On Orders Of Elliptic Curves Over Finite Fields, 2018 Columbia University

#### On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim

*Rose-Hulman Undergraduate Mathematics Journal*

In this work, we completely characterize by $j$-invariant the number of orders of elliptic curves over all finite fields $F_{p^r}$ using combinatorial arguments and elementary number theory. Whenever possible, we state and prove exactly which orders can be taken on.

A Comparison Of Algorithms For Finding An Efficient Theme Park Tour, 2018 Furman University

#### A Comparison Of Algorithms For Finding An Efficient Theme Park Tour, Liz Bouzarth, Richard J. Forrester, Kevin Hutson, Rahul Isaac, James Midkiff, Danny Rivers, Leonard J. Testa

*Mathematics Publications*

The problem of efficiently touring a theme park so as to minimize the amount of time spent in queues is an instance of the Traveling Salesman Problem with Time-Dependent Service Times (TSP-TS). In this paper, we present a mixed-integer linear programming formulation of the TSP-TS and describe a branch-and-cut algorithm based on this model. In addition, we develop a lower bound for the TSP-TS and describe two metaheuristic approaches for obtaining good quality solutions: a genetic algorithm and a tabu search algorithm. Using test instances motivated by actual theme park data, we conduct a computational study to compare the effectiveness ...

On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, 2018 Poznań University Of Technology

#### On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, Katarzyna Filipiak, Augustyn Markiewicz, Adam Mieldzioc, Aneta Sawikowska

*Electronic Journal of Linear Algebra*

We consider approximation of a given positive definite matrix by nonnegative definite banded Toeplitz matrices. We show that the projection on linear space of Toeplitz matrices does not always preserve nonnegative definiteness. Therefore we characterize a convex cone of nonnegative definite banded Toeplitz matrices which depends on the matrix dimensions, and we show that the condition of positive definiteness given by Parter [{\em Numer. Math. 4}, 293--295, 1962] characterizes the asymptotic cone. In this paper we give methodology and numerical algorithm of the projection basing on the properties of a cone of nonnegative definite Toeplitz matrices. This problem can be ...

Explicit Block-Structures For Block-Symmetric Fiedler-Like Pencils, 2018 University of California, Santa Barbara

#### Explicit Block-Structures For Block-Symmetric Fiedler-Like Pencils, M. I. Bueno, Madeline Martin, Javier Perez, Alexander Song, Irina Viviano

*Electronic Journal of Linear Algebra*

In the last decade, there has been a continued effort to produce families of strong linearizations of a matrix polynomial $P(\lambda)$, regular and singular, with good properties, such as, being companion forms, allowing the recovery of eigenvectors of a regular $P(\lambda)$ in an easy way, allowing the computation of the minimal indices of a singular $P(\lambda)$ in an easy way, etc. As a consequence of this research, families such as the family of Fiedler pencils, the family of generalized Fiedler pencils (GFP), the family of Fiedler pencils with repetition, and the family of generalized Fiedler pencils with ...

On The Largest Distance (Signless Laplacian) Eigenvalue Of Non-Transmission-Regular Graphs, 2018 East China Normal University

#### On The Largest Distance (Signless Laplacian) Eigenvalue Of Non-Transmission-Regular Graphs, Shuting Liu, Jinlong Shu, Jie Xue

*Electronic Journal of Linear Algebra*

Let $G=(V(G),E(G))$ be a $k$-connected graph with $n$ vertices and $m$ edges. Let $D(G)$ be the distance matrix of $G$. Suppose $\lambda_1(D)\geq \cdots \geq \lambda_n(D)$ are the $D$-eigenvalues of $G$. The transmission of $v_i \in V(G)$, denoted by $Tr_G(v_i)$ is defined to be the sum of distances from $v_i$ to all other vertices of $G$, i.e., the row sum $D_{i}(G)$ of $D(G)$ indexed by vertex $v_i$ and suppose that $D_1(G)\geq \cdots \geq D_n(G)$. The $Wiener~ index$ of $G$ denoted by $W ...

Spectral Bounds For The Connectivity Of Regular Graphs With Given Order, 2018 Maastricht University

#### Spectral Bounds For The Connectivity Of Regular Graphs With Given Order, Aida Abiad, Boris Brimkov, Xavier Martinez-Rivera, Suil O, Jingmei Zhang

*Electronic Journal of Linear Algebra*

The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to connectivity attributes such as the vertex- and edge-connectivity, isoperimetric number, and characteristic path length. In this paper, two upper bounds are presented for the second-largest eigenvalues of regular graphs and multigraphs of a given order which guarantee a desired vertex- or edge-connectivity. The given bounds are in terms of the order and degree of the graphs, and hold with equality for infinite families of graphs. These results ...

Bounded Linear Operators That Preserve The Weak Supermajorization On $\Ell^1(I)^+$, 2018 Faculty of Mechanical Engineering, Department of Mathematics,University of Niš, Serbia

#### Bounded Linear Operators That Preserve The Weak Supermajorization On $\Ell^1(I)^+$, Martin Z. Ljubenović, Dragan S. Djordjevic

*Electronic Journal of Linear Algebra*

Linear preservers of weak supermajorization which is defined on positive functions contained in the discrete Lebesgue space $\ell^1(I)$ are characterized. Two different classes of operators that preserve the weak supermajorization are formed. It is shown that every linear preserver may be decomposed as sum of two operators from the above classes, and conversely, the sum of two operators which satisfy an additional condition is a linear preserver. Necessary and sufficient conditions under which a bounded linear operator is a linear preserver of the weak supermajorization are given. It is concluded that positive linear preservers of the weak supermajorization ...

Color Space Standardization And Image Analysis For High-Throughput Phenotyping Of Sorghum Bicolor, 2018 Department of Mathematics, Illinois State University

#### Color Space Standardization And Image Analysis For High-Throughput Phenotyping Of Sorghum Bicolor, Alexandria A. Pokorny

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

No abstract provided.

Transformations On Double Occurrence Words Motivated By Dna Rearrangement, 2018 University of South Florida

#### Transformations On Double Occurrence Words Motivated By Dna Rearrangement, Daniel Cruz, Margherita Maria Ferrari, Lukas Nabergall, Natasa Jonoska, Masahico Saito

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

No abstract provided.

Semi-Tensor Product Representations Of Boolean Networks, 2018 Illinois State University

#### Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

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

No abstract provided.

The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, 2018 Illinois State University

#### The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

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

No abstract provided.

Combinatorial Geometry Of Threshold-Linear Networks, 2018 Illinois State University

#### Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon

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

No abstract provided.

Topological Detection Of The Dimension Of The Stimuli Space, 2018 Illinois State University

#### Topological Detection Of The Dimension Of The Stimuli Space, Aliaksandra Yarosh

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

No abstract provided.

Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, 2018 Illinois State University

#### Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

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

No abstract provided.

Weighted Composition Operators On Analytic Function Spaces: Some Recent Progress, 2018 Embry-Riddle Aeronautical University

#### Weighted Composition Operators On Analytic Function Spaces: Some Recent Progress, Dip Acharyya

*Publications*

Theory of Composition Operators is a steady point of interest for almost 100 years. While studying these operators, our general goal is to describe their operator theoretic properties in terms of the associated function symbols. In this talk, I will discuss some recent results concerning linear combinations (sums, differences, etc.) of weighted composition operators in certain spaces of Analytic functions.

Reducing The Maximum Degree Of A Graph By Deleting Vertices: The Extremal Cases, 2018 University of Malta

#### Reducing The Maximum Degree Of A Graph By Deleting Vertices: The Extremal Cases, Peter Borg, Kurt Fenech

*Theory and Applications of Graphs*

Let $\lambda(G)$ denote the smallest number of vertices that can be removed from a non-empty graph $G$ so that the resulting graph has a smaller maximum degree. In a recent paper, we proved that if $n$ is the number of vertices of $G$, $k$ is the maximum degree of $G$, and $t$ is the number of vertices of degree $k$, then $\lambda (G) \leq \frac{n+(k-1)t}{2k}$. We also showed that $\lambda (G) \leq \frac{n}{k+1}$ if $G$ is a tree. In this paper, we provide a new proof of the first bound and use ...

Math Active Learning Lab: Math 93 Notebook, 2018 University of North Dakota

#### Math Active Learning Lab: Math 93 Notebook, Michele Iiams, Gwennie Byron

*Open Educational Resources*

This course notebook has been designed for students of Math 93 (Algebra Prep III) at the University of North Dakota. It has been designed to help you get the most out of the ALEKS resources and your time.

- Topics in the Notebook are organized by weekly learning module.
- Space for notes from ALEKS learning pages, e-book and videos directs you to essential concepts.
- Examples and “You Try It” problems have been carefully chosen to help you focus on these essential concepts.
- Completed Notebook is an invaluable tool when studying for exams.

Otto Holder's Formal Christening Of The Quotient Group Concept, 2018 Colorado State University-Pueblo

#### Otto Holder's Formal Christening Of The Quotient Group Concept, Janet Heine Barnett

*Abstract Algebra*

No abstract provided.

Vaccination Strategies And Herd Immunity Thresholds In Small World Models, 2018 University of Portland

#### Vaccination Strategies And Herd Immunity Thresholds In Small World Models, Emily Mcclung, Sam Rivas, Emma Soriano, Caelan Thomas, Hannah Highlander

*Mathematics Undergraduate Publications, Presentations and Projects*

Infectious diseases pose a serious threat to humans, plants, and animals. Though vaccines can help control outbreaks of infectious diseases, there is typically not enough vaccine available for the entire population. In this case, certain vaccination strategies can be employed to maximize the benefits for the entire population. Using results from graph theory and the simulation tool lONTW (Infections On NeTWorks), we investigated various vaccination strategies on certain types of so-called contact networks that model the patterns of interactions within a population. In particular, we focused on a certain class of contact networks known as small world models, where individuals ...

Dual Perspectives On Desargues' Theorem, 2018 Ursinus College