P Alibasyah, Mursito S. Bialangi, Yulia Windarsih

Jurnal Pendidikan Sains

This study aims to describe the profile of gadget use and learning motivation among Grade XI students in biology learning at SMA Negeri 5 Palu and to explore students’ and teachers’ experiences of gadgets as learning support tools and potential sources of digital distraction. A qualitative descriptive design was employed, supported by descriptive questionnaire profiling. A total of 74 students completed a 50-item questionnaire on gadget use and learning motivation, while 10 students and two biology teachers participated in semi-structured interviews. Questionnaire data were analyzed using frequencies and percentages, while interview data were analyzed thematically. The descriptive findings showed that …

The Application Of The Group Investigation (Gi) Model Of Cooperative Learning To Improve Students’ Understanding Of Biodiversity In Year 10 At Sman 2 Mori Atas, Nadia Rosmita Lumako, Mohammad Jamhari, Yulia Windarsih, Lilies Lilies, Rafiqa Rafiqa, Amalia Buntu

Jurnal Pendidikan Sains

Biology instruction at SMAN 2 Mori Atas was predominantly conducted through conventional teaching practices. Preliminary observations revealed that students had difficulty understanding biodiversity concepts, and several students did not meet the minimum passing criterion of 70. These conditions highlighted the need for learning activities that promote active investigation, discussion, and conceptual connections. This classroom action research examined the use of the Group Investigation (GI) cooperative learning model to improve Grade 10 students’ classroom engagement and conceptual understanding of biodiversity, as assessed through Higher-Order Thinking Skills (HOTS) questions based on the Structure of Observed Learning Outcomes (SOLO) taxonomy. The study involved …

The Effect Of The Problem-Based Learning Model On Biology Learning Outcomes In The 8th Grade Science Class At Smp Negeri 19 Palu, Delfi Srieviyani, Mursito S. Bialangi, Masrianih Masrianih, Abd Hakim Laenggeng, Vita Indri Febriani, Bustamin Bustamin

Jurnal Pendidikan Sains

Research background: The low student achievement in biology at SMP Negeri 19 Palu specifically regarding the human respiratory system is attributed to the conventional teaching methods still employed by teachers. Purpose and scope of the article: This study examines the effect of the Problem-Based Learning (PBL) model on students’ learning outcomes in biology, specifically regarding the human respiratory system. Method: This study used a quasi-experimental design with a quantitative approach. The research design employed was a nonequivalent control group design using two groups: an experimental group (Class VIII D) consisting of 25 students who received the PBL model, and a …

Generalized Apostol-Bernoulli Functions And The Evaluation Of Character Sums, Brad Isaacson

Publications and Research

We introduce two types of generalized Apostol–Bernoulli functions attached to Dirichlet characters and express them by generalized Apostol–Bernoulli numbers. As a corollary, we obtain formulas expressing two families of character sums by generalized Apostol–Bernoulli numbers. These sums are twisted generalizations of sums introduced and studied by Arakawa, Berndt, Ibukiyama, Kaneko, Kim, Ramanujan, and Zaharescu in the context of modular forms and theta function identities.

Powers' Conjecture On The Third Largest Eigenvalue Of A Graph, Kevin Schmidt

Master's Theses

In 1989, David Powers conjectured that for any connected graph G on n vertices, the k-th largest eigenvalue of the adjacency matrix satisfies λk(G) ≤ ⌊n/k⌋ for every 1 ≤ k ≤ n/2. The conjecture has since been resolved case by case, in the sharper form λk(G) ≤ n/k − 1: the case k = 1 is classical, k = 2 was settled independently by Hong and by Powers in 1988, and k ≥ 4 was shown to fail by Nikiforov and Linz. This thesis surveys the resolution of the remaining case, k = 3, achieved in March 2026 by …

A Study On Some Distance Based Domination Parameters In Graphs And Their Applications, Shanmugavelan S Mr

Theses and Dissertations

Distance-based domination has emerged as a significant development in graph theory, attributed to its applications in communication systems, interconnection networks, parallel architectures, and chemical graph models. This thesis focuses on two such graph invariants: hop domination number and 2-hop domination number of graphs. The hop domination number of some generalized graph structures like generalized thorn paths, generalized theta graphs, and snake graph families is studied along with a newly introduced family, namely generalized ciliates.

