Discrete Wiener Algebra In The Bicomplex Setting, Spectral Factorization With Symmetry, And Superoscillations,
2023
Chapman University
Discrete Wiener Algebra In The Bicomplex Setting, Spectral Factorization With Symmetry, And Superoscillations, Daniel Alpay, Izchak Lewkowicz, Mihaela Vajiac
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we present parallel theories on constructing Wiener algebras in the bicomplex setting. With the appropriate symmetry condition, the bicomplex matrix valued case can be seen as a complex valued case and, in this matrix valued case, we make the necessary connection between bicomplex analysis and complex analysis with symmetry. We also write an application to superoscillations in this case.
An Explicit Construction Of Sheaves In Context,
2023
CUNY Graduate Center
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.
Pairings In A Ring Spectrum-Based Bousfield-Kan Spectral Sequence,
2023
CUNY Graduate Center
Pairings In A Ring Spectrum-Based Bousfield-Kan Spectral Sequence, Jonathan Toledo
Dissertations, Theses, and Capstone Projects
Bousfield and Kan traditionally formulated their homotopy spectral sequence over a simplicial set X resolved with respect to a ring R. By considering an adequate category of ring spectra, one can take a ring spectrum E, create from it a functor of a triple on the category of simplicial sets, and build a cosimplicial simplicial set EX. The homotopy spectral sequence can then be formed over such cosimplicial spaces by a similar construction to the original. Pairings can be established on these spectral sequences, and, for nice enough spaces, these pairings on the E2-terms coincide with certain …
Quantifying Separability In Limit Groups,
2023
CUNY Graduate Center
Quantifying Separability In Limit Groups, Keino Brown
Dissertations, Theses, and Capstone Projects
We show that for any finitely generated non-abelian subgroup H of a limit group L, there exists a finite-index subgroup K which is fully residually H. This generalizes the result of Wilton that limit groups admit local retractions. We also show that for any finitely generated subgroup of a limit group, there is a finite-dimensional representation of the limit group which separates the subgroup in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate a finitely generated subgroup in a limit group. This generalizes results of Louder, …
Abstract Algebra: An Inquiry-Based Approach, Second Edition, Supplemental Material,
2023
St. Edward's University
Abstract Algebra: An Inquiry-Based Approach, Second Edition, Supplemental Material, Jonathan K. Hodge, Steven Schlicker, Ted Sundstrom
Open Textbooks
This text is a supplement to Abstract Algebra: An Inquiry-Based Approach, Second Edition. It includes applications of algebra to RSA encryption, check digits, the games of NIM and the 15 Puzzle, and the determination of groups of small order. In addition, reference material that could be useful for some students appears in the appendices, such as background material on functions, methods of proof (including the equivalencies of the Well-Ordering Principle and different versions of mathematical induction), and complex roots of unity. The appendices also contain a complete proof that polynomial rings are rings, a proof of the Fundamental Theorem of …
Hospital-Acquired Pressure Injuries In Adults With Prone Positioning Using Manual Method Versus Specialty Bed: A Retrospective Comparison Cohort Study,
2023
St. Joseph's Medical Center, Stockton
Hospital-Acquired Pressure Injuries In Adults With Prone Positioning Using Manual Method Versus Specialty Bed: A Retrospective Comparison Cohort Study, Jacqueline M. Demellow, Harbir Dhillon, Mouchumi Bhattacharyya, Daniel Pacitto, Teri M. Kozik
Pacific Faculty Work
Purpose: The purpose of this study was to compare the incidence of hospital-acquired pressure injuries (HAPIs) in patients with acute respiratory distress syndrome (ARDS) and placed in a prone position manually or using a specialty bed designed to facilitate prone positioning. A secondary aim was to compare mortality rates between these groups. Design: Retrospective review of electronic medical records. SUBJECTS AND SETTING: The sample comprised 160 patients with ARDS managed by prone positioning. Their mean age was 61.08 years (SD = 12.73); 58% (n = 96) were male. The study setting was a 355-bed community hospital in the Western United …
Production Functions Of Ncaa Men And Women Water Polo Matches,
2023
University of the Pacific
Production Functions Of Ncaa Men And Women Water Polo Matches, Joey Gullikson, Lewis R. Gale, John Mayberry, Lara Killick, John Kim
College of the Pacific Faculty Articles
Previous research has adapted the use of economic production functions to estimate the scoring production of teams in professional sports. Most of these studies have focused on professional male team sports, most notably, US baseball, basketball, and association football. This study adds to the literature by utilizing a new and distinctive data set of shooting statistics from 88 men’s and 38 women’s NCAA water polo contests to estimate production functions for United States’ collegiate water polo games and identify the most important variables for predicting margin of victory in such competitions. The results show that shots on goal, average shot …
