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Full-Text Articles in Mathematics

Agent-Based Modeling: Introduction And Actuarial Applications, Rick Gorvett May 2025

Agent-Based Modeling: Introduction And Actuarial Applications, Rick Gorvett

Mathematics and Economics Faculty Working Papers

Agent-based modeling (ABM) has become an important and valued approach to modeling complex systems. In this paper, I advocate for actuaries to recognize the complex systems-nature of socioeconomic and risk processes and for ABM models to become a regular resource in our actuarial toolkits. These models allow for the observation of potential macro-behavior emerging from the underlying agent-level micro-activity and characteristics. Therefore, ABM models can provide significant insight into the quantification of risk and the identification of optimal strategies. This paper is an introduction and guide to ABM models, and it includes several case studies to illustrate their utility.

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A Selective Discontinuous Galerkin Implicit Particle-In-Cell Method For Plasma Simulation With Improved Interpolation, Siyu Wu, Yang Li, Hongtao Liu, Xiaoming He, Yong Cao May 2025

A Selective Discontinuous Galerkin Implicit Particle-In-Cell Method For Plasma Simulation With Improved Interpolation, Siyu Wu, Yang Li, Hongtao Liu, Xiaoming He, Yong Cao

Mathematics and Statistics Faculty Research & Creative Works

This article dynamically incorporates multiple ideas into the existing direct implicit particle-in-cell (DIPIC) method for plasma simulation, in order to dramatically improve the DIPIC method for its local mesh refinement needs based on Cartesian meshes as well as its interpolation needs based on the locally refined meshes. One key tool is to utilize the selective discontinuous Galerkin method, which is based on the interior penalty discontinuous Galerkin formulation and the regular local finite element basis functions, as the electric field solver in the DIPIC simulation. This hybrid type finite element method combines the advantages of both continuous and discontinuous finite …

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A Short Proof Of The Lemma Of The Logarithmic Derivative In Several Complex Variables, Qi Han, Jingbo Liu May 2025

A Short Proof Of The Lemma Of The Logarithmic Derivative In Several Complex Variables, Qi Han, Jingbo Liu

All Faculty Scholarship (Archived)

In this work, we provide a concise proof of the logarithmic derivative lemma in Cn. We start by giving a complete proof of a critical result by Biancofiore and Stoll (Ann. of Math. Stud., No. 100, 29–45, 1981) via matrix theory, which is central to this area of study. Then, we follow Li (Trans. Amer. Math. Soc. 363, 6257–6267, 2011) and Ye (Math. Z. 222, 81–95, 1996) to present the shortest proof to date.

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Math 115: College Algebra Instructor Guide, Seth Lehman May 2025

Math 115: College Algebra Instructor Guide, Seth Lehman

Open Educational Resources

OER instructor guide for Math 115, College Algebra, Queens College

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Conditional Quantization For Some Discrete Distributions, Edgar A. Gonzalez, Mrinal Kanti Roychowdhury, David A. Salinas, Vishal Veeramachaneni May 2025

Conditional Quantization For Some Discrete Distributions, Edgar A. Gonzalez, Mrinal Kanti Roychowdhury, David A. Salinas, Vishal Veeramachaneni

School of Mathematical & Statistical Sciences Faculty Publications

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the finite support are preselected, then the quantization is called a conditional quantization. In this paper, we have determined the conditional quantization, first for two different finite discrete distributions with a same conditional set, and for a finite discrete distribution with two different conditional sets. Next, we have determined the conditional and unconditional quantization for an infinite discrete distribution with support {12𝑛:𝑛∈ℕ}. We have …

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All Graphs Of Order N With Distinguishing Number N−1 Or N − 2, Andi Pujo Rahadi, Edy Tri Baskoro, Suhadi Wido Saputro May 2025

All Graphs Of Order N With Distinguishing Number N−1 Or N − 2, Andi Pujo Rahadi, Edy Tri Baskoro, Suhadi Wido Saputro

Theory & Applications of Graphs

Let G be a simple connected graph. The distinguishing number of G, denoted by D(G), is the least integer d such that G has a vertex d-labeling preserved only by the trivial automorphism. In this paper, we characterize all graphs of order n with distinguishing number n − 1, or n − 2.

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Similarity Metrics, Metrics, And Conditionally Negative Definite Functions, Daniel Alpay, Liora Mayats-Alpay May 2025

Similarity Metrics, Metrics, And Conditionally Negative Definite Functions, Daniel Alpay, Liora Mayats-Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

We give an example of a similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.

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Global Attractivity Of Positive Solutions Of Higher Order Nonlinear Difference Equations And Its Applications, Abdulaziz Almaslokh May 2025

Global Attractivity Of Positive Solutions Of Higher Order Nonlinear Difference Equations And Its Applications, Abdulaziz Almaslokh

Theses and Dissertations

Difference equations play an effective role in many mathematical models that represent some phenomena in different fields such as physics, economics, engineering and biology. From this perspective, studying and analyzing such equations are interesting issues for the advancement of scientific research. In particular, studying the asymptotic behavior of positive solutions of some population models that are a system of difference equations has become a necessity. In this dissertation, we examine the global attractivity of positive solutions of certain higher order nonlinear difference equations and apply these results to some population models.

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Entanglement Distribution Of Universal Quantum Cloners, James B. Daughtry May 2025

Entanglement Distribution Of Universal Quantum Cloners, James B. Daughtry

Student Scholarship

Szab`o et al. [4] show that universal quantum cloning machines may be used to manipulate entanglement between bipartite states. Entanglement is measured with concurrence, C, and it is shown that as the fidelity of the cloner improves, more entanglement transfers from the reference to the cloned state. This thesis characterizes the nature of this entanglement transfer by analyzing the entanglement distribution of the cloner. In this analysis we will show that entanglement is generally destroyed after cloning except in cases where there is no cloning, two identical qubits are created, or there is complete qubit transfer. Along with …

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On The Special Cases Of Carmichael’S Totient Conjecture, Christopher Saito May 2025

On The Special Cases Of Carmichael’S Totient Conjecture, Christopher Saito

UNLV Theses, Dissertations, Professional Papers, and Capstones

Euler’s totient function, φ(n), is the arithmetic function defined as the number of positive integers less than or equal to n that are relatively prime to n. In his 1922 paper [3], Professor R. D. Carmichael conjectured that for each positive integer n, there exists at least one positive integer m̸ = n such that φ(m) = φ(n).In this thesis, we consider some relevant literature and explore Carmichael’s totient conjecture for particular values of φ(n) = k. Our main consideration will be the set X_k = {n ∈ N : φ(n) = k}. In identifying X_k for k = 2^t, …

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The Concept Of T-Basis And Vector-Valued Hardy Classes, Bilal Bilalov, Sabina Rahib Sadigova May 2025

The Concept Of T-Basis And Vector-Valued Hardy Classes, Bilal Bilalov, Sabina Rahib Sadigova

Turkish Journal of Mathematics

This paper introduces the concept of a t-basis generated by some bilinear mapping t(·;·). It is considered the vector-valued class Lp(X) := Lp(J; X), 1 ≤ p < +∞, where J = [−π, π] and X is a Banach space with the UMD property, and it is proven that the classical system of exponents {eint}n∈ℤ forms a t-basis for Lp(X), 1 < p < +∞. Using this fact, the Hardy vector classes nHp±(X), 1 < p < +∞, different from the classical ones, are defined, and an equivalent definition of these classes is given and some of their properties are studied. In addition, the concept of t-Riesz property of a system of exponentials is introduced in Lp(X), 1 < p < +∞, and it is proved that this system has the t-Riesz property. A new method is given for establishing the Plemelj–Sokhotski formulas for X-valued Cauchy type integrals when X has the UMD property. An abstract analogue of the “1/4-Kadets” theorem is obtained for …

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Independent Vs. Signed Musicians: Does Thier Status Affect Their Success?, Zachary Vincent May 2025

Independent Vs. Signed Musicians: Does Thier Status Affect Their Success?, Zachary Vincent

Honors Projects in Mathematics and Economics

As technology has advanced and become more widely available, and as the public learns more about the recording industry and its workings, more musicians are choosing not to sign with record labels, becoming independent musicians. This now raises the question: does a musician’s status of independent or signed determine their level of success? It has been previously found that independent musicians have a more difficult time competing with signed musicians due to the resources provided by record labels and the way labels negotiate with large streaming platforms, giving signed labels more opportunities to be seen in the public eye, but …

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Algorithms To Estimate Contours: Two Applications Of Analytical Tools In Differential Geometry And Topology, Mohammad Abirul Islam May 2025

Algorithms To Estimate Contours: Two Applications Of Analytical Tools In Differential Geometry And Topology, Mohammad Abirul Islam

Computer Science ETDs

We develop distributed robotics algorithms with analytical tools needed to define and analyze angle turned and distance traversed by robots executing geometric algorithms. We then use these analytical tools to obtain information, via sensor measurements, about an a priori unknown surface. Our contributions are threefold. First, we develop the Sketch Algorithm, which estimates the boundary of any unknown contour and is asymptotically optimal in terms of distance traversed and angle turned. Second, we present experimental field work that validates the Sketch Algorithm. Finally, we propose an approach to find multiple sources of a surface with potential applications to approximate that …

