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 p(n). Using a result of Shimura we also relate …

Coloring Complexes And Combinatorial Hopf Monoids, 2023 The University of Texas Rio Grande Valley

#### Coloring Complexes And Combinatorial Hopf Monoids, Jacob A. White

*Mathematical and Statistical Sciences Faculty Publications and Presentations*

We generalize the notion of a coloring complex of a graph to linearized combinatorial Hopf monoids. We determine when a linearized combinatorial Hopf monoid has such a construction, and discover some inequalities that are satisfied by the quasisymmetric function invariants associated to the combinatorial Hopf monoid. We show that the collection of all such coloring complexes forms a linearized combinatorial Hopf monoid, which is the terminal object in the category of combinatorial Hopf monoids with convex characters. We also study several examples of combinatorial Hopf monoids.

Supplementary Files For "Adaptive Mapping Of Design Ground Snow Loads In The Conterminous United States", 2023 University of Utah

#### Supplementary Files For "Adaptive Mapping Of Design Ground Snow Loads In The Conterminous United States", Jadon Wagstaff, Jesse Wheeler, Brennan Bean, Marc Maguire, Yan Sun

*Browse all Datasets*

Recent amendments to design ground snow load requirements in ASCE 7-22 have reduced the size of case study regions by 91% from what they were in ASCE 7-16, primarily in western states. This reduction is made possible through the development of highly accurate regional generalized additive regression models (RGAMs), stitched together with a novel smoothing scheme implemented in the R software package remap, to produce the continental- scale maps of reliability-targeted design ground snow loads available in ASCE 7-22. This approach allows for better characterizations of the changing relationship between temperature, elevation, and ground snow loads across the Conterminous United …

Counting Power Domination Sets In Complete M-Ary Trees, 2023 Gonzaga University

#### Counting Power Domination Sets In Complete M-Ary Trees, Hays Whitlatch, Katharine Shultis, Olivia Ramirez, Michele Ortiz, Sviatlana Kniahnitskaya

*Theory and Applications of Graphs*

Motivated by the question of computing the probability of successful power domination by placing k monitors uniformly at random, in this paper we give a recursive formula to count the number of power domination sets of size k in a labeled complete m-ary tree. As a corollary we show that the desired probability can be computed in exponential with linear exponent time.

From Mirrors To Wallpapers: A Virtual Math Circle Module On Symmetry, 2023 Central New Mexico Community College

#### From Mirrors To Wallpapers: A Virtual Math Circle Module On Symmetry, Nicole A. Sullivant, Christina L. Duron, Douglas T. Pfeffer

*Journal of Math Circles*

Symmetry is a natural property that children see in their everyday lives; it also has deep mathematical connections to areas like tiling and objects like wallpaper groups. The Tucson Math Circle (TMC) presents a 7-part module on symmetry that starts with reflective symmetry and culminates in the deconstruction of wallpapers into their ‘generating tiles’. This module utilizes a scaffolded, hands-on approach to cover old and new mathematical topics with various interactive activities; all activities are made available through free web-based platforms. In this paper, we provide lesson plans for the various activities used, and discuss their online implementation with Zoom, …

Hs-Integral And Eisenstein Integral Mixed Circulant Graphs, 2023 Indian Institute of Technology Guwahati

#### Hs-Integral And Eisenstein Integral Mixed Circulant Graphs, Monu Kadyan, Bikash Bhattacharjya

*Theory and Applications of Graphs*

A mixed graph is called \emph{second kind hermitian integral} (\emph{HS-integral}) if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers. A mixed graph is called \emph{Eisenstein integral} if the eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. We characterize the set $S$ for which a mixed circulant graph $\text{Circ}(\mathbb{Z}_n, S)$ is HS-integral. We also show that a mixed circulant graph is Eisenstein integral if and only if it is HS-integral. Further, we express the eigenvalues and the HS-eigenvalues of unitary oriented circulant graphs in terms of generalized M$\ddot{\text{o}}$bius 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 *APS(L)*. Our …

Slices Of C_2, Klein-4, And Quaternionic Eilenberg-Mac Lane Spectra, 2023 University of Kentucky

#### Slices Of C_2, Klein-4, And Quaternionic Eilenberg-Mac Lane Spectra, Carissa Slone

*Theses and Dissertations--Mathematics*

We provide the slice (co)towers of \(\Si{V} H_{C_2}\ul M\) for a variety of \(C_2\)-representations \(V\) and \(C_2\)-Mackey functors \(\ul M\). We also determine a characterization of all 2-slices of equivariant spectra over the Klein four-group \(C_2\times C_2\). We then describe all slices of integral suspensions of the equivariant Eilenberg-MacLane spectrum \(H\ulZ\) for the constant Mackey functor over \(C_2\times C_2\). Additionally, we compute the slices and slice spectral sequence of integral suspensions of $H\ulZ$ for the group of equivariance $Q_8$. Along the way, we compute the Mackey functors \(\mpi_{k\rho} H_{K_4}\ulZ\) and $\mpi_{k\rho} H_{Q_8}\ulZ$.

Conceptual Mathematics In Society, 2023 Northern Illinois University

#### Conceptual Mathematics In Society, Ricela Feliciano-Semidei

*Books, Book Chapters, & Supplemental Materials*

This textbook is a compilation of chapters with educational purposes for the course MATH 103 in Spring 2023. The first part (Chapters 1 and 2) includes logic and critical thinking. Understanding the thinking process and strategies for solving problems in an effective way will provide students with skills that will be required to succeed in all college math courses. The second part (Chapters 3 & 4) is an opportunity to develop numbers sense through strengthening conceptual understanding of fractions and algebraic thinking. This will help develop foundational mathematical knowledge for college mathematics courses. The third and fourth parts of this …

Runge-Kutta Methods For Rough Differential Equations, 2022 Martin Luther University Halle-Wittenberg, Institute of Mathematics, Theodor-Lieser-Str. 5, 06120 Halle (Saale), Germany

#### Runge-Kutta Methods For Rough Differential Equations, Martin Redmann, Sebastian Riedel

*Journal of Stochastic Analysis*

No abstract provided.

A Jump-Diffusion Process For Asset Price With Non-Independent Jumps, 2022 Hofstra University, Hempstead, NY 11549 USA

#### A Jump-Diffusion Process For Asset Price With Non-Independent Jumps, Yihren Wu, Majnu John

*Journal of Stochastic Analysis*

No abstract provided.

Continuous Semi-Supervised Nonnegative Matrix Factorization, 2022 The University of Texas Rio Grande Valley

#### Continuous Semi-Supervised Nonnegative Matrix Factorization, Michael R, Lindstrom, Xiaofu Ding, Feng Liu, Anand Somayajula, Deanna Needell

*Mathematical and Statistical Sciences Faculty Publications and Presentations*

Nonnegative matrix factorization can be used to automatically detect topics within a corpus in an unsupervised fashion. The technique amounts to an approximation of a nonnegative matrix as the product of two nonnegative matrices of lower rank. In this paper, we show this factorization can be combined with regression on a continuous response variable. In practice, the method performs better than regression done after topics are identified and retrains interpretability.

Quantization Of The Monotone Poisson Central Limit Theorem, 2022 Università di Bari, n.4, Via E. Orabona, 70125 Bari, Italy

#### Quantization Of The Monotone Poisson Central Limit Theorem, Yungang Lu

*Journal of Stochastic Analysis*

No abstract provided.

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 are …

Applications Of A Superposed Ornstein-Uhlenbeck Type Processes, 2022 African Institute for Mathematical Sciences (AIMS), Cameroon

#### Applications Of A Superposed Ornstein-Uhlenbeck Type Processes, Santatriniaina Avotra Randrianambinina, Julius Esunge

*Journal of Stochastic Analysis*

No abstract provided.

Multi-Trace Matrix Models From Noncommutative Geometry, 2022 The University of Western Ontario

#### Multi-Trace Matrix Models From Noncommutative Geometry, Hamed Hessam

*Electronic Thesis and Dissertation Repository*

Dirac ensembles are finite dimensional real spectral triples where the Dirac operator is allowed to vary within a suitable family of operators and is assumed to be random. The Dirac operator plays the role of a metric on a manifold in the noncommutative geometry context of spectral triples. Thus, integration over the set of Dirac operators within a Dirac ensemble, a crucial aspect of a theory of quantum gravity, is a noncommutative analog of integration over metrics.

Dirac ensembles are closely related to random matrix ensembles. In order to determine properties of specific Dirac ensembles, we use techniques from random …

Algorithmic Methods For Covering Arrays Of Higher Index, 2022 United States Military Academy

#### Algorithmic Methods For Covering Arrays Of Higher Index, Ryan Dougherty, Kristoffer Kleine, Michael Wagner, Charles J. Colbourn, Dimitris E. Simos

*West Point Research Papers*

Covering arrays are combinatorial objects used in testing large-scale systems to increase confidence in their correctness. To do so, each interaction of at most a specified number t of factors is represented in at least one test; that is, the covering array has strength t and index 1. For certain systems, the outcome of running a test may be altered by variability of the interaction effect or by measurement error of the test result. To improve the efficacy of testing, one can ensure that each interaction of t or fewer factors is represented in at least λ tests. When λ …

Meertens Number And Its Variations, 2022 International Business Machines

#### Meertens Number And Its Variations, Chai Wah Wu

*Communications on Number Theory and Combinatorial Theory*

In 1998, Bird introduced Meertens numbers as numbers that are invariant under a map similar to the Gödel encoding. In base 10, the only known Meertens number is 81312000. We look at some properties of Meertens numbers and consider variations of this concept. In particular, we consider variations of Meertens numbers where there is a finite time algorithm to decide whether such numbers exist, exhibit infinite families of these variations and provide bounds on parameters needed for their existence.

On The Diagonalizability And Factorizability Of Quadratic Boson Fields, 2022 Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy

#### On The Diagonalizability And Factorizability Of Quadratic Boson Fields, Luigi Accardi, Andreas Boukas, Yungang Lu, Alexander Teretenkov

*Journal of Stochastic Analysis*

No abstract provided.

On The Spatial Modelling Of Biological Invasions, 2022 The University of Western Ontario

#### On The Spatial Modelling Of Biological Invasions, Tedi Ramaj

*Electronic Thesis and Dissertation Repository*

We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …