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Articles 2281 - 2310 of 27232
Full-Text Articles in Mathematics
Largeness And Accessibility Of Sparse Sets, Oscar Quester
Largeness And Accessibility Of Sparse Sets, Oscar Quester
Honors Program Theses and Projects
One of the main goals in the study of Ramsey Theory is to find “order” in seemingly “random” structures. For example, Van der Waerden’s Theorem tells us that given any r-coloring of the positive integers, there will exist arbitrarily long monochromatic arithmetic progressions. The theorem places no requirement on the gap (common difference), d, of the arithmetic progression – it can be any natural number. With this in mind, we ask if we are still guaranteed arbitrarily long monochromatic arithmetic progressions when we restrict the possible values of d to some subset D ⊆ N. We also ask a similar …
A Tale Of Two Toroidal Graphs, Akshat Gulgulia
A Tale Of Two Toroidal Graphs, Akshat Gulgulia
Honors Theses
A graph is toroidal if it can be embedded on a torus which is a doughnut-shaped surface. Two well-known examples of toroidal graphs are the complete graph K5 and the complete bipartite graph K3,3. In this thesis we elucidate the association of the subject matter with two renowned enigmas in graph theory, namely the Five Princes Problem and the Three Utilities Problems. Additionally, we look at their association with several renowned theorems in topological graph theory. We explore the link between these two graphs and a contemporary labeling concept.
Numerical Investigation To Produce A Fundamental Polygon, Elizabeth Sipes
Numerical Investigation To Produce A Fundamental Polygon, Elizabeth Sipes
Honors College Theses
There exist multiple types of geometry, differing in the postulates they are based on, and therefore the theorems and proofs that make up said geometry. Hyperbolic geometry differs from others by allowing there to exist multiple lines through a single point not on a given line, that are parallel to the given line. Every geometry has the idea of distance and isometries, distance preserving maps. By considering special collections of isometries called discrete groups, we can construct interesting surfaces, such as the torus and genus-g surface. The connection between the surface and the discrete group can be understood through …
Euler Archive Spotlight: Multiple Search Options, Christopher Goff
Euler Archive Spotlight: Multiple Search Options, Christopher Goff
Euleriana
The Euler Archive houses PDF versions of almost all of Euler's original publications. While most visitors search the archive via a work's Eneström number, the Archive can be searched via source publication name, date written, or decade of publication. The Archive also provides context for Euler's publications through short pieces of historical information.
Euler And A Proof Of The Functional Equation For The Riemann Zeta-Function He Could Have Given, Alexander Aycock
Euler And A Proof Of The Functional Equation For The Riemann Zeta-Function He Could Have Given, Alexander Aycock
Euleriana
We explain how Euler could have proved a functional equation, which is equivalent to the one for the Riemann zeta-function, that he conjectured in his paper {\it ``Remarques sur un beau rapport entre les series des puissances tant directes que reciproques"} \cite{E352} (E352: ``Remarks on the beautiful relation between the series of the direct and reciprocal powers").
Euler And The Gaussian Summation Formula For The Hypergeometric Series, Alexander Aycock
Euler And The Gaussian Summation Formula For The Hypergeometric Series, Alexander Aycock
Euleriana
We show that in his paper {\it ``Plenior expositio serierum illarum memorabilium, quae ex unciis potestatum binomii formantur"} \cite{E663} (E663: ``A more thorough exposition of those memorable series that are formed from the binomial coefficients") Euler could have found the Gaussian summation formula for the hypergeometric series from his own formulas in that same paper, if he actually set the task for himself.
Euler And Homogeneous Difference Equations With Linear Coefficients, Alexander Aycock
Euler And Homogeneous Difference Equations With Linear Coefficients, Alexander Aycock
Euleriana
We present a method outlined by Euler in his paper{\it ``De fractionibus continuis observationes"} \cite{E123} (E123: ``Observations on continued fractions") that can be used to solve homogeneous difference equations with linear coefficients. We will illustrate his ideas by applying it to two familiar examples and explain how it can be understood from a more modern point of view.
On The Cases In Which The Formula X^4+Kxxyy+Y^4 Can Be Reduced To A Square, Georg Ehlers
On The Cases In Which The Formula X^4+Kxxyy+Y^4 Can Be Reduced To A Square, Georg Ehlers
Euleriana
Euler’s key idea for equating the Quartic in the title to a square is to set k=P+surd(Q). From this he derives P=f·x^2 and Q=4f·y^2+4 and solves the Pell equation for y. He then discusses various extensions to rational numbers that leave k an integer. Euler provides incomplete tables for integers k with |k|square.
Research On Arithmetic, Erik R. Tou
Research On Arithmetic, Erik R. Tou
Euleriana
In this English translation, some of Joseph-Louis Lagrange's early number theory is presented. Here, he laid out a theory of binary quadratic forms with special attention to the representation problem: determining those integers which may be represented by a given form, and cataloguing the possible forms of their divisors.
Number Theory And More, Christopher Goff, Erik Tou
Number Theory And More, Christopher Goff, Erik Tou
Euleriana
An introduction to the contents in Issue 1, Volume 4 of Euleriana.
Caterpillar, Lobster, X Graphs, Gerald Melin, Landon Seward, Will Mahowald, Xavier Jones
Caterpillar, Lobster, X Graphs, Gerald Melin, Landon Seward, Will Mahowald, Xavier Jones
Celebrating Scholarship and Creativity Day (2018-)
We studied a combinatorial game played between two players ("Alpha", who goes first, and "Beta", who goes second). The idea is that there are a lot of lightbulbs in a large warehouse, and they take turns turning a light bulb on. When a light bulb is turned on, it illuminates the area directly by it as well as the areas immediately surrounding it. The player who is the one to make all of the warehouse illuminated is the winner. This can be modeled on a graph. The two players take turns (1) selecting a vertex that has not yet been …
Finite State And Sequential Automata, Kriti Gulgulia
Finite State And Sequential Automata, Kriti Gulgulia
Honors Theses
No abstract provided.
Skeletal 2-Groups And Category Theory, Nicholas Small '25, Alexander Stepanov '26, Haley Waiksnis '25
Skeletal 2-Groups And Category Theory, Nicholas Small '25, Alexander Stepanov '26, Haley Waiksnis '25
Mathematics & Computer Science Student Scholarship
Nicholas Small ’25, Mathematics and Computer Science major
Alexander Stepanov ’26, Mathematics and Studio Art major
Haley Waiksnis ’25, Mathematics major
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science
Autonomous Remote Erosion Monitoring Using Computer Vision, Emily Gelchie '24, Gabriel Benz '25
Autonomous Remote Erosion Monitoring Using Computer Vision, Emily Gelchie '24, Gabriel Benz '25
Mathematics & Computer Science Student Scholarship
Emily Gelchie ’24, Computer Science major
Gabriel Benz ’25, Computer Science major
Faculty Mentor: Dr. Martin Helwig, Mathematics and Computer Science
Media Portrayals Of Mathematics And Mathematicians: An Annotated Bibliography Of Published Journal Articles, Sarah O'Connor '26
Media Portrayals Of Mathematics And Mathematicians: An Annotated Bibliography Of Published Journal Articles, Sarah O'Connor '26
Education Student Scholarship
Sarah O'Connor ’26, Mathematics major
Faculty Mentor: Dr. Kevin O’Conner, Secondary Education and Dr. Olga Limnios, English
Avatars Runnin' On Dunkin, Keelin Robbins '26
Avatars Runnin' On Dunkin, Keelin Robbins '26
Mathematics & Computer Science Student Scholarship
Keelin Robbins ’26, Computer Science major, Finance minor
Faculty Mentor: Dr. Martin Helwig, Mathematics and Computer Science
Blueberry Drone Ai: Estimating Crop Yield Using Deep Learning & Smart Drones, Luke Tonon, Brandon Mchenry, Anthony Thompson, Harper Zappone, Jacob Green, Hieu Nguyen, Thanh Nguyen
Blueberry Drone Ai: Estimating Crop Yield Using Deep Learning & Smart Drones, Luke Tonon, Brandon Mchenry, Anthony Thompson, Harper Zappone, Jacob Green, Hieu Nguyen, Thanh Nguyen
STEM Student Research Symposium Posters
This project seeks to assist blueberry growers in New Jersey estimate crop yield by developing software that allows autonomous drones to capture aerial images of blueberry bushes in the field, perform berry count, and identify blueberry conditions using deep learning models & computer vision.
