Other Mathematics Commons^™

Uniform Random Variate Generation With The Linear Congruential Method, Joseph Free

PANDION: The Osprey Journal of Research and Ideas

This report considers the issue of using a specific linear congruential generator (LCG) to create random variates from the uniform(0,1) distribution. The LCG is used to generate multiple samples of pseudo-random numbers and statistical computation techniques are used to assess whether those samples could have resulted from a uniform(0,1) distribution. Source code is included with this report in the appendix along with annotations.

Exact And Strongly Exact Filters, M. A. Moshier, A. Pultr, A. L. Suarez

Mathematics, Physics, and Computer Science Faculty Articles and Research

A meet in a frame is exact if it join-distributes with every element, it is strongly exact if it is preserved by every frame homomorphism. Hence, finite meets are (strongly) exact which leads to the concept of an exact resp. strongly exact filter, a filter closed under exact resp. strongly exact meets. It is known that the exact filters constitute a frame FiltE(L) somewhat surprisingly isomorphic to the frame of joins of closed sublocales. In this paper we present a characteristic of the coframe of meets of open sublocales as the dual to the frame of strongly exact filters FiltsE(L).

Plithogenic Cognitive Maps In Decision Making, Florentin Smarandache, Nivetha Martin

Branch Mathematics and Statistics Faculty and Staff Publications

Plithogenic sets introduced by Smarandache (2018) have disclosed new research vistas and this paper introduces the novel concept of plithogenic cognitive maps (PCM) and its applications in decision making. The new approach of defining instantaneous state neutrosophic vector with the confinement of indeterminacy to (0,1] is proposed to quantify the degree of indeterminacy. The resultant vector is obtained by applying instantaneous state vector through the connection matrix together with plithogenic operators comprising the contradiction degrees. The connection matrix is represented as fuzzy matrix and neutrosophic matrix and the resultant vector is determined by applying plithogenic fuzzy operators and plithogenic neutrosophic …

Discrete-Time Control With Non-Constant Discount Factor, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau

Mathematics Faculty Research Publications

This paper deals with discrete-time Markov decision processes (MDPs) with Borel state and action spaces, and total expected discounted cost optimality criterion. We assume that the discount factor is not constant: it may depend on the state and action; moreover, it can even take the extreme values zero or one. We propose sufficient conditions on the data of the model ensuring the existence of optimal control policies and allowing the characterization of the optimal value function as a solution to the dynamic programming equation. As a particular case of these MDPs with varying discount factor, we study MDPs with stopping, …

Superposed Ornstein-Uhlenbeck Processes, Julius Esunge, Auguste Muhau

Journal of Stochastic Analysis

No abstract provided.

Von Neumann's Minimax Theorem For Continuous Quantum Games, Luigi Accardi, Andreas Boukas

Journal of Stochastic Analysis

No abstract provided.

On The Extension Of Positive Definite Kernels To Topological Algebras, Daniel Alpay, Ismael L. Paiva

Mathematics, Physics, and Computer Science Faculty Articles and Research

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.

Taylor Expansions And Castell Estimates For Solutions Of Stochastic Differential Equations Driven By Rough Paths, Qi Feng, Xuejing Zhang

Journal of Stochastic Analysis

No abstract provided.

At The Interface Of Algebra And Statistics, Tai-Danae Bradley

Dissertations, Theses, and Capstone Projects

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals …

Derivable Single Valued Neutrosophic Graphs Based On Km-Fuzzy Metric, Florentin Smarandache, Mohammad Hamidi

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we consider the concept of KM-fuzzy metric spaces and we introduce a novel concept of KM-single valued neutrosophic metric graphs based on KM-fuzzy metric spaces. Then we investigate the finite KM-fuzzy metric spaces with respect to KM-fuzzy metrics and we construct the KMfuzzy metric spaces on any given non-empty sets. We try to extend the concept of KM-fuzzy metric spaces to a larger class of KM-fuzzy metric spaces such as union and product of KM-fuzzy metric spaces and in this regard we investigate the class of products of KM-single valued neutrosophic metric graphs. In the final, we …

Permutation And Monomial Progenitors, Crystal Diaz

Electronic Theses, Projects, and Dissertations

We searched monomial and permutation progenitors for symmetric presentations of important images, nonabelian simple groups, their automorphism groups, or groups that have these as their factor groups. In this thesis, we described our search for the homomorphic images through the permutation progenitor 2^*15:(D₅ X 3) and construction of a monomial representation through the group 2³:3.

We constructed PGL(2,7) over 2³:3 on 6 letters and L₂(11) over 2²:3 on 8 letters. We also give our construction of S₅ X 2 and L₂(25) as homomorphic images of the …

Realizations Of Holomorphic And Slice Hyperholomorphic Functions: The Krein Space Case, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we treat realization results for operator-valued functions which are analytic in the complex sense or slice hyperholomorphic over the quaternions. In the complex setting, we prove a realization theorem for an operator-valued function analytic in a neighborhood of the origin with a coisometric state space operator thus generalizing an analogous result in the unitary case. A main difference with previous works is the use of reproducing kernel Krein spaces. We then prove the counterpart of this result in the quaternionic setting. The present work is the first paper which presents a realization theorem with a state space …

Acoustic Versus Electromagnetic Field Theory: Scalar, Vector, Spinor Representations And The Emergence Of Acoustic Spin, Lucas Burns, Konstantin Y. Bliokh, Franco Nori, Justin Dressel

Mathematics, Physics, and Computer Science Faculty Articles and Research

We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a scalar potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement vector potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether …

Strategies And Algorithms Of Sudoku, Callie Weaver

Mathematics Senior Capstone Papers

This paper discusses different strategies for the game of Sudoku and how those strategies relate to other problem solving techniques while also attempting to use those other techniques in a way that improves the strategies for Sudoku. This includes a thorough analysis of the general algorithm and an algorithm that is formed by the Occupancy Theorem and Preemptive Sets. This paper also compares these algorithms that directly relate to Sudoku with algorithms to similar combinatorial problems such as the Traveling Salesman problem and more. With the study of game theory becoming more popular, these strategies have also been shown to …

Introductory Calculus: Through The Lenses Of Covariation And Approximation, Caleb Huber

Graduate Student Portfolios, Professional Papers, and Capstone Projects

Over the course of a year, I investigated reformative approaches to the teaching of calculus. My research revealed the substantial findings of two educators, Michael Oehrtman and Pat Thompson, and inspired me to design a course based upon two key ideas, covariation and approximation metaphors. Over a period of six weeks, I taught a course tailored around these ideas and documented student responses to both classroom activities and quizzes. Responses were organized intonarratives, covariation, rates of change, limits, and delta notation. Covariation with respect to rates of change was found to be incredibly complex, and students would often see it …

From Branches To Fibers - Investigating F-Actin Networks With Biochemistry And Mathematical Modeling, Melissa A. Riddle

Senior Honors Projects, 2020-current

F-actin networks have different structures throughout the cell depending on their location or mechanical role. For example, at the leading edge of a migrating cell, F-actin is organized in a region called the lamellipodia as a branched network responsible for pushing the membrane outwards. Behind the lamellipodia is a lamellar actin network where focal adhesions and stress fibers originate, and then within the cell cortex, actin is arranged in a gel-like network. Stress fibers are an important organization of F-actin and how they arise from either the branched lamellipodia network or the gel-like cortex network is poorly understood. Our approach …

An Analysis And Comparison Of Knot Polynomials, Hannah Steinhauer

Senior Honors Projects, 2020-current

Knot polynomials are polynomial equations that are assigned to knot projections based on the mathematical properties of the knots. They are also invariants, or properties of knots that do not change under ambient isotopy. In other words, given an invariant α for a knot K, α is the same for any projection of K. We will define these knot polynomials and explain the processes by which one finds them for a given knot projection. We will also compare the relative usefulness of these polynomials.

Structure Theorems For Idempotent Residuated Lattices, José Gil-Férez, Peter Jipsen, George Metcalfe

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we study structural properties of residuated lattices that are idempotent as monoids. We provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras in various subclasses. We also establish the finite embeddability property for certain varieties generated by classes of residuated lattices that are conservative in the sense that monoid multiplication always yields one of its arguments. We then make use of a more symmetric version of Raftery’s characterization theorem for totally ordered commutative idempotent residuated lattices to prove that the variety generated by this class has …

Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems, Subagya Perera

Master's Theses

In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao in 1992. The modified HAM can be viewed as a more generalized method that encloses many perturbation and non-perturbation methods. It is different from perturbation or other analytical methods in that it allows considerable freedomformanyvariables. Using the modified HAM, especially zero-order and higher-order deformation equations, we solve a nonlinear initial value problem and a nonlinear eigenvalue problem. We adjust the convergence region of a solution by modifying auxiliary parameter values. The results converge in very few …

Exploring Pedagogical Empathy Of Mathematics Graduate Student Instructors, Karina Uhing

Department of Mathematics: Dissertations, Theses, and Student Research

Interpersonal relationships are central to the teaching and learning of mathematics. One way that teachers relate to their students is by empathizing with them. In this study, I examined the phenomenon of pedagogical empathy, which is defined as empathy that influences teaching practices. Specifically, I studied how mathematics graduate student instructors conceptualize pedagogical empathy and analyzed how pedagogical empathy might influence their teaching decisions. To address my research questions, I designed a qualitative phenomenological study in which I conducted observations and interviews with 11 mathematics graduate student instructors who were teaching precalculus courses at the University of Nebraska—Lincoln.

In the …