University of Nebraska-Lincoln
Louisiana Tech University
Bard College
University of Texas at Tyler
University of New Mexico
Hofstra University, Hempstead, NY 11549, USA
Missouri State University
Rhode Island College
An Extension Of The Complex–Real (C–R) Calculus To The Bicomplex Setting, With Applications,
2023
Chapman University
An Extension Of The Complex–Real (C–R) Calculus To The Bicomplex Setting, With Applications, Daniel Alpay, Kamal Diki, Mihaela Vajiac
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we extend notions of complex ℂ−ℝ-calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms.
Multiplication Operators By White Noise Delta Functions And Associated Differential Equations,
2023
Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy
Multiplication Operators By White Noise Delta Functions And Associated Differential Equations, Luigi Accardi, Un Cig Ji, Kimiaki Saitô
Journal of Stochastic Analysis
No abstract provided.
Random Variables With Overlapping Number And Weyl Algebras Ii,
2023
Missouri State University, Springfield, MO 65897, U.S.A.
Random Variables With Overlapping Number And Weyl Algebras Ii, Ruma Dutta, Gabriela Popa, Aurel Stan
Journal of Stochastic Analysis
No abstract provided.
An Explicit Construction Of Sheaves In Context,
2023
The Graduate Center, City University of New York
An Explicit Construction Of Sheaves In Context, Tyler A. Bryson
Dissertations, Theses, and Capstone Projects
This document details the body of theory necessary to explicitly construct sheaves of sets on a site together with the development of supporting material necessary to connect sheaf theory with the wider mathematical contexts in which it is applied. Of particular interest is a novel presentation of the plus construction suitable for direct application to a site without first passing to the generated grothendieck topology.
Operators Induced By Certain Hypercomplex Systems,
2023
Chapman University
Operators Induced By Certain Hypercomplex Systems, Daniel Alpay, Ilwoo Choo
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we consider a family {Ht}t∈R of rings of hypercomplex numbers, indexed by the real numbers, which contain both the quaternions and the split-quaternions. We consider natural Hilbert-space representations {(C2, πt)}t∈R of the hypercomplex system {Ht}t∈R, and study the realizations πt(h) of hypercomplex numbers h ∈ Ht, as (2 × 2)-matrices acting on C2, for an arbitrarily fixed scale t ∈ R. Algebraic, operator-theoretic, spectral-analytic, and free-probabilistic properties of them are considered.
Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods,
2023
Memorial University of Newfoundland, St Johns, NL A1C 5S7, Canada
Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods, Will Hicks
Journal of Stochastic Analysis
No abstract provided.
Modelling Nuclear Weapon Effects In Wargaming Using Monte Carlo Simulations,
2023
United States Military Academy
Modelling Nuclear Weapon Effects In Wargaming Using Monte Carlo Simulations, Tyler Guetzke, Alexander Withenbury, Zachary Dugger
West Point Research Papers
The United States Army’s interpretation of nuclear weapon effects needs change and modernization. Wargaming exercises are commonplace in today’s military, however, despite the growing threat of non-strategic nuclear weapons (NSNW), little has been done to inform battlefield commanders on their true effects. Our research seeks to develop a tool for commanders to easily interpret quantifiable effects of a NSNW. Utilizing Monte Carlo simulation, we are developing a new methodology to analyze NSNW effects. Our model allows a commander to calculate the expected unit strength following a NSNW strike which will aid in their operational decision making ability. The Monte Carlo …
Adaptive And Topological Deep Learning With Applications To Neuroscience,
2023
University of Tennessee, Knoxville
Adaptive And Topological Deep Learning With Applications To Neuroscience, Edward Mitchell
Doctoral Dissertations
Deep Learning and neuroscience have developed a two way relationship with each informing the other. Neural networks, the main tools at the heart of Deep Learning, were originally inspired by connectivity in the brain and have now proven to be critical to state-of-the-art computational neuroscience methods. This dissertation explores this relationship, first, by developing an adaptive sampling method for a neural network-based partial different equation solver and then by developing a topological deep learning framework for neural spike decoding. We demonstrate that our adaptive scheme is convergent and more accurate than DGM -- as long as the residual mirrors the …
G(10,30): A Minor-Minimal Intrinsically Knotted Graph,
2023
University of South Alabama
G(10,30): A Minor-Minimal Intrinsically Knotted Graph, Johanthan R. Herron
Theses and Dissertations
In this paper, we shall lay the groundwork for a proof of the minor-minimal intrinsic knotting of the graph G(10, 30). We show that this graph is in fact minor minimal with respect to the property of intrinsic knotting, i.e that no minor of G(10, 30) is intrinsically knotted. Moreover, we discuss the procedure for showing that G(10, 30) itself is intrinsically knotted, and provide a collection of subgraphs that can be used to aid in a proof. In this way, we hope to contribute to the growing list of known minor-minimal intrinsically knotted graphs.
Knot Equivalence,
2023
California State University, San Bernardino
Knot Equivalence, Jacob Trubey
Electronic Theses, Projects, and Dissertations
A knot is a closed curve in R3. Alternatively, we say that a knot is an embedding f : S1 → R3 of a circle into R3. Analogously, one can think of a knot as a segment of string in a three-dimensional space that has been knotted together in some way, with the ends of the string then joined together to form a knotted loop. A link is a collection of knots that have been linked together.