Moreover, a variant of hop domination number, namely, the 2-hop domination number, is studied for some grid families like ladder, hexagonal grid, and its variants. Furthermore, …

Non-Gradient Quaternion Training Matrix Modifications For Color-Image Distillation, Tahsin Shahnewaz, Megdam Ahmed Chowdhury, Nikolay Metodiev Sirakov

Student Publications

This paper develops a new multi-stage image distillation method that combines two well known techniques. In the first stage, our method creates a matrix from all training images. In the next stage, it adapts a modified principal component analysis (M-PCA) approach to transform the training matrix. In the third stage, Singular Value Decomposition (SVD) fur ther refines the training-image matrix through low-rank reconstruction and controlled row selection. In the fourth stage, rotation of small 2 ×2 matrix blocks on the entire left singular matrix is conducted. The upper m (user-selected number) rows of the reconstructed matrix are selected and transformed …

Relationship Between Aleks Use, Implementation Models, And Grade 9 Students’ Achievement On Algebra 1 Summative Assessments, Deneen Alfordburke

Walden Dissertations and Doctoral Studies

The problem that was addressed through this study was Grade 9 students’ achievement on the Algebra 1 New Jersey Student Learning Assessment (NJSLA) continued to be below the proficiency level that is defined by the state, despite implementation of Assessment and Learning in Knowledge Spaces (ALEKS) Algebra 1 software. The study was grounded in Doignon and Falmagne’s knowledge space theory (KST) which evaluates students’ current knowledge levels and guides them along individualized learning paths based on what they are ready to learn next. The purpose of this nonexperimental quantitative study was to determine whether the predictor variables Grade 9 students’ …

Differential Equation Modeling For Sustainable Resource Management: A Steady-State Optimal Harvesting Approach, Iordanka N. Panayotova, Aleksei Talonov

CODEE Journal

Mathematical models based on differential equations provide a powerful framework for connecting real-world data to informed decision-making. In this work, we present a student-accessible project that uses an optimal-control framework to study the sustainable management of biological resources.

Motivated by fisheries management, we examine a predator--prey system in which harvesting decisions must balance ecological and economic considerations. The model is formulated as an optimal control problem that seeks to maximize the total discounted net revenue from harvesting. Rather than solving for the complete time-dependent harvesting trajectory, we restrict the analysis to positive controlled coexistence equilibria and characterize an interior stationary …

Continuous-Time Quantum Markov Chains And Discretizations Of P-Adic Schrödinger Equations: Comparisons And Simulations, Wilson A. Zuniga-Galindo, L. F. Chacón-Cortés

School of Mathematical & Statistical Sciences Faculty Publications

Continuous-time quantum walks (CTQWs) are a fundamental tool in the development of quantum algorithms. Recently, it was shown that discretizations of p-adic Schrödinger equations give rise to continuous-time quantum Markov chains (CTQMCs); this type of Markov chain includes the CTQWs constructed using adjacency matrices of graphs as a particular case. Unlike classical continuous-time Markov chains (CTMCs), the CTQMCs studied here do not satisfy the classical Chapman–Kolmogorov equation; this is a genuine quantum effect, due to the fact that the underlying unitary evolution composes at the level of probability amplitudes rather than probabilities, and we make precise the sense in …

Describing Preservice Secondary Mathematics Teachers’ Critical Statistical Literacy Habits Of Mind Enactment, Nina G. Bailey, Allison W. Mcculloch

Department of Mathematics Faculty Scholarship and Creative Works

Globally, school standards documents increasingly emphasize statistical literacy from the consumer orientation (making sense of real-world data representations). This orientation requires the adoption of a Critical lens (e.g., focus on power and equity) because how statistics are used (e.g., decision making) cannot be separated from the fact that social issues operate within systems of marginalization, privilege, and power. This study aims to explore how preservice secondary mathematics teachers enact critical statistical literacy habits of mind (CSLHM) when presented with data representations from the media. Findings reveal that preservice mathematics teachers typically emergently enact CSLHM, and some robustly. There is no …

How Euler Could Have Done It: Euler And An Integral Of Ramanujan, Alexander Aycock

Euleriana

We present a derivation of a definite integral discovered by Ramanujan (1887–1920) in his 1915 paper "Some Definite Integrals," from formulas and ideas already developed by Euler (1707–1783). Additionally, it is argued why Euler did not discover Ramanujan's integral himself, although he had all tools required for this task at his disposal.

A Note On Euler's Definition Of The Sum Of A Divergent Series, Alexander Aycock

Euleriana

We outline Euler's theory of divergent series and present another approach he could have taken to sum his ``factorial series". Finally, we address the contradictions that arise from his concept of a sum of a divergent series.

