Applied Mathematics Commons^™

A Uniform Chevalley Theorem For Direct Summands Of Polynomial Rings In Mixed Characteristic, Alessandro De Stefani, Eloisa Grifo, Jack Jeffries

Department of Mathematics: Faculty Publications

We prove an explicit uniform Chevalley theorem for direct summands of graded polynomial rings in mixed characteristic. Our strategy relies on the introduction of a new type of differential powers that does not require the existence of a p-derivation on the direct summand.

Bistability And Switching Behavior In Moving Animal Groups, Daniel Strömbom, Stephanie Nickerson, Catherine Futterman, Alyssa Difazio, Cameron Costello, Kolbjørn Tunstrøm

Northeast Journal of Complex Systems (NEJCS)

Moving animal groups such as schools of fish and flocks of birds frequently switch between different group structures. Standard models of collective motion have been used successfully to explain how stable groups form via local interactions between individuals, but they are typically unable to produce groups that exhibit spontaneous switching. We are only aware of one model, constructed for barred flagtail fish that are known to rely on alignment and attraction to organize their collective motion, that has been shown to generate this type of behavior in 2D (or 3D). Interestingly, another species of fish, golden shiners, do exhibit switching …

Proceedings State Of Stem 2022: How Does Virtual Hands-On Stem Work?, Cristo Leon, James Lipuma, Michele Rittenhouse, Louis Wells, Edgar Meritano, Ricardo Morales-Carbajal, Miguel Angel Bastarrachea Magnani, Ten80 Education, Llc, New Jersey School Boards Association, International Stem League, Inc (Insl), Red De Investigadores De Juegos De Rol

STEM for Success Resources

Proceedings of the "State of STEM 2022: How does virtual hands-on STEM work?"

Application Of The Riemann-Hilbert Method To Soliton Solutions Of A Nonlocal Reverse-Spacetime Sasa-Satsuma Equation And A Higher-Order Reverse-Time Nls-Type Equation, Ahmed Ahmed

USF Tampa Graduate Theses and Dissertations

For many years, the study of integrable systems has been one of the most fascinating branches of mathematics and has been thought to be an interesting area for both mathematicians and physicists alike.Many natural phenomena can be predicted by using integrable systems, particularly by studying their different solutions, as well as analyzing and exploring their properties and structures. They are commonly found in nonlinear optics, plasmas, ocean and water waves, gravitational fields, and fluid dynamics. Typical examples of integrable systems include the Korteweg-de Vries (KdV) equation, the nonlinear Schrödinger (NLS) equation, and the Kadomtsev-Petviashvili (KP) equation. Solitons are intrinsic solutions …

Image Classification Based On Sparse Representation In The Quaternion Wavelet Domain, Long H. Ngo, Nikolay Metodiev Sirakov, Marie Luong, Emmanuel Viennet

Faculty Publications

In this study, we propose a novel sparse representation learning method in the Quaternion Wavelet (QW) domain for multi-class image classification. The proposed method takes advantages from: i) the QW decomposition, which promotes sparsity and provides structural information about the image data while allowing approximate shift-invariance, to extract meaningful features from low-frequency QW subbands, ii) the dimensionality reduction method using Principal Component Analysis (PCA) for reducing the complexity of the problem, and iii) the sparse representation of the generated QW features to efficiently learn and capture the meaningful and compact information of this data. After the QW decomposition, the features …

On Efficacy And Effectiveness Of Vaccines: A Mathematical Approach Based On Conditional Probability With Applications To The Covid-19 Context, Flavius Guias

Spora: A Journal of Biomathematics

This paper presents a mathematically formalized approach which points out the relation between efficacy and effectiveness of vaccines. The first term denotes the relative degree of protection in clinical trials or under ideal conditions, while the latter is based on observed real-life data. We define the efficacy by a similar formula to the effectiveness, but the probabilities involved in the relative risk are conditional with respect to the exposure to the virus. If exposure and vaccination status are independent, the two quantities are equal. Otherwise, the observed value of the effectiveness is a biased one, as it could be seen …

Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons

Spora: A Journal of Biomathematics

We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of R₀ to changes in sociological parameter values.

Numerical Study Of Highly Efficient Centrifugal Cyclones, Murodil Madaliev

Scientific-technical journal

Centrifugal cyclones have been developing for 100 years, while the efficiency of all cyclones for fine dust does not increase by 80%. The widespread use of cyclones in all branches of industrial production is determined by the simplicity of the design and sufficient reliability in operation. Along with this, the process carried out in a cyclone presents a complex scientific problem that has not been solved from the standpoint of aerohydromechanics. This is confirmed by various cyclone designs. Currently, the efficiency of cyclone cleaning of technological flows does not meet the requirements of sanitary standards and largely determines the level …

Human Impact On Planetary Temperature And Glacial Volume: Extending A Toy Climate Model To A New Millennium, Samantha Secor, Jennifer Switkes

CODEE Journal

Starting with a toy climate model from the literature, we employ a system of two nonlinear differential equations to model the reciprocal effects of the average temperature and the percentage of glacial volume on Earth. In the literature, this model is used to demonstrate the potential for a stable periodic orbit over a long time span in the form of an attracting limit cycle. In the roughly twenty five years since this model appeared in the literature, the effects of global warming and human-impacted climate change have become much more well known and apparent. We demonstrate modification of initial conditions …

Translation Of: Dupin’Sche Hyperflächen, Doctoral Dissertation, Universität Freiburg (1981) By Ulrich Pinkall, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

This is an unofficial translation of the original dissertation which was written in German. A few minor typographical errors have been corrected by the translator. All references should be made to the original dissertation. The classification of Dupin hypersurfaces in E⁴ contained in this dissertation is also contained in the journal article by Ulrich Pinkall, Dupin’sche Hyperflächen in E⁴, Manuscr. Math. 51 (1985), 89–119.

