Mathematics Commons^™

On Extending Hansel's Theorem To Hypergraphs, Gregory Sutton Churchill

USF Tampa Graduate Theses and Dissertations

For integers $n \geq k \geq 2$, let $V$ be an $n$-element set, and let $\binom{V}{k}$ denote the family of all $k$-element subsets of $V$. For disjoint subsets $A, B \subseteq V$, we say that $\{A, B\}$ {\it covers} an element $K \in \binom{V}{k}$ if $K \subseteq A \dot\cup B$ and $K \cap A \neq \emptyset \neq K \cap B$. We say that a collection $\cC$ of such pairs {\it covers} $\binom{V}{k}$ if every $K \in \binom{V}{k}$ is covered by at least one $\{A, B\} \in \cC$. When $k=2$, covers $\cC$ of $\binom{V}{2}$ were introduced in~1961 by R\'enyi~\cite{Renyi}, where they …

A Geometric Formulation Of Lax Integrability For Nonlinear Equationsin Two Independent Variables, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

A geometric formulation of Lax integrability is introduced which makes use of a Pfaffan formulation of Lax integrability. The Frobenius theorem gives a necessary and suffcient condition for the complete integrability of a distribution, and provides a powerful way to study nonlinear evolution equations. This permits an examination of the relation between complete integrability and Lax integrability. The prolongation method is formulated in this context and gauge transformations can be examined in terms of differential forms as well as the Frobenius theorem.

Borges And The Subjective-Idealism In Relativity Theory And Quantum Mechanics, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper is intended to be a follow-up to our previous paper with title: "Reinterpreting Tlon, Uqbar, Orbis Tertius: On the antirealism tendency in modern physics." We will give more background for our propositions in the previous paper. Our message here is quite simple: allow us to remind fellow physicists and cosmologists to become more aware of Berkeley-idealism tendency, which can lead us to so many distractions instead of bringing us closer to the truth. We observe that much of the progress of modern physics in the last few decades only makes us as confused as before, but at a …

The Classification Of Infinite Abelian Groups With Partial Decomposition Bases In L∞Ω, Carol Jacoby, Peter Loth

Mathematics Faculty Publications

We consider the class of abelian groups with partial decomposition bases, which includes groups classified by Ulm, Warfield, Stanton and others. We define an invariant and classify these groups in the language L∞ω, or equivalently, up to partial isomorphism. This generalizes a result of Barwise and Eklof and builds on Jacoby's classification of local groups with partial decomposition bases in L∞ω.

Relativity From Mathematics Or Why Newton Could Have Beaten Einstein To The Punch, Diego Castano

Mathematics Colloquium Series

Special Relativity was developed by Albert Einstein and relied crucially on Electromagnetism, a theory not fully developed until 1873. Yet there is nothing in the basic theory's development that requires physics beyond what Newton knew. A derivation of the theory based on Newton's laws and mathematical consistency is presented.

Convergence Analysis And Error Estimates For A Second Order Accurate Finite Element Method For The Cahn–Hilliard–Navier–Stokes System, Amanda E. Diegel, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn–Hilliard–Navier–Stokes equations with matched densities. the scheme combines a standard second order Crank–Nicolson method for the Navier–Stokes equations and a modification to the Crank–Nicolson method for the Cahn–Hilliard equation. in particular, a second order Adams-Bashforth extrapolation and a trapezoidal rule are included to help preserve the energy stability natural to the Cahn–Hilliard equation. We show that our scheme is unconditionally energy stable with respect to a modification of the continuous free energy of the PDE system. Specifically, the discrete phase variable is shown …

Combustion-Derived Nanoparticles, The Neuroenteric System, Cervical Vagus, Hyperphosphorylated Alpha Synuclein And Tau In Young Mexico City Residents, Lilian Calderón-Garcidueñas, Rafael Reynoso-Robles, Beatriz Pérez-Guillé, Partha S. Mukherjee, Angélica Gónzalez-Maciel

Mathematics Faculty Publications and Presentations

Mexico City (MC) young residents are exposed to high levels of fine particulate matter (PM_2.5), have high frontal concentrations of combustion-derived nanoparticles (CDNPs), accumulation of hyperphosphorylated aggregated α-synuclein (α-Syn) and early Parkinson's disease (PD). Swallowed CDNPs have easy access to epithelium and submucosa, damaging gastrointestinal (GI) barrier integrity and accessing the enteric nervous system (ENS). This study is focused on the ENS, vagus nerves and GI barrier in young MC v clean air controls. Electron microscopy of epithelial, endothelial and neural cells and immunoreactivity of stomach and vagus to phosphorylated ɑ-synuclein Ser129 and Hyperphosphorylated-Tau (Htau) …

Biomarkers Of Cardiovascular Disease, Ying Huang, Kailash Gulshan, Truc Nguyen, Yuping Wu

Mathematics and Statistics Faculty Publications

No abstract provided.

2017: "Lighting Up The Night", Shyam Sai, Istvan Kovach, Abhay Gupta, James Wei

Distinguished Student Work

Drone technology is beginning to permeate many aspects of life in the modern world, and for good reason. Delivery drones can efficiently deliver packages better than any existing methods. Medical drones can reach emergency patients faster than any ambulance. Security drones can surveil areas more quickly and more thoroughly than a team of human guards. The advent of commercial and industrial uses for drones, however, begets the vital question of how can drones be used outside the workplace. Intel's answer? Entertainment.

