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Full-Text Articles in Mathematics

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski Dec 2018

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


Regularity Radius: Properties, Approximation And A Not A Priori Exponential Algorithm, David Hartman, Milan Hladik Dec 2018

Regularity Radius: Properties, Approximation And A Not A Priori Exponential Algorithm, David Hartman, Milan Hladik

Electronic Journal of Linear Algebra

The radius of regularity, sometimes spelled as the radius of nonsingularity, is a measure providing the distance of a given matrix to the nearest singular one. Despite its possible application strength this measure is still far from being handled in an efficient way also due to findings of Poljak and Rohn providing proof that checking this property is NP-hard for a general matrix. There are basically two approaches to handle this situation. Firstly, approximation algorithms are applied and secondly, tighter bounds for radius of regularity are considered. Improvements of both approaches have been recently shown by Hartman and Hlad\'{i ...


Subsets Of Vertices Of The Same Size And The Same Maximum Distance, Maria Axenovich, Dominik Duerrschnabel Dec 2018

Subsets Of Vertices Of The Same Size And The Same Maximum Distance, Maria Axenovich, Dominik Duerrschnabel

Theory and Applications of Graphs

For a simple connected graph $G=(V,E)$ and a subset $X$ of its vertices, let $$d^*(X) = \max\{{\rm dist}_G(x,y): x,y\in X\}$$ and let

$h^*(G)$ be the largest $k$ such that there are disjoint vertex subsets $A$ and $B$ of $G$, each of size $k$ such that $d^*(A) = d^*(B).$

Let $h^*(n) = \min \{h^*(G): |V(G)|=n\}$. We prove that $h^*(n) = \lfloor (n+1)/3 \rfloor,$ for $n\geq 6.$ This solves the homometric set problem restricted to the largest distance exactly. In addition we compare $h^*(G)$ with ...


Context Is Critical: Three-Act Math Tasks, Lindsey Herlehy Dec 2018

Context Is Critical: Three-Act Math Tasks, Lindsey Herlehy

Publications & Research

Mathematicians view mathematics within interesting and natural contexts. In this session, participants will engage and explore Three-Act Math Tasks; a story-telling pedagogical strategy that elicits student curiosity, collaboration, and questioning while redefining the term “real-world context” and the role that students play in the learning process. Resources will be provided


Multi-Resolution Analysis Using Wavelet Basis Conditioned On Homogenization, Abibat Adebisi Lasisi Dec 2018

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 ...


Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg Dec 2018

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 ...


Pentagons In Triangle-Free Graphs, Bernard Lidicky, Florian Pfender Dec 2018

Pentagons In Triangle-Free Graphs, Bernard Lidicky, Florian Pfender

Mathematics Publications

For all n≥9, we show that the only triangle-free graphs on n vertices maximizing the number 5-cycles are balanced blow-ups of a 5-cycle. This completely resolves a conjecture by Erd\H{o}s, and extends results by Grzesik and Hatami, Hladky, Kral, Norin and Razborov, where they independently showed this same result for large n and for all n divisible by 5.


Symmetric Presentations And Double Coset Enumeration, Charles Seager Dec 2018

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 ...


Exploring Flag Matroids And Duality, Zachary Garcia Dec 2018

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 ...


Italian Domination On Ladders And Related Products, Bradley Gardner Dec 2018

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 ...


Commutators Involving Matrix Functions, Osman Kan, Süleyman Solak Nov 2018

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, James B. Hart, Brian Frazier Nov 2018

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, Jaroslav Horáček, Milan Hladík, Josef Matějka Nov 2018

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 $\Mid A^{*} \Mid + \Mid B^{*} \Mid$, Yun Zhang Nov 2018

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, Nancy C. Wrinkle Nov 2018

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, Emma A. Turian Nov 2018

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, Matthew D. Graham Nov 2018

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, Zhonggang Zeng Nov 2018

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, Cecily Corrine Froemke, Martin Zwick Nov 2018

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, Christopher A. Sobecki, Jie Zhang, Yanzhi Zhang, Cheng Wang Nov 2018

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, Yali Gao, Xiaoming He, Liquan Mei, Xiaofeng Yang Nov 2018

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 ...


Teaching Differential Equations Without Computer Graphics Solutions Is A Crime, Beverly H. West Nov 2018

Teaching Differential Equations Without Computer Graphics Solutions Is A Crime, Beverly H. West

CODEE Journal

In the early 1980s computer graphics revolutionized the teaching of ordinary differential equations (ODEs). Yet the movement to teach and learn the qualitative methods that interactive graphics affords seems to have lost momentum. There still exist college courses, even at big universities, being taught without the immense power that computer graphics has brought to differential equations. The vast majority of ODEs that arise in mathematical models are nonlinear, and linearization only approximates solutions sufficiently near an equilibrium. Introductory courses need to include nonlinear DEs. Graphs of phase plane trajectories and time series solutions allow one to see and analyze the ...


Experiences Using Inquiry-Oriented Instruction In Differential Equations, Keith Nabb Nov 2018

Experiences Using Inquiry-Oriented Instruction In Differential Equations, Keith Nabb

CODEE Journal

Student-centered instruction can be a challenging endeavor for teachers and students. This article reports on the use of the Inquiry-Oriented Differential Equations (IO-DE) curriculum (Rasmussen, 2002) in an undergraduate differential equations course. Examples of student work are shared with specific reference to research in mathematics education.