Flow Patterns For Newtonian And Non-Newtonian Fluids In A Cylindrical Pipe,
2023
The University of Texas Rio Grande Valley
Flow Patterns For Newtonian And Non-Newtonian Fluids In A Cylindrical Pipe, Erick Sanchez, Dambaru Bhatta
School of Mathematical & Statistical Sciences Faculty Publications
A fully developed laminar steady flow of an incompressible, viscous fluid in a horizontal cylindrical pipe is considered here. Flow patterns for an incompressible, viscous fluid for both Newtonian and non-Newtonian fluids such as shear-thinning, shear-thickening and Bingham plastic fluids are analyzed in this study. Assuming that the flow is only due to the wall shear stress and the pressure drop, the velocity component in the axial direction for these cases is derived. Computational results of the velocity profiles for various cases are obtained using MATLAB and presented in graphical forms. It is observed that the velocity profile is parabolic …
The Coupled Modified Yajima–Oikawa System: Model Derivation And Soliton Solutions,
2023
The University of Texas Rio Grande Valley
The Coupled Modified Yajima–Oikawa System: Model Derivation And Soliton Solutions, Junchao Chen, Bao-Feng Feng, Ken-Ichi Maruno
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we consider a coupled modified Yajima–Oikawa (YO) system which describes the nonlinear resonant interaction between one long wave (LW) and two short waves (SWs). It is shown that this coupled system can be derived from a three-component modified nonlinear Schrödinger equations through asymptotic reductions. Furthermore, the bright, dark multi-soliton and multi-breather solutions in terms of determinants are obtained respectively by virtue of the bilinear Kadomtsev–Petviashvili-hierarchy reduction technique. The detailed analysis of dynamical properties for one- and two-solitons and breathers is performed, which show the interesting collision properties for the bright and dark solitons. Particularly, differing from …
Deep Learning Recommendations For The Acl2 Interactive Theorem Prover,
2023
California Polytechnic State University, San Luis Obispo
Deep Learning Recommendations For The Acl2 Interactive Theorem Prover, Robert K. Thompson, Robert K. Thompson
Master's Theses
Due to the difficulty of obtaining formal proofs, there is increasing interest in partially or completely automating proof search in interactive theorem provers. Despite being a theorem prover with an active community and plentiful corpus of 170,000+ theorems, no deep learning system currently exists to help automate theorem proving in ACL2. We have developed a machine learning system that generates recommendations to automatically complete proofs. We show that our system benefits from the copy mechanism introduced in the context of program repair. We make our system directly accessible from within ACL2 and use this interface to evaluate our system in …
Groups Of Non Positive Curvature And The Word Problem,
2023
California Polytechnic State University, San Luis Obispo
Groups Of Non Positive Curvature And The Word Problem, Zoe Nepsa
Master's Theses
Given a group $\Gamma$ with presentation $\relgroup{\scr{\scr{A}}}{\scr{R}}$, a natural question, known as the word problem, is how does one decide whether or not two words in the free group, $F(\scr{\scr{A}})$, represent the same element in $\Gamma$. In this thesis, we study certain aspects of geometric group theory, especially ideas published by Gromov in the late 1980's. We show there exists a quasi-isometry between the group equipped with the word metric, and the space it acts on. Then, we develop the notion of a CAT(0) space and study groups which act properly and cocompactly by isometries on these spaces, such groups …
Topics On Asymmetric Classification,
2023
New Jersey Institute of Technology
Topics On Asymmetric Classification, Subhrasish Chakraborty
Dissertations
Asymmetric classification refers to a situation where the cost of misclassifying one class is significantly higher than the cost of misclassifying the other class. This problem is common in many real-world scenarios, such as medical diagnosis or fraud detection. In this dissertation two of the common types of asymmetric classification problems have been dealt with — imbalanced classification and ordinal classification. An example of imbalanced classification is to detect fraudulent credit card transactions where the distribution of the normal and fraud transactions are extremely skewed. On the other hand, ordinal classification, also known as ordinal regression, is widely used in …
Bright Light Therapy And Depression: Assessing Suitability Using Entrainment Maps,
2023
New Jersey Institute of Technology
Bright Light Therapy And Depression: Assessing Suitability Using Entrainment Maps, Charles A. Mainwaring
Theses
Bright Light Therapy has been shown to be efficacious to mood disorders including Major Depression. Researchers use the Jewett-Forger-Kronauer model of the circadian rhythm with the Unified Model of melatonin including a mathematical term implementing feedback from the melatonin system into the circadian system to quantify the effects of bright light. Early investigations into intrinsic period, light sensitivity, and the circadian pacemaker's sensitivity to blood melatonin concentration may be indicators of subsets of patients with long intrinsic periods exhibiting symptoms of depression.
