Mathematics Commons^™

Trees With Unique Italian Dominating Functions Of Minimum Weight, Alyssa England

Electronic Theses and Dissertations

An Italian dominating function, abbreviated IDF, of $G$ is a function $f \colon V(G) \rightarrow \{0, 1, 2\}$ satisfying the condition that for every vertex $v \in V(G)$ with $f(v)=0$, we have $\sum_{u \in N(v)} f(u) \ge 2$. That is, either $v$ is adjacent to at least one vertex $u$ with $f(u) = 2$, or to at least two vertices $x$ and $y$ with $f(x) = f(y) = 1$. The Italian domination number, denoted $\gamma_I$(G), is the minimum weight of an IDF in $G$. In this thesis, we use operations that join two trees with a single edge in order …

A Mathematical Development Of Minimal Surface Theory: From Soap Films To Black Holes, Timothy Pitts

Theses and Dissertations

Minimal surfaces are a special subset of surfaces that have gone through a long and extensive development and have also led to many fruitful findings in mathematics. Several periods that are key to the progression of the theory are coined as Golden Ages for the field’s development. Here, a historical and mathematical development of minimal surface theory is presented that spans from its inception in the late 18th century to the present day. Along with the development, there is an emphasis on showing connections of minimal surfaces to various natural phenomena that occur such as soap films, black holes, biological …

Bases Of Infinite-Dimensional Representations Of Orthosymplectic Lie Superalgebras, Dwight Anderson Williams Ii

Mathematics Dissertations - Archive

We provide explicit bases of representations of the Lie superalgebra osp(1|2n) obtained by taking tensor products of infinite-dimensional representation and the standard representation. This infinite-dimensional representation is the space of polynomials C[x₁,...,xn]. Also, we provide a new differential operator realization of osp(1|2n) in terms of differential operators of n commuting variables x₁,...,xn and 2n anti-commuting variables ξ1; : : : ; ξ2n.

Boundary, Costs And Trade-Offs In Reserve Design Systems, Justus Hurd

Honors Theses

Due to limitations in funding and natural resources, it is infeasible to construct perfect reserve systems for large populations of critical species. For this project, our objective is to formulate a reserve design model that minimizes the distance between reserve sites meeting a threshold of biodiversity features subject to a species coverage constraints. Coupled with other spatial characteristics including reserve size and configuration, the boundary of a reserve system is of key importance. While positive area effects are gained when selecting additional sites, negative boundary length effects are also experienced. For example, it is costly to implement and maintain boundary …

Predictive Modeling Of Iphone 7 Charge Rates Using Least Squares Curve Fitting, Grace Cahill

Honors Theses

In a time where individuals depend on their cell phones, the need for a long lasting and quick charging battery life is imperative. As information regarding how long a battery can remained charged is highly advertised, there is no information regarding how long it would take for a dead phone battery to completely charge. This study determined the amount of time it will take an iPhone 7 to charge from 0% to 100% using the standard charging cable under four different charging conditions. The charge percentage was recorded every two minutes until it was fully charged with this process being …

Mathematical Modeling Of Nonlinear Dynamics Of Blood Hormones On The Regulatory System, Gabriela Urbina

Theses and Dissertations

We study a mathematical modeling of nonlinear dynamics of blood hormones, which includes glucose and insulin. On Chapter I, II, III and IV, we introduce this work, analyze an effect of the secreted insulin by the pancreatic beta cells and glucagon hormones and state concluding remarks, respectively. This model considers the time evolution of nonlinear dynamics of the equations for glucose, glucagon and insulin concentrations plus insulin and glucagon actions and the secreted insulin as a result of elevation of glucose in the blood plasma. Using both analytical and numerical procedures, we determine such quantities using different parameters for different …

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 …

Winding Numbers And Full Extendability In Holomorphic Motions, Yunping Jiang

Publications and Research

We construct an example of a holomorphic motion of a five-point subset of the Riemann sphere over an annulus such that it satisfies the zero winding number condition but is not fully extendable.

Discontinuity-Driven Mesh Alignment For Evolving Discontinuities In Elastic Solids, Mihhail Berezovski, Arkadi Berezovski

Publications

A special mesh adaptation technique and a precise discontinuity tracking are presented for an accurate, efficient, and robust adaptive-mesh computational procedure for one-dimensional hyperbolic systems of conservation laws, with particular reference to problems with evolving discontinuities in solids. The main advantage of the adaptive technique is its ability to preserve the modified mesh as close to the original fixed mesh as possible. The constructed method is applied to the martensitic phase-transition front propagation in solids.

Nonlinear Photonics In Twisted And Nonlocal Structures, Austin Copeland

Mathematics Theses and Dissertations

We provide a theoretical framework for the observed confinement of light modes within a twisted coreless photonic crystal fiber. Asymptotic methods are applied through ray theory and field theory in both the linear and nonlinear regime. We find the modes have a radially symmetric chirp and the envelope will decay away from the axis of propagation. Secondly, we study the stability and singularity formation of unidirectional beams as described by the Schrodinger equation. We propose a novel extension to the modeling equation to include a fractional Laplacian in one spatial dimension and a standard second derivative in a second dimension. …

Partial Differential Equations In Curved Spacetimes, Jorge A. Garcia

Theses and Dissertations

It is the ambition of this thesis to analyze in a concise and coherent manner the idiosyncratic nature of partial differential equations and their mathematical structure in distinct curved spacetimes. In our work special interest is taken in quantum fields dwelling within the de-Sitter geometry. In Chapters I, II, III, and IV, a meticulous study of general relativity is undertaken with one of its solutions derived, an introduction of quantum mechanics is posed, the relativistic quantum theory of fermions is defined, and a “merging” of the former chapters and results are considered, respectively. With what has been derived we seek …

Solitary And Periodic Wave Solutions For Several Short Wave Model Equations, Andrey V. Stukopin

Theses and Dissertations

We study the periodic and solitary wave solutions to several short wave model equations arising from a so-called $\beta$-family equation for $\beta=1,2,4$. These are integrable cases which possess Lax pair and multi-soliton solutions. By phase plane analysis, either the loop or cuspon type solutions are predicted. Then, by introducing a hodograph, or reciprocal, transformation, a coupled system is derived for each $\beta$. Applying a travelling wave setting, we are able to find the periodic solutions exactly expressed in terms of Jacobi Elliptic functions. In the limiting cases of modulus k=1, they all converge to the known solitary waves.

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 …

The Directed Forest Complex Of Cayley Graphs, Kennedy Courtney

Boise State University Theses and Dissertations

Let Γ be a directed graph. The directed forest complex, DF(Γ), is a simplicial complex whose vertices are the edges of Γ and whose simplices are sets of edges that form a directed forest in Γ. We study the directed forest complex of Cayley graphs of finite groups. The homology of DF(Γ) contains information about the graph, Γ and about the group, G. The ultimate goal is to classify DF(Γ) up to homotopy, compute its homology, and interpret the findings in terms of properties of DF(Γ). In this thesis, we present progress made toward this goal.

Beginning Algebra Made Useful, Charlene E. Beckmann

Open Textbooks

Beginning Algebra Made Useful addresses the needs of learners to make sense of algebra by quantifying and generalizing everyday occurrences such as commuting to work, buying gas or pizza, and determining the better deal. It requires learners to actively engage with algebraic concepts through physical and thought experiments in ways that help them connect ideas, representations, and contexts, and solve problems that arise in their daily lives. The text helps learners grow their brains and develop growth mindsets as they learn algebra conceptually. Problem sets continue the process, extending work begun in each lesson, applying new understandings to new contexts, …

An Analysis Of The First Passage To The Origin (Fpo) Distribution, Aradhana Soni

Electronic Theses and Dissertations

What is the probability that in a fair coin toss game (a simple random walk) we go bankrupt in n steps when there is an initial lead of some known or unknown quantity $m? What is the distribution of the number of steps N that it takes for the lead to vanish? This thesis explores some of the features of this first passage to the origin (FPO) distribution. First, we explore the distribution of N when m is known. Next, we compute the maximum likelihood estimators of m for a fixed n and also the posterior distribution of m when …

A Formula For The Cohomology And K-Class Of A Regular Hessenberg Variety, Erik Insko, Julianna Tymoczko, Alexander Woo

Mathematics Sciences: Faculty Publications

Hessenberg varieties are subvarieties of the flag variety parametrized by a linear operator X and a nondecreasing function h. The family of Hessenberg varieties for regular X is particularly important: they are used in quantum cohomology, in combinatorial and geometric representation theory, in Schubert calculus and affine Schubert calculus. We show that the classes of a regular Hessenberg variety in the cohomology and K-theory of the flag variety are given by making certain substitutions in the Schubert polynomial (respectively Grothendieck polynomial) for a permutation that depends only on h. Our formula and our methods are different from a recent result …

The Marshmallow Lab: A Project-Based Approach To Understanding Functional Responses, Melissa Pulley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper presents a three-part lesson plan to improve student’s understanding of Holling’s type II functional response model. This model describes the interaction between a predator and how much it is able to consume given a constant number of prey. According to the model, while increased availability of prey allows predators to consume portionately more prey for low values, after some number of prey, predators will only be able to capture a limited number of prey even as the prey continues to increase. This phenomenon is known as saturation. Holling first develop this important ecological theory through his “disc experiment” …

Some Asymptotic Properties Of Seirs Models Withnonlinear Incidence And Random Delays, Divine Wanduku, Broderick O. Oluyede

Mathematical Sciences: Faculty Publications

This paper presents the dynamics of mosquitoes and humans with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless version is derived; analytical techniques are applied to find conditions for deterministic extinction and permanence of disease. The BRN R0* and ESPR E(e–(μvT1+μT2)) are computed. Conditions for deterministic extinction and permanence are expressed in terms of R0* and E(e–(μvT1+μT2)) and applied to a P. vivax malaria scenario. Numerical results are given.

Periodic Triangulations Of Zn, Mathieu Dutour Sikiric, Alexey Garber

School of Mathematical & Statistical Sciences Faculty Publications

We consider in this work triangulations of Z n that are periodic along Z n . They generalize the triangulations obtained from Delaunay tessellations of lattices. In certain cases we impose additional restrictions on such triangulations such as regularity or invariance under central symmetry with respect to the origin; both properties hold for Delaunay tessellations of lattices. Full enumeration of such periodic triangulations is obtained for dimension at most 4 . In dimension 5 several new phenomena happen: there are centrally-symmetric triangulations that are not Delaunay, there are non-regular triangulations (it could happen in dimension 4 ) and a given …