Mathematics Commons^™

Modeling The Probability Of N Clonal Rosettes In A Bromeliaceae Genetic Individual, Erin N. Bodine, Layla K. Lammers

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Infographic: Pisa Insights – Encouraging Mathematical Thinking, Dominique Russell

Teacher infographics

Each cycle of the global Programme for International Student Assessment (PISA) includes a teacher questionnaire. One questionnaire topic – encouraging mathematical thinking – can help foster critical thinking, enhance problem-solving skills and allow students to see the relevance and connectedness of mathematics in their lives.

Analysis Of An Effective Training Curriculum: Solutions Toincrease Participants' Interest In Training Teachingmaterials, Maulidya Husnul Khatimah, Yoto Yoto

Jurnal Pendidikan Sains

This research is important because it analyzes the curriculum as a primary tool for generating and maintaining participant interest. Curricula that are irrelevant, monotonous, or misaligned with participant needs are often the main causes of low motivation and participation. Furthermore, this research encourages the exploration and implementation of more innovative teaching methods and materials in training curricula. External pressure in the form of demands or instructions, rather than internal motivation, drives most training activities. This can reduce engagement and learning effectiveness. To overcome this, training institutions need to design programs that are relevant, flexible, and able to encourage participants' intrinsic …

Augmented Reality-Assisted E-Module On Temperature Andheat Content (Emarks), Tetri Sabrina, Ika Mustika Sari, Dedi Sasmita

Jurnal Pendidikan Sains

Temperature and heat content (calor) material in physics often involves concepts and phenomena that are difficult to observe directly or are abstract (such as energy transfer, particle movement, and changes in state). EMARKS (AR-based E-modules) are important because Augmented Reality (AR) allows the visualization of these abstract concepts in the form of interactive 3D models in the user's real environment. This helps students understand the concepts more concretely and easily. The development of E-modules is an innovation in learning media that is relevant to the demands of the digital era and the needs of modern students. The use of advanced …

The Effect Of Guided Inquiry Model With Deep Learningapproach On Student’S Hots In Elements, Compounds,And Mixtures At Junior High School, Friska Pakpahana, Retno Dwi Suyanti

Jurnal Pendidikan Sains

The current education curriculum places a strong emphasis on developing HOTS skills (such as analyzing, evaluating, and creating) to prepare students for the challenges of the 21st century. School learning often focuses on lower-level cognitive domains (memorizing and understanding). This research seeks to address this gap by offering a potentially effective learning model. The guided inquiry model positions students as active participants in learning, encouraging them to investigate, discover, and formulate concepts independently with teacher guidance. This strongly supports the development of critical thinking and problem-solving skills. Therefore, this study aims to analyze the effect of the guided inquiry model …

Development Of Problem-Based Learning Worksheet Toenhance Ecoliteracy: Human Impact On Ecosystem, Ulina M.S. Simangunsong, B. Manurung, Martina Asiati Napitupulu

Jurnal Pendidikan Sains

Ecoliteracy (ecological literacy) is an individual's ability to understand basic ecological principles and make environmentally responsible decisions. Improving ecoliteracy is a crucial foundation for realizing Education for Sustainable Development (ESD), which prepares students to become proactive citizens in protecting the environment. The problem-based learning model helps students learn on their own by using real-world environmental cases to get them to think critically and solve problems. Therefore, this research aims to determine the effectiveness of using problem-based learning worksheets to enhance the ecoliteracy of seventh-grade students. The development model used is 4-D. The research instruments include expert validation forms for subject, …

Development Of E-Lkpd Assisted By Phet Colorado Basedon Discovery Learning: Critical Thinking Skills On Lightmaterial At Junior High School, Flora Yani Saragih, Pintor Simamora

Jurnal Pendidikan Sains

Critical thinking is necessary for 21st-century pupils, but PISA data suggest that Indonesian students, especially junior high school students, lack it. The junior high science/physics light material is abstract and involves in-depth reasoning (reflection, refraction, and shadow generation). Without critical thinking, kids memorize formulas or notions without analyzing real phenomena. Discovery learning involves pupils discovering concepts via observation and experimentation. Critical thinking requires initiative, exploration, and reasoning, which these foster. Therefore, this study aims to develop E-LKPD based on Discovery Learning assisted by an interactive simulation of PhET Colorado to strengthen the critical thinking skills of grade VIII students on …

Guided Inquiry Learning Assisted By Crossword Puzzlemedia: Student Scientific Literacy And Critical Thinkingability For Middle School, Agis Putri Niswa, Mariati Purnama Simanjuntak, Ramlan Silaban, Fauziyah Harahap, Ridwan Abdullah Sani

