Positive Semidefinite 3 X 3 Block Matrices, 2014 University of Wyoming

#### Positive Semidefinite 3 X 3 Block Matrices, Minghua Lin, Pauline Van Den Driessche

*Electronic Journal of Linear Algebra*

Several results related to positive semidefinite 3 by 3 block matrices are presented. In particular, a question of Audenaert is answered affirmatively and some determinantal inequalities are proved.

Gifted Students In Mathematics: A Problem Solving Approach To Enrichment, 2014 The College at Brockport: State University of New York

#### Gifted Students In Mathematics: A Problem Solving Approach To Enrichment, Caylin Depuy

*Education and Human Development Master's Theses*

** **In the United States mathematically gifted students frequently go unnoticed and most often receive the same education as their at-level peers (Ysseldyke, Tardrew, Betts, Thill, Hannigan, 2004). There is very limited funding available for gifted students and the identification and classification varies by state, often being decided by school district (National Association, 2014). Gifted American students are exposed to less challenging problems than those in other countries and, as a result, are falling behind in academic performance (Ross, 1993). This curriculum is designed to supplement the existing Geometry curriculum by offering eight unique, challenging problems that can be used for ...

An Algebra Unit On Quadratics For Teachers With Students With Ebd, 2014 The College at Brockport: State University of New York

#### An Algebra Unit On Quadratics For Teachers With Students With Ebd, Christopher Williams

*Education and Human Development Master's Theses*

The number of students identified as having an emotional and behavioral disorder (EBD) are increasing rapidly and still underreported. These students often have significant behavioral, social and academic deficits that pose challenges within and outside the school setting and are among some of the most difficult students to teach with the bleakest post-school success or employment rates. Research reveals several effective procedures for conducting interventions to increase performance, participation and engagement and in lowering the number of inappropriate behavior occurrences within the classroom. Based on these findings, an algebra unit plan on quadratics has been developed to assist and direct ...

The Structure And Properties Of Clique Graphs Of Regular Graphs, 2014 The University of Southern Mississippi

#### The Structure And Properties Of Clique Graphs Of Regular Graphs, Jan Burmeister

*Master's Theses*

In the following thesis, the structure and properties of *G *and its clique graph *cl*_{t}* *(*G*) are analyzed for graphs *G *that are non-complete, regular with degree *δ *, and where every edge of *G *is contained in a *t *-clique. In a clique graph *cl*_{t}* *(*G*), all cliques of order *t *of the original graph *G *become the clique graph’s vertices, and the vertices of the clique graph are adjacent if and only if the corresponding cliques in the original graph have at least 1 vertex in common. This thesis mainly investigates if properties of regular graphs ...

Introduction To Mathematical Analysis, 2014 Portland State University

#### Introduction To Mathematical Analysis, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

*Open Access Textbooks: PDX Open*

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract ...

Mixed Variational Formulation For The Wellposedness And Numerical Approximation Of A Pde Model Arising In A 3-D Fluid-Structure Interaction, 2014 Dordt College

#### Mixed Variational Formulation For The Wellposedness And Numerical Approximation Of A Pde Model Arising In A 3-D Fluid-Structure Interaction, George Avalos, Tom Clark

*Faculty Work*

We present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. Wellposedness is established by constructing for it a nonstandard semigroup generator representation; this representation is accomplished by an appropriate elimination of the pressure. This coupled PDE model involves the Stokes system which evolves on a three dimensional domain O coupled to a fourth order plate equation, possibly with rotational inertia parameter ρ>0. This plate PDE evolves on a flat portion Ω of the boundary of O. The coupling on Ω is implemented via the Dirichlet trace of the Stokes system ...

Ogden College News, 2014 Western Kentucky University

#### Ogden College News, Cheryl Stevens, Dean, Odgen College Of Science & Engineering, Western Kentucky University

*Ogden College of Science & Engineering Publications*

No abstract provided.