Euler's Explorations Of Extremal Ellipses, Jonathan David Evans

Euleriana

In the 1770s, Euler wrote a series of papers (E563, E691 and E692) about finding the ellipse with minimal area or perimeter in the family of all ellipses passing through a fixed set of points. This is a translation of all three papers from the original Latin, together with a commentary which discusses Euler's results and an appendix which addresses a question from E691 which Euler left for others to consider.

Arithmetic Theorems, Demonstrated By A New Method: An English Translation Of E271, Brendon Lasell

Euleriana

After defending in general terms the value of arithmetic demonstrations, where, according to Euler, the force of genius shines more brightly than in any other kind of demonstration, he goes on to let the force of his own genius shine forth in demonstrating the fact that, for any pair of relatively prime numbers a and N, a^ϕ(N) − 1 is always divisible by N, where we anachronistically denote by ϕ(N) the number of numbers less than N that are relatively prime to it. He approaches this theorem by considering the remainders that result when the numbers in an arithmetic …

On Double Integral Formulas: An English Translation Of E391, Thomas W. Polaski

Euleriana

In this paper, Euler investigates the theory of double intergrals to uses them to find areas, volumes and surface areas. He considers transformations of variables in double integrals. After showing that simple multiplication of the transformed differentials is not appropriate, he derives the formula for a change of variables in double integrals. Euler then uses such changes of variables to investigate areas and volumes, and then turns his attention to the so-called ``Florentine problem.'' This problem requires one to remove four equal windows from a hemispherical surface so that the remaining area is equal to the area of a square. …

Eulerian Problem Solving, Christopher Goff, Erik Tou

Euleriana

An introduction to the contents in Volume 6 (Issue 2) of Euleriana.

Taut And Dupin Submanifolds (Updated Version), Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

This is an updated version of the paper [29] by the author which originally appeared in 1997. The original paper was a survey of the closely related fields of taut and Dupin submanifolds of Euclidean space, and this updated version includes many results in the field that have appeared since the publication of the original version. The emphasis is on stating results in their proper context and noting areas for future research, and relatively few proofs are given. The important class of isoparametric hypersurfaces is surveyed in detail, as is the relationship between the two concepts of taut and Dupin. …

Fast Computation And Model Order Reduction Of The Friction Stir Welding Process With Pod-Deim, Joshua Kay, Zilong Song

Mathematics and Statistics Student Research and Class Projects

Friction stir welding (FSW) is a solid-state manufacturing process widely used in joining aluminum and other metal workpieces. The FSW process can be modeled by a coupled system of non-Newtonian Navier–Stokes and heat-transfer equations. However, solving this non-linear system with high accuracy requires significant computational power. This work refines the system by introducing corrected coefficients and new treatments for boundary conditions near the tool. Then, model order reduction, including the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), is applied to efficiently solve the FSW system in a low-dimensional space. To enhance accuracy and effectiveness, two novel treatments …

Using Approximations Of Practice To Support Calculus Instructors’ Enactment Of Equitable Active Learning Teaching Practices, Kaitlyn Stephens Serbin, Karina Uhing

School of Mathematical & Statistical Sciences Faculty Publications

We implemented a semester-long professional development workshop series to help Calculus I and II instructors implement active learning and equitable teaching practices. The workshops actively engaged instructors in approximations of practice (Grossman et al., 2009) in which they learned to enact various teaching practices like designing tasks; eliciting, noticing, and responding to evidence of student thinking; orchestrating class discussions; fostering inclusive social norms; and equitably managing student participation. After they participated in the workshops, we interviewed the instructors about their decisions to implement the teaching practices from the approximations of practice in their teaching. We analyzed the instructors’ resources, orientations, …

Health-Related Quality-Of-Life Profiles In Adults With Tinnitus, Preeti Pandey, Hansapani Rodrigo, Megan Kruger, Eldré W. Beukes, De Wet Swanepoel, Anu Sharma, Gerhard Andersson, Vinaya Manchaiah

School of Mathematical & Statistical Sciences Faculty Publications

Purpose: The study aimed to characterize the multidimensional burden of tinnitus on health-related quality of life (HRQoL) using the EuroQol 5-Dimension 5-Level (EQ-5D-5L) dimensions (mobility, self-care, usual activities, pain/discomfort, and anxiety/depression) moving beyond symptom severity alone.

Method: A cross-sectional analysis was conducted using baseline data (N = 428, Mage = 54.9 years, 51.9% female) from several clinical trials examining the efficacy of internet-based cognitive behavioral therapy for tinnitus. Data were collected using a series of online questionnaires including demographic, audiological, and clinical variables. HRQoL was assessed using the EQ-5D-5L profile dimensions.