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Analyticity, Superoscillations And Supershifts In Several Variables, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Alain Yger May 2025

Analyticity, Superoscillations And Supershifts In Several Variables, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Alain Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing their highest Fourier component. A different way of thinking about superoscillations consists in realizing that it is possible to reproduce the exponential function far away from the origin by only knowing its value in a countable set of points near the origin. By using this perspective, one can extend the idea of superoscillations to functions that are not a sum of exponential functions, namely to the notion of supershift. The study …

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Applications Of The Mathieu Groups And Information Theory In Dna Encoding Functions, Juan C. Nava Jr May 2025

Applications Of The Mathieu Groups And Information Theory In Dna Encoding Functions, Juan C. Nava Jr

Theses and Dissertations

A foundational idea in mathematics lies in breaking down existing components into their bare fundamentals. As evidenced by prime numbers and composites, we learn this idea at an early age. Categorizing these broken-down components into their simplest form allows mathematicians to construct proofs from emergent patterns. John Conway’s Atlas of Finite Groups in the 1990s was particularly concerned with the categorization of structures known as groups. There are certain axioms a group must adhere to, which amount to the retention of symmetry; ultimately a group helps us to better understand symmetric actions performed on a set with a binary operation. …

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Pluricomplex Green Functions And Transform Methods For The Laplacian, Jesse Joel Hulse May 2025

Pluricomplex Green Functions And Transform Methods For The Laplacian, Jesse Joel Hulse

Dissertations - ALL

There are two research themes within complex analysis presented. The first is developing generalizations of the Unified Transform Method as a novel way to compute fluid flows and numerically solve boundary value problems for holomorphic functions and solutions to the Laplacian and complex Helmholtz equation. The second is finding a formula for the pluricomplex Green function with two poles of equal weights for the bidisk. The Unified Transform Method (also sometimes known as the Fokas Method) is a technique for numerically solving boundary value problems for linear and integrable nonlinear PDEs. Crowdy reformulated the Unified Transform Method in the complex …

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Asymptotics Of Fubini-Study Currents For Sequences Of Line Bundles, Melody Ann Wolff May 2025

Asymptotics Of Fubini-Study Currents For Sequences Of Line Bundles, Melody Ann Wolff

Dissertations - ALL

Let $(X,\omega)$ be a Kähler manifold, and $L_p$ be a sequence of line bundles on $X$ equipped with continuous hermitian metrics $h_p$. Let $\gamma_p$ be the Fubini-Study current and $h_p^{eq}$ the equilibrium metric corresponding to the metric $h_p$. Our goal is to generalize a theorem of Tian in Complex Geometry to a setting using arbitrary line bundles equipped with metrics with non-positive curvature. This amounts to finding sufficient conditions for $\gamma_p-c_1(L_p,h_p^{eq})$, when appropriately scaled, to converge to $0$ in the sense of currents. To achieve this goal, we imply methods of Demailly and the Oshawa-Takegoshi Extension Theorem to bound a …

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Encircling Chains Around 4- And 6-Clusters In Fullerenes, Hannah Melissa Kimbrell May 2025

Encircling Chains Around 4- And 6-Clusters In Fullerenes, Hannah Melissa Kimbrell

Dissertations - ALL

Fullerenes are purely carbon molecules which can be represented by a 3-regular planar graph consisting of only hexagonal and (exactly 12) pentagonal faces. Since carbon atoms have valence 4 but our graphs are trivalent we need to double the edges in a perfect matching to bring the valence up to 4. The edges in a perfect matching form a Kekulé structure and the hexagonal faces bound by three Kekulé edges are called benzene rings. A maximal independent set of benzene rings for a given Kekulé structure is called a Clar set, and the maximum possible size of a Clar set …

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Maximal Simple Regular Matroids, Elana Joy Israel May 2025

Maximal Simple Regular Matroids, Elana Joy Israel

Dissertations - ALL

In 1980, Seymour completely classified regular matroids. In this thesis, we use this classification to provide a complete list of maximal simple regular matroids up through rank six. In each rank, exactly one of these is graphic. Additionally, there are one, two, and eight cographic, but not graphic, maximal simple regular matroids in ranks four, five, and six, respectively. In rank five, we also have the 10-element sporadic matroid, and in rank six we have a 12-element maximal simple regular matroid and 16-element maximal simple regular matroid, both of which are decomposable matroids that are not graphic, cographic, or sporadic. …

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On The Embeddability Of Small Cubic Graphs Into The Torus, Marie Kramer May 2025

On The Embeddability Of Small Cubic Graphs Into The Torus, Marie Kramer

Dissertations - ALL

The embeddability of graphs into different surfaces has been studied for nearly a century. In 1930, Kuratowski famously proved that a graph is planar if and only if it does not contain the complete graph K5 or the complete bipartite graph K3,3 as a topological minor. In particular, K3,3 is the only cubic obstructions for the plane. This sparked interest in two different directions: What are analogous results for other surfaces, and what can be said about embeddings of K5 and K3,3 into other surfaces? Regarding the first question, it was shown in the 1970s and 80s by Glover, Huneke, …

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Exploration Into Homotopy Equivalence And Vietoris-Rips Complexes, Alexander J. Mobley May 2025

Exploration Into Homotopy Equivalence And Vietoris-Rips Complexes, Alexander J. Mobley

Honors Theses

An important question in discrete topology and geometry is how to recover the structure and characteristics of a manifold when only given a finite set of points sampled from that manifold. Thus, if mathematicians have a point cloud of data which induces a discrete metric space, they look for some structure to these points. Understanding the structure of these points often gives needed insight to solve this problem. One such way to determine structure to these points is to use these points to construct a Vietoris-Rips complex. In abstract, Latschev shows that this allows us to recover the homotopy type …

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Crystallization Of The Quantized Function Algebras Of Suq(N + 1), Manabendra Giri May 2025

Crystallization Of The Quantized Function Algebras Of Suq(N + 1), Manabendra Giri

Doctoral Theses

The $q$-deformation of a connected, simply connected Lie group $G$ is typically studied through two Hopf algebras associated with it: the quantized universal enveloping algebra $\mathcal{U}_q(\mathfrak{g})$ and the quantized function algebra $\mathcal{O}(G_q)$. If $G$ has a compact real form $K$, one can use the Cartan involution to give a $*$-structure on $\mathcal{O}(G_q)$. The QFA $\mathcal{O}(G_q)$ with this $*$ structure is denoted by $\mathcal{O}(K_q)$ and its $C^*$-completion by $C(K_q)$. Here we study the crystal limits of $\mathcal{O}(SU_q(n+1))$ and $C(SU_q(n+1))$ and classify all irreducible representations of the crystallized algebras. We also prove that the crystallized algebra carries a natural bialgebra structure.

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Understanding Student And Teacher Perceptions Of A Checking For Accuracy Method In Algebra Class, Abigail A. Jameson May 2025

Understanding Student And Teacher Perceptions Of A Checking For Accuracy Method In Algebra Class, Abigail A. Jameson

Masters of Education in Teaching and Learning

Mathematics encompasses learning from one’s mistakes and developing accuracy with problem-solving. This action research study analyzed the classroom teacher’s and students' perceptions of a checking for accuracy math method that was implemented in an eighth-grade algebra classroom. Additionally, the researcher wanted to understand how the participants felt about the accuracy method and its influence on students’ attitudes toward math and mastery of math concepts. Student surveys, individual teacher (with student artifacts) and student interviews and focus groups (with individual artifacts) were the qualitative data collected using the constant comparative method. Descriptive statistics was used to collect quantitative data with calculated …

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Derived $P$-Adic Heights And The Leading Coefficient Of The Bertolini–Darmon–Prasanna $P$-Adic $L$-Function, Francesc Castella, Chi-Yun Hsu, Debanjana Kundu, Yu-Sheng Lee, Zheng Liu May 2025

Derived $P$-Adic Heights And The Leading Coefficient Of The Bertolini–Darmon–Prasanna $P$-Adic $L$-Function, Francesc Castella, Chi-Yun Hsu, Debanjana Kundu, Yu-Sheng Lee, Zheng Liu

School of Mathematical & Statistical Sciences Faculty Publications

Let E/Q be an elliptic curve and let p be an odd prime of good reduction for E. Let K be an imaginary quadratic field satisfying the classical Heegner hypothesis and in which p splits. The goal of this paper is two-fold: (1) we formulate a p-adic BSD conjecture for the p-adic L-function LBDP p introduced by Bertolini–Darmon–Prasanna [Duke Math. J. 162 (2013), pp. 1033–1148]; and (2) for an algebraic analogue F BDP p of LBDP p , we show that the “leading coefficient” part of our conjecture holds, and that the “order of vanishing” part follows from the expected …

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Statistics - What Does My Data Say About Me?, Taylor Gadsden-Deterville May 2025

Statistics - What Does My Data Say About Me?, Taylor Gadsden-Deterville

Student Scholar Symposium Abstracts and Posters

For my Introduction to Statistics Class, I have been tasked with collecting unique, personal data to give insight into my daily routine. I decided to record nine different outcomes (two qualitative and seven quantitative). On February 6, 2025, I began with a blank Excel sheet, and so far, I have 57 full days of data collected. I will continue monitoring my findings for the remainder of the Spring 2025 Semester. Per my project instructions, I must include tables and graphs for my qualitative and quantitative outcomes. So far, I have collected daily quantitative data on my screen time (Instagram and …

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A Preliminary Study Of Hilbert–Kunz Functions: Coefficient Behavior In A Normal Affine Semigroup Ring, Jesus A. Mendiola Herrera May 2025

A Preliminary Study Of Hilbert–Kunz Functions: Coefficient Behavior In A Normal Affine Semigroup Ring, Jesus A. Mendiola Herrera

Theses and Dissertations

In 1890, David Hilbert published a set of notes on what now constitutes one of the bases of Commutative Algebra; his work would eventually influence the efforts of mathematicians like Ernst Kunz. In 1969, Ernst Kunz introduced a particular mapping regarding modules of regular local rings. His goal was to characterize Noetherian local rings of prime characteristic by computing the length of the composition series under Frobenius power transformations. In this thesis, the focus will be on stating the initial steps on finding the coefficients of the Hilbert-Kunz function of the normal affine semigroup ring of the form R = …

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Adding Libraries To The Equation: Mathematical Sciences’ Underutilization Of Academic Librarians, Jennifer L.C. Burke, Elizabeth C. Novosel, Daniel G. Kipnis, Rasitha R. Jayesekere May 2025

Adding Libraries To The Equation: Mathematical Sciences’ Underutilization Of Academic Librarians, Jennifer L.C. Burke, Elizabeth C. Novosel, Daniel G. Kipnis, Rasitha R. Jayesekere

Libraries Scholarship

Academic librarians do not engage with all disciplinary departments equally. Despite equal or even greater efforts, some departments are less responsive to librarian outreach. One such department is mathematics. To understand mathematics departments’ relationships with their academic librarians, three mathematics librarians created a 20-question survey that was disseminated to mathematics faculty, instructors, and instructional staff in the United States and Canada. Of the 188 survey participants, more than a third reported that they never engage with their librarians, approximately half only do so occasionally, and a mere eight percent of participants collaborated with librarians to provide information literacy instruction (IL) …

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A Zariski-Nagata Theorem For Smooth Toric Surfaces, Jordan Vincent Barrett May 2025

A Zariski-Nagata Theorem For Smooth Toric Surfaces, Jordan Vincent Barrett

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

The Affine Zariski-Nagata theorem is a classical result in commutative algebra that gives an expression for the nth symbolic power of a radical ideal I in a polynomial ring over a field in terms of the nth ordinary powers of the maximal ideals in [affine variety]max(I). In this thesis we discuss a well-known projective analog of Zariski-Nagata and provide the necessary background on toric varieties to present a generalization of this result to toric surfaces. We conclude with a brief discussion about work toward characterizing which abstract toric varieties have smooth point fibers with …

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Oriented Matroid Circuit Polytopes, Jodi Mcwhirter May 2025

Oriented Matroid Circuit Polytopes, Jodi Mcwhirter

Arts & Sciences Graduate Student Theses and Dissertations

Matroids give rise to several natural constructions of polytopes. Inspired by this, we examine polytopes that arise from the signed circuits of an oriented matroid. We give the dimensions of these polytopes arising from graphical oriented matroids and their duals. Moreover, we consider polytopes constructed from cocircuits of oriented matroids generated by the positive roots in any type A root system. We give an explicit description of their face structure and determine the Ehrhart series. We also study an action of the symmetric group on these polytopes, giving a full description the subpolytopes fixed by each permutation. These type A …

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Transformations Of Bound Quivers, Ari Pincus-Kazmar May 2025

Transformations Of Bound Quivers, Ari Pincus-Kazmar

Mathematics, Statistics, and Computer Science Honors Projects

A quiver Q is a directed multigraph. Representations of Q are assignments of vector spaces and linear maps to the vertices and arrows of Q; these are categorically equivalent to the modules over the path algebra kQ. The indecomposable representations of a given quiver and the irreducible morphisms between them are summarized combinatorially in the Auslander-Reiten quiver which, in the case of algebras of finite representation type, gives almost complete information about the category of representations. We introduce an intuitive transformation from a family of bound quivers to a family of A-type quivers which preserves properties of the Auslander-Reiten quiver.

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