Mathematics Commons^™

Testing The Reliability Of Chatgpt In Providing Spectral Information Of Organic Molecules, Ana Fraiman, Paola Barron, Brooke Dorsey, Sofia A. Delgado, Emanuel Sanchez

School of Mathematical & Statistical Sciences Faculty Publications

ChatGPT has emerged as a tool for predicting Hydrogen-1 Nuclear Magnetic Resonance (1HNMR), Infrared (IR), and Mass Spectrometry (MS) spectra. In order to rely on ChatGPT as a tool, a proof of concept for its application was essential. Having the ChatGPT outputs be validated by experimental data and databases (SDBS) has proven valuable for future uses. By inference, ChatGPT spectra output can be used to design problems without interference of copyright infringement of existing databases.

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (El–Rk–Fv) Method For Scalar Nonlinear Conservation Laws, Jiajie Chen, Joseph Nakao, Jing Mei Qiu, Yang Yang

Michigan Tech Publications

We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for …

Trends In U.S. Smoking And Cessation: Insights From 2015-2022, Nhan Phan '26, Thinh Nguyen '26, Naima Shifa

Annual Student Research Poster Session

Our project focuses on analyzing trends in smoking and cessation rates among U.S. adults between 2015 and 2022, using data from the Behavioral Risk Factor Surveillance System (BRFSS). The goal of the study was to explore how key demographic factors such as age, gender, income, and education impact smoking behaviors and quitting efforts. By employing both descriptive statistics and logistic regression, we identified disparities in smoking prevalence and cessation rates across these demographic groups. The findings suggest that while smoking rates have generally declined, there remain significant differences in outcomes based on socio-demographic variables. This work provides insights that could …

A Novel Bipolar Valued Fuzzy Group Based On Dib’S Approach, Fadi Al-Zu’Bi, Abdul Ghaffur Ahmad, Abd Ulazeez Alkouri, Maslina Darus

All Works

The numerous extensions of fuzzy groups (FG) and fuzzy subgroups are complicated. Several results depending on different approaches of FG theory were introduced. This study introduces a novel extension, named bipolar-valued fuzzy groups (BVF-groups), which are based on bipolar-valued fuzzy space (BVF-space) and are created using Dib’s methodology. The BVF-space replaces the universal set in conventional set theory. The BVF-space generalizes the notion of fuzzy space (F-space) from [0, 1] to [−1, 0] × [0, 1] for the range of membership function. The novel theory of BVF-group is achieved through the BVF-space and bipolar valued binary operation (BVFBO) to build …

Comparative Analysis In The Effectiveness Of Real Vs. Virtual Labs In Enhancing Students’ Conceptual Understanding Of Archimedes’ Principle, Judeanto Edy, Sutopo Sutopo, Edi Supriana

Jurnal Pendidikan Sains

This research aimed to investigate the effectiveness of virtual laboratories compared to real laboratories in improving students’ conceptual understanding of Archimedes’ principle. A quantitative approach was employed using a pretest-posttest design. The measurement instrument used in this study was a concept mastery test, consisting of 15 multiple-choice questions. Data were analyzed using an independent sample T-test. The research involved students from two XI IPA classes, each consisting of 33 students. The findings indicated that both virtual and real laboratories in the learning process could enhance students’ conceptual understanding. The study concluded that there was no significant difference between the virtual …

Development Of E-Modules Based On Pjbl-Steam And Virtual Simulation Media On Work And Energy Topic As An Effort To Improve Students’ Critical Thinking Skills, Farah Rafidah, Parno Parno, Nasikhudin Nasikhudin, Marlina Ali

Jurnal Pendidikan Sains

Work and energy are fundamental topics in physics. However, enhancing students’ critical thinking skills in these areas remains a challenge. This research aimed to develop and assess the validity and readability of e-modules designed with PjBL-STEAM and virtual simulation media to address this issue. The development process followed a 4D model, and the resulting e-modules were evaluated as strongly valid category. The validation tests yielded percentage scores of 91.6% for media, 89.3% for content, and 88.0% for lesson plans. Additionally, the readability test achieved a score of 84.6%, indicating a excellent level of comprehensibility. These findings suggest that the e-modules …

Exploration Of Students’ Scientific Argumentation Skills On Static Fluid Topics, Trio Junira Fernando, Parno Parno, Markus Diantoro

Jurnal Pendidikan Sains

The weakness in students’ scientific argumentation, particularly in providing evidence-based arguments, has become a significant concern in education. This study aims to assess students’ scientific argumentation skills specifically on the topic of static fluids. The survey was conducted with 78 twelfth-grade students from private high schools in East Java, Indonesia, who had previously studied this topic. A scientific argumentation test instrument, consisting of an essay format with five questions, was employed to collect data. The data were analyzed using descriptive statistics, followed by a classification based on static fluid subtopics and the level of scientific argumentation skill. The results indicated …

Impact Of Problem-Based Learning Integrated With Blended Learning On Students’ Collaborative Skills, Angel Regina, Yustina Febblina Daryanes, Riki Apriyandi Putra

Jurnal Pendidikan Sains

This study investigates the impact of implementing a Problem-Based Learning (PBL) model integrated with Blended Learning on enhancing students’ collaborative abilities. Conducted in class XI of SMA Negeri Plus Riau Province during the 2021/2022 academic year, the research utilized a control group design to compare the collaborative skills of students in an experimental class, which employed the PBL model, with those in a control class. The study assessed four key indicators of collaborative ability: working productively, valuing opinions, compromising, and sharing responsibility. The findings revealed that students in the experimental class showed significant improvements in all four indicators compared to …

Influencing Factors Of Competency Achievement In Fiber Optic Installation Engineering: A Study On Vocational School Graduates In Indonesia, Pangadongan Elfin Pujianto, Djoko Kustono, Hakkun Elmunsyah

Jurnal Pendidikan Sains

This study investigates the factors influencing the achievement of competencies in the field of Fiber Optic Installation Engineering (TIFO) among vocational school graduates in Indonesia and their subsequent performance in the workforce. Utilizing a quantitative approach, the research examines the relationship between several key variables, including national examination scores, quality of infrastructure, teaching competence, and telecommunication systems subject scores. Path analysis structural equation modeling was employed to determine the direct and indirect effects of these variables on TIFO competency achievement and graduates’ performance. The findings reveal that the quality of infrastructure is the most significant contributor to competency achievement, accounting …

Predicting Students' Academic Performance Via Machine Learning Algorithms: An Empirical Review And Practical Application, Edmund F. Agyemang, Joseph A. Mensah, Obu-Amoah Ampomah, Louis Agyekum, Justice Akuoko-Frimpong, Amma Quansah, Oluwaferanmi M. Akinlosotu

School of Mathematical & Statistical Sciences Faculty Publications

Predicting academic outcomes is complex and influenced by factors like socioeconomic background, motivation, and learning style. Machine Learning (ML) algorithms have become increasingly important due to their ability to analyze large data volumes and identify prediction patterns. Results show ML’s success in predicting academic performance, though effectiveness varies by dataset, algorithm choice, and training features. There is no consensus on the most effective ML method for predicting student performance with broad applicability. Among the five algorithms evaluated in this study, the Random Forest Classifier emerged as the best model, achieving the highest G-Mean and accuracy of 0.9243 and 85.42% respectively. …

Collaborative Practices In Virtual Group Work On Dynamic Geometry Tasks, Younggon Bae, V. Rani Satyam, Zareen G. Aga

School of Mathematical & Statistical Sciences Faculty Publications

The goal of this study is to explore productive ways to engage students in groupwork using dynamic geometry tasks in online synchronous classroom environments. In particular, we aim to understand the social, mathematical, and technological aspects of student collaboration in virtual spaces. We analyzed how three online groups of students collaboratively worked on dynamic geometry tasks of exploring interactive kaleidoscope applets in Desmos and producing visual representations and written descriptions of geometric transformations used in the applets. The students shared their screens in Zoom as they shared their findings and discussed how to draw and write to represent the kaleidoscopes. …

A Garch-Midas Approach To Modelling Stock Returns, Ezekiel N.N. Nortey, Ruben Agbeli, Godwin Debrah, Theophilus Ansah-Narh, Edmund F. Agyemang

School of Mathematical & Statistical Sciences Faculty Publications

Measuring stock market volatility and its determinants is critical for stock market participants, as volatility spillover effects affect corporate performance. This study adopted a novel approach to analysing and implementing GARCH-MIDAS modelling methods. The classical GARCH as a benchmark and the univariate GARCH-MIDAS framework are the GARCH family models whose forecasting outcomes are examined. The outcome of GARCH-MIDAS analyses suggests that inflation, interest rate, exchange rate, and oil price are significant determinants of the volatility of the Johannesburg Stock Market All Share Index. While for Nigeria, the volatility reacts significantly to the exchange rate and oil price. Furthermore, inflation, exchange …

Relative Equilibria Of Pinwheel Point Mass Systems In A Planar Gravitational Field, Ritwik Gaur

Rose-Hulman Undergraduate Mathematics Journal

In this paper, we consider a planar case of the full two-body problem (F2BP) where one body is a pinwheel (four point masses connected via two perpendicular massless rods) and the other is a point mass. Relative equilibria (RE) are defined to be ordered pairs (r, θ) such that there exists a rotating reference frame under which the two bodies are in equilibrium when the distance between the point mass and the center of the pinwheel is r and the angle of the pinwheel within its orbit is θ. We prove that relative equilibria exist for …

Noncrystallographic Tail-Triangle C-Groups Of Rank 4 And Interlacing Number 2, Mark L. Loyola, Nonie Elvin S. Leyrita, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

This work applies the modular reduction technique to the Coxeter group of rank 4 having a star diagram with labels 5, 3, and k = 3,4,5, or 6. As moduli, we use the primes in the quadratic integer ring Z[τ], where τ = (1+√5)/2, the golden ratio. We prove that each reduced group is a C-group, regardless of the prime used in the reduction. We also classify each reduced group as a reflection group over a finite field, whenever applicable.

A Preliminary Fuzzy Inference System For Predicting Atmospheric Ozone In An Intermountain Basin, John R. Lawson, Seth N. Lyman

Mathematics and Statistics Faculty Publications

High concentrations of ozone in the Uinta Basin, Utah, can occur after sufficient snowfall and a strong atmospheric anticyclone creates a persistent cold pool that traps emissions from oil and gas operations, where sustained photolysis of the precursors builds ozone to unhealthy concentrations. The basin's winter-ozone system is well understood by domain experts and supported by archives of atmospheric observations. Rules of the system can be formulated in natural language ("sufficient snowfall and high pressure leads to high ozone"), lending itself to analysis with a fuzzy-logic inference system. This method encodes human expertise as machine intelligence in a more prescribed …

Fractional Derivative-Based Analysis Of The Heat Transfer Properties Of Fluid Flow Over A Contracting Permeable Infinite-Length Cylinder, Anas Saeb Alhasan

Thesis/ Dissertation Defenses

Understanding the complex interplay between the contracting behavior of the cylinder and the fluid flow dynamics has implications for the design of porous structures for heat exchange and filtration systems. In this study, we investigate the dynamics and thermal behavior of fluid flow past a contracting permeable infinite cylinder. First, we developed a mathematical model based on the Navier-Stokes equations to describe the fluid dynamics around the contracting permeable infinite cylinder. A new simple well-behaved definition of fractional derivative called conformable fractional derivative introduced by authors Khalil et al. is employed to generalize the PDE’s of momentum and energy. The …

Hierarchical Neural Networks, P-Adic Pdes, And Applications To Image Processing, Wilson A. Zuniga-Galindo, B. A. Zambrano-Luna, Baboucarr Dibba

School of Mathematical & Statistical Sciences Faculty Publications

The first goal of this article is to introduce a new type of p-adic reaction–diffusion cellular neural network with delay. We study the stability of these networks and provide numerical simulations of their responses. The second goal is to provide a quick review of the state of the art of p-adic cellular neural networks and their applications to image processing.

Q-Rational Functions And Interpolation With Complete Nevanlinna–Pick Kernels, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we introduce the concept of matrix-valued q-rational functions. In comparison to the classical case, we give different characterizations with principal emphasis on realizations and discuss algebraic manipulations. We also study the concept of Schur multipliers and complete Nevanlinna–Pick kernels in the context of q-deformed reproducing kernel Hilbert spaces and provide first applications in terms of an interpolation problem using Schur multipliers and complete Nevanlinna–Pick kernels.

Euler Archive Spotlight: Ed Sandifer's Influence, Erik Tou

Euleriana

The Euler Archive owes its existence to the work and enthusiasm of C. Edward Sandifer. In this issue, we give a history of Ed's work and influence on the creation and growth of the Euler Archive.

Translating Scientific Latin Texts With Artificial Intelligence: The Works Of Euler And Contemporaries, Sylvio R. Bistafa

Euleriana

The major hindrance in the study of earlier scientific literature is the availability of Latin translations into modern languages. This is particularly true for the works of Euler who authored about 850 manuscripts and wrote a thousand letters and received back almost two thousand more. The translation of many of these manuscripts, books and letters have been published in various sources over the last two centuries, but many more have not yet appeared. Fortunately, nowadays, artificial intelligence (AI) translation can be used to circumvent the challenges of translating such substantial number of texts. To validate this tool, benchmark tests have …

On The Vibration Of Strings: An English Translation Of Leonhard Euler’S `Sur La Vibration Des Cordes' (E140), Reilly R. Fortune

Euleriana

We present an English translation of E140 - 'Sur la Vibration des cordes.'

About The Cases In Which The Formula X^4+Mxxyy+Y^4 Can Be Reduced To A Square, Georg Ehlers

Euleriana

Euler continues a previous study on the title Quartic (E696) with a new approach. His starting point here is the observation that, when the title Quartic is solved for m, the resulting fraction becomes an integer when z=ax^2y^2-(x^2±y^2). He provides many quadratic forms for m that allow special solutions, and tables for |m|≤200. Even though the tables are known today to be incomplete, they allow an insight into the enormous amount of work that was needed for their compilation.

The interest in the title Quartic predates Euler, and the fact that he resumed the study indicates a …

Ed Sandifer: A Running Mathematician And Mathematical Runner, Rick Cleary

Euleriana

Historian of mathematics C. Edward Sandifer was an outstanding marathon runner as well as a first rate mathematician. This note is a review of Prof. Sandifer's athletic successes, and a look at the attributes that he brought to both his professional and running careers.

How Ed Did It - A Memorial Conference To Honor Ed Sandifer, Lawrence D'Antonio

Euleriana

I look back at the virtual conference from February 2023 that was organized to honor the memory of the historian of mathematics Ed Sandifer, who had died in August 2022. The program of the conference is given at the end of the article.

Looking Back And Looking Forward, Christopher Goff, Erik Tou

Euleriana

An introduction to the contents in Issue 2, Volume 4 of Euleriana.

Some Studies On Mathematical Morphology In Remotely Sensed Data Analysis, Geetika Barman

Doctoral Theses

The application of Mathematical Morphology (MM) techniques has proven to be beneficial in the extraction of shapebased and texture-based features during remote sensing image analysis. The characteristics of these techniques, such as nonlinear adaptability and comprehensive lattice structure, make them useful for contextual spatial feature analysis. Despite the advancements, there are still persistent challenges, including the curse of dimensionality, maintaining spatial correlation, and the adaptability of morphological operators in higher dimensions. The focus of this thesis is to explore the potential of MM-based methods to analyse spatial features in addressing these challenges, specifically in the context of spatialcontextual feature analysis …

A Correspondence Between Deep Boltzmann Machines And P-Adic Statistical Field Theories, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

There is a strong interest in studying the correspondence between Euclidean quantum fields and neural networks. This correspondence takes different forms depending on the type of networks considered. In this work, we study this correspondence in the case of deep Boltzmann machines (DBMs) having a tree-like topology. We use p-adic numbers to encode this type of topology. A p-adic continuous DBM is a statistical field theory (SFT) defined by an energy functional on the space of square-integrable functions defined on a p-adic N-dimensional ball. The energy functionals are non-local, meaning they depend on the interaction of all the neurons forming …

The Heat Kernel On A Finite Graph In Different Time-Scales, Yang Chen, Jay Jorgenson, Luis Lopez, Lejla Smajlovic

Turkish Journal of Mathematics

Let G be a finite, weighted graph, and let [[EQUATION]] be a Time-scale with a fixed point [[EQUATION]] such that sup[[EQUATION]]. In this paper we construct the heat kernel on G in Time-scale [[EQUATION]] in terms of a certain convolution series involving he heat operator acting on a parametrix, which is a fairly general function depending on the vertex set of G and the time variable [[EQUATION]]. We develop some applications by choosing different parametrices and various Time-scales. The results we obtain here do extend, in part, aspects of the recent articles in that the Time-scale considered in this paper …

Φ−Pluriharmonicity And Φ−Invariance Of Pointwise Bislant Riemanniansubmersions, Grayson Light, Cem Sayar, Mehmet Aki̇f Akyol

Turkish Journal of Mathematics

In this research, we investigate the intriguing realm of pointwise bislant Riemannian submersions, a generalizationof many previous submersions, such as antiinvariant, slant, semislant, pointwise slant, pointwise semislant,and bislant submersions, within the framework of almost product manifolds. After giving an original example, wedelve into the submersion’s integrability conditions and geodesics. We explore the concept of φ−pluriharmonicity andφ−invariance within this context. The study sheds light on the profound interplay between pointwise bislant submersions’fibers and their being either geodesic or mixed geodesic, offering valuable insights into these intriguing mappings’geometric properties.

Ideals In Semigroups Of Partial Transformations With Invariant Set, Jitsupa Srisawat, Yanisa Chaiya

Turkish Journal of Mathematics

This paper explores the ideals and their structural properties in two generalizations of the partial transformationsemigroup. Furthermore, principal, maximal, and minimal ideals within these semigroups are elucidated.