Digital Commons Network^™

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, …

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, …

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 …

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.

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 …

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 …

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 …

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) …

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 …

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 …

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 …

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) …

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 …

Topology Across Scales On Heterogeneous Cell Data, M. Torras-Pérez, Iris Yoon , '13, P. Weeratunga, L.-P. Ho, H. M. Byrne, U. Tillmann, H. A. Harrington

Mathematics & Statistics Faculty Works

Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides multiscale descriptors of “shape" suitable for the analysis of such spatial data. Here we propose a novel visualisation of persistent homology (PH) and fine-tune vectorisations thereof (exploring the effect of different weightings for persistence images, a prominent vectorisation of PH). These approaches offer new biological interpretations and promising avenues for improving the analysis of complex spatial biological data especially in multiple cell type data. To illustrate our methods, we apply them …

On Algebraic Aspects And Functoriality Of The Set Of Unbounded Operators Affiliated With A Von Neumann Algebra, Indrajit Ghosh

Doctoral Theses

In quantum theory, physically meaningful observables such as position and momentum are modeled by unbounded self-adjoint operators on Hilbert spaces. To study such operators in a rigorous mathematical framework, Murray and von Neumann introduced the concept of affiliation with a von Neumann algebra, giving rise to what are now known as Murray–von Neumann affiliated operators. For a single (unbounded) self-adjoint operator, its spectral projections span an abelian von Neumann algebra to which the operator is affiliated. If we want a common framework to study families of (unbounded) self-adjoint operators which do not necessarily commute with each other, it is instructive …

Needs Analysis Of Interactive Learning Media For Teachingheat Transfer In Physics: Students’ And Teachers’Perspectives, Rizki Eka Shintya, Ika Mustika Sari, Ida Kaniawati

Jurnal Pendidikan Sains

Heat transfer material in physics is known to be abstract. This study specifically analyzes the conceptual difficulties, and visualization needs specific to this material, which is different from the analysis of physics needs in general. This analysis does not only look for the need for traditional media but explicitly looks for the need for interactive media (simulation, animation, virtual laboratory). Therefore, this study aims to identify the need for interactive learning media in physics education, specifically in the teaching of heat transfer, from the perspective of students and teachers in West Java, Indonesia. Using a quantitative descriptive survey, data were …

Efficacy Of Teaching At The Right Level Approach Combined With The Problem-Based Learning Model On Science Learning Outcomes At Middle School, Heri Syahputra Azhar Panjaitan, Ryan Dwi Puspita

Jurnal Pendidikan Sains

This research seeks to evaluate the efficacy of the Teaching at the Right Level (TaRL) strategy in conjunction with the Problem-Based Learning (PBL) model on the scientific learning outcomes of eighth-grade students at middle school Islam Terpadu Khairul Imam. This research addresses the inadequate scientific problem-solving abilities and science learning outcomes of Indonesian students, necessitating a more interactive and individualized instructional technique. The methodology used is a quasi-experimental design with a nonequivalent control group. The sample included two purposively chosen eighth-grade classes: one experimental class (n=25) underwent the TaRL–PBL intervention, whereas the control class (n=25) simply used the lecture approach. …

Second Moment Of Degree Three L-Functions, Sampurna Pal

Doctoral Theses

Let $F$ be a Hecke-Maa\ss\  cusp form for $SL(3,\mathbb{Z})$. In this dissertation, we obtain a non-trivial upper bound of the second moment of $L(F,s)$ in the $t$-aspect: $$ \int_{T}^{2T}|L(F,1/2+it)|^2 dt\ll_{F,\epsilon} T^{3/2-3/32+\epsilon}.$$ Immediate corollaries include improvements over the existing results on the Subconvexity bound for self-dual $GL(3)$ $L$-functions in the $t$-aspect and for self-dual $GL(3)\times GL(2)$ $L$-functions in the $GL(2)$ spectral aspect, the error term in the Rankin-Selberg problem, and the zero density estimate for $GL(3)$ $L$-functions.

Development Of Students Worksheet Based On Project-Based Learning To Train Critical Thinking Skills At Vocational High School, Dia Ayu Permatasari, Harun Nasruddin

Jurnal Pendidikan Sains

Critical thinking is a cognitive skill that helps identify problems and generate solutions, leading to logical decisions or considerations for solving those problems. Students' critical thinking skills can be trained through learning activities to further improve students' critical thinking skills with learning tools. Therefore, this research intends to produce a student worksheet based on project-based learning to train students' critical thinking skills on the colligative properties of solutions. The development research uses the 4D development model from Thiagarajan, limited to the development stage. A limited trial was conducted with 30 students of industrial chemical engineering expertise at Vocational High School …

Development Of Digital Comic Learning Media Based On Mobile Learning On Media: Making Media Materials In Plant Tissue Culture, Sufina Intan Pertiwi, Fauziyah Harahap, Aline Gusti Yolanda Harahap, Marsya Amira Indrawati, Aline Jelita Christiani Simanullang, Yanda Febry Gracea Br Tarigan, Maureen Efriyanti Sitinjak

Jurnal Pendidikan Sains

his research was conducted based on student needs analysis, analysis of learner characteristics, and curriculum analysis, namely the lack of visualization and presentation of concepts and the lack of utilization of interactive technology in the learning process on media material and media making in tissue culture for college students. This study intends to develop digital comic media based on mobile learning and making media materials in tissue culture. This research method used research and development (R&D) with the ADDIE model: analyze, design, develop, implement, and evaluate. The subjects of this study were students of the Department of Biology, Universitas Negeri …

Problem-Based Learning Assisted By Augmented Reality On The Respiratory System Topic: A Study Of Students’ Critical Thinking Skills And Learning Motivation, Nyimas Dilviana, Ade Yeti Nuryantini, Sumiyati Sa'adah

Jurnal Pendidikan Sains

This study aims to examine the effectiveness of the Problem-Based Learning (PBL) model assisted by Augmented Reality (AR) technology regarding the respiratory system in improving students’ critical thinking skills and learning motivation. The research method used was a quasi-experimental design with a one-group pretest-posttest model. The subjects were 30 eleventh-grade students from a public high school in Garut City. Research instruments included a critical thinking test and a learning motivation questionnaire. The results showed a significant improvement in students’ critical thinking scores after the implementation of PBL with AR support. Additionally, learning motivation data analyzed from 16 statement items revealed …

An Ode-Based Analytical Approach To Rayleigh Flow Of Kelvin–Voigt Fluid, Kamille Garcia, Mahanthesh Basavarajappa

CODEE Journal

We present some results from a project carried out in the Under- graduate Research in Mathematics (MATH 4380) course at TAMIU. The main goal of this study is to demonstrate that analytical solutions for a system of partial differential equations (PDEs) can be obtained using methods typically taught in an undergraduate ordinary differential equations (ODE) course, such as power series, undetermined coefficients, and Laplace transforms. In this study, we provide semi-analytical solutions for Rayleigh flow type problem utilizing the Kelvin-Voigt fluid model, which describes the behavior of vis- coelastic materials by incorporating both elastic and viscous properties. Heat transfer analysis …

A Bdg Inequality For Stochastic Volterra Integrals, Alexandre Pannier

Journal of Stochastic Analysis

We establish Burkholder-Davis-Gundy-type inequalities for stochastic Volterra integrals with a completely monotone convolution kernel, which may exhibit singular behaviour at the origin. When the supremum is taken over a finite interval, the upper bound depends linearly on the Lγ-norm of the kernel, for any γ > 2. We demonstrate the utility of this inequality in quantifying the pathwise distance between two stochastic Volterra equations with distinct kernels, with a particular emphasis on the multifactor Markovian approximation. For kernels that decay sufficiently fast, we derive an alternative inequality valid over an infinite time interval, providing uniformin- time bounds for mean-reverting stochastic Volterra …