Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, 2016 University of Tennessee, Chattanooga

#### Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, Hayley Little

*Honors Theses*

Since their introduction in 2010, the Common Core State Standards (CCSS) have been a highly controversial topic in educational reform. Though the standards are not a product of the federal government and are not federally mandated, they do represent a push towards national academic standards in America. For states such as Tennessee, educational policies of the past pushed them to lower their academic standards in order to create the illusion of success. Those states are now some of the places that have seen the most change with the adoption of the CCSS. It still remains somewhat unclear, however, which changes ...

Mathematical Analysis Ii, 2016 Payame Noor University

Homological Characterizations Of Quasi-Complete Intersections, 2016 University of Nebraska - Lincoln

#### Homological Characterizations Of Quasi-Complete Intersections, Jason M. Lutz

*Dissertations, Theses, and Student Research Papers in Mathematics*

Let R be a commutative ring, (**f**) an ideal of R, and E = K(**f**; R) the Koszul complex. We investigate the structure of the Tate construction T associated with E. In particular, we study the relationship between the homology of T, the quasi-complete intersection property of ideals, and the complete intersection property of (local) rings.

Advisers: Luchezar L. Avramov and Srikanth B. Iyengar

Hybrid Chebyshev Polynomial Scheme For The Numerical Solution Of Partial Differential Equations, 2016 University of Southern Mississippi

#### Hybrid Chebyshev Polynomial Scheme For The Numerical Solution Of Partial Differential Equations, Balaram Khatri Ghimire

*Dissertations*

In the numerical solution of partial differential equations (PDEs), it is common to find situations where the best choice is to use more than one method to arrive at an accurate solution. In this dissertation, hybrid Chebyshev polynomial scheme (HCPS) is proposed which is applied in two-step approach and one-step approach. In the two-step approach, first, Chebyshev polynomials are used to approximate a particular solution of a PDE. Chebyshev nodes which are the roots of Chebyshev polynomials are used in the polynomial interpolation due to its spectral convergence. Then, the resulting homogeneous equation is solved by boundary type methods including ...

Multilevel Models For Longitudinal Data, 2016 East Tennessee State University

#### Multilevel Models For Longitudinal Data, Aastha Khatiwada

*Electronic Theses and Dissertations*

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each ...

On Fixed Points, Diagonalization, And Self-Reference, 2016 Indiana University - Purdue University Fort Wayne

#### On Fixed Points, Diagonalization, And Self-Reference, Bernd Buldt

*Philosophy Faculty Publications*

We clarify the respective roles fixed points, diagonalization, and self- reference play in proofs of Gödel’s first incompleteness theorem.

Ogden College Of Science & Engineering Newsletter (Summer 2016), 2016 Western Kentucky University

#### Ogden College Of Science & Engineering Newsletter (Summer 2016), Cheryl Stevens, Dean

*Ogden College of Science & Engineering Publications*

No abstract provided.

On Rank Driven Dynamical Systems, 2016 Portland State University

#### On Rank Driven Dynamical Systems, J.J. P. Veerman, F. J. Prieto

*J.J.P. Veerman*

We investigate a class of models related to the Bak-Sneppen model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of “complex behavior” such as self-organized criticality that is often observed in physical and biological systems. In this model, random fitnesses in [0, 1] are associated to agents located at the vertices of a graph G. Their fitnesses are ranked from worst (0) to best (1). At every time-step the agent with the worst fitness and some others with a priori given rank probabilities are replaced by new agents with random fitnesses. We ...

Kernels Of Directed Graph Laplacians, 2016 Portland State University

#### Kernels Of Directed Graph Laplacians, John S. Caughman Iv, J. J. P. Veerman

*J.J.P. Veerman*

Let G denote a directed graph with adjacency matrix Q and in- degree matrix D. We consider the *Kirchhoff matrix* L = D − Q, sometimes referred to as the *directed Laplacian*. A classical result of Kirchhoff asserts that when G is undirected, the multiplicity of the eigenvalue 0 equals the number of connected components of G. This fact has a meaningful generalization to directed graphs, as was observed by Chebotarev and Agaev in 2005. Since this result has many important applications in the sciences, we offer an independent and self-contained proof of their theorem, showing in this paper that the algebraic ...

On A Convex Set With Nondifferentiable Metric Projection, 2016 Portland State University

#### On A Convex Set With Nondifferentiable Metric Projection, Shyan S. Akmal, Nguyen Mau Nam, J.J. P. Veerman

*J.J.P. Veerman*

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with smooth boundary which possesses the same property.

Rearranging Algebraic Equations Using Electrical Circuit Applications: A Unit Plan Aligned To The New York State Common Core Learning Standards, 2016 SUNY Brockport

#### Rearranging Algebraic Equations Using Electrical Circuit Applications: A Unit Plan Aligned To The New York State Common Core Learning Standards, Susan L. Sommers

*Education and Human Development Master's Theses*

As a response to both the implementation of the Common Core State Standards (CCSS) and a recent approval of a change by the New York State Board of Regents to allow multiple pathways for graduation, this curriculum project, which will be referred to as a unit plan throughout the paper, was designed to meet the need for more units of study that apply mathematical modeling in algebra to real world situations that allow students to explore applications of mathematics in careers. The unit plan on rearranging algebraic equations using electrical circuit applications is aligned to the New York State Common ...

Topological Data Analysis Of Biological Aggregation Models, 2016 Macalester College

#### Topological Data Analysis Of Biological Aggregation Models, Chad M. Topaz, Lori B. Ziegelmeir, Tom Halverson

*Lori Beth Ziegelmeier*

No abstract provided.

Topological Data Analysis Of Biological Aggregation Models, 2016 Macalester College

#### Topological Data Analysis Of Biological Aggregation Models, Chad M. Topaz, Lori B. Ziegelmeir, Tom Halverson

*Chad M. Topaz*

No abstract provided.

Biological Aggregation Driven By Social And Environmental Factors: A Nonlocal Model And It Degenerate Cahn-Hilliard Approximation, 2016 Harvey Mudd College

#### Biological Aggregation Driven By Social And Environmental Factors: A Nonlocal Model And It Degenerate Cahn-Hilliard Approximation, Andrew J. Bernoff, Chad Topaz

*Chad M. Topaz*

No abstract provided.

Flipped Calculus: A Study Of Student Performance And Perceptions, 2016 Macalester College

#### Flipped Calculus: A Study Of Student Performance And Perceptions, Lori B. Ziegelmeir, Chad M. Topaz

*Chad M. Topaz*

No abstract provided.

Norm Retrievable Frames In $\Mathbb{R}^N$, 2016 Department of Mathematics Vali-e-Asr University of Rafsanjan

#### Norm Retrievable Frames In $\Mathbb{R}^N$, Mohammad Ali Hasankhani Fard

*Electronic Journal of Linear Algebra*

This paper is concerned with the norm retrievable frames in $\mathbb{R}^n$. We present some equivalent conditions to the norm retrievable frames in $\mathbb{R}^n$. We will also show that the property of norm retrievability is stable under enough small perturbation of the frame set only for phase retrievable frames.

Tridiagonal Matrices And Boundary Conditions, 2016 Portland State University

#### Tridiagonal Matrices And Boundary Conditions, J.J. P. Veerman, David K. Hammond

*J.J.P. Veerman*

We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end of a one-dimensional flock. We apply our results to demonstrate how asymptotic stability for consensus and flocking systems depends on the imposed boundary condition.

Classifying Resolving Lists By Distances Between Members, 2016 University of Texas of the Permian Basin

#### Classifying Resolving Lists By Distances Between Members, Paul Feit

*Theory and Applications of Graphs*

L

Let $G$ be a connected graph and let $w_1,\cdots w_r$ be a list of vertices. We refer the choice of a triple $(r;G;w_1,\cdots w_r)$, as a {\em metric selection.} Let $\rho$ be the shortest path metric of $G$. We say that $w_1,\cdots w_r$ {\em resolves $G$ (metricly)\/} if the function $c:V(G)\mapsto\bbz^r$ given by

\[ x\mapsto (\rho (w_1,x),\cdots ,\rho (w_r,x))\]

is injective. We refer to this function the {\em code map,} and to its image as the {\em codes\/} of the triple $(r;G;w_1,\cdots ,w_r ...

Transients Of Platoons With Asymmetric And Di#11;Erent Laplacians, 2016 Czech Technical University, Prague

#### Transients Of Platoons With Asymmetric And Di#11;Erent Laplacians, Ivo Herman, Dan Martinee, J.J. P. Veerman

*J.J.P. Veerman*

We consider an asymmetric control of platoons of identical vehicles with nearest-neighbor interaction. Recent results show that if the vehicle uses different asymmetries for position and velocity errors, the platoon has a short transient and low overshoots. In this paper we investigate the properties of vehicles with friction. To achieve consensus, an integral part is added to the controller, making the vehicle a third-order system. We show that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities. Simulations suggest that our system has a better performance than other nearest-neighbor scenarios. Moreover ...

Group-Antimagic Labelings Of Multi-Cyclic Graphs, 2016 Illinois Wesleyan University

#### Group-Antimagic Labelings Of Multi-Cyclic Graphs, Dan Roberts, Richard M. Low

*Theory and Applications of Graphs*

Let $A$ be a non-trivial abelian group. A connected simple graph $G = (V, E)$ is $A$-\textbf{antimagic} if there exists an edge labeling $f: E(G) \to A \backslash \{0\}$ such that the induced vertex labeling $f^+: V(G) \to A$, defined by $f^+(v) = \Sigma$ $\{f(u,v): (u, v) \in E(G) \}$, is a one-to-one map. The \textit{integer-antimagic spectrum} of a graph $G$ is the set IAM$(G) = \{k: G \textnormal{ is } \mathbb{Z}_k\textnormal{-antimagic and } k \geq 2\}$. In this paper, we analyze the integer-antimagic spectra for various classes of multi-cyclic graphs.