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2024

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Articles 91 - 120 of 1077

Full-Text Articles in Mathematics

Coloring Trivalent Graphs: A Defect Tft Approach, Amit Kumar Oct 2024

Coloring Trivalent Graphs: A Defect Tft Approach, Amit Kumar

LSU Doctoral Dissertations

We show that the combinatorial matter of graph coloring is, in fact, quantum in the sense of satisfying the sum over all the possible intermediate state properties of a path integral. In our case, the topological field theory (TFT) with defects gives meaning to it. This TFT has the property that when evaluated on a planar trivalent graph, it provides the number of Tait-Coloring of it. Defects can be considered as a generalization of groups. With the Klein-four group as a 1-defect condition, we reinterpret graph coloring as sections of a certain bundle, distinguishing a coloring (global-sections) from a coloring …

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Pedagogical Moves Related To Analogy That Support A Unified Understanding Of Eigentheory Concepts In A Quantum Mechanics Class, Kaitlyn Stephens Serbin, Megan Wawro Oct 2024

Pedagogical Moves Related To Analogy That Support A Unified Understanding Of Eigentheory Concepts In A Quantum Mechanics Class, Kaitlyn Stephens Serbin, Megan Wawro

School of Mathematical & Statistical Sciences Faculty Publications

It is beneficial for quantum mechanics students to have a unified understanding of eigentheory concepts, so they can recognize the shared structure of mathematized phenomena from the different quantum mechanical systems of spin, energy, or position and recognize those as instantiations of the same overarching concept. Quantum mechanics instructors should, therefore, provide opportunities for their class community to develop a shared unified understanding of eigentheory concepts. One such opportunity can arise by engaging students in analogizing eigentheory concepts in one context with those from another context. We investigate the pedagogical moves related to analogies that can be used by a …

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Pricing Variance Swaps For The Discrete Bn-S Model, Semere Gebresilasie Oct 2024

Pricing Variance Swaps For The Discrete Bn-S Model, Semere Gebresilasie

Journal of Stochastic Analysis

No abstract provided.

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Group Representations & Quantum Theory, Vehbi Paksoy Oct 2024

Group Representations & Quantum Theory, Vehbi Paksoy

Mathematics Colloquium Series

What is the common thing between some integers and symmetries of an equilateral triangle? How studying rotations on a circle helps us understand quantum mechanics? Groups and their representations provide an amazing framework for many physics and chemistry theories. Understanding how certain groups act on physical systems, both classical and quantum, helps us to build models and make predictions. In this talk, we discover how abstract mathematical notions such as groups and representation theory and counterintuitive nature of quantum mechanics come together to guide us in our journey to explore the world we live in. This talk is designed to …

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A Phenomenological Study Of Persistence For Black Women In Mathematics Doctoral Programs, Shushannah Marie Smith Oct 2024

A Phenomenological Study Of Persistence For Black Women In Mathematics Doctoral Programs, Shushannah Marie Smith

Doctoral Dissertations and Projects

The purpose of this phenomenological study was to describe the doctoral persistence experiences of Black women mathematicians. Guided by McGee’s fragile and robust mathematical identity framework, the research design followed Moustakas’ qualitative transcendental phenomenological approach. The researcher explored the contributing factors to the phenomenon guided by the central research question, “What are the doctoral persistence experiences of Black women mathematicians?” The study involved 11 Black women participants who hold or were within one year of holding a doctoral degree in mathematics and were selected to ensure diversity and representativeness. Data collection encompassed three methods: a mathematical identity development timeline, one-on-one …

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Uniqueness Of Maximum Points Of A Sequence Of Functions Arising From An Adapted Algorithm For ‘The Secretary Problem’, Boning Wang, Giang Vu Thanh Nguyen Oct 2024

Uniqueness Of Maximum Points Of A Sequence Of Functions Arising From An Adapted Algorithm For ‘The Secretary Problem’, Boning Wang, Giang Vu Thanh Nguyen

OUR Journal: ODU Undergraduate Research Journal

This paper is aimed at a sequence of functions that is extended from an adaptive algorithm of the classical ‘secretary problem’. It was proved in Nguyen et al. (2024) the uniqueness of maximizers of a function sequence that represents the expected score of an element in a ‘candidate’ sequence. This function sequence is indeed considered as a special case of an extended function sequence that corresponds to the case α = 0. More specifically, we are motivated to prove the uniqueness of maximizers for this extended function sequence in the case α = 1. Nevertheless, the corresponding proof is rather …

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Scaled Global Operators And Fueter Variables On Non-Zero Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Choo, Mihaela Vajiac Oct 2024

Scaled Global Operators And Fueter Variables On Non-Zero Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Choo, Mihaela Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we describe the rise of global operators in the scaled quaternionic case, an important extension from the quaternionic case to the family of scaled hypercomplex numbers Ht, t ∈ R∗ , of which the H−1 = H is the space of quaternions and H1 is the space of split quaternions.We also describe the scaled Fueter-type variables associated to these operators, developing a coherent theory in this field. We use these types of variables to build different types of function spaces on Ht. Counterparts of the Hardy space and of the …

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Integrable Semi-Discretization For A Modified Camassa-Holm Equation With Cubic Nonlinearity, Bao-Feng Feng, Heng-Chun Hu, Han-Han Sheng, Wei Yin, Guo-Fu Yu Oct 2024

Integrable Semi-Discretization For A Modified Camassa-Holm Equation With Cubic Nonlinearity, Bao-Feng Feng, Heng-Chun Hu, Han-Han Sheng, Wei Yin, Guo-Fu Yu

School of Mathematical & Statistical Sciences Faculty Publications

In the present paper, an integrable semi-discretization of the modified Camassa-Holm (mCH) equation with cubic nonlinearity is presented. The key points of the construction are based on the discrete Kadomtsev-Petviashvili (KP) equation and appropriate definition of discrete reciprocal transformations. First, we demonstrate that these bilinear equations and their determinant solutions can be derived from the discrete KP equation through Miwa transformation and some reductions. Then, by scrutinizing the reduction process, we obtain a set of semi-discrete bilinear equations and their general soliton solutions in the Gram-type determinant form. Finally, we obtain an integrable semi-discrete analog of the mCH equation by …

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Counting The Classes Of Projectively-Equivalent Pentagons On Finite Projective Planes Of Prime Order, Maxwell Hosler Oct 2024

Counting The Classes Of Projectively-Equivalent Pentagons On Finite Projective Planes Of Prime Order, Maxwell Hosler

Rose-Hulman Undergraduate Mathematics Journal

In this paper, we examine the number of equivalence classes of pentagons on finite projective planes of prime order under projective transformations. We are interested in those pentagons in general position, meaning that no three vertices are collinear. We consider those planes which can be constructed from finite fields of prime order, and use algebraic techniques to characterize them by their symmetries. We are able to construct a unique representative for each pentagon class with nontrivial symmetries. We can then leverage this fact to count classes of pentagons in general. We discover that there are (1/10)((p+3)(p-3)+4 …

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Nano Topology And Decision Making In Medical Applications, Samir Mukhtar, Mohamed Shokry, Manar Omran Oct 2024

Nano Topology And Decision Making In Medical Applications, Samir Mukhtar, Mohamed Shokry, Manar Omran

Journal of Engineering Research

Nano Topology is one of the essential topics that receive special attention from some athletes in the field of General Topology, Operations Research, and Computer Science, because it has a vital role in the generalizing most of the various mathematical concepts. Recently, many efforts have been made to study many types of Nano Topology, as the previous studies lacked real applications in Engineering, Medicine, Pharmacy, and Social Sciences. In this paper, we present some different applications of these studies. The paper is divided into two parts: Firstly, we study the theory of The Nano Topology and investigate its relation with …

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New Operation Defined Over Dual-Hesitant Fuzzy Set And Its Application In Diagnostics In Medicine, Manar Mohamed Omran, Reham Abdel-Aziz Abo-Khadra Oct 2024

New Operation Defined Over Dual-Hesitant Fuzzy Set And Its Application In Diagnostics In Medicine, 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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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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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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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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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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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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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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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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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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