Combinatorial Identities Associated With A Bivariate Generating Function For Overpartition Pairs, 2023 The University of Texas Rio Grande Valley

#### Combinatorial Identities Associated With A Bivariate Generating Function For Overpartition Pairs, Atul Dixit, Ankush Goswami

*Mathematical and Statistical Sciences Faculty Publications and Presentations*

We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with N(r,s,m,n), a function counting certain overpartition pairs recently introduced by Bringmann, Lovejoy and Osburn. For example, one of our identities gives a closed-form evaluation of a double series in terms of Chebyshev polynomials of the second kind, thereby resulting in an analogue of Euler's pentagonal number theorem. Another of our results expresses a multi-sum involving N(r,s,m,n) in terms of just the partition function ...

Spectral Sequences And Khovanov Homology, 2023 Dartmouth College

#### Spectral Sequences And Khovanov Homology, Zachary J. Winkeler

*Dartmouth College Ph.D Dissertations*

In this thesis, we will focus on two main topics; the common thread between both will be the existence of spectral sequences relating Khovanov homology to other knot invariants. Our first topic is an invariant *MKh(L)* for links in thickened disks with multiple punctures. This invariant is different from but inspired by both the Asaeda-Pryzytycki-Sikora (APS) homology and its specialization to links in the solid torus. Our theory will be constructed from a *Z^n*-filtration on the Khovanov complex, and as a result we will get various spectral sequences relating *MKh(L)* to *Kh(L)*, *AKh(L)*, and ...

Geometry And Dynamics Of Rolling Systems, 2022 Washington University in St. Louis

#### Geometry And Dynamics Of Rolling Systems, Bowei Zhao

*Arts & Sciences Electronic Theses and Dissertations*

Billiard systems, broadly speaking, may be regarded as models of mechanical systems in which rigid parts interact through elastic impulsive collision forces. When it is desired or necessary to account for linear/angular momentum exchange in collisions involving a spherical body, a type of billiard system often referred to as no-slip has been used. Previous work indicated that no-slip billiards resemble non-holonomic systems, speciﬁcally, systems consisting of a ball rolling on surface. In prior research, such connections were only observed numerically and were restricted to very special surfaces. In this thesis, it is shown that no-slip billiard and rolling systems ...

Data Visualization, Dimensionality Reduction, And Data Alignment Via Manifold Learning, 2022 Utah State University

#### Data Visualization, Dimensionality Reduction, And Data Alignment Via Manifold Learning, Andrés Felipe Duque Correa

*All Graduate Theses and Dissertations*

The high dimensionality of modern data introduces significant challenges in descriptive and exploratory data analysis. These challenges gave rise to extensive work on dimensionality reduction and manifold learning aiming to provide low dimensional representations that preserve or uncover intrinsic patterns and structures in the data. In this thesis, we expand the current literature in manifold learning developing two methods called DIG (Dynamical Information Geometry) and GRAE (Geometry Regularized Autoencoders). DIG is a method capable of finding low-dimensional representations of high-frequency multivariate time series data, especially suited for visualization. GRAE is a general framework which splices the well-established machinery from kernel ...

The History Of Mathematics: A Source-Based Approach, Volume Ii (Book Review), 2022 Dordt University

#### The History Of Mathematics: A Source-Based Approach, Volume Ii (Book Review), Calvin Jongsma

*Faculty Work Comprehensive List*

Reviewed Title: *The History of Mathematics: A Source-Based Approach, Volume II *by June Barrow-Green, Jeremy Gray, and Robin Wilson. Providence, Rhode Island: MAA Press, an imprint of the American Mathematical Society, 2022. 687 pp. ISBN: 978-1-4704-4382-5

Mathematics In The Woods: Exploring Low-Income Parents’ Perceptions Of And Involvement In Their Children’S Mathematical Learning, 2022 St.John's University

#### Mathematics In The Woods: Exploring Low-Income Parents’ Perceptions Of And Involvement In Their Children’S Mathematical Learning, Lulu Sun

*Northwest Journal of Teacher Education*

This article features data from a three-day mathematics camping trip that offered parents and their children time and space to enjoy non-digital activities and mathematics-building tasks. Drawing upon data from a larger qualitative study of children and their parents, this article specifically focuses on 10 parents’ perceptions of their children’s mathematics learning, problem-solving, and wellbeing. Findings suggest that, although parents are interested in their children’s mathematics learning, they are most concerned with their children’s development of problem-solving abilities and social skills. Moreover, students’ own learning experience is important for their mathematics learning.

On Rainbow Cycles And Proper Edge Colorings Of Generalized Polygons, 2022 Middle Georgia State University

#### On Rainbow Cycles And Proper Edge Colorings Of Generalized Polygons, Matt Noble

*Theory and Applications of Graphs*

An edge coloring of a simple graph G is said to be *proper rainbow-cycle-forbidding* (PRCF, for short) if no two incident edges receive the same color and for any cycle in G, at least two edges of that cycle receive the same color. A graph G is defined to be *PRCF-good* if it admits a PRCF edge coloring, and G is deemed *PRCF-bad* otherwise. In recent work, Hoffman, et al. study PRCF edge colorings and find many examples of PRCF-bad graphs having girth less than or equal to 4. They then ask whether such graphs exist having girth greater than ...

On The Uniqueness Of Continuation Of A Partially Defined Metric, 2022 Institute of Applied Mathematics and Mechanics of the NAS of Ukraine

#### On The Uniqueness Of Continuation Of A Partially Defined Metric, Evgeniy Petrov

*Theory and Applications of Graphs*

The problem of continuation of a partially defined metric can be efficiently studied using graph theory. Let $G=G(V,E)$ be an undirected graph with the set of vertices $V$ and the set of edges $E$. A necessary and sufficient condition under which the weight $w\colon E\to\mathbb R^+$ on the graph $G$ has a unique continuation to a metric $d\colon V\times V\to\mathbb R^+$ is found.