Results: Participants primarily reported no problems with mobility (76.6%), …

On The Existence, Uniqueness And Stability Of Solutions Of Sdes With State-Dependent Variable Exponent, Mustafa Avci

Journal of Stochastic Analysis

We study a time-inhomogeneous nonlinear SDE with drift and diffusion governed by state-dependent variable exponents. This framework generalizes models like the geometric Brownian motion (GBM) and the constant elasticity of variance (CEV), offering flexibility to capture complex dynamics while posing analytical challenges. Using a fixed-point approach, we prove existence and uniqueness, analyze higher-order moments, derive asymptotic estimates, and assess stability. Finally, we illustrate an application where Poisson’s equation admits a probabilistic representation via a timehomogeneous nonlinear SDE with state-dependent variable exponents.

Companion Matrices Associated To Stochastic Matrices, Andreas Boukas, Philip Feinsilver

Journal of Stochastic Analysis

Starting with a stochastic matrix, we study the behavior of powers of an associated companion matrix, which has the same characteristic polynomial as the original matrix. In general the companion matrix will have negative entries while maintaining rowsums equal to 1. We will find the growth rate even if the Ces`aro limit of the sums of the companion matrix diverge. Surprisingly, in the irreducible aperiodic case the powers of the companion matrix will converge even though the norm of the matrix exceeds 1 and it has possibly negative entries.

Z+-Valued Additive Processes In Law With Nonnegative Increments, Nadjib Bouzar

Journal of Stochastic Analysis

The goal of this article is to study in depth the subclass of Z+- valued additive processes in law with nonnegative increments. We establish key distributional properties of these processes and obtain some existence results under a variety of conditions. We show that they form a subclass of the family of inhomogeneous Markov chains with spatial homogeneity. We extend the notion of factoring introduced by Sato (2004, [9]) for Rd-valued additive processes in law to their Z+-valued counterparts with nonnegative increments. We give a sufficient condition for the existence of a factoring for these processes. Lastly, we obtain their representation …

Motivating Second-Order Differential Equation Models Beyond The Spring–Mass System, Katherine E. Rutherford, John C. Borger

CODEE Journal

Students in introductory differential equations courses often learn to associate specific equation types with familiar physical systems. While this approach supports procedural fluency, it can inhibit transfer learning: students recognize familiar forms rather than construct models from first principles. This paper presents a modeling-first instructional approach designed to help students recognize the shared structure of second-order differential equations across diverse contexts. Students derive governing equations from fundamental physical laws for multiple systems, including an Inductor, Resistor, and Capacitor (LRC) electrical circuit, a simple pendulum, and viscous pipe flow. Through guided comparison, students identify common components such as inertia, damping, restoring …

Generalized Spectral Bound For Quasi-Twisted Codes, Buket Özkaya

Turkish Journal of Mathematics

Minimum distance bounds play a central role in the analysis of algebraic codes. For cyclic and constacyclic codes, several bounds based on their zero set have been developed. However, analogous results for quasi-twisted (QT) codes are comparatively limited. In this paper, we further investigate the spectral theory of QT codes and derive a general spectral bound on their minimum distance. Our bound unifies and generalizes previously known spectral bounds for quasi-cyclic (QC) and QT codes, and contains them as special cases. We present a new proof technique and show that the bound can be formulated with respect to an arbitrary …

A Novel Iterative Algorithm For Approximating Common Fixed Points Of Generalized Α-Nonexpansive Multivalued Mappings In Kohlenbach Hyperbolic Spaces, Makbule Kaplan Özekes

Turkish Journal of Mathematics

In this paper, we propose a new iterative scheme involving three multivalued mappings in Kohlenbach hyperbolic spaces. Strong and ∆-convergence theorems are established for approximating common fixed points of nonexpansive multivalued mappings under suitable conditions. A numerical example is also presented to illustrate the efficiency and faster convergence of the proposed method. The results obtained extend and unify several related contributions in the existing literature.

On Families Of Finsler Metrics, İsmai̇l Sağlam, Ken'ichi Ohshika, Athanase Papadopoulos

Turkish Journal of Mathematics

In this paper, we answer some natural questions concerning symmetrisation and more general combinations of Finsler metrics, with a view to applications to Funk and Hilbert geometries and metrics on Teichmüller spaces. The metrics on Teichmüller space that we consider are the Thurston metric and the earthquake metric, both introduced by Thurston. The first metric has been thoroughly studied over the last couple of decades, and the second over the last few years. The Funk metric and its symmetrisation, the Hilbert metric, are classical metrics that have been investigated in the contexts of hyperbolic geometry and geometric function theory and, …