Thus, the Intel Shooting Star^TM drone was born, a quadcopter explicitly built for producing breathtaking aerial light shows …

2017: "The Wasatch Range Ski-Matic", Andy Liu, Bert Cao, Joshua Eberhardt, Allen Chen

Distinguished Student Work

Ski resorts are very popular among both avid skiers and families who are looking to have fun. In fact, winter resorts account for over 3 billion dollars in revenue, with an annual growth of 2.6% [IBI]. In addition to their use as recreational areas, ski resorts are also used for various winter competitions, most famously the Olympics. Our job was to design and create a suitable ski resort for both the Olympics and for recreational use in the Wasatch Peaks Range property. In addition, we were advised to create over 160km of trails and maintain a 20%- 40%-40% balance between …

2017: Himcm International Mathematics Modeling Contest: Finalist Rating, Aryan Walia, Katie Lu, Mia Ye, Kevin Mikos

Distinguished Student Work

The integration of drones for light shows, alongside modes of delivery, have seen soaring popularity with modernity: both literally and physically. With the employment of drones in events like the Superbowl, and Intel light shows, drones’ uses have widespread implications that are quickly gaining momentum. In an order to implement these drones in light shows, adherence to regulations alongside quantifying and monitoring the path for a set number of drones is crucial.

For an outdoor aerial light show that will display a Ferris wheel, a dragon, and another unique image, various factors need to be taken into account including the …

2017: Himcm International Mathematics Modeling Contest: Meritorious Rating, Spoorthi Jakka, Claire Wang, Amy Wang, Claudia Zhu '18

Distinguished Student Work

Restatement of the Problem:

The integration of drones for light shows, alongside modes of delivery, have seen soaring popularity with modernity: both literally and physically. With the employment of drones in events like the Superbowl, and Intel light shows, drones’ uses have widespread implications that are quickly gaining momentum. In an order to implement these drones in light shows, adherence to regulations alongside quantifying and monitoring the path for a set number of drones is crucial.

For an outdoor aerial light show that will display a Ferris wheel, a dragon, and another unique image, various factors need to be taken …

A High Quality, Eulerian 3d Fluid Solver In C++, Lejon Anthony Mcgowan

Computer Science and Software Engineering

Fluids are a part of everyday life, yet are one of the hardest elements to properly render in computer graphics. Water is the most obvious entity when thinking of what a fluid simulation can achieve (and it is indeed the focus of this project), but many other aspects of nature, like fog, clouds, and particle effects. Real-time graphics like video games employ many heuristics to approximate these effects, but large-scale renderers aim to simulate these effects as closely as possible.

In this project, I wish to achieve effects of the latter nature. Using the Eulerian technique of discrete grids, I …

Cardinal Characteristics And Countable Borel Equivalence Relations, Samuel Coskey, Scott Schneider

Mathematics Faculty Publications and Presentations

Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we introduce a family of properties of countable Borel equivalence relations which correspond to combinatorial cardinal characteristics of the continuum in the same way that Borel boundedness corresponds to the bounding number ��. We analyze some of the basic behavior of these properties, showing, e.g., that the property corresponding to the splitting number �� coincides with smoothness. We then settle many of the implication relationships between the properties; …

Perpetual Integral Functionals Of Brownian Motion And Blowup Of Semilinear Systems Of Spdes, Eugenio Guerrero, José Alfredo López-Mindela

Communications on Stochastic Analysis

No abstract provided.

The Moments Of Lévy's Area Using A Sticky Shuffle Hopf Algebra, Robin Hudson, Uwe Schauz, Yue Wu

Communications on Stochastic Analysis

No abstract provided.

A Note On Time-Dependent Additive Functionals, Adrien Barrasso, Francesco Russo

Communications on Stochastic Analysis

No abstract provided.

Essential Sets For Random Operators Constructed From An Arratia Flow, Andrey A. Dorogovtsev, Ia. A. Korenovska

Communications on Stochastic Analysis

No abstract provided.

One Dimensional Complex Ornstein-Uhlenbeck Operator, Yong Chen

Communications on Stochastic Analysis

No abstract provided.

Hybrid Extended Kalman Filtering And Noise Statistics Optimization For Produce Wash State Estimation, Vahid Azimi, Daniel Munther, Seyed Abolfazl Fakoorian, Thang Tien Nguyen, Daniel J. Simon

Mathematics and Statistics Faculty Publications

Food-borne diseases associated with fresh produce consistently cause serious public health issues. Although sanitization measures are utilized to enhance the safety of fresh produce, strategies that neglect the dynamic nature of commercial wash processes are limited, creating the potential for pathogen cross-contamination and major disease outbreaks. In light of this risk, there is an urgent need for new control approaches during produce washing to reduce the probability of outbreaks. As an important step in this direction, a hybrid extended Kalman filter (HEKF) and particle swarm optimization (PSO)-based noise statistics optimization are designed for a produce wash system. The HEKF uses …