# Mathematics Commons™

Articles 1 - 30 of 17785

## Full-Text Articles in Mathematics

Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. Deloach Jan 2020

#### Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. Deloach

##### University Honors Program Theses

Mathematics is a discipline of academia that can be found everywhere in the world around us. Mathematicians and scientists are not the only people who need to be proficient in numbers. Those involved in social sciences and even the arts can benefit from a background in math. In fact, connections between mathematics and various forms of art have been discovered since as early as the fourth century BC. In this thesis we will study such connections and related concepts in mathematics, dances, and music.

Gehring Inequalities On Time Scales, Martin Bohner, S. H. Saker Jan 2020

#### Gehring Inequalities On Time Scales, Martin Bohner, S. H. Saker

##### Mathematics and Statistics Faculty Research & Creative Works

In this paper, we first prove a new dynamic inequality based on an application of the time scales version of a Hardy-type inequality. Second, by employing the obtained inequality, we prove several Gehring-type inequalities on time scales. As an application of our Gehring-type inequalities, we present some interpolation and higher integrability theorems on time scales. The results as special cases, when the time scale is equal to the set of all real numbers, contain some known results, and when the time scale is equal to the set of all integers, the results are essentially new.

Individual Based Modeling And Analysis Of Pathogen Levels In Poultry Chilling Process, Zachary Mccarthy, Ben Smith, Aamir Fazil, Jianhong Wu, Shawn D. Ryan, Daniel Munther Dec 2019

#### Individual Based Modeling And Analysis Of Pathogen Levels In Poultry Chilling Process, Zachary Mccarthy, Ben Smith, Aamir Fazil, Jianhong Wu, Shawn D. Ryan, Daniel Munther

##### Mathematics Faculty Publications

Pathogen control during poultry processing critically depends on more enhanced insight into contamination dynamics. In this study we build an individual based model (IBM) of the chilling process. Quantifying the relationships between typical Canadian processing specifications, water chemistry dynamics and pathogen levels both in the chiller water and on individual carcasses, the IBM is shown to provide a useful tool for risk management as it can inform risk assessment models. We apply the IBM to Campylobacter spp. contamination on broiler carcasses, illustrating how free chlorine (FC) sanitization, organic load in the water, and pre-chill carcass pathogen levels affect pathogen levels ...

Laplacian Spectral Characterization Of Signed Sun Graphs, Fatemeh Motialah, Mohammad Hassan Shirdareh Haghighi Oct 2019

#### Laplacian Spectral Characterization Of Signed Sun Graphs, Fatemeh Motialah, Mohammad Hassan Shirdareh Haghighi

##### Theory and Applications of Graphs

A sun $SG_{n}$ is a graph of order $2n$ consisting of a cycle $C_{n}$, $n\geq 3$, to each vertex of it a pendant edge is attached. In this paper, we prove that unbalanced signed sun graphs are determined by their Laplacian spectra. Also we show that a balanced signed sun graph is determined by its Laplacian spectrum if and only if $n$ is odd.

Inequalities For Sector Matrices And Positive Linear Maps, Fuping Tan, Huimin Chen Oct 2019

#### Inequalities For Sector Matrices And Positive Linear Maps, Fuping Tan, Huimin Chen

##### Electronic Journal of Linear Algebra

Ando proved that if $A, B$ are positive definite, then for any positive linear map $\Phi$, it holds \begin{eqnarray*} \Phi(A\sharp_\lambda B)\le \Phi(A)\sharp_\lambda \Phi(B), \end{eqnarray*} where $A\sharp_\lambda B$, $0\le\lambda\le 1$, means the weighted geometric mean of $A, B$. Using the recently defined geometric mean for accretive matrices, Ando's result is extended to sector matrices. Some norm inequalities are considered as well.

