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Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski 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, David Hartman, Milan Hladik 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, Maria Axenovich, Dominik Duerrschnabel 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, Lindsey Herlehy 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, Abibat Adebisi Lasisi 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, Jacob Kullberg 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, Bernard Lidicky, Florian Pfender 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, Charles Seager 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, Zachary Garcia 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, Bradley Gardner 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, Osman KAN, Süleyman Solak 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, James B. Hart, Brian Frazier 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, Jaroslav Horáček, Milan Hladík, Josef Matějka 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 $\Mid A^{*} \Mid + \Mid B^{*} \Mid$, Yun Zhang 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, Nancy C. Wrinkle 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, Emma A. Turian 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, Matthew D. Graham 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, Zhonggang Zeng 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, Cecily Corrine Froemke, Martin Zwick 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, Christopher A. Sobecki, Jie Zhang, Yanzhi Zhang, Cheng Wang 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 ...


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