An important question in the mathematical study of knot theory is that of how we can tell when two knots are, or are …
Symmetric Functions Algebras (Sfa) Ii: Induced Matrices,
2023
Southern Illinois University, Carbondale, Illinois 62901, USA
Symmetric Functions Algebras (Sfa) Ii: Induced Matrices, Philip Feinsilver
Journal of Stochastic Analysis
No abstract provided.
The Theatre Of Math: The Stage As A Tool For Abstract Math Education,
2023
Bowling Green State University
The Theatre Of Math: The Stage As A Tool For Abstract Math Education, Blaine Hudak
Honors Projects
So often in the education of Mathematics does instruction solely consist of the lecture. While this can be an effective method of communicating the ideas of math, it leaves much to be desired in gathering the interest and intrigue of those who have not dedicated their lives to the study of the subject. Theatre, by contrast, is a tool that has been used in the past as means of teaching complicated and difficult to understand moral and emotional subjects. While Theatre and Mathematics have been used in combination many times in the past, it is most often done in the …
Optimal Control Problems For Stochastic Processes With Absorbing Regime,
2023
University of Connecticut, Storrs, CT 06269, USA
Optimal Control Problems For Stochastic Processes With Absorbing Regime, Yaacov Kopeliovich
Journal of Stochastic Analysis
No abstract provided.
Sl(2,Z) Representations And 2-Semiregular Modular Categories,
2023
Louisiana State University and Agricultural and Mechanical College
Sl(2,Z) Representations And 2-Semiregular Modular Categories, Samuel Nathan Wilson
LSU Doctoral Dissertations
We address the open question of which representations of the modular group SL(2,Z) can be realized by a modular category. In order to investigate this problem, we introduce the concept of a symmetrizable representation of SL(2,Z) and show that this property is necessary for the representation to be realized. We then prove that all congruence representations of SL(2,Z) are symmetrizable. The proof involves constructing a symmetric basis, which greatly aids in further calculation. We apply this result to the reconstruction of modular category data from representations, as well as to the classification of semiregular categories, which are defined via an …
Discovering Dune: Essays On Frank Herbert’S Epic Saga., Edited By Dominic J. Nardi And N. Trevor Brierly,
2023
Independent Scholar
Discovering Dune: Essays On Frank Herbert’S Epic Saga., Edited By Dominic J. Nardi And N. Trevor Brierly, G. Connor Salter
Mythlore: A Journal of J.R.R. Tolkien, C.S. Lewis, Charles Williams, and Mythopoeic Literature
G. Connor Salter reviews Discovering Dune: Essays on Frank Herbert’s Epic Saga, edited by Dominic J. Nardi and N. Trevor Brierly, considering its new contributions to studies of Frank Herbert's work. Essays included fit into four categories (Politics and Power, History and Religion, Biology and Ecology, and Philosophy, Choice and Ethics) and range from Herbert's use of ecology in Dune to how game theory may help explain certain characters' apparent ability to see the future. Discovering Dune also includes an appendix which contains the only up-to-date bibliography of Herbert's work (primary and secondary sources).
Hörmander’S L2 -Method, ∂-Problem And Polyanalytic Function Theory In One Complex Variable,
2023
Chapman University
Hörmander’S L2 -Method, ∂-Problem And Polyanalytic Function Theory In One Complex Variable, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we consider the classical ∂-problem in the case of one complex variable both for analytic and polyanalytic data. We apply the decomposition property of polyanalytic functions in order to construct particular solutions of this problem and obtain new Hörmander type estimates using suitable powers of the Cauchy-Riemann operator. We also compute particular solutions of the ∂-problem for specific polyanalytic data such as the Itô complex Hermite polynomials and polyanalytic Fock kernels.
Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience,
2023
University of Nebraska at Omaha
Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, Jordan M. Sahs, Brad Horner
UNO Student Research and Creative Activity Fair
Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy …
Modelling Illiquid Stocks Using Quantum Stochastic Calculus,
2023
Memorial University of Newfoundland, St Johns, NL A1C 5S7, Canada
Modelling Illiquid Stocks Using Quantum Stochastic Calculus, Will Hicks
Journal of Stochastic Analysis
No abstract provided.
Symmetric Functions Algebras I: Introduction And Basic Features,
2023
Southern Illinois University, Carbondale, Illinois 62901, USA
Symmetric Functions Algebras I: Introduction And Basic Features, Philip Feinsilver
Journal of Stochastic Analysis
No abstract provided.
Using Game Theory To Model Tripolar Deterrence And Escalation Dynamics,
2023
University of Nebraska - Lincoln
Using Game Theory To Model Tripolar Deterrence And Escalation Dynamics, Grace Farson
Honors Theses, University of Nebraska-Lincoln
The study investigated how game theory can been utilized to model multipolar escalation dynamics between Russia, China, and the United States. In addition, the study focused on analyzing various parameters that affected potential conflict outcomes to further new deterrence thought in a tripolar environment.
A preliminary game theoretic model was created to model and analyze escalation dynamics. The model was built upon framework presented by Zagare and Kilgour in their work ‘Perfect Deterrence’. The model is based on assumptions and rules set prior to game play. The model was then analyzed based upon these assumptions using a form of mathematical …