Jurnal Pendidikan Sains

Scientific literacy and critical thinking skills are two fundamental competencies that students need in the 21st century. Scientific literacy is essential for students to understand and use scientific knowledge to make informed decisions, while critical thinking trains students to analyze information, evaluate arguments, and solve problems logically. Therefore, the intent of this study was to determine the effect of the guided inquiry learning model assisted by crossword puzzle media on students’ scientific literacy and critical thinking skills. The type of research used was quasi-experimental with a two-group pretest-posttest design. The sample consisted of two classes: class VII-8 as the control …

Site Specific Reliability-Targeted Snow Loads And Winter Wind Parameters Across The World, Brennan Bean, Nicholas Brimhall, Bikram Bhusal, Marc Maguire, Maha Moussa

Mathematics and Statistics Faculty Publications

This report presents a framework for estimating Reliability Targeted Snow Loads (RTSLs) and Winter Wind Parameters (WWPs) at locations outside the Conterminous United States (OCONUS). The methodology integrates ground-based in-situmeasurements with gridded global climate products to generate spatially continuous RTSL estimates for nearly any location in OCONUS. RTSLs are computed at qualifying in-situ stations, and predictive models relating gridded climate products to in-situRTSLs enable estimation at locations lacking direct measurements. This report describes the development of the in-situ annual maximum snow load database, the construction of global gridded climate summaries, the estimation of site-specific RTSLs and Service Targeted …

Developing Middle School Students’ Systems Thinking In Earth Science Through Dynamic Simulations: The Case Of The Rock Cycle, Nicole Panorkou, Amanda Provost, Gabriella Migliore

Department of Mathematics Faculty Scholarship and Creative Works

In this paper, we discuss the development of students’ systems thinking about the rock cycle as they interact with an instructional module that includes three interactive simulations and accompanying questioning. We present the reasoning of six students from a whole-class design experiment in a sixth-grade classroom to describe how students’ systems thinking may be constructed and reorganized through activity with our design. Our findings highlight a framework of students’ systems thinking about the rock cycle that builds and expands prior work to specific sub-components. We also discuss an emerging framework for supporting students’ systems thinking through careful design of simulation …

Expanding Ode Examples: Introducing Gene Regulation Dynamics Through Hill Functions, Maila Hallare, Jane M. Santamore

CODEE Journal

Gene regulation is a fundamental biological process that controls gene expression. It can explain phenomena such as cell differentiation, circadian rhythms, disease progression, and metabolic control, among many others. Despite their importance in mathematical biology, gene regulation models are rarely featured in traditional ODE textbooks, which focus mainly on examples from engineering, physics, chemistry, and population biology. This article introduces gene regulation dynamics as a valuable addition to ODE curricula, presenting the models from a mathematical perspective and building on properties of the Hill function. These models deepen the understanding of biology-inspired ODE applications, provide accessible research opportunities for students, …

Pfaffian Solution For Dark–Dark Soliton To The Coupled Complex Modified Korteweg–De Vries Equation, Chenxi Li, Xiaochuan Liu, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study the coupled complex modified Korteweg–de Vries (ccmKdV) equation by combining the Hirota’s method and the Kadomtsev–Petviashvili (KP) reduction method. First, we show that the bilinear form of the ccmKdV equation under nonzero boundary condition is linked to the discrete BKP hierarchy through Miwa transformation. Based on this finding, we construct the dark–dark soliton solution in the pfaffian form. The dynamical behaviors for one- and two-soliton are analyzed and illustrated.

Ecophysiological Benefits Of Industrial Organic Wastes On Alfalfa Yield And Stress Mitigation In Saline Soils, Shugao Fan, Zhuanzhuan Ma, Jiawei Wu, Tianhui Yang, Jincheng Hao, Shumei Chen, Xutong Hu, Ying Zhao

School of Mathematical & Statistical Sciences Faculty Publications

Rising soil salinity and water scarcity demand sustainable solutions to maintain crop productivity. This study evaluated four agro-industrial organic amendments—fish emulsion, neem cake, coffee grounds, and seaweed extract on alfalfa (Medicago sativa) under combined salinity and drought stress, assessing their effects on soil respiration, plant physiology, and yield. Soil CO₂ efflux varied significantly among treatments: coffee grounds induced the highest microbial activity (6.2 μmol m⁻² s⁻¹), suggesting rapid decomposition, while neem cake exhibited stable emissions (3.8 μmol m⁻² s⁻¹), indicating slower organic matter turnover. Fish emulsion showed intermediate dynamics, peaking at 4.8 μmol m⁻² s⁻¹ by week 4, …

Paclobutrazol Enhances Tall Fescue Salt Tolerance Via Physiological And Root System Architecture Modulation, Shugao Fan, Xindi Sun, Guohao Liang, Zhuanzhuan Ma, Jincheng Hao, Jiawei Wu, Ying Zhao

School of Mathematical & Statistical Sciences Faculty Publications

Background: Salinity represents a major global constraint on crop productivity. Promoting the cultivation of tall fescue in saline environments offers not only nutritional advantages for livestock but also enhances its potential for ornamental use. In this mesocosm study, we examined the effects of paclobutrazol (PBZ) on tall fescue performance under salt stress, focusing on key physiological traits to evaluate salt tolerance.

Results: Under high salt stress, paclobutrazol application increased the total number of lateral roots by 85%, from 18.39 to 34.04, and widened their growth angle by 24%, from 24.10° to 29.88°, fundamentally enhancing topsoil exploration. This reconfigured root system …

Problems In Extremal Graph Theory And Spectral Graph Theory, Fareeha Jamal

Dissertations

Spectral graph theory is a subfield of algebraic graph theory that studies the matrices associated with graphs. It lives at the nexus of Linear Algebra and Combinatorics. Many intriguing results in the domains of Matrix Theory and Combinatorics have come from studying the eigenvalues of graph matrices; in fact, several open problems in both areas have been resolved. Beyond its theoretical appeal, spectral graph theory has found meaningful applications in theoretical chemistry, particularly in the mathematical classification of chemical graphs. These classifications underpin quantitative structure–property relationships (QSPRs), facilitating the prediction of physicochemical properties such as enthalpy of vaporization, molar refractivity, …

Causal Predictive Modeling Of Survival Of Lung And Bronchus Cancer Patients Diagnosed During 2010–2011 In Texas, Zeinab Mohamed, Sidketa Fofana, Everardo Cobos, Manish K. Tripathi, Tamer Oraby

School of Mathematical & Statistical Sciences Faculty Publications

Background: Lung and Bronchus cancer is the most fatal type of cancer in the United States. According to the American Cancer Society, there were more than 127,000 deaths from lung cancer in 2023. Lung cancer care cost 23.8 billion dollars in 2020. In Texas, only 22.8% of lung cancer patients survived 5 years or more past diagnosis based on 2012-2018 data.

Aim: This study evaluates the survival length of lung and bronchus cancer patients in Texas using advanced statistical and machine learning methods applied to an 11-year cohort study from Surveillance, Epidemiology, and End Results Program. It also quantifies the …

Tight Spherical Embeddings (Updated Version), Thomas E. Cecil, Patrick J. Ryan

Mathematics and Computer Science Department Faculty Scholarship

This is an updated version of the paper [14] which appeared in the proceedings of the 1979 Berlin Colloquium on Global Differential Geometry. This paper contains the original exposition together with some notes by the authors made in 2025 (as indicated in the text) that give references to descriptions of progress made in the field since the time of the original version of the paper. The main result of this paper is that every compact isoparametric hypersurface Mⁿ ⊂ Sⁿ⁺¹ ⊂ Rⁿ⁺² is tight, i.e., every non-degenerate linear height function ℓ_p, p ∈ …

Existence, Uniqueness, Stability And Exact Expression Of Periodic Traveling Wave Solutions Of The Higher-Order Cubic-Quintic Nonlinear Schrödinger Equation, Nan Wang, Yuqian Zhou, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, the high-order cubic-quintic nonlinear Schrödinger equation is considered. By overcoming the difficulties caused by its non-integrability, we completely explore the existence, uniqueness and stability of the limit cycle of the equation. It enables us to accurately give the explicit parameter representation of its periodic wave solution in a special form for the first time. These results provide not only a new idea of obtaining periodic solutions in complex nonlinear systems, but also the important theoretical support for understanding related wave phenomena.

Restricted Mean Value Property On Riemannian Manifolds And Carleson's Problem On Damek-Ricci Spaces, Utsav Dewan

Doctoral Theses

One of the most key aspects of Harmonic Analysis is the study of the boundary behaviour of solutions of Partial Differential Equations. The central theme of this thesis is to study such problems for some suitable classes of Riemannian manifolds. We first study the restricted mean value property (RMVP for short) in the context of Riemannian manifolds. For a pre-compact domain D with smooth boundary in a Riemannian manifold M, we first prove that any real-valued, bounded, continuous function u satisfying the RMVP in D, having boundary limits in a full measure subset of the boundary, is harmonic in D. …

Italian Mathematics Prison Teachers’ Perspective On The Teaching/Learning Of Mathematics In Prison School, Andrea Maffia, Luca Decembrotto, Chiara Giberti, Federica Mennuni, Gabriella Pocalana, Silvia Regola, Agnese Telloni

Journal of Prison Education Research

Teaching in the prison context is characterized by a high complexity level; it is a multifaced activity influenced by several factors depending on the specific context. We present a preliminary but overall picture of schooling in Italian prisons by considering teachers’ reflections regarding their experiences in teaching mathematics in correctional facilities. To address the gap in the current literature on this issue, we conducted a SWOT analysis on the reflection provided by a group of nine Italian mathematics teachers who teach in different prisons and with different experiences and backgrounds. Their reflection allowed us to identify and describe six theory-driven …

A New Scheme For Simple Asymmetric Bivariate Copulas And Applications, Rachid Bentoumi, Farid El Ktaibi, Christophe Chesneau

All Works

Bivariate copulas play a central role in modeling the dependence structure between two random variables and serve as a fundamental tool in various applied fields. In this article, we develop a new theoretical framework aimed at constructing simple asymmetric bivariate copulas of the form C(u, v) = uv [ϕ(v) + u(1 − ϕ(v))^], (u, v) ∈ [0, 1]². This framework relies on a tuning univariate function to achieve the desired asymmetry. We study this pioneering scheme, emphasizing its theoretical foundations, and illustrating it with several examples. More precisely, we establish important properties of the proposed copulas …

Energy-Saving Simple Adaptive Recursive Terminal Sliding Mode Control For Industrial Feed Drive Systems, Haryson Johanes Nyobuya

Tanzania Journal of Science

This paper proposes a simple adaptive recursive terminal sliding mode control approach for industrial feed drive systems. The design employs a recursive sliding mode structure that eliminates the reaching phase and ensures finite-time convergence of the tracking error. To mitigate chattering, a second-order nonsingular terminal sliding mode is used and the parameters to compensate for disturbances are obtain in terms of integral form and a proportional terminal term, which enhances disturbance rejection and further guarantees finite-time convergence. The proposed controller significantly reduces the tracking error and saves energy for the feed drive system. Numerical simulations on an industrial feed drive …

A Comparative Study For Classical Machine Learning Models For Swahili Social Media Sentiment Analysis, Mahadia Tunga, Davis David

Tanzania Journal of Science

Despite sentiment analysis being one of the most popular applications in Natural Language Processing (NLP), most studies are skewed towards languages with a rich corpus (language database). Less emphasis has been placed on low-resource languages like Swahili. Swahili is the official language of the African Union and of 4 countries in East Africa, and is spoken by many people on the African continent. This study performed sentiment analysis using 3,000 tweets hosted on the Zindi Africa platform. Data was processed using a term frequency-inverse document frequency vectorization method, and five classical machine learning algorithms (RandomForest, XgBoost, and CatBoost, HistogramGradientBoost, LightGradientBoos) …

Mathematical Analysis Of Toxicants And Diseases Impact On A Prey-Predator System With Control Interventions, Nuru Yazidi Juma, Thadei Damas Sagamiko, James Philbert Mpele

Tanzania Journal of Science

This study developed a generic prey-predator mathematical model incorporating logistic growth for prey and a Holling Type I functional response for predator consumption. Prey-predator interactions form the foundation of ecological balance, but in recent decades these systems have been increasingly threatened by toxicants and infectious diseases. The combined effect of these challenges can lead to severe population declines, biodiversity loss, and ecosystem instability, making their study important for conservation and environmental management. The model includes the effects of diseases and toxicants on prey and toxicants only on predators, and explores optimal control strategies to mitigate these threats. Without considering time …

Comparative Study On The Application Of Gra, Psi And Hybrid Psi-Gra Techniques For Optimising Turning Parameters In Multi-Criteria Problems, Mussa Iddi Mgwatu

Tanzania Journal of Science

The optimum turning parameters help to justify the investment in machine tools for manufacturing industries. However, solving optimisation models to achieve optimum turning parameters in multi-criteria environment is complex leading to the application of multi-criteria decision-making techniques. This paper compares three multi-criteria decision-making techniques in determining optimum turning process parameters namely spindle speed, feed rate and depth of cut. The performance criteria are material removal rate, consumed electrical energy and tool wear rate. Example data for turning process were obtained from other studies while the analyses for multi-criteria decision-making were performed using grey relational analysis (GRA), preference selection index (PSI) …

