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Articles 1861 - 1890 of 27234

Full-Text Articles in Mathematics

Decision-Making In Diagnosing Heart Failure Problems Using Dual Hesitant Fuzzy Sets, Manar Mohamed Omran, Reham Abdel-Aziz Abo-Khadra Oct 2024

Decision-Making In Diagnosing Heart Failure Problems Using Dual Hesitant Fuzzy Sets, Manar Mohamed Omran, Reham Abdel-Aziz Abo-Khadra

Journal of Engineering Research

In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type n fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multi-sets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, and then propose an extension principle of DHFSs. Additionally, we give an example to illustrate …

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A Comparison Of Gaussian Processes And Polynomial Chaos Emulators In The Context Of Haemodynamic Pulse–Wave Propagation Modelling, L. Mihaela Paun, Mitchel J. Colebank, Dirk Husmeier Oct 2024

A Comparison Of Gaussian Processes And Polynomial Chaos Emulators In The Context Of Haemodynamic Pulse–Wave Propagation Modelling, L. Mihaela Paun, Mitchel J. Colebank, Dirk Husmeier

Faculty Publications

Computational modelling of the cardiovascular system is a promising future direction for patient-specific healthcare. However, the computational cost of these simulators is a bottleneck for their practical use in clinic for real-time digital twins. Emulation can overcome this, yet an extensive investigation into cardiovascular emulators is warranted. In this study, we emulate two one-dimensional haemodynamics models of the pulmonary circulation and compare two common emulation strategies: Gaussian processes (GPs) and polynomial chaos expansions (PCEs). We start by reducing the parameter space of the models through global sensitivity analysis, and then compare both emulation strategies using a multivariate, time-series output …

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Stability Of Optimal Spherical Codes, Károly J. Böröczky, Alexey Glazyrin Oct 2024

Stability Of Optimal Spherical Codes, Károly J. Böröczky, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

For many extremal configurations of points on a sphere, the linear programming approach can be used to show their optimality. In this paper we establish the general framework for showing stability of such configurations and use this framework to prove the stability of the two spherical codes formed by minimal vectors of the lattice E8 and of the Leech lattice.

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Further Results On Vanishing Coefficients In The Series Expansion Of Lacunary Eta Quotients, Timothy Huber, James Mclaughlin, Dongxi Ye Oct 2024

Further Results On Vanishing Coefficients In The Series Expansion Of Lacunary Eta Quotients, Timothy Huber, James Mclaughlin, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

In a previous paper the authors proved the existence of various pairs\break (A(q),B(q)) of lacunary eta quotients with identically vanishing coefficients. Further experiments indicated that the results in this previous paper were just the "tip of the iceberg". We provide a comprehensive description of what experiment suggests and employ a variety of methods to prove experimentally-derived results. The work is a template and atlas for the subsequent study of lacunary eta quotients. A broad range of proof strategies are applied to confirm the vanishing structure. These comprise a representative sample of techniques that may be used to study the remaining …

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Discrete Time Series Forecasting Of Hive Weight, In-Hive Temperature, And Hive Entrance Traffic In Non-Invasive Monitoring Of Managed Honey Bee Colonies: Part I, Vladimir A. Kulyukin, Daniel Coster, Aleksey V. Kulyukin, William Meikle, Milagra Weiss Oct 2024

Discrete Time Series Forecasting Of Hive Weight, In-Hive Temperature, And Hive Entrance Traffic In Non-Invasive Monitoring Of Managed Honey Bee Colonies: Part I, Vladimir A. Kulyukin, Daniel Coster, Aleksey V. Kulyukin, William Meikle, Milagra Weiss

Computer Science Faculty and Staff Publications

From June to October, 2022, we recorded the weight, the internal temperature, and the hive entrance video traffic of ten managed honey bee (Apis mellifera) colonies at a research apiary of the Carl Hayden Bee Research Center in Tucson, AZ, USA. The weight and temperature were recorded every five minutes around the clock. The 30 s videos were recorded every five minutes daily from 7:00 to 20:55. We curated the collected data into a dataset of 758,703 records (208,760–weight; 322,570–temperature; 155,373–video). A principal objective of Part I of our investigation was to use the curated dataset to investigate …

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Quantifying The Impact Of Rain-On-Snow Induced Flooding In The Western United States, Brennan Lynn Bean, Emma Watts Oct 2024

Quantifying The Impact Of Rain-On-Snow Induced Flooding In The Western United States, Brennan Lynn Bean, Emma Watts

Mathematics and Statistics Faculty Publications

The potentially destructive flooding resulting from rain-on-snow (ROS) events motivates efforts to better incorporate these events and their residual effects into flood-related infrastructure design. This paper examines relationships between measured streamflow surges at streamgages across the Western United States and the meteorological conditions preceding them at SNOTEL stations within the same water catchment. Relevant stream surges are identified using a peak detection algorithm via time series analysis, which are then labeled ROS- or non-ROS-induced based on the preceding meteorological conditions. Both empirical and model-derived differences between ROS- and non-ROS-induced stream surges are then explored, which suggest that ROS-induced stream surges …

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Fibonacci Numbers And Symmetry In Tai-Chi Motions, Matthew He Oct 2024

Fibonacci Numbers And Symmetry In Tai-Chi Motions, Matthew He

Mathematics Colloquium Series

In this talk, we first briefly review Fibonaccinumbers and its growth and development inmath, science, arts, culture, and nature, followedby an overview of Tao’s thoughts as an energysource of Tai-Chi motion. We then show thatFibonacci numbers are rooted in Tai-Chi motionand demonstrate that golden rectangle simulatesthe core space of Tai-Chi motions, and circular,spiral, and symmetrical motions can be used todescribe Tai-Chi movements. This talk is broadlydivided into the following three parts: 1.FIBONACCI NUMBERS, GROWTH AND DEVELOPMENT 2.TAO’S THOUGHTS, GROWTH AND DEVELOPMENT 3.TAI-CHI: MOTION OF FIBONACCI NUMBERS AND SYMMETRY

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Two Is Enough, But Three (Or More) Is Better: In Ai And Beyond, Olga Kosheleva, Vladik Kreinovich, Victor L. Timchenko, Yury P. Kondratenko Oct 2024

Two Is Enough, But Three (Or More) Is Better: In Ai And Beyond, Olga Kosheleva, Vladik Kreinovich, Victor L. Timchenko, Yury P. Kondratenko

Departmental Technical Reports (CS)

At present, the most successful AI technique is deep learning -- the use of neural networks that consist of multiple layers. Interestingly, it is well known that neural networks with two data processing layers are sufficient -- in the sense that they can approximate any function with any given accuracy. Because of this, until reasonably recently, researchers and practitioners used such networks. However, recently it turned out, somewhat unexpectedly, that using three or more data processing layers -- i.e., using what is called deep learning -- makes the neural networks much more efficient. In this paper, on numerous examples from …

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Exploring The Roles Of Genetics, Gender, Nurturing, And Learning Methods In Mathematical Skills Development, Laura Alinani, Jana Shyti Oct 2024

Exploring The Roles Of Genetics, Gender, Nurturing, And Learning Methods In Mathematical Skills Development, Laura Alinani, Jana Shyti

Honors Projects

This research explores the multifaceted factors influencing the development of mathematical competence through a combination of cognitive, psychological, and sociocultural frameworks. The study aims to address how genetic predispositions, nurturing environments, teaching methods, and societal influences interact to shape mathematical abilities. Using insights from genetic research, cognitive psychology, and education theory, we analyze the role of effective teaching methods, such as active knowledge construction and differentiated instruction, in fostering mathematical skills. The study also examines how societal biases, particularly gender stereotypes, impact students' confidence and interest in math. The findings highlight the importance of promoting gender-inclusive practices and early exposure …

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Mathematics In Contemporary Society, Patrick J. Wallach Oct 2024

Mathematics In Contemporary Society, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

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Zermelo's Theorem: How To Reach A Standard Of Perfect Play In Chess, Elisha Amadasu '26 Oct 2024

Zermelo's Theorem: How To Reach A Standard Of Perfect Play In Chess, Elisha Amadasu '26

Annual Student Research Poster Session

Zermelo’s theorem establishes that in any two player zero-sum game with perfect information (without the element of chance), either one side can force a win regardless of how the other side plays, or both sides can force a draw (if allowed in the rules). This theorem encouraged me to see how I could better my chess to see if I could exploit the existence of this perfect standard. I considered how chess engines play, as they are currently the strongest at playing chess. I understood that they often look 60-70 moves deep from the opening stage of the game, which …

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Festival Of Research Abstracts, Fall 2024, College Of Science And Mathematics, Wright State University Oct 2024

Festival Of Research Abstracts, Fall 2024, College Of Science And Mathematics, Wright State University

Festival of Research

The collection of abstracts accepted for the Fall 2024 Festival of Research hosted by the Wright State University College of Science and Mathematics.

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(Si13-07) Optimal Range For Value Of Two-Person Zero-Sum Game Models With Uncertain Payoffs, Sana Afreen, Ajay Kumar Bhurjee Oct 2024

(Si13-07) Optimal Range For Value Of Two-Person Zero-Sum Game Models With Uncertain Payoffs, Sana Afreen, Ajay Kumar Bhurjee

Applications and Applied Mathematics: An International Journal (AAM)

Game theory deals with the decision-making of individuals in conflicting situations with known payoffs. However, these payoffs are imprecisely known, which means they have uncertainty due to vagueness in the data set of most real-world problems. Therefore, we consider a two-person zero-sum game model on a larger scale where the payoffs are imprecise and lie within a closed interval. We define the pure and mixed strategy as well as value for the game models. The proposed method computes the optimal range for the value of the game model using interval analysis. To derive some important results, we establish some lemmas …

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(Si13-06) Analysis Of Some Unified Integral Equations Of Fredholm Type Associated With Multivariable Incomplete H And I-Functions, Rahul Sharma, Vinod Gill, Naresh Kumar, Kanak Modi, Yudhveer Singh Oct 2024

(Si13-06) Analysis Of Some Unified Integral Equations Of Fredholm Type Associated With Multivariable Incomplete H And I-Functions, Rahul Sharma, Vinod Gill, Naresh Kumar, Kanak Modi, Yudhveer Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we examine various effective methods for addressing the problem of solving Fredholm-type integral equations. Our investigation commences by applying the principles of fractional calculus theory. We employ series representations and products of multivariable incomplete H-functions and multivariable incomplete I-functions to solve these integrals. The outcomes derived from our analysis possess a general nature and hold the potential to yield numerous results.

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The P-Adic Schrödinger Equation And The Two-Slit Experiment In Quantum Mechanics, Wilson A. Zuniga-Galindo Oct 2024

The P-Adic Schrödinger Equation And The Two-Slit Experiment In Quantum Mechanics, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

p-Adic quantum mechanics is constructed from the Dirac-von Neumann axioms identifying quantum states with square-integrable functions on the N-dimensional p-adic space, Q_{p}^{N}. This choice is equivalent to the hypothesis of the discreteness of the space. The time is assumed to be a real variable. p-Adic quantum mechanics is the response to the question: what happens with the standard quantum mechanics if the space has a discrete nature? The time evolution of a quantum state is controlled by a nonlocal Schrödinger equation obtained from a p-adic heat equation by a temporal Wick rotation. This p-adic heat equation describes a particle performing …

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On Helly Numbers For Crystals And Cut-And-Project Sets, Alexey Garber Oct 2024

On Helly Numbers For Crystals And Cut-And-Project Sets, Alexey Garber

School of Mathematical & Statistical Sciences Faculty Publications

We prove existence of Helly numbers for crystals and for cut-and-project sets with convex windows. Also we show that for a two-dimensional crystal consisting of 𝑘 copies of a single lattice the Helly number does not exceed 𝑘 + 6.

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Testing The Reliability Of Chatgpt In Providing Spectral Information Of Organic Molecules, Ana Fraiman, Paola Barron, Brooke Dorsey, Sofia A. Delgado, Emanuel Sanchez Oct 2024

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.

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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 Oct 2024

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 …

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Trends In U.S. Smoking And Cessation: Insights From 2015-2022, Nhan Phan '26, Thinh Nguyen '26, Naima Shifa Oct 2024

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 …

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A Novel Bipolar Valued Fuzzy Group Based On Dib’S Approach, Fadi Al-Zu’Bi, Abdul Ghaffur Ahmad, Abd Ulazeez Alkouri, Maslina Darus Oct 2024

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 …

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Comparative Analysis In The Effectiveness Of Real Vs. Virtual Labs In Enhancing Students’ Conceptual Understanding Of Archimedes’ Principle, Judeanto Edy, Sutopo Sutopo, Edi Supriana Sep 2024

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 …

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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 Sep 2024

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 …

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Exploration Of Students’ Scientific Argumentation Skills On Static Fluid Topics, Trio Junira Fernando, Parno Parno, Markus Diantoro Sep 2024

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 …

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Impact Of Problem-Based Learning Integrated With Blended Learning On Students’ Collaborative Skills, Angel Regina, Yustina Febblina Daryanes, Riki Apriyandi Putra Sep 2024

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 …

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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 Sep 2024

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 …

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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 Sep 2024

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. …

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Collaborative Practices In Virtual Group Work On Dynamic Geometry Tasks, Younggon Bae, V. Rani Satyam, Zareen G. Aga Sep 2024

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. …

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A Garch-Midas Approach To Modelling Stock Returns, Ezekiel N.N. Nortey, Ruben Agbeli, Godwin Debrah, Theophilus Ansah-Narh, Edmund F. Agyemang Sep 2024

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 …

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Relative Equilibria Of Pinwheel Point Mass Systems In A Planar Gravitational Field, Ritwik Gaur Sep 2024

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 …

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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 Sep 2024

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.

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