A Survey On Online Matching And Ad Allocation,
2023
New Jersey Institute of Technology
A Survey On Online Matching And Ad Allocation, Ryan Lee
Theses
One of the classical problems in graph theory is matching. Given an undirected graph, find a matching which is a set of edges without common vertices. In 1990s, Richard Karp, Umesh Vazirani, and Vijay Vazirani would be the first computer scientists to use matchings for online algorithms [8]. In our domain, an online algorithm operates in the online setting where a bipartite graph is given. On one side of the graph there is a set of advertisers and on the other side we have a set of impressions. During the online phase, multiple impressions will arrive and the objective of …
A Strong-Type Furstenberg–Sárközy Theorem For Sets Of Positive Measure,
2023
Chapman University
A Strong-Type Furstenberg–Sárközy Theorem For Sets Of Positive Measure, Polona Durcik, Vjekoslav Kovač, Mario Stipčić
Mathematics, Physics, and Computer Science Faculty Articles and Research
For every β ∈ (0,∞), β ≠ 1, we prove that a positive measure subset A of the unit square contains a point (x0, y0) such that A nontrivially intersects curves y − y0 = a(x −x0)β for a whole interval I ⊆ (0,∞) of parameters a ∈ I . A classical Nikodym set counterexample prevents one to take β = 1, which is the case of straight lines. Moreover, for a planar set A of positive density, we show that the interval I can be arbitrarily large on the logarithmic scale. These results can …
Decomposition Of Beatty And Complementary Sequences,
2023
Smith College
Decomposition Of Beatty And Complementary Sequences, Geremías Polanco
Mathematics Sciences: Faculty Publications
In this paper we express the difference of two complementary Beatty sequences, as the sum of two Beatty sequences closely related to them. In the process we introduce a new Algorithm that generalizes the well known Minimum Excluded algorithm and provides a method to generate combinatorially any pair of complementary Beatty sequences.
Motion Planning Algorithm In A Y-Graph,
2023
Wright College, City Colleges, Chicago
Motion Planning Algorithm In A Y-Graph, David Baldi
Rose-Hulman Undergraduate Mathematics Journal
We present an explicit algorithm for two robots to move autonomously and without collisions on a track shaped like the letter Y. Configuration spaces are of practical relevance in designing safe control schemes for automated guided vehicles. The topological complexity of a configuration space is the minimal number of continuous instructions required to move robots between any initial configuration to any final one without collisions. Using techniques from topological robotics, we calculate the topological complexity of two robots moving on a Y-track and exhibit an optimal algorithm realizing this exact number of instructions given by the topological complexity.
Δ-Small Intersection Graphs Of Modules,
2023
Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq
Δ-Small Intersection Graphs Of Modules, Ahmed H. Alwan
Al-Bahir
Let R be a commutative ring with unit and M be a unitary left R-module. The δ-small intersection graph of non-trivial submodules of , denoted by , is an undirected simple graph whose vertices are the non-trivial submodules of , and two vertices are adjacent if and only if their intersection is a -small submodule of . In this article, we study the interplay between the algebraic properties of , and the graph properties of such as connectivity, completeness and planarity. Moreover, we determine the exact values of the diameter and girth of , as well as give a formula …
Using Deep Neural Networks To Classify Astronomical Images,
2023
Seattle Pacific University
Using Deep Neural Networks To Classify Astronomical Images, Andrew D. Macpherson
Honors Projects
As the quantity of astronomical data available continues to exceed the resources available for analysis, recent advances in artificial intelligence encourage the development of automated classification tools. This paper lays out a framework for constructing a deep neural network capable of classifying individual astronomical images by describing techniques to extract and label these objects from large images.
Identifiability Of Phylogenetic Models,
2023
College of the Holy Cross
Identifiability Of Phylogenetic Models, Thomas J. Yacovone
Math and Computer Science Honors Theses
An algebraic statistical model is a parametrized family of probability distributions. Identifiability is a crucial property of a statistical model; when it holds, probability distributions in the model uniquely determine the parameters that produce them. In phylogenetics, models that are identifiable can be used to ascertain evolutionary relationships between species based on observed data, such as amino acid and DNA sequence data. However, global identifiability is a strong condition that may not always hold. A discrete parameter of a model is said to be generically identifiable if the set of probability distributions that do not uniquely determine the discrete parameter …