P-Periodic Solutions Of A Q-Integral Equation With Finite Delay, Muhammad N. Islam, Jeffrey T. Neugebauer

EKU Faculty and Staff Scholarship

A Volterra type integral equation with a finite delay is considered on a discrete nonadditive time scale domain q(N0) = {q(n) : n is an element of N-0}, where k is an element of N, q > 1. The existence of periodic solutions of this equation, which we call a q-integral equation, are shown employing the contraction mapping principle and a fixed point theorem due to Krasnosel'skii.

Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer, Jose Alvarez, Kathleen M. Storey, Pavitra Kannan, Heyrim Cho

Spora: A Journal of Biomathematics

Radiation therapy remains as one of the main cancer treatment modalities. Typical regimens for radiotherapy comprise a constant dose administered on weekdays, and no radiation on weekends. In this paper, we examine adaptive dosages of radiation treatment strategies for heterogeneous tumors using a dynamical system model that consist of radiation-resistant and parental populations with unique interactive properties, namely, PC3 and DU145 prostate cancer cell lines. We show that stronger doses of radiation given in longer time intervals, while keeping the overall dosage the same, are effective in PC3 cell lines, but not in DU145 cell lines. In addition, we tested …

Lefschetz Properties Of Some Codimension Three Artinian Gorenstein Algebras, Nancy Abdallah, Nasrin Altafi, Anthony Iarrobino, Alexandra Seceleanu, Joachim Yaméogo

Department of Mathematics: Faculty Publications

Codimension two Artinian algebras A have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three AG algebras - the most promising results so far have concerned the weak Lefschetz property for such algebras. We here show that every standard-graded codimension three Artinian Gorenstein algebra A having low maximum value of the Hilbert function - at most six - has the strong Lefschetz property, provided that the characteristic is zero. When the characteristic is greater than the socle degree of …

Classification And Keyword Identification Of Covid 19 Misinformation On Social Media: A Framework For Semantic Analysis, Grace Y. Smith

Theses and Dissertations

The growing surge of misinformation among COVID-19 communication can pose great hindrance to truth, magnify distrust in policy makers and/or degrade authorities’ credibility, and it can even harm public health. Classification of textual context on social media data relating to COVID-19 is an effective tool to combat misinformation on social media platforms. In this research, Twitter data was leveraged to 1) develop classification methods to detect misinformation and identify Tweet sentiment with respect to COVID-19 and 2) develop a human-in-the-loop interactive framework to enable identification of keywords associated with social context, here, being misinformation regarding COVID-19. 1) Six fusion-based classification …

Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper

Honors Program: Senior Projects (Public)

Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of …

An Optimization Model For Minimization Of Systemic Risk In Financial Portfolios, Zachary Alexander Gelber

Master's Theses

In this thesis, we study how sovereign credit default swaps are able to measure systemic risk as well as how they can be used to construct optimal portfolios to minimize risk. We define the clustering coefficient as a proxy for systemic risk and design an optimization problem with the goal of minimizing the mean absolute deviation of the clustering coefficient on a group of nine European countries. Additionally, we define a metric we call the diversity score that measures the diversification of any given portfolio. We solve this problem for a baseline set of parameters, then spend the remainder of …

Covid-19 Pandemic Analysis By The Volterra Integral Equation Models: A Preliminary Study Of Brazil, Italy, And South Africa, Yajni Warnapala, Emma Dehetre, Kate Gilbert

Arts & Sciences Faculty Publications

The COVID-19 pandemic has affected many people throughout the world. The objective of this research project was to find numerical solutions through the Gaussian Quadrature Method for the Volterra Integral Equation Model. The non-homogenous Volterra Integral Equation of the second kind is used to capture a broader range of disease distributions. Volterra Integral equation models are used in the context of applied mathematics, public health, and evolutionary biology. The mathematical models of this integral equation gave valid convergence results for the COVID-19 data for 3 countries Italy, South Africa and Brazil. The modeling of these countries was done using the …

Framing And Mapping A Project To The Five Elements And Systems Change While Developing A Project Proposal, Cristo Leon, James Lipuma

STEM for Success Resources

Presentation at the “Office Hour Featuring Caitlin Howley and Cristo Leon”

NSF INCLUDES National Network

Resilient Modulus Of Siliciclastic Unbound Granular Materials Under Repeated Wheel Loading, Siya Rimoyi

Tanzania Journal of Engineering and Technology (TJET)

The Resilient Modulus (Mr) is a fundamental material property input in modern Mechanistic-Empirical (M-E) pavements structural design. Empirical pavement design methods have been in use over a long period during which large databases of four- days-soaked California Bearing Ratio (CBR) values at or near the Maximum Dry Density have been generated in the strength assessments for Unbound Granular Materials (UGMs). In the adoption of the M-E design approach researchers have so far attempted with various degrees of success to develop models to derive resilient modulus from the conventional CBR-based databases. This study provides an extensive laboratory experimental study to investigate …

Real-Time Complex Hand Gestures Recognition Based On Multi- Dimensional Features, Isack Bulugu

Tanzania Journal of Engineering and Technology (TJET)

Gesture recognition is broadly utilized within the field of sensing. There are basically three gesture recognition methods based on computer vision, depth sensor and motion sensor. Motion sensor-based gesture recognition has few input data, fast speed, and direct access to three- dimensional information of the hand. The advantages of traditional motion sensor-based gesture recognition have gradually become a current research hotspot. The essence of traditional motion sensor-based gesture recognition is a pattern recognition problem, and its accuracy depends heavily on the feature dataset extracted from prior experience. Unlike traditional pattern recognition methods, deep learning can be used to a large …