Italian Domination On Ladders And Related Products, 2018 East Tennessee State University

#### Italian Domination On Ladders And Related Products, Bradley Gardner

*Electronic Theses and Dissertations*

An Italian dominating function on a graph $G = (V,E)$ is a function such that $f : V \to \{0,1,2\}$, and for each vertex $v \in V$ for which $f(v) = 0$, we have $\sum_{u\in N(v)}f(u) \geq 2$. The weight of an Italian dominating function is $f(V) = \sum_{v\in V(G)}f(v)$. The minimum weight of all such functions on a graph $G$ is called the Italian domination number of $G$. In this thesis, we will consider Italian domination in various types of products of a graph $G$ with the complete ...

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, 2018 Utah State University

#### Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

*All Graduate Plan B and other Reports*

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms ...

Euclidian Geometry: Proposed Lesson Plans To Teach Throughout A One Semester Course, 2018 Boise State University

#### Euclidian Geometry: Proposed Lesson Plans To Teach Throughout A One Semester Course, Joseph Willert

*Mathematics Undergraduate Theses*

Overview We provide several engaging lesson plans that would aid in the teaching of geometry, specifically targeting Euclidian Geometry, towards students of high school age. The audience of this piece would be high school or college students who have not yet had an introduction to geometry, but have completed the standard mathematical courses leading up to this point (i.e. algebra, elementary math, etc.). This being the case the lessons and concepts realized in Chapter 1 target a basic understanding of what Euclidian Geometry is and the subsequent chapters aim specifically at underlying properties of a geometry. The main source ...

Multi-Resolution Analysis Using Wavelet Basis Conditioned On Homogenization, 2018 Utah State University

#### Multi-Resolution Analysis Using Wavelet Basis Conditioned On Homogenization, Abibat Adebisi Lasisi

*All Graduate Theses and Dissertations*

This dissertation considers an approximation strategy using a wavelet reconstruction scheme for solving elliptic problems. The foci of the work are on (1) the approximate solution of differential equations using multiresolution analysis based on wavelet transforms and (2) the homogenization process for solving one and two-dimensional problems, to understand the solutions of second order elliptic problems. We employed homogenization to compute the average formula for permeability in a porous medium. The structure of the associated multiresolution analysis allows for the reconstruction of the approximate solution of the primary variable in the elliptic equation. Using a one-dimensional wavelet reconstruction algorithm proposed ...

The Strong Law Of Large Numbers For U-Statistics Under Random Censorship, 2018 University of Wisconsin-Milwaukee

#### The Strong Law Of Large Numbers For U-Statistics Under Random Censorship, Jan Höft

*Theses and Dissertations*

We introduce a semi-parametric U-statistics estimator for randomly right censored data. We will study the strong law of large numbers for this estimator under proper assumptions about the conditional expectation of the censoring indicator with re- spect to the observed life times. Moreover we will conduct simulation studies, where the semi-parametric estimator is compared to a U-statistic based on the Kaplan- Meier product limit estimator in terms of bias, variance and mean squared error, under different censoring models.

Generalized Line Graphs, 2018 Western Michigan University

#### Generalized Line Graphs, Mohra Abdullah Z. Alqahtani

*Dissertations*

With every nonempty graph, there are associated many graphs. One of the best known and most studied of these is the line graph *L (G)* of a graph *G*, whose vertices are the edges of *G* and where two vertices of *L (G)* are adjacent if the corresponding edges of *G* are adjacent. This concept was implicitly introduced by Whitney in 1932. Over the years, characterizations of graphs that are line graphs have been given, as well as graphs whose line graphs have some specified property. For example, Beineke characterized graphs that are line graphs by forbidding certain graphs that ...

Topological Properties Of A 3-Rung Möbius Ladder, 2018 Stephen F. Austin State University

#### Topological Properties Of A 3-Rung Möbius Ladder, Rebecca Woods

*Electronic Theses and Dissertations*

In this work, we discuss the properties of the 3-rung Möbius ladder on the torus. We also prove ℤ_{2} is an orientation preserving topological symmetry group of the 3-rung Möbius ladder with sides and rungs distinct, embedded in the torus.

