Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, 2018 Wojciech Budzianowski Consulting Services

#### 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, 2018 Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics, Prague, Czech Republic and Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic.

#### 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, 2018 Karlsruhe Institute of Technology

#### 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, 2018 Illinois Mathematics and Science Academy

#### 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, 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 ...

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 ...

Pentagons In Triangle-Free Graphs, 2018 Iowa State University

#### 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, 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 ...

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 ...

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 ...

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 ...