Second-Order Know-How Strategies, 2018 Lafayette College

#### Second-Order Know-How Strategies, Pavel Naumov, Jia Tao

*Faculty Research and Reports*

The fact that a coalition has a strategy does not mean that the coalition knows what the strategy is. If the coalition knows the strategy, then such a strategy is called a know-how strategy of the coalition. The paper proposes the notion of a second-order know-how strategy for the case when one coalition knows what the strategy of another coalition is. The main technical result is a sound and complete logical system describing the interplay between the distributed knowledge modality and the second-order coalition know-how modality.

From Sets To Metric Spaces To Topological Spaces, 2018 Ursinus College

#### From Sets To Metric Spaces To Topological Spaces, Nicholas A. Scoville

*Topology*

No abstract provided.

Mixed Categories Of Sheaves On Toric Varieties, 2018 Louisiana State University and Agricultural and Mechanical College

#### Mixed Categories Of Sheaves On Toric Varieties, Sean Michael Taylor

*LSU Doctoral Dissertations*

In [BGS96], Beilinson, Ginzburg, and Soergel introduced the notion of mixed categories. This idea often underlies many interesting "Koszul dualities." In this paper, we produce a mixed derived category of constructible complexes (in the sense of [BGS96]) for any toric variety associated to a fan. Furthermore, we show that it comes equipped with a t-structure whose heart is a mixed version of the category of perverse sheaves. In chapters 2 and 3, we provide the necessary background. Chapter 2 concerns the categorical preliminaries, while chapter 3 gives the background geometry. This concerns both some basics of toric varieties as well ...

The Hermitian Null-Range Of A Matrix Over A Finite Field, 2018 University of Trento

#### The Hermitian Null-Range Of A Matrix Over A Finite Field, Edoardo Ballico

*Electronic Journal of Linear Algebra*

Let $q$ be a prime power. For $u=(u_1,\dots ,u_n), v=(v_1,\dots ,v_n)\in \mathbb {F} _{q^2}^n$, let $\langle u,v\rangle := \sum _{i=1}^{n} u_i^qv_i$ be the Hermitian form of $\mathbb {F} _{q^2}^n$. Fix an $n\times n$ matrix $M$ over $\mathbb {F} _{q^2}$. In this paper, it is considered the case $k=0$ of the set $\mathrm{Num} _k(M):= \{\langle u,Mu\rangle \mid u\in \mathbb {F} _{q^2}^n, \langle u,u\rangle =k\}$. When $M$ has coefficients in $\mathbb {F ...

Algorithmic Trading With Prior Information, 2018 Washington University in St. Louis

#### Algorithmic Trading With Prior Information, Xinyi Cai

*Arts & Sciences Electronic Theses and Dissertations*

Traders utilize strategies by using a mix of market and limit orders to generate profits. There are different types of traders in the market, some have prior information and can learn from changes in prices to tweak her trading strategy continuously(Informed Traders), some have no prior information but can learn(Uninformed Learners), and some have no prior information and cannot learn(Uninformed Traders). In this thesis. Alvaro C, Sebastian J and Damir K \cite{AL} proposed a model for algorithmic traders to access the impact of dynamic learning in profit and loss in 2014. The traders can employ the ...

The Properties Of Partial Trace And Block Trace Operators Of Partitioned Matrices, 2018 Poznań University Of Technology

#### The Properties Of Partial Trace And Block Trace Operators Of Partitioned Matrices, Katarzyna Filipiak, Daniel Klein, Erika Vojtková

*Electronic Journal of Linear Algebra*

The aim of this paper is to give the properties of two linear operators defined on non-square partitioned matrix: the partial trace operator and the block trace operator. The conditions for symmetry, nonnegativity, and positive-definiteness are given, as well as the relations between partial trace and block trace operators with standard trace, vectorizing and the Kronecker product operators. Both partial trace as well as block trace operators can be widely used in statistics, for example in the estimation of unknown parameters under the multi-level multivariate models or in the theory of experiments for the determination of an optimal designs under ...

Preface: International Conference On Matrix Analysis And Its Applications -- Mattriad 2017, 2018 University of Tampere

#### Preface: International Conference On Matrix Analysis And Its Applications -- Mattriad 2017, Oskar Maria Baksalary, Natalia Bebiano, Heike Fassbender, Simo Puntanen

*Electronic Journal of Linear Algebra*

No abstract provided.

