Mathematics Commons^™

Application Of The Tridiagonal Representation Approach And The J Matrix Method Of Scattering In Theoretical Physics, Tunde Joseph Osunmusanmi

Thesis/ Dissertation Defenses

This dissertation investigates the application of the Tridiagonal Representation Approach (TRA) to linear systems and introduces, for the first time, an extension of the J-matrix method of scattering to nonlinear phenomena. The TRA provides an algebraic framework for solving second-order linear ordinary differential equations by combining algebraic structure with the analytical properties of orthogonal polynomials and special functions. Computationally, the method benefits from efficient numerical techniques for tridiagonal matrices. Within the TRA, solutions of differential equations, including the Schrödinger equation, are expressed as convergent expansions in square-integrable basis functions chosen to yield a tridiagonal representation of the differential operator. This …

Literature Review Of Local Culture-Based Mathematics E-Module With Islamic Values In Probability, Maya Puspita Sari, Surya Sari Faradiba

Jurnal Pendidikan Sains

This study is grounded in the need to address the limitations of probability learning that is often procedural, decontextualized, and disconnected from students’ cultural and religious values. It aims to develop a comprehensive understanding of how local cultural contexts and Islamic values can be systematically integrated into mathematics e-modules, particularly for probability learning, and to formulate structured design principles and quality indicators for their development. This paper adopts a Systematic Literature Review (SLR) approach by analyzing empirical studies published between 2020 and 2025, using a structured selection process involving identification, screening, eligibility, and inclusion stages. A total of 11 high-quality …

The Effect Of Virtual Laboratories On Students Interest And Learning Outcomes In Spermatophyta At Sma Negeri 1 Sojol, Ismawati Ismawati, Sutrisnawati Sutrisnawati, Manap Trianto, Masrianih Masrianih, Abd Rauf, Musdalifah Nurdin

Jurnal Pendidikan Sains

Limited access to physical laboratory facilities and the abstract nature of Spermatophyta material reduce students’ learning interest and outcomes, necessitating the use of innovative digital learning media such as virtual laboratories. This study aims to analyze the effect of Virtual Laboratory (V-Lab) implementation on students’ learning interest and cognitive learning outcomes in Spermatophyta material at the senior high school level. A quantitative quasi-experimental design with a posttest-only control group was employed involving 66 eleventh-grade students divided into experimental and control classes; data were collected using a learning interest questionnaire and a multiple-choice test, and analyzed using independent samples t-test after …

Exploring The Thinking Processes Of Female Students In Solving Number Pattern Problems Based On Self-Directed Learning, Lailia Maghfiroh, Yayan Eryk Setiawan, Sikky El Walida

Jurnal Pendidikan Sains

Problem solving in mathematics requires integrating conceptual understanding, procedural knowledge, and logical reasoning. This qualitative exploratory case study investigates the intuitive and analytical thinking processes of two female students with contrasting levels of Self-Directed Learning (SDL) in solving number pattern problems. Data were collected through written problem-solving tasks and semi-structured interviews and analyzed descriptively. In this case study, the student with high SDL tends to use analytical thinking, including systematic data organization, strategic planning, and reflective evaluation, while the student with low SDL tends to rely on intuitive thinking, using rapid pattern recognition and prior experience without systematic verification. These …

Development Of Problem-Based Teaching Modules On Linear Systems Of Equations And Inequalities To Improve Mathematical Problem-Solving Skills, Elsya Suharnita, Kartini Kartini, Sehatta Saragih

Jurnal Pendidikan Sains

This study addresses the low mathematical problem-solving competency among Indonesian students, as evidenced by the PISA 2018 results that showed 71% failed to meet the minimum mathematical competency level. This study aims to develop a problem-based learning (PBL) module for systems of equations and inequalities content to improve Phase E students' mathematical problem-solving abilities. Using the ADDIE (Analysis, Design, Development, Implementation, Evaluation) model, this study involved expert validation, a small group trial with 12 students, and field implementation using a posttest-only control group design with 24 students in the experimental group and 25 students in the control group. The results …

Cognitive Conflict In Iconic Visual Representations: Comparing Conventional And Ai Approaches, Endrayana Putut Laksminto Emanuel, Herfa Maulina Dewi Soewardini, Radhitya Duta Pradana, Sikky El Walida

Jurnal Pendidikan Sains

Background of study: The rapid integration of Artificial Intelligence (AI) in higher education has transformed mathematical problem-solving practices, yet it introduces potential discrepancies in students’ visual understanding, particularly in geometric contexts, leading to commognitive conflicts in visual mediators. Aims and scope of paper: This study aims to analyze and compare the sources of commognitive conflict in iconic visual representations when students solve flat shape problems using conventional methods versus AI-assisted approaches. Methods: A qualitative design was employed involving 20 first-year mathematics education students divided into two groups (AI-assisted and conventional). Data were collected through students’ written work and semi-structured interviews …

Asymmetrical S-Curve For Residual Load Sways Suppression For Double-Pendulum Rotary Crane Using Bayesian Optimization, Haryson Johanes Nyobuya

Tanzania Journal of Science

In rotary crane operations, one of the main difficulties lies in suppressing the load sway during its movement. This can be achieved using only horizontal boom motion, offering a solution that is energy-saving, simple, and safe. However, this approach renders the system under actuated, making the suppression objective more difficult to achieve. In this study, a double-pendulum model is adopted to capture the coupled dynamics of the suspended load and hook, which shows a realistic basis for sway suppression. An asymmetric S-curve velocity trajectory is proposed to shape the horizontal boom motion, effectively minimizing residual vibrations without requiring direct sway …

Quantitative Analysis Of Cholera Dynamics And The Impact Of Integrated Control Measures., Kazeem Abidoye Odeyemi, Mutairu Kayode Kolawole

Tanzania Journal of Science

A comprehensive mathematical evaluation of cholera dynamics, emphasizing the crucial role of optimal control strategies which include vaccination, treatment in endemic region and environmental hygiene in controlling the disease spread in Western and Mid-Eastern regions of African setting. Through analysis of the local and global stability of the model and assessing the reproduction number (��0), this research highlights how targeted interventions can influence transmission rates of cholera disease. Sensitivity analysis identifies key parameters driving cholera dynamics, underlining the urgency of timely and adequate intervention. Utilizing the innovative Homotopy Perturbation Method for the numerical simulation, the study explores the interplay between …

Non-Redundant Rovibrational Hamiltonians By Molien Generating Functions And Gröbner-Basis Reduction, Leandro Ajo

University Libraries Undergraduate Research Award

High-resolution molecular spectroscopy requires an effective Hamiltonian whose operator content is both complete, containing every term allowed by molecular symmetry and nonredundant, free of any algebraically dependent operators that would cause ill-conditioned parameter fits. Traditional derivations based on Van Vleck contact transformations satisfy neither criterion automatically. This paper develops a rigorous, algorithmic pipeline that guarantees both properties simultaneously. Starting from the permutation– inversion (PI) group GPI of a molecule (Longuet-Higgins, 1963), we apply Molien’s theorem (Molien, 1897) to the symplectic normal-coordinate representation to obtain the vibrational generating function Φvib(t); integrate over the Haar measure of SO(3) (Weyl, 1946) to obtain …

Multiple Variable Regression Assignment, Sam Loyd

Distinguished Student Scholarship Collection

This paper applies multiple linear regression analysis to examine whether life outlook and sociability predict happiness. Using a dataset of 38 observations, the study employs IBM SPSS to conduct exploratory data analysis, assess regression assumptions, and evaluate model validity. Key assumptions—including linearity, homoscedasticity, independence of residuals, multicollinearity, normality, and the presence of influential outliers—are systematically examined using statistical tests and visual diagnostics. While some deviations from normality and potential nonlinear patterns are identified, the analysis proceeds based on sample size considerations and overall assumption adequacy. Results indicate that the regression model is not statistically significant and explains only a small …

The Kaczmarz Algorithm In Hilbert C∗-Modules, Daniel Alpay, Chad Berner, Eric S. Weber

Mathematics and Statistics Faculty Research & Creative Works

The Kaczmarz algorithm in Hilbert spaces is a classical iterative method for stably recovering vectors from inner product data. In this paper, we extend the algorithm to the setting of Hilbert C^∗-modules and establish analogues of its effectiveness in both finite-dimensional and stationary cases. Consequently, we demonstrate that continuous families of elements in a Hilbert space can be uniformly recovered using the Kaczmarz algorithm. Additionally, we develop a normalized Cauchy transform for continuous families of measures and use it to provide sufficient conditions under which standard frames in Hilbert C(X)-modules can be generated by the Kaczmarz algorithm and …

A Fully Discrete Decoupled Scheme And Applications For Non-Isothermal Two-Phase Flow Model With Different Viscosities And Thermal Diffusivities, Jian Li, Chunhao Chen, Xiaoyong Chen, Rui Li, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

To study natural convection problems in two-phase flows, a non-isothermal two-phase flow model incorporating differential viscosities and thermal diffusivities is considered and analyzed via the phase-field method. This modeling framework involves the Multiphysics coupling of the Cahn-Hilliard phase field equations, heat transfer equation, and Navier-Stokes equations, resulting in a strongly nonlinear system. To efficiently solve the sophisticated system, we develop, analyze, and demonstrate a decoupled linear fully discrete scheme, which leverages the invariant energy quadratization strategy for the Cahn-Hilliard phase field system, the artificial compressibility method without artificial pressure boundary condition, an explicit-implicit treatment of nonlinear terms, and the addition …

Sequences That Do Frame Reconstruction, Chad Berner

Mathematics and Statistics Faculty Research & Creative Works

Frames allow all elements of a Hilbert space to be reconstructed by inner product data in a stable manner. Recently, there is interest in relaxing the definition of frames to understand the implications for stable signal recovery. In this paper, we relax the definition of a frame by allowing the operator in the frame decomposition formula to not be invertible. We provide a complete classification of sequences that allow this decomposition via a type of frame operator. In addition, we provide several examples of sequences that allow this reconstruction property that are not frames and illustrate in which ways they …

Statistical Investigation Project, Ahmad Almomani Ph.D.

School of Arts & Sciences

The assignment was developed by SUNY Geneseo Professor Ahmad Almomani for the course, MATH 242: Elements of Probability and Statistics in the spring 2026 semester.

The objective for this assignment is that students will apply statistical methods to analyze real-world data and communicate meaningful conclusions.

Math 242: Elements Of Probability And Statistics (Syllabus), Ahmad Almomani Ph.D.

School of Arts & Sciences

This syllabus was developed by SUNY Geneseo Professor Ahmad Almomani during the spring 2026 semester.

Course Objectives:

Upon successful completion of Math 242, R/Elements of Probability and Statistics, a student will be able to: 

• Organize, present and interpret statistical data, both numerically and graphically; 
• Use various methods to compute the probabilities of events; 
• Analyze and interpret statistical data using appropriate probability distributions, e.g. binomial and normal. 
• Apply central limit theorem to describe inferences; 
• Construct and interpret confidence intervals to estimate means, standard deviations and proportions for populations; 
• Perform parameter testing techniques, including single and multi-sample tests for means, standard deviations …

Evolution As Spatial Projection, Charles H. Smith, Ngoc Nguyen

Faculty/Staff Personal Papers

A theory combining explanations for the nature of three-dimensional systems and evolutionary processes is advanced, set to a geometric simulation, and then discussed in the context of several empirical studies bearing on its validity. The concept “evolution” is first discussed, then related to Baruch de Spinoza’s ideas on natural philosophy, including his concept of the conatus. These ideas are then extended by posing the possible existence of a general form of natural systems subsystemization leading to the extended space condition. A geometrical/topological simulation study projecting spatial relations among subsystem structures interpretable through entropy maximization and multidimensional scaling methods is presented, …

Algorithm Performance In The Search For Hamiltonian Cycles, Chance Davis

Honors Theses

The Hamiltonian cycle problem is ubiquitous in both computer science and graph theory: Given a connected graph, a solution would either confirm the existence of a cycle which visits each vertex only once or its nonexistence. The importance of this problem, as well as its difficulty, is described in the Clay Mathematics Institute’s Millenium Prize Problems and Karp’s 21 NP-complete problems. Despite its “hardness,” solutions to the Hamiltonian cycle problem are desired in logistics, electronic circuit design, and network routing, among other fields. In this work, we benchmark a promising exhaustive enumeration algorithm on various graphs, including ones derived from …

Transport Of Quantum Walks In Electric Fields, Yousef Mohammad Yousef Salah

Theses

This thesis presents an analysis of transport in one-dimensional discrete-time quantum walks (DTQWs) on the Hilbert space ℓ²(ℤ) ⊗ ℂ². Quantum walks serve as fundamental models of coherent quantum transport and exhibit ballistic spreading driven by superposition and interference. The primary focus of this work is the review and derivation of sharp maximal velocity bounds for several classes of quantum walk step operators, including the shift-coin walk, the split-step walk, and models with constant as well as position-dependent coin operators. We establish general a priori bounds that remain valid beyond the translation-invariant regime. For homogeneous models, Fourier and spectral analysis …

Dissection Of The Quintuple Product, With Applications, Tim Huber, James Mclaughlin, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

This work considers the m-dissection (for m≢0(mod3)">m≢0(mod3)) of the general quintuple productQ(z,q)=(z,q/z,q;q)∞(qz2,q/z2;q2)∞.">Q(z,q)=(z,q/z,q;q)∞(qz2,q/z2;q2)∞.Multiple novel applications arise from this m-dissection. For example, we derive the general partition identityDS(mn+(m2−1)/24)=(−1)(m+1)/6bm(n), for all n≥0,">DS(mn+(m2−1)/24)=(−1)(m+1)/6bm(n), for all n≥0,where m≡5(mod6)">m≡5(mod6) is a square-free positive integer relatively prime to 6; DS(n)">DS(n) is defined, for S the set of positive integers containing no multiples of m, to be the number of partitions of n into an even number of distinct parts from S minus the number of partitions of n into an odd number of distinct parts from S; and …

Soliton Solutions To The Coupled Sasa–Satsuma Equation Under Mixed Boundary Conditions, Changyan Shi, Xiyao Chen, Guangxiong Zhang, Chengfa Wu, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we derive general bright–dark soliton solutions to the coupled Sasa–Satsuma (CSS) equation using the Kadomtsev–Petviashvili reduction method. Since the CSS equation is a special case of the four-component Hirota equation, our approach begins with the construction of two-bright-two-dark soliton solutions for the four-component Hirota equation. By imposing specific parameter constraints, these solutions are subsequently reduced to the bright–dark soliton solutions of the CSS equation. Finally, the dynamical behaviours of the one- and two-bright–dark soliton solutions are thoroughly analysed and illustrated.