An Introduction To Psychological Statistics, Garett C. Foster, David Lane, David Scott, Mikki Hebl, Rudy Guerra, Dan Osherson, Heidi Zimmer Nov 2018

An Introduction To Psychological Statistics, Garett C. Foster, David Lane, David Scott, Mikki Hebl, Rudy Guerra, Dan Osherson, Heidi Zimmer

Open Educational Resources Collection

We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through the lens of statistics, we learn to find the signal hidden in the noise when it is there and to know when an apparent trend or pattern is really just randomness. The study of statistics involves math and relies upon calculations of numbers. But it also relies heavily on how the numbers are chosen and how the ...


Erasure Coding For Distributed Matrix Multiplication For Matrices With Bounded Entries, Li Tang, Konstantinos Konstantinidis, Aditya Ramamoorthy Nov 2018

Erasure Coding For Distributed Matrix Multiplication For Matrices With Bounded Entries, Li Tang, Konstantinos Konstantinidis, Aditya Ramamoorthy

Electrical and Computer Engineering Publications

Distributed matrix multiplication is widely used in several scientific domains. It is well recognized that computation times on distributed clusters are often dominated by the slowest workers (called stragglers). Recent work has demonstrated that straggler mitigation can be viewed as a problem of designing erasure codes. For matrices A and B, the technique essentially maps the computation of ATB into the multiplication of smaller (coded) submatrices. The stragglers are treated as erasures in this process. The computation can be completed as long as a certain number of workers (called the recovery threshold) complete their assigned tasks. We present a novel ...


Inducibility Of Directed Paths, Ilkyoo Choi, Bernard Lidicky, Florian Pfender Nov 2018

Inducibility Of Directed Paths, Ilkyoo Choi, Bernard Lidicky, Florian Pfender

Mathematics Publications

A long standing open problem in extremal graph theory is to describe all graphs that maximize the number of induced copies of a path on four vertices. The character of the problem changes in the setting of oriented graphs, and becomes more tractable. Here we resolve this problem in the setting of oriented graphs without transitive triangles.


Catalytic Deoxygenation Of Model And Realistic Feeds To Fuel-Like Hydrocarbons Over Supported Nickel-Copper Catalysts, Deyshon Ward, Kazi Javed Nov 2018

Catalytic Deoxygenation Of Model And Realistic Feeds To Fuel-Like Hydrocarbons Over Supported Nickel-Copper Catalysts, Deyshon Ward, Kazi Javed

Posters-at-the-Capitol

The goal was to make a renewable fuel by using catalysts to remove oxygen molecules from fats. This is a current issue that society faces today because nonrenewable fossil fuels hurt the environment more than they help it. There are two components that make up a heterogeneous catalyst, a support and a reduced metal active phase. The active metal phases Nickel, Palladium, Platinum have been studied in the past on an alumina and carbon supports. We were investigating other supports using Nickel as the active phase component to determine the effect the support has on the catalyst removing oxygen of ...


33 - On The Existence Of An Arbitrarily Large Number Of Generators For The Presentation Ideal Of A Semigroup Ring., Arun Suresh Nov 2018

33 - On The Existence Of An Arbitrarily Large Number Of Generators For The Presentation Ideal Of A Semigroup Ring., Arun Suresh

Georgia Undergraduate Research Conference (GURC)

Consider K to be an arbitrary field, and P(n1,…, nm) be the ideal of polynomials given by

P(n1,…, nm) = {f(x1, … , xm) : f(x1,…,xm) ∈ K[x1,…,xm], f(tn1, … ,tnm) = 0, where t is transcendental over K}.

In 1970, J. Herzog showed that the least upper bound on the number of generators of K, for m = 3, is 3. It can be lowered to two, if n1, n2, n3 satisfy a few symmetry conditions. Following that, Bresinsky in 1975, showed ...


Predicting Time To Dementia Using A Quantitative Template Of Disease Progression, Murat Bilgel, Bruno Jedynak Nov 2018

Predicting Time To Dementia Using A Quantitative Template Of Disease Progression, Murat Bilgel, Bruno Jedynak

Portland Institute for Computational Science Publications

Introduction: Characterization of longitudinal trajectories of biomarkers implicated in sporadic Alzheimer's disease (AD) in decades prior to clinical diagnosis is important for disease prevention and monitoring.

Methods: We used a multivariate Bayesian model to temporally align 1369 AD Neuroimaging Initiative participants based on the similarity of their longitudinal biomarker measures and estimated a quantitative template of the temporal evolution cerebrospinal fluid (CSF) Aβ1-42, p-tau181p, and t-tau, hippocampal volume, brain glucose metabolism, and cognitive measurements. We computed biomarker trajectories as a function of time to AD dementia, and predicted AD dementia onset age in a disjoint sample.

Results ...


The Dpg-Star Method, Leszek Demkowicz, Jay Gopalakrishnan, Brendan Keith Nov 2018

The Dpg-Star Method, Leszek Demkowicz, Jay Gopalakrishnan, Brendan Keith

Portland Institute for Computational Science Publications

This article introduces the DPG-star (from now on, denoted DPG*) finite element method. It is a method that is in some sense dual to the discontinuous Petrov– Galerkin (DPG) method. The DPG methodology can be viewed as a means to solve an overdetermined discretization of a boundary value problem. In the same vein, the DPG* methodology is a means to solve an underdetermined discretization. These two viewpoints are developed by embedding the same operator equation into two different saddle-point problems. The analyses of the two problems have many common elements. Comparison to othermethods in the literature round out the newly ...