On The Distance And Distance Signless Laplacian Eigenvalues Of Graphs And The Smallest Gersgorin Disc, 2018 Indian Institute of Technology Kharagpur

#### On The Distance And Distance Signless Laplacian Eigenvalues Of Graphs And The Smallest Gersgorin Disc, Fouzul Atik, Pratima Panigrahi

*Electronic Journal of Linear Algebra*

The \emph{distance matrix} of a simple connected graph $G$ is $D(G)=(d_{ij})$, where $d_{ij}$ is the distance between the $i$th and $j$th vertices of $G$. The \emph{distance signless Laplacian matrix} of the graph $G$ is $D_Q(G)=D(G)+Tr(G)$, where $Tr(G)$ is a diagonal matrix whose $i$th diagonal entry is the transmission of the vertex $i$ in $G$. In this paper, first, upper and lower bounds for the spectral radius of a nonnegative matrix are constructed. Applying this result, upper and lower bounds for the distance and distance signless ...

Block Representation And Spectral Properties Of Constant Sum Matrices, 2018 School of Mathematics Cardiff University

#### Block Representation And Spectral Properties Of Constant Sum Matrices, Sally L. Hill, Matthew C. Lettington, Karl Michael Schmidt

*Electronic Journal of Linear Algebra*

An equivalent representation of constant sum matrices in terms of block-structured matrices is given in this paper. This provides an easy way of constructing all constant sum matrices, including those with further symmetry properties. The block representation gives a convenient description of the dihedral equivalence of such matrices. It is also shown how it can be used to study their spectral properties, giving explicit formulae for eigenvalues and eigenvectors in special situations, as well as for quasi-inverses when these exist.

Re-Evaluating Performance Measurement: New Mathematical Methods To Address Common Performance Measurement Challenges, 2018 Duquesne University

#### Re-Evaluating Performance Measurement: New Mathematical Methods To Address Common Performance Measurement Challenges, Jordan David Benis

*Electronic Theses and Dissertations*

Performance Measurement is an essential discipline for any business. Robust and reliable performance metrics for people, processes, and technologies enable a business to identify and address deficiencies to improve performance and profitability. The complexity of modern operating environments presents real challenges to developing equitable and accurate performance metrics. This thesis explores and develops two new methods to address common challenges encountered in businesses across the world. The first method addresses the challenge of estimating the relative complexity of various tasks by utilizing the Pearson Correlation Coefficient to identify potentially over weighted and under weighted tasks. The second method addresses the ...

Developmental Mathematics: A Quantitative Investigation Of Instructor Classification As Related To Student Success, 2018 Stephen F Austin State University

#### Developmental Mathematics: A Quantitative Investigation Of Instructor Classification As Related To Student Success, Brittany A. Fish

*Electronic Theses and Dissertations*

The purpose of this quantitative study was to examine what type of predictive power exists between an instructor’s employment classification, student gender, student race, and first-generation status on a student’s academic success in developmental mathematics, as measured by final semester grades at a regionally comprehensive state university in Texas between fall 2013 and spring 2017. Data were collected from the institution under study and the sample population included 1932 unique student observations. The data collected in this study were analyzed through a binary logistic regression model to determine whether an instructor’s employment classification, student gender, student race ...

Packing Tight Hamilton Cycles In Uniform Hypergraphs, 2018 Carnegie Mellon University

#### Packing Tight Hamilton Cycles In Uniform Hypergraphs, Deepak Bal, Alan Frieze

*Deepak Bal*

We say that a k-uniform hypergraph C is a Hamilton cycle of type ℓ, for some 1 ≤ ℓ ≤ k, if there exists a cyclic ordering of the vertices of C such that every edge consists of k consecutive vertices and for every pair of consecutive edges Ei−1, Ei in C (in the natural ordering of the edges) we have |Ei−1 \ Ei | = ℓ. We define a class of (ε, p)-regular hypergraphs, that includes random hypergraphs, for which we can prove the existence of a decomposition of almost all edges into type ℓ Hamilton cycles, where ℓ < k/2.

Rainbow Arborescence In Random Digraphs, 2018 Carnegie Mellon University

#### Rainbow Arborescence In Random Digraphs, Deepak Bal, Patrick Bennett, Colin Cooper, Alan Frieze, Pawel Pralat

*Deepak Bal*

We consider the Erd˝os-R´enyi random directed graph process, which is a stochastic process that starts with n vertices and no edges, and at each step adds one new directed edge chosen uniformly at random from the set of missing edges. Let D(n, m) be a graph with m edges obtained after m steps of this process. Each edge ei (i = 1, 2, . . . , m) of D(n, m) independently chooses a colour, taken uniformly at random from a given set of n(1 + O(log log n/ log n)) = n(1 + o(1)) colours. We stop the process ...