Classical And Motivic Adams Charts, 2014 Wayne State University

#### Classical And Motivic Adams Charts, Daniel C. Isaksen

*Mathematics Research Reports*

This document contains large-format Adams charts that compute 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. The charts are essentially complete through the 59-stem and contain partial results to the 70-stem. In the classical context, we believe that these are the most accurate charts of their kind. We also include Adams charts for the motivic homotopy groups of the cofiber of τ.

Classical And Motivic Adams-Novikov Charts, 2014 Wayne State University

#### Classical And Motivic Adams-Novikov Charts, Daniel C. Isaksen

*Mathematics Research Reports*

This document contains large-format Adams-Novikov charts that compute the classical 2-complete stable homotopy groups. The charts are essentially complete through the 59-stem. We believe that these are the most accurate and extensive charts of their kind. We also include a motivic Adams-Novikov E∞ chart.

The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, 2014 Brigham Young University

#### The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, Michael Steven Andersen

*All Theses and Dissertations*

Conner and Spencer used ultrafilters to construct homomorphisms between fundamental groups that could not be induced by continuous functions between the underlying spaces. We use methods from Shelah and Pawlikowski to prove that Conner and Spencer could not have constructed these homomorphisms with a weak version of the Axiom of Choice. This led us to define and examine a class of pathological objects that cannot be constructed without a strong version of the Axiom of Choice, which we call the class of inscrutable objects. Objects that do not need a strong version of the Axiom of Choice are scrutable. We ...

On The Estrada Index Of Cacti, 2014 University of Wyoming

#### On The Estrada Index Of Cacti, Erfang Shan, Hongzhuan Wang, Liying Kang

*Electronic Journal of Linear Algebra*

Let G be a simple connected graph on n vertices and λ_1, λ_2, . . . , λ_n be the eigenvalues of the adjacency matrix of G. The Estrada index of G is defined as EE(G) = \sum_{i=1}^n e^{λi}. A cactus is a connected graph in which any two cycles have at most one common vertex. In this work, the unique graph with maximal Estrada index in the class of all cacti with n vertices and k cycles was determined. Also, the unique graph with maximal Estrada index in the class of all cacti with n vertices and k cut ...

Exact Results For Perturbation To Total Positivity And To Total Nonsingularity, 2014 University of Wyoming

#### Exact Results For Perturbation To Total Positivity And To Total Nonsingularity, Miriam Farber, Mitchell Faulk, Charles R. Johnson, Evan Marzion

*Electronic Journal of Linear Algebra*

A study of the maximum number of equal entries in totally positive and totally nonsingular m-by-n, matrices for small values of m and n, is presented. Equal entries correspond to entries of the totally nonnegative matrix J that are not changed in producing a TP or TNS matrix. It is shown that the maximum number of equal entries in a 7-by-7 totally positive matrix is strictly smaller than that for a 7-by-7 totally non-singular matrix, but, this is the first pair (m; n) for which these maximum numbers differ. Using point-line geometry in the projective plane, a family of values ...

The Combinatorial Inverse Eigenvalue Problem Ii: All Cases For Small Graphs, 2014 University of Wyoming

#### The Combinatorial Inverse Eigenvalue Problem Ii: All Cases For Small Graphs, Wayne Barrett, Curtis G. Nelson, John Henry Sinkovic, Tianyi Yang

*Electronic Journal of Linear Algebra*

Let G be a simple undirected graph on n vertices and let S(G) be the class of real symmetric n by n matrices whose nonzero off-diagonal entries correspond to the edges of G. Given 2n - 1 real numbers \lambda_1\geq \mu_1 \geq \lambda_2 \geq \mu_2 \geq \cdots \geq \lambda_{n-1} \geq \mu_{n-1} \geq \lambda_{n-1}, and a vertex v of G, the question is addressed of whether or not there exists A in S(G) with eigenvalues \lambda_1, \ldots, \lambda_ n such that A(v) has eigenvalues \mu_1, \ldots, \mu_{n-1}, where A(v) denotes the matrix with ...