Blueberry Drone Ai: Smart Farming Of Blueberries Using Artificial Intelligence And Autonomous Drones, Robert Czarnota, Anthony Segrest, Anthony Thompson, Harper Zappone, Hieu Nguyen, Nguyen Thanh, Ik Jae Lee, Lori Green, Tuan Le
Blueberry Drone Ai: Smart Farming Of Blueberries Using Artificial Intelligence And Autonomous Drones, Robert Czarnota, Anthony Segrest, Anthony Thompson, Harper Zappone, Hieu Nguyen, Nguyen Thanh, Ik Jae Lee, Lori Green, Tuan Le
STEM Student Research Symposium Posters
This project seeks to assist blueberry growers in New Jersey with preventing blueberry scorch disease. Plants can’t be cured of scorch, so they have to be removed to prevent the disease from spreading to other bushes. This project aims to use object detection and classifier machine learning models in order to detect scorch disease with photos from intelligent drones. Images are first tiled, then processed through and convolutional neural network that detects scorch symptoms. Lastly, a fully connected neural network is implemented to make a final prediction.
Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, Mahdiyeh Soltaninejad
Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, Mahdiyeh Soltaninejad
Dissertations
The high prevalence of dental caries among children and adolescents, especially those from lower socio-economic backgrounds, is a significant nationwide health concern. Early prevention, such as dental sealants and fluoride varnish (FV), is essential, but access to this care remains limited and disparate. In this research, a national dataset is utilized to assess sealants' reach and effectiveness in preventing tooth decay, particularly focusing on 2nd molars that emerge during early adolescence, a current gap in the knowledge base. FV is recommended to be delivered during medical well-child visits to children who are not seeing a dentist. Challenges and facilitators in …
The Effect Of Fixed Time Delays On The Synchronization Phase Transition, Shaizat Bakhytzhan
The Effect Of Fixed Time Delays On The Synchronization Phase Transition, Shaizat Bakhytzhan
USF Tampa Graduate Theses and Dissertations
Nature is full of synchronization phenomena, which are essential to many scientific fields like biology, chemistry, physics, and neuroscience. The Kuramoto model is a well-known theoretical model that helps explain the fundamental ideas behind synchronization dynamics [6]. Nevertheless, in practical situations, systems frequently display intrinsic latency, which can greatly impact their behavior during synchronization. This insight inspired our work, which looks at the results of adding temporal delays to the Kuramoto model. In particular, we investigate how the system’s synchronization dynamics are affected by delays. We shed light on the mechanisms underpinning synchronization in the face of temporal delays and …
Extending Natural Mates In Euclidean 3-Space And Applications To Bertrand Pairs, Alexander Navarro
Extending Natural Mates In Euclidean 3-Space And Applications To Bertrand Pairs, Alexander Navarro
Honors Theses
In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced in relation to the natural mate. A complete characterization of co-successors is proved, followed by an application of the co-successor towards describing Bertrand curves and their mates.
Geometries Gon Wild, Naat Ambrosino
Geometries Gon Wild, Naat Ambrosino
Undergraduate Theses
A circle is mathematically defined as the collection of points a given distance away from a set point. Thus, the appearance of a circle varies dramatically across different metrics—for example, the taxicab metric (as popularized by Krause and Reynolds) has a circle that is a Euclidean square. As such, metrics can be partially defined by the appearance of their unit circles. This paper focuses on creating and analyzing an infinite set of metrics defined by their circles being regular polygons. Additionally, it provides a method of exactly generating a regular n-gon given a center, included point, and specified orientation.
Green Function In Metric Measure Spaces, Mario Bonk, Luca Capogna, Xiaodan Zhou
Green Function In Metric Measure Spaces, Mario Bonk, Luca Capogna, Xiaodan Zhou
Mathematics Sciences: Faculty Publications
We study existence and uniqueness of Green functions for the Cheeger QLaplacian in metric measure spaces that are Ahlfors Q-regular and support a Q-Poincar´e inequality with Q > 1. We prove uniqueness of Green functions both in the case of relatively compact domains, and in the global (unbounded) case. We also prove existence of global Green functions in unbounded spaces, complementing the existing results in relatively compact domains proved recently in [BBL20].
Solvability And Difficulty Of The Snake Puzzle In The Cube And Its Topological Variants, Jamie Shepard
Solvability And Difficulty Of The Snake Puzzle In The Cube And Its Topological Variants, Jamie Shepard
Honors Theses
A snake cube is a puzzle made by a sequence of n3 straight and turn pieces that can fold into a n x n x n cube. Solving the puzzle is comparable to the problem of finding a Hamiltonian path in the grid graph of the cube. By using computer algorithms, we find and count all sequences that are solutions. Furthermore, we can count the unique folding configurations of each sequence giving us an idea of its difficulty. Finally, we expand on this by exploring the problem in other topological variants of the cube, which sheds insight into the problem …
Analyzing The Effect Of Targeted Activities On Linear Concept Understanding, Jenae Rogers
Analyzing The Effect Of Targeted Activities On Linear Concept Understanding, Jenae Rogers
Honors Theses
Despite previously showing mastery of all test topics in ALEKS, Andrews’ remedial math students continue to struggle with some of them on the paper tests. After previous research, additional teaching activities, including one targeting word problems, were implemented to address student misconceptions about linear equations. My current research compares student performance on the paper tests before and after these activities on questions regarding linear relationship word problems. My findings show no statistically significant difference in student performance after these activities. These results will lead to further curriculum changes, in an attempt to increase students’ long-term conceptual understanding and problem-solving skills.
Rsa Algorithm, Evalisbeth Garcia Diazbarriga
Rsa Algorithm, Evalisbeth Garcia Diazbarriga
ATU Scholars Symposium
I will be presenting about the RSA method in cryptology which is the coding and decoding of messages. My research will focus on proving that the method works and how it is used to communicate secretly.
Data Analytics Internship At Fastenal, Jacob J. Haines
Data Analytics Internship At Fastenal, Jacob J. Haines
Research & Creative Achievement Day
The poster will present the results from an analysis of Fastenal's customer base to find characteristics among them that serve as useful predictors of their spending habits. This will allow Fastenal to create more accurate control groups when assessing the effectiveness of various marketing initiatives. This poster acts as the communication of capstone experience outcomes which is required for Data Science majors in addition to the capstone experience.
Using Data Visualizations To Analyze Employee Performance At Xcel Energy, Abby Venz
Using Data Visualizations To Analyze Employee Performance At Xcel Energy, Abby Venz
Research & Creative Achievement Day
Companies often are curious about their employee performance. But how, exactly, do they analyze this? As a Data Analytics Intern for Xcel Energy, I was in charge of doing just this. This poster will walk you through the methods used to analyze and model employee performance, as well as the results found and the different ways managers at Xcel Energy used them
My Experience As An It Data Intern, Annajo V. Vonseth
My Experience As An It Data Intern, Annajo V. Vonseth
Research & Creative Achievement Day
This poster presentation is focused on my internship as an IT Data Intern with B’nai B’rith Youth Organization (BBYO). I was able to use the skills already learned through courses here at WSU to help project and produce high-end reports. Additionally, I was in-charge of the creation of the survey all the way to creating the PowerPoint presentation with the results. I will also discuss how Microsoft Suites played a huge role in my day-to-day work, from large, complex data sets to cleaning and refining old data, I will be discussing the skills I learned during my time as an …
Finding Combinatorial Patterns In Real Valued Omics Data, Kenneth Smith
Finding Combinatorial Patterns In Real Valued Omics Data, Kenneth Smith
Dissertations
Precision medicine is a healthcare approach which tailors disease prevention and treatment to an individual, based on their genetics, environment, lifestyle, and physiological state. These factors interact to produce biological changes that can be measured to produce data called omics, and include genomics, lipidomics, and proteomics. Despite the abundance of omics data and analysis techniques, researchers still struggle to identify biological findings that replicate across data sets and translate into clinical applications. In this dissertation, we employ combinatorial optimization techniques to improve upon three steps in the precision medicine analysis pipeline: 1) data cleaning, 2) community detection, and 3) feature …