Extension Of Fundamental Transversals And Euler’S Polyhedron Theorem, 2022 University of South Florida

#### Extension Of Fundamental Transversals And Euler’S Polyhedron Theorem, Joy Marie D'Andrea

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Solving Clostridioides Difficile: Mathematical Models Of Transmission And Control In Healthcare Settings, 2022 Lewis University

#### Solving Clostridioides Difficile: Mathematical Models Of Transmission And Control In Healthcare Settings, Cara Sulyok, Max Lewis, Laila Mahrat, Brittany Stephenson, Malen De La Fuente Arruabarrena, David Kovalev, Justyna Sliwinska

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Modularity And Boolean Network Decomposition, 2022 University of Florida

#### Modularity And Boolean Network Decomposition, Matthew Wheeler

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Canalization And Other Design Principles Of Gene Regulatory Networks, 2022 Illinois State University

#### Canalization And Other Design Principles Of Gene Regulatory Networks, Claus Kadelka

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Stochastic Models Of Zoonotic Avian Influenza With Multiple Hosts, Environmental Transmission, And Migration In The Natural Reservoir, 2022 Illinois State University

#### Stochastic Models Of Zoonotic Avian Influenza With Multiple Hosts, Environmental Transmission, And Migration In The Natural Reservoir, Kaia Smith

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Model-Free Identification Of Relevant Variables From Response Data, 2022 University of Dayton

#### Model-Free Identification Of Relevant Variables From Response Data, Alan Veliz-Cuba, David Murrugarra

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, 2022 Illinois State University

#### On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, Prihantini Prihantini

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Collation Model For Ljs 232: Trattato Delle Proportioni Et Proportionalità, 2022 University of Pennsylvania

#### Collation Model For Ljs 232: Trattato Delle Proportioni Et Proportionalità, Dot Porter

*Collation Models*

Treatise by Benedetto Varchi on proportion as the basis for rithmomachia, a mathematical game played on a chessboard with pieces that each have a shape and a number; a dialogue written by Carlo di Ruberto Strozzi, in which Cosimo Rucellai, who introduced the game to Benedetto Varchi, teaches the rules to Strozzi and Jacopo di Piero Vettori; and other notes on the game. Later unrelated notes and pen trials on leaves before and after main texts. Damage and bleed-through due to oxidation on many leaves.

One Iteration For The Second Boundary Condition For The Nonlinear One Dimensional Monge-Ampere Equation, 2022 University of Illinois at Chicago

#### One Iteration For The Second Boundary Condition For The Nonlinear One Dimensional Monge-Ampere Equation, Gerard Awanou

*Mathematics Colloquium Series*

The design of lenses and mirrors, in free form i.e. with no a priori symmetry assumption, has a long list of applications including materials processing, energy concentrators, medicine, antennas, computing lithography, laser weapons, optical data storage, imaging etc. The design process can be reduced to solving a generalized Monge-Ampere equation where the unknown is a function with a convexity property and subject to a constraint that a generalized gradient maps a given domain onto a prescribed one. The latter type of constraint is known as second boundary condition. The model one dimensional Monge-Ampere equation is nonlinear in the first ...

Fractal Like Snowflakes Generated By Non-Contractive Function Systems, 2022 Louisiana State University and Agricultural and Mechanical College

#### Fractal Like Snowflakes Generated By Non-Contractive Function Systems, William H. Kelly Iii

*LSU Master's Theses*

At the heart of this thesis is the examination of a non-contractive iterative function system T on the Hausdorff metric space of all compact subset of ℝ . Despite the absence of an 2 attracting fixed point, an examination reveals the appearance of fractal-like shapes (snowflakes) when applying the Barnsley’ random walk method to study the iterative sequence 𝑇^{n}(0) (𝑛 ∈ ℕ) for 𝑇 = 𝑇^{1} ∪ 𝑇^{2} ∪ 𝑇^{3}, where 𝑇_{1}(𝑧) = 𝑟𝑧, 𝑇_{2}(𝑧) = 𝑟𝑧 + 𝑏, and 𝑇_{3}(𝑧) = 𝑟𝑧 - 𝑏, and 𝑟 = 𝑒^{𝑖π/3}.

Studying Extended Sets From Young Tableaux, 2022 Butler University

#### Studying Extended Sets From Young Tableaux, Eric Nofziger

*Rose-Hulman Undergraduate Mathematics Journal*

Young tableaux are combinatorial objects related to the partitions of an integer and have various applications in representation theory. They are particularly useful in the study of the fibers arising from the Springer resolution. In recent work of Graham-Precup-Russell, an association has been made between a given row-strict tableau and three disjoint subsets of {1,2,...,n}. These subsets are then used in the study of extended Springer fibers, so we call them extended sets. In this project, we use combinatorial techniques to classify which of these extended sets correlate to a valid row-strict or standard tableau and give bounds ...

On The Smallest Non-Trivial Action Of Saut(Fn) For Small N, 2022 Hertford College, University of Oxford

#### On The Smallest Non-Trivial Action Of Saut(Fn) For Small N, Reemon Spector

*Rose-Hulman Undergraduate Mathematics Journal*

In this paper we investigate actions of SAut(*F _{n}*), the unique index 2 subgroup of Aut(

*F*), on small sets, improving upon results by Baumeister--Kielak--Pierro for several small values of

_{n}*n*. Using a computational approach for

*n*⩾ 5, we show that every action of SAut(

*F*) on a set containing fewer than 20 elements is trivial.

_{n}