Exploring Flag Matroids And Duality, 2018 California State University, San Bernardino

#### Exploring Flag Matroids And Duality, Zachary Garcia

*Electronic Theses, Projects, and Dissertations*

Matroids capture an abstraction of independence in mathematics, and in doing so, connect discrete mathematical structures that arise in a variety of contexts. A matroid can be defined in several cryptomorphic ways depending on which perspective of a matroid is most applicable to the given context. Among the many important concepts in matroid theory, the concept of matroid duality provides a powerful tool when addressing difficult problems. The usefulness of matroid duality stems from the fact that the dual of a matroid is itself a matroid. In this thesis, we explore a matroid-like object called a flag matroid. In particular ...

Symmetric Presentations And Double Coset Enumeration, 2018 California State University, San Bernardino

#### Symmetric Presentations And Double Coset Enumeration, Charles Seager

*Electronic Theses, Projects, and Dissertations*

In this project, we demonstrate our discovery of original symmetric presentations and constructions of important groups, including nonabelian simple groups, and groups that have these as factor groups. The target nonabelian simple groups include alternating, linear, and sporadic groups. We give isomorphism types for each finite homomorphic image that has been found. We present original symmetric presentations of $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ as homomorphism images of the progenitors $2^{*20}$ $:$ $A_{5}$, $2^{*10}$ $:$ $PGL(2,9)$, $2^{*10}$ $:$ $Aut ...

Commutators Involving Matrix Functions, 2018 P.h.D student

#### Commutators Involving Matrix Functions, Osman Kan, Süleyman Solak

*Electronic Journal of Linear Algebra*

Some results are obtained for matrix commutators involving matrix exponentials $\left(\left[e^{A},B\right],\left[e^{A},e^{B}\right]\right)$ and their norms.

Finite Simple Graphs And Their Associated Graph Lattices, 2018 Middle Tennessee State University

#### Finite Simple Graphs And Their Associated Graph Lattices, James B. Hart, Brian Frazier

*Theory and Applications of Graphs*

In his 2005 dissertation, Antoine Vella explored combinatorical aspects of finite graphs utilizing a topological space whose open sets are intimately tied to the structure of the graph. In this paper, we go a step further and examine some aspects of the open set lattices induced by these topological spaces. In particular, we will characterize all lattices that constitute the opens for finite simple graphs endowed with this topology, explore the structure of these lattices, and show that these lattices contain information necessary to reconstruct the graph and its complement in several ways.

Determinants Of Interval Matrices, 2018 Charles University, Prague, Czech Republic

#### Determinants Of Interval Matrices, Jaroslav Horáček, Milan Hladík, Josef Matějka

*Electronic Journal of Linear Algebra*

In this paper we shed more light on determinants of real interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both relative and absolute approximation is proved. Next, methods computing verified enclosures of interval determinants and their possible combination with preconditioning are discussed. A new method based on Cramer's rule was designed. It returns similar results to the state-of-the-art method, however, it is less consuming regarding computational time. Other methods transferable from real matrices (e.g., the Gerschgorin circles, Hadamard's inequality ...

Inequalities Between $\Mid A\Mid + \Mid B\Mid $ And $\Mid A^{*} \Mid + \Mid B^{*} \Mid$, 2018 Huaibei Normal University

#### Inequalities Between $\Mid A\Mid + \Mid B\Mid $ And $\Mid A^{*} \Mid + \Mid B^{*} \Mid$, Yun Zhang

*Electronic Journal of Linear Algebra*

Let $A$ and $B$ be complex square matrices. Some inequalities between $\mid A \mid + \mid B \mid$ and $\mid A^{*} \mid + \mid B^{*} \mid$ are established. Applications of these inequalities are also given. For example, in the Frobenius norm, $$ \parallel\, A+B \,\parallel_{F} \leq \sqrt[4]{2} \parallel \mid A\mid + \mid B\mid \, \parallel_{F}. $$

Distance And Intersection Number In The Curve Complex Of A Closed Surface, 2018 Northeastern Illinois University

#### Distance And Intersection Number In The Curve Complex Of A Closed Surface, Nancy C. Wrinkle

*Faculty Research and Creative Activities Symposium*

No abstract provided.

Linear Analysis Of Tumor Morphology During Growth Using Bending Energy, 2018 Northeastern Illinois University

#### Linear Analysis Of Tumor Morphology During Growth Using Bending Energy, Emma A. Turian

*Faculty Research and Creative Activities Symposium*

No abstract provided.

Punctuated Cognitive Psychological Interventions On Student's Disposition To Learn And The Effects On Mathematical Achievement, 2018 Northeastern Illinois University

#### Punctuated Cognitive Psychological Interventions On Student's Disposition To Learn And The Effects On Mathematical Achievement, Matthew D. Graham

*Faculty Research and Creative Activities Symposium*

No abstract provided.

Singular And Ill-Conditioned Linear Systems, 2018 Northeastern Illinois University

#### Singular And Ill-Conditioned Linear Systems, Zhonggang Zeng

*Faculty Research and Creative Activities Symposium*

No abstract provided.

Enhancing Value-Based Healthcare With Reconstructability Analysis: Predicting Cost Of Care In Total Hip Replacement, 2018 Portland State University

#### Enhancing Value-Based Healthcare With Reconstructability Analysis: Predicting Cost Of Care In Total Hip Replacement, Cecily Corrine Froemke, Martin Zwick

*Systems Science Faculty Publications and Presentations*

Legislative reforms aimed at slowing growth of US healthcare costs are focused on achieving greater value per dollar. To increase value healthcare providers must not only provide high quality care, but deliver this care at a sustainable cost. Predicting risks that may lead to poor outcomes and higher costs enable providers to augment decision making for optimizing patient care and inform the risk stratification necessary in emerging reimbursement models. Healthcare delivery systems are looking at their high volume service lines and identifying variation in cost and outcomes in order to determine the patient factors that are driving this variation and ...

Dynamics Of Paramagnetic And Ferromagnetic Ellipsoidal Particles In Shear Flow Under A Uniform Magnetic Field, 2018 Missouri University of Science and Technology

#### Dynamics Of Paramagnetic And Ferromagnetic Ellipsoidal Particles In Shear Flow Under A Uniform Magnetic Field, Christopher A. Sobecki, Jie Zhang, Yanzhi Zhang, Cheng Wang

*Yanzhi Zhang*

We investigate the two-dimensional dynamic motion of magnetic particles of ellipsoidal shapes in shear flow under the influence of a uniform magnetic field. In the first part, we present a theoretical analysis of the rotational dynamics of the particles in simple shear flow. By considering paramagnetic and ferromagnetic particles, we study the effects of the direction and strength of the magnetic field on the particle rotation. The critical magnetic-field strength, at which particle rotation is impeded, is determined. In a weak-field regime (i.e., below the critical strength) where the particles execute complete rotations, the symmetry property of the rotational ...

Decoupled, Linear, And Energy Stable Finite Element Method For The Cahn-Hilliard-Navier-Stokes-Darcy Phase Field Model, 2018 Missouri University of Science and Technology

#### Decoupled, Linear, And Energy Stable Finite Element Method For The Cahn-Hilliard-Navier-Stokes-Darcy Phase Field Model, Yali Gao, Xiaoming He, Liquan Mei, Xiaofeng Yang

*Xiaoming He*

In this paper, we consider the numerical approximation for a phase field model of the coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn—Hilliard—Navier—Stokes equations in the free flow region and Cahn—Hilliard—Darcy equations in the porous media region that are coupled by seven interface conditions. The coupled system is decoupled based on the interface conditions and the solution values on the interface from the previous time step. A fully discretized scheme with finite elements for the spatial discretization is developed to solve the decoupled system. In order to deal with ...