#### The Grass Grows Green In Virginia: A Grassroots Effort Leading To Comprehensive Change In Removing Mathematics Barriers For Students., Patricia Parker

##### Inquiry: The Journal of the Virginia Community Colleges

The Virginia Community College System (VCCS) embarked on a comprehensive mathematics pathways project in October 2015 with a move from design to implementation in spring 2017. The VCCS Mathematics Pathways Project (VMPP) aimed not only to develop strategies to improve retention and completion, but also to address foundational barriers to students’ success. This grassroots effort involved collaboration among all 23 community colleges, over 200 mathematics faculty, and staff from career and technical support departments. Collaboration extended to the K–12 and university sectors, professional organizations, publishers, and foundations. VMPP goals focused on creating structured mathematics pathway courses for all program ...

Reinforcing The Number Of Disjoint Spanning Trees, Damin Liu, Hong-Jian Lai, Zhi-Hong Chen Oct 2019

#### Reinforcing The Number Of Disjoint Spanning Trees, Damin Liu, Hong-Jian Lai, Zhi-Hong Chen

##### Zhi-Hong Chen

The spanning tree packing number of a connected graph G, denoted by T(G), is the maximum number of edge-disjoint spanning trees of G. In this paper, we determine the minimum number of edges that must be added to G so that the resulting graph has spanning tree packing number at least k, for a given value of k.

Making Kr+1-Free Graphs R-Partite, József Balogh, Felix Christian Clemen, Mikhail Lavrov, Bernard Lidický, Florian Pfender Oct 2019

#### Making Kr+1-Free Graphs R-Partite, József Balogh, Felix Christian Clemen, Mikhail Lavrov, Bernard Lidický, Florian Pfender

##### Bernard Lidický

The Erdős–Simonovits stability theorem states that for all ε > 0 there exists α > 0 such that if G is a Kr+1-free graph on n vertices with e(G) > ex(n, Kr+1) − αn2, then one can remove εn2 edges from G to obtain an r-partite graph. Fu¨redi gave a short proof that one can choose α = ε. We give a bound for the relationship of α and ε which is asymptotically sharp as ε → 0.

Oct 2019

#### Sdrap: An Annotation Pipeline For Highly Scrambled Genomes, Jasper Braun

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Mathematical Models For Describing Molecular Self-Assembly, Margherita Maria Ferrari Oct 2019

#### Mathematical Models For Describing Molecular Self-Assembly, Margherita Maria Ferrari

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt Oct 2019

#### Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra Oct 2019

#### Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Loop Homology Of Bi-Secondary Structures, Andrei Bura Oct 2019

#### Loop Homology Of Bi-Secondary Structures, Andrei Bura

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Design Of Experiments For Unique Wiring Diagram Identification, Elena Dimitrova Oct 2019

#### Design Of Experiments For Unique Wiring Diagram Identification, Elena Dimitrova

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

The Energy-Spectrum Of Bicompatible Sequences, Wenda Huang Oct 2019

#### The Energy-Spectrum Of Bicompatible Sequences, Wenda Huang

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

On An Enhancement Of Rna Probing Data Using Information Theory, Thomas J.X. Li, Christian M. Reidys Oct 2019

#### On An Enhancement Of Rna Probing Data Using Information Theory, Thomas J.X. Li, Christian M. Reidys

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Oct 2019

#### Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Modeling Control Methods To Manage The Sylvatic Plague In Black-Tailed Prairie Dog Towns, David C. Elzinga, Shelby R. Stowe, Leland Russell Oct 2019

#### Modeling Control Methods To Manage The Sylvatic Plague In Black-Tailed Prairie Dog Towns, David C. Elzinga, Shelby R. Stowe, Leland Russell

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Using Agent-Based Modeling To Investigate The Existence Of Herd Immunity Thresholds For Infectious Diseases On Randomly Generated Contact Networks, Hannah Callender Highlander, Owen Price Oct 2019

#### Using Agent-Based Modeling To Investigate The Existence Of Herd Immunity Thresholds For Infectious Diseases On Randomly Generated Contact Networks, Hannah Callender Highlander, Owen Price

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Oscillation In Mathematical Epidemiology, Meredith Greer Oct 2019

#### Oscillation In Mathematical Epidemiology, Meredith Greer

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Oct 2019

#### A Concise Workbook For College Algebra 2nd Edition, Fei Ye

##### Open Educational Resources

This is the second edition of the book "A Concise Workbook for College Algebra". In this new edition, some tips and notes, more exercises and examples were added.