Fahp-Topsis Model In Ranking Critical Success Factors Of E-Learning: A Comparative Analysis Of Normalization Methods, Judith R. Pande, David Koloseni, Septimi Kitta

Tanzania Journal of Science

The teaching and learning process has become effective and explicit due to the progressive development of e-learning. This has significantly transformed the education framework. As a result, evaluating the usefulness of e-learning requires a detailed understanding of the critical success factors that impact the success of e-learning environments. This study ranked these factors using Multi-Criteria Decision-Making techniques. Specifically, the Fuzzy Analytical Hierarchy Process was used to determine the weight of each factor, while the Technique for Order of Preference by Similarity to Ideal Solution was used to rank the factors of e-learning. The study also examined and compared four normalization …

Modeling The Effects Of Screening, Vaccination, Treatment, And Non-Pharmaceutical Controls On Leptospirosis Transmission Dynamics, Janeth Michael, Herieth Rwezaura, Goodluck Mlay, Nyimvua Shaban Mbare

Tanzania Journal of Science

Leptospirosis is the world’s most common zoonotic disease and remains a significant public health challenge, particularly in regions with poor sanitation and high exposure risks. This study aims to evaluate the effectiveness of combined interventions: screening, vaccination, treatment, and non-pharmaceutical controls in reducing leptospirosis transmission in human and domestic animal populations. The study develops and analyzes a deterministic compartmental model with eleven compartments representing human, domestic animal, and bacterial populations. Stability analysis reveals that the Disease-Free Equilibrium (DEF) is globally asymptotically stable when the effective reproduction number is less than a unit ( < 1), ensuring disease eradication under these conditions, whereas the Endemic Equilibrium Point (EEP) remains stable when > 1. The study employs the normalized forward …

Evaluating Weather Research And Forecasting Model In Simulating March-May Rainfall In Tanzania: Implications Of Selecting Parameterization Schemes, Mohamed H. Mohamed, Makungu James Ng'oga

Tanzania Journal of Science

The current study evaluates the performance of the Weather Research and Forecasting (WRF) model in simulating seasonal rains of March-May (MAM) in Tanzania, based on the implication of selecting parameterization scheme combinations. The model was configured into two domains with horizontal resolutions of 36 km and 12 km and the initial and lateral boundary conditions were provided by the Climate Forecast System Version 2 at 00 UTC. However, only the inner domain of 12 km was used for analysis, which has a fine horizontal resolution that accounts for small scale features such as terrains. Twelve simulations have been performed using …

Forbidden Triples For $2$-Connected Graphs With Minimum Degree Three Which Contain $K_4$ And $K_{2,2}$, Takafumi Kotani, Yoshimi Egawa

Theory & Applications of Graphs

For a family $\mathcal{H}$ of graphs, a graph $G$ is said to be $\mathcal{H}$-free if $G$ contains no member of $\mathcal{H}$ as an induced subgraph. Let $\mathcal{G}_2^{(3)}}(\mathcal{H})$ denote the family of $2$-connected $\mathcal{H}$-free graphs having minimum degree at least $3$. This paper is concerned with families $\mathcal{H}$ of connected graphs with $|\mathcal{H}| = 3$ such that $\mathcal{G}_2^{(3)}}(\mathcal{H})$ is a finite family. In particular, we show that for a connected graph $T$ of order at least $3$ that is not a star, $\mathcal{G}_2^{(3)}(\{K_4,K_{2,2},T\})$ is finite if and only if $T$ is a path of order at most $6$.

Star-Critical Weakened Ramsey Numbers, Mark R. Budden, Monu Moun, Jagjeet Jakhar

Theory & Applications of Graphs

The weakened Ramsey number $r^{s,t}(G)$ is defined to be the least $p\in \mathbb{N}$ such that every $t$-coloring of the edges of the complete graph $K_p$ contains a subgraph isomorphic to $G$ that is spanned by edges that use at most $s$ colors ($1\le s\le t-1$). The star-critical weakened Ramsey number $r^{s,t}_*(G)$ then determines the minimum number of edges that must join a vertex to $K_{r^{s,t}(G)-1}$ in order for this Ramsey property to hold. We begin by showing that $r_*^{s,t}(K_n)=r^{s,t}(K_n)-1$ for all $n\in \mathbb{N}$. Then, building off of Khamseh and Omidi's recent determination of $r^{s,t}(K_{1,n})$ when $s=t-1$ and $s=t-2$, we focus …