Interdisciplinary Fun With Knapp Chairs, Mit's Erik And Martin Demaine, 2018 University of San Diego

#### Interdisciplinary Fun With Knapp Chairs, Mit's Erik And Martin Demaine, Ryan T. Blystone

*Research Week*

No abstract provided.

Norm Inequalities Related To Clarkson Inequalities, 2018 University of Jordan

#### Norm Inequalities Related To Clarkson Inequalities, Fadi Alrimawi, Omar Hirzallah, Fuad Kittaneh

*Electronic Journal of Linear Algebra*

Let $A$ and $B$ be $n\times n$ matrices. It is shown that if $p=2$, $4\leq p<\infty$, or $2

Bounds For The Completely Positive Rank Of A Symmetric Matrix Over A Tropical Semiring, 2018 University of Ljubljana

#### Bounds For The Completely Positive Rank Of A Symmetric Matrix Over A Tropical Semiring, David Dolžan, Polona Oblak

*Electronic Journal of Linear Algebra*

In this paper, an upper bound for the CP-rank of a matrix over a tropical semiring is obtained, according to the vertex clique cover of the graph prescribed by the positions of zero entries in the matrix. The graphs that beget the matrices with the lowest possible CP-ranks are studied, and it is proved that any such graph must have its diameter equal to $2$.

Golden Arm: A Probabilistic Study Of Dice Control In Craps, 2018 Monmouth University

#### Golden Arm: A Probabilistic Study Of Dice Control In Craps, Donald R. Smith, Robert Scott Iii

*UNLV Gaming Research & Review Journal*

This paper calculates how much control a craps shooter must possess on dice outcomes to eliminate the house advantage. A golden arm is someone who has dice control (or a rhythm roller or dice influencer). There are various strategies for dice control in craps. We discuss several possibilities of dice control that would result in several different mathematical models of control. We do not assert whether dice control is possible or not (there is a lack of published evidence). However, after studying casino-legal methods described by dice-control advocates, we can see only one realistic mathematical model that describes the resulting ...

Creating A Predictive Model For Flowering Of Virginia Orchid, Cypripedium Pubescens, 2018 Lynchburg College

#### Creating A Predictive Model For Flowering Of Virginia Orchid, Cypripedium Pubescens, Emily Horton

*Undergraduate Theses and Capstone Projects*

This research investigates the native Virginia orchid, *Cyprepedium* *pubescens,* or the large yellow lady-slipper. Researchers at Lynchburg College, located in central Virginia, collected orchid activity data over the span of nine years from 2006-2014. This data included the following information: when the first sprout appeared, the number of leaves, the number of flowers, and the number of flowers per each plant. Using collected data about nine orchids on the campus of Lynchburg College as a basis, we wanted create a model that would predict when we might see flowering on a yearly basis. Flowering is important because researchers are investigating ...

Examples Of Solving The Wave Equation In The Hyperbolic Plane, 2018 Liberty University

#### Examples Of Solving The Wave Equation In The Hyperbolic Plane, Cooper Ramsey

*Senior Honors Theses*

The complex numbers have proven themselves immensely useful in physics, mathematics, and engineering. One useful tool of the complex numbers is the method of conformal mapping which is used to solve various problems in physics and engineering that involved Laplace’s equation. Following the work done by Dr. James Cook, the complex numbers are replaced with associative real algebras. This paper focuses on another algebra, the hyperbolic numbers. A solution method like conformal mapping is developed with solutions to the one-dimensional wave equation. Applications of this solution method revolve around engineering and physics problems involving the propagation of waves. To ...

Supporting English Language Learners Inside The Mathematics Classroom: One Teacher’S Unique Perspective Working With Students During Their First Years In America, 2018 University of Nebraska - Lincoln

#### Supporting English Language Learners Inside The Mathematics Classroom: One Teacher’S Unique Perspective Working With Students During Their First Years In America, Amy Marie Fendrick

*Research and Evaluation in Literacy and Technology*

Reflecting upon my personal experiences teaching mathematics to English Language Learners (ELL) in a public high school in Lincoln, Nebraska, this essay largely focuses on the time I spent as the only Accelerated Math teacher in my school building. From 2012 – 2017, I taught three different subjects at this high school: Advanced Algebra, Algebra, and Accelerated Math. This essay highlights why I chose to become a math and ELL teacher, as well as the challenges, issues, struggles, and successes I experienced during my time teaching. I focus on the challenges I faced teaching students who did not share my native ...