Oct 2019

#### A Study On Discrete And Discrete Fractional Pharmacokinetics-Pharmacodynamics Models For Tumor Growth And Anti-Cancer Effects, Ferhan Atici, Ngoc Nguyen

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Oct 2019

#### Research For Educators: Modeling Graph Theory For Nontraditional Math Researchers, Erwin Cornelius

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Oct 2019

#### A Model For Cross-Institutional Collaboration: Addressing Diminishing Resources In Academia, Claudia Kolakowski

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, X. Zhang, Y. Zhang, John R. Singler Oct 2019

#### An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, X. Zhang, Y. Zhang, John R. Singler

##### Mathematics and Statistics Faculty Research & Creative Works

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their uxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.

Exercises Integrating High School Mathematics With Robot Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal Oct 2019

#### Exercises Integrating High School Mathematics With Robot Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal

##### Computer Science: Faculty Publications and Other Works

This paper presents progress in developing exercises for high school students incorporating level-appropriate mathematics into robotics activities. We assume mathematical foundations ranging from algebra to precalculus, whereas most prior work on integrating mathematics into robotics uses only very elementary mathematical reasoning or, at the other extreme, is comprised of technical papers or books using calculus and other advanced mathematics. The exercises suggested are relevant to any differerential-drive robot, which is an appropriate model for many different varieties of educational robots. They guide students towards comparing a variety of natural navigational strategies making use of typical movement primitives. The exercises align ...

Oct 2019

#### Beauty, Bees, And God: The Fibonacci Sequence As A Theological Springboard In Secondary Mathematics, John D. Brahier

##### Journal of Catholic Education

Catholic schools primarily should be in the business of making saints. This article identifies and explores a meaningful, engaging point of contact between mathematics and theology for high school math classes, the Fibonacci Sequence. This sequence serves as an engaging introduction to sequences and series; more importantly, the topic can be used as a springboard to theological discussions. The paper will provide a brief historical background to the Fibonacci Sequence, an explanation of how it can be used in a high school math classroom, and an exploration of three different theological touchpoints that the Fibonacci Sequence offers.

Diffusion And Consensus On Weakly Connected Directed Graphs, J. J. P. Veerman, Ewan Kummel Oct 2019

#### Diffusion And Consensus On Weakly Connected Directed Graphs, J. J. P. Veerman, Ewan Kummel

##### Mathematics and Statistics Faculty Publications and Presentations

Let G be a weakly connected directed graph with asymmetric graph Laplacian L. Consensus and diffusion are dual dynamical processes defined on G by x˙=−Lx for consensus and p˙=−pL for diffusion. We consider both these processes as well their discrete time analogues. We define a basis of row vectors {γ¯i}ki=1 of the left null-space of L and a basis of column vectors {γi}ki=1 of the right null-space of L in terms of the partition of G into strongly connected components. This allows for complete characterization of the asymptotic behavior of both diffusion and ...

Sep 2019

#### Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, Olusegun M. Otunuga

##### Olusegun Michael Otunuga

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to ...

Making Kr+1-Free Graphs R-Partite, József Balogh, Felix Christian Clemen, Mikhail Lavrov, Bernard Lidický, Florian Pfender Sep 2019

#### Making Kr+1-Free Graphs R-Partite, József Balogh, Felix Christian Clemen, Mikhail Lavrov, Bernard Lidický, Florian Pfender

##### Mathematics Publications

The Erdős–Simonovits stability theorem states that for all ε > 0 there exists α > 0 such that if G is a Kr+1-free graph on n vertices with e(G) > ex(n, Kr+1) − αn2, then one can remove εn2 edges from G to obtain an r-partite graph. Fu¨redi gave a short proof that one can choose α = ε. We give a bound for the relationship of α and ε which is asymptotically sharp as ε → 0.