Commuting Maps On Rank-K Matrices, 2014 University of Wyoming

#### Commuting Maps On Rank-K Matrices, Xiao-Wei Xu, Xiaofei Yi

*Electronic Journal of Linear Algebra*

In this short note we give a new proof and a slight improvement of the Franca Theorem. More precisely we prove: Let n \geq 3 be a natural number, and let Mn(K) be the ring of all n × n matrices over an arbitrary field K with center Z. Fix a natural number 2≤s≤n. If G:Mn(K)→Mn(K) is an additive map such that G(x)x=xG(x) for every rank-s matrix x ∈ Mn(K), then there exist an element λ ∈ Z and an additive map μ : Mn(K) → Z such that G(x) = λx ...

Traces Of Matrix Products, 2014 University of Wyoming

#### Traces Of Matrix Products, John Greene

*Electronic Journal of Linear Algebra*

Given two noncommuting matrices, A and B, it is well known that AB and BA have the same trace. This extends to cyclic permutations of products of A’s and B’s. It is shown here that for 2×2 matrices A and B, whose elements are independent random variables with standard normal distributions, the probability that Tr(ABAB) > Tr(AB) is exactly 1/\sqrt{2} .

Note On Rainbow Connection In Oriented Graphs With Diameter 2, 2014 Georgia Southern University

#### Note On Rainbow Connection In Oriented Graphs With Diameter 2, Rebecca Holliday, Colton Magnant, Pouria Salehi Nowbandegani

*Theory and Applications of Graphs*

In this note, we provide a sharp upper bound on the rainbow connection number of tournaments of diameter $2$. For a tournament $T$ of diameter $2$, we show $2 \leq \overrightarrow{rc}(T) \leq 3$. Furthermore, we provide a general upper bound on the rainbow $k$-connection number of tournaments as a simple example of the probabilistic method. Finally, we show that an edge-colored tournament of $k^{th}$ diameter $2$ has rainbow $k$-connection number at most approximately $k^{2}$.

The Scope Of Gödel’S First Incompleteness Theorem, 2014 Indiana University – Purdue University Fort Wayne

#### The Scope Of Gödel’S First Incompleteness Theorem, Bernd Buldt

*Philosophy Faculty Publications*

Guided by questions of scope, this paper provides an overview of what is known about both the scope and, consequently, the limits of Gödel’s famous first incompleteness theorem.

Hamiltonicity And $\Sigma$-Hypergraphs, 2014 Georgia Southern University

#### Hamiltonicity And $\Sigma$-Hypergraphs, Christina Zarb

*Theory and Applications of Graphs*

We define and study a special type of hypergraph. A $\sigma$-hypergraph $H= H(n,r,q$ $\mid$ $\sigma$), where $\sigma$ is a partition of $r$, is an $r$-uniform hypergraph having $nq$ vertices partitioned into $ n$ classes of $q$ vertices each. If the classes are denoted by $V_1$, $V_2$,...,$V_n$, then a subset $K$ of $V(H)$ of size $r$ is an edge if the partition of $r$ formed by the non-zero cardinalities $ \mid$ $K$ $\cap$ $V_i \mid$, $ 1 \leq i \leq n$, is $\sigma$. The non-empty intersections $K$ $\cap$ $V_i$ are called the parts of $K$, and $s ...

Online Resource Platform For Mathematics Education, 2014 Dublin Institute of Technology

#### Online Resource Platform For Mathematics Education, Marisa Llorens, Edmund Nevin, Eileen Mageean

*Conference Papers*

Engineering education is facing many challenges: a decline in core mathematical skills; lowering entry requirements; and the diversity of the student cohort. One approach to confronting these challenges is to make subject content appropriate to the communication styles of today’s student. To achieve this, a pedagogical shift from the traditional hierarchical approach to learning to one that embraces the use of technology as a tool to enhance the student learning experience is required. By including the student as co-creator of course content, a greater sense of engagement is achieved and a change to one where students become agents of ...

Rainbow Generalizations Of Ramsey Theory - A Dynamic Survey, 2014 Georgia Southern University

#### Rainbow Generalizations Of Ramsey Theory - A Dynamic Survey, Shinya Fujita, Colton Magnant, Kenta Ozeki

*Theory and Applications of Graphs*

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs.