Mathematics Commons^™

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 …

(Si17-06) Green-Naghdi Theory Of Two-Temperature Fractional Thermoelasticity Under Thermal Shock And Ramp-Type Heating, Sagar Sankeshwari, Vinayak Kulkarni

Applications and Applied Mathematics: An International Journal (AAM)

The linear thermoelasticity theory without energy dissipation developed by Green-Naghdi has been reconstructed by using two temperature theory in the context of a time fractional derivative. In half-space, the mathematical model is discussed for one-dimensional wave propagation subject to two different problems, viz., thermal shock and ramp-type heating at the bounding surface. Assume the bounding surface is traction-free. The analytical solutions are obtained in the Laplace domain. The Gaver-Stehfest technique is numerically used to perform time domain inversion of the Laplace transform, satisfying Kuznetsov’s convergence condition. The impact of fractional order parameters on the variations of various fields inside the …

(Si17-15) On Becker’S Conjecture, Jitender ., Shiv Datt Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we explore identities that involve higher-degree versions of widely recognized composition formulae, specifically focusing on expressions of the form

(x^k₁ + x^k₂ + · · · + x^k_r ) · (y^k₁ + y^k₂ + · · · + y^k_s ) = (z^k₁ + z^k₂ + · · · + z^k_n),

where k ≥ 2, y = (y₁, y₂, . . . , y_s), x = (x₁, x₂, . …

(Si17-05) Properties Of The Fermatean Fuzzy Matrix And Its Applications, Vineet Kumar, Anjana Gupta, H. C. Taneja

Applications and Applied Mathematics: An International Journal (AAM)

All real-world problems involve a significant amount of imprecision. To deal with the unpredictable environment, various methods and tools have been introduced. The Fermatean fuzzy matrix (FFM) is one of the important concepts for dealing with imprecision. In this paper, we explore the concept of Fermatean fuzzy matrix and introduce certain significant definitions. Some propositions and theorems of Fermatean fuzzy matrix are introduced with their proofs. The adjoint and determinant methods of Fermatean fuzzy matrices are also introduced. Finally, we have proposed a similarity measure and illustrated it via an application of Fermatean fuzzy matrix in decision-making problems.

Ranking Stocks In The S&P 500 And Nasdaq-100 Using An Entropy-Weighted Topsis Method, Hyeseong Oh '27

Annual Student Research Poster Session

This project ranks stocks in the S&P 500 and NASDAQ-100 using TOPSIS, a multi-criteria decision-making method. Instead of relying on a single financial ratio, each stock is scored on ten indicators covering valuation, profitability, cash flow, leverage, growth, efficiency, volatility, and momentum. Weights are set with the entropy method, which gives more weight to indicators that vary more across stocks, so the weights come from the data rather than personal judgment. TOPSIS then measures how close each stock is to a hypothetical best case and how far it is from a worst case. The S&P 500 is analyzed as two …

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, …

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 …