Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

10664 Full-Text Articles 9688 Authors 1723329 Downloads 209 Institutions

All Articles in Mathematics

Faceted Search

10664 full-text articles. Page 1 of 291.

The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown 2016 Western Michigan University

The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown

Honors Theses

The Creation of a Video Review Guide for the Free-Response Section of the Advanced Placement Calculus Exam follows the creation of a resource to help students prepare for the College Board’s Advanced Placement Calculus Exam. This project originated out of the authors personal experiences in preparing for this exam. The goal of the project was to create an accessible resource that reviews content, provides insights into the Advanced Placement exam, and creates successful habits in student responses. This paper, chronologically, details the development of the resource and a reflection on the final product and future uses.


Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, Hayley Little 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, Ismail Nikoufar 2016 Payame Noor University

Mathematical Analysis Ii, Ismail Nikoufar

Ismail Nikoufar

No abstract provided.


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


Multilevel Models For Longitudinal Data, Aastha Khatiwada 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 ...


Breaking Spaces And Forms For The Dpg Method And Applications Including Maxwell Equations, Carsten Carstensen, Leszek Demkowicz, Jay Gopalakrishnan 2016 Humboldt-Universität zu Berlin

Breaking Spaces And Forms For The Dpg Method And Applications Including Maxwell Equations, Carsten Carstensen, Leszek Demkowicz, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

Discontinuous Petrov Galerkin (DPG) methods are made easily implementable using `broken' test spaces, i.e., spaces of functions with no continuity constraints across mesh element interfaces. Broken spaces derivable from a standard exact sequence of first order (unbroken) Sobolev spaces are of particular interest. A characterization of interface spaces that connect the broken spaces to their unbroken counterparts is provided. Stability of certain formulations using the broken