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(R2165) Two Different Stages With Two Distinct Harvesting Processes, S. Vijaya, Krishika M

Applications and Applied Mathematics: An International Journal (AAM)

This study extends the classical Lotka-Volterra prey-predator model by incorporating a stage structured prey population consisting of juvenile and adult stages, while considering a single predator species governed by a Holling type II functional response. The growth of the juvenile prey depends on the adult prey population and since the juvenile prey has no reproduction capability. Two distinct harvesting strategies are introduced in the model. Constant-yield harvesting is applied to the juvenile stage of the prey population and represents a fixed amount of harvest regardless of population size. Constant effort harvesting is applied to the adult stage of the prey …

Toward Mapping Multiphase Multicomponent Mixtures With Neural Networks, Kristen L. Hallas, Melissa De Jesus, Christine J. Wu, Jianzhi Li, Jason Bernstein, Philip C. Myint

School of Mathematical & Statistical Sciences Faculty Publications

Equation of state (EOS) tables are commonly used in hydrodynamic simulations of high-pressure, high-temperature phenomena in fields like planetary science, astrophysics, and high-energy-density science. However, generating and storing EOS tables for multiphase, multicomponent mixtures over a wide range of pressures and temperatures is computationally infeasible due to their memory-intensive nature. To address this issue, we have developed a neural network-based machine learning model to predict new EOS tables for binary mixtures. In particular, a deep feedforward neural network trained on a set of ten EOS tables at particular mixture compositions is able to predict nine new (hold-out) EOS tables at …

Revisiting Ulam Stability For Boundary Value Problems, Martin Bohner, Snezhana Hristova, Agnieszka B. Malinowska, Ewa Girejko

Mathematics and Statistics Faculty Research & Creative Works

The main goal of this paper is to apply Ulam stability theory to boundary value problems for dynamic equations, while addressing several common misconceptions found in the existing literature. We identify the key issues that arise when applying Ulam stability to such problems and propose three distinct approaches to overcome them. To enhance clarity and accessibility, we begin with nonlinear ordinary differential equations and subsequently extend the analysis to nonlinear dynamic equations on time scales. Since a time scale is defined as any nonempty closed subset of the real numbers, our results are applicable to dynamic equations on continuous, discrete, …

Quasi-Poisson Analogs Of Regular Poisson Varieties, Casen Thompson

All Graduate Theses and Dissertations, Fall 2023 to Present

Let G be a complex semisimple linear algebraic group with 𝐶 a conjugacy class of parabolic subgroups of G. In previous work, Dr. Crooks defines 𝑢_𝐶→ B_𝐶 , a universal flat family of a fine Hamiltonian Lagrangian G-bundles over 𝐶, and shows that 𝑢_𝐶 is a family of regular Poisson varieties. This manuscript introduces a natural candidate for a quasi-Poisson analog of Dr. Crooks’s construction, 𝑢_𝐶, using the framework of quasi-Poisson geometry established by Alekseev, Kosmann-Scwarzbach, and Meinrenken. It will be shown that this proposed quasi-Poisson analog indeed has a valid quasi-Poisson structure and …

Peakon Solutions And Analytical Properties For The Camassa–Holm-Type Equations With Quadratic Nonlinearities, Yonghong Chen, Zhijun Qiao, Mingxuan Zhu

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we derive the multi-peakon dynamical system of a class of Camassa-Holm-type equations with quadratic nonlinearities. We also consider the analytical properties for the Cauchy problem. Firstly, we establish local well-posedness of solutions in Besov spaces and then provide the blow-up criteria. Subsequently, we impose appropriate sufficient conditions on the initial data to guarantee that the corresponding solution either exists globally or blows up in a finite time. Finally, we prove the ill-posedness in the Besov space B2,∞^3/2 by utilizing the non-traveling wave solutions.

Pattern Formation In Quantum Hierarchical Cellular Neural Networks, Wilson A. Zuniga-Galindo, B. A. Zambrano-Luna, Chayapuntika Indoung

School of Mathematical & Statistical Sciences Faculty Publications

We present a new class of quantum neural networks (QNNs) whose states are solutions of p -adic Schrödinger equations with a non-local potential that controls the interaction between the neurons. These equations are obtained as Wick rotations of the state equations of p -adic cellular neural networks (CNNs). The p -adic CNNs arise as continuous limits of large discrete hierarchical neural networks (NNs). The CNNs are bio-inspired by the Wilson–Cowan model, which describes the macroscopic dynamics of large populations of neurons. We provide a detailed study of the discretization of the new p -adic Schrödinger equations, which allows the construction …

A Finite Element Model For Thermomechanical Stress-Strain Fields In Transversely Isotropic Strain-Limiting Materials, Saugata Ghosh, Dambaru Bhatta, S. M. Mallikarjunaiah

School of Mathematical & Statistical Sciences Faculty Publications

This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress concentrations. We address the challenge of unphysical strain singularities at crack tips by employing a strain-limiting theory of elasticity. This theory is characterized by an algebraically nonlinear constitutive relationship between stress and strain, which intrinsically enforces a limit on the norm of the strain tensor. This approach allows the development of very large stresses, as expected near a crack tip, while ensuring that the corresponding strains remain physically bounded. A loosely coupled system …

Beyond Intent: Teacher Capacity, Opportunity To Learn, And The Persistence Of Math Equity Gaps In Tennessee (2000-2025), Soso Dede

The Journal of the Research Association of Minority Professors

For a quarter-century (2000–2025), Tennessee pursued mathematics reforms aiming for equity, yet stark racial and socioeconomic achievement gaps endure. Framed by Opportunity to Learn (OTL) and Mathematical Knowledge for Teaching (MKT), this study investigates the intersection of equity, teacher capacity, and policy. By synthesizing assessment data, program evaluations, policy documents, and research literature, this study reveals that systemic OTL inequities—disparate access to quality instruction, adequate resources, and teachers possessing strong MKT—are primary drivers of these enduring gaps. Such inequities deny marginalized students a fair chance at mathematical proficiency. The interplay between OTL and MKT is critical: inadequate OTL constrains knowledgeable …

Exact Formulas For Restricted Coprime Representations Of Even Integers, Andres Mauricio Salazar

Communications on Number Theory and Combinatorial Theory

Let p ≥ 5 be prime, and let g(2n,p) denote the number of unordered representations by positive integers 2n = h + k, with h ≤ k and gcd(h,6p) = gcd(k,6p) = 1. Every positive integer coprime to 6 belongs to exactly one of the families 6z + 1 and 6z + 5. In each family, divisibility by p excludes one explicit residue class of z modulo p. We use these two excluded classes to derive an exact formula for g(2n,p) from finite residue counts and nonnegative lift counts. The formula is valid for every positive integer n, including all …

Finite Mathematics: A Course Guide, Angela West Dixon, Hillary Dosser

Faculty Publications

Finite Mathematics: A Course Guide is a supplement to Mathematics for Business and Social Sciences by Kathryn Bollinger and Vanessa Coffelt. The authors of this Course Guide, Angela Dixon and Hilary Dosser, are instructors of Mathematics at Stephen F. Austin State University in Nacogdoches, Texas. This Course Guide was developed in response to adapting MATH 1324, Finite Mathematics to a zero-cost course, using an Open Educational Resource (OER) implemented in the Fall semester of 2026. According to the Texas Higher Education Coordinating Board’s Academic Course Guide Manual (ACGM), MATH 1324 Mathematics for Business and Social Sciences concerns the application of …

Quantum Mechanics, Non-Locality, And The Space Discreteness Hypothesis, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space X as a model for the physical space at short distances. However, we consider the time as a real variable. In this framework, the Dirac–von Neumann formalism can be used. This discreteness hypothesis implies that given two different points in space, there is no continuous curve (a world line) joining them. Consequently, this hypothesis is not compatible with the theory of relativity. We propose R×(R×X)3 as …

Study Of A Nonlinear Delayed Parabolic Model For Prion Disease Dynamics With The Unfolded Protein Response, Gangadhara Boregowda, Laurent Pujo-Menjouet, Zhaosheng Feng, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Prion diseases are neurodegenerative disorders characterized by the dynamic spread of misfolded toxic proteins in the brain. In this process, the normal cellular prion protein (PrPC) produced by neurons misfolds into a toxic form known as scrapie prion protein (PrPSc). These misfolded proteins propagate through the brain by converting healthy prions into their toxic form. This biological mechanism can be modeled by a system of nonlinear parabolic partial differential equations, accompanied by a nonlinear delayed integral boundary condition. Our primary objective is to establish the existence of nonnegative classical solutions to this system. Furthermore, we derive a priori estimates for …

Implementation Of The Problem-Based Learning Model On The Topic Of The Immune System To Enhance The Critical Thinking Skills Of Grade Xi B Students At Sman 1 Tojo, Nani Sofyanti, Sutrisnawati Sutrisnawati, Vita Indri Febriani, Mohammad Jamhari, Bustamin Bustamin, Raya Agni

Jurnal Pendidikan Sains

Critical-thinking skills are essential competencies for students in 21st-century learning. Preliminary classroom observations in Class XI B at SMAN 1 Tojo indicated that instruction remained predominantly teacher-centered and provided limited opportunities for students to engage in activities involving interpretation, analysis, evaluation, and inference. This study aimed to improve students’ critical-thinking skills through the implementation of Problem-Based Learning (PBL) on the immune system topic. The study employed a Classroom Action Research (CAR) design conducted over two cycles, involving 28 students in Class XI B. Data were collected using a teacher activity observation sheet and critical-thinking skills tests assessing four indicators: interpretation, …

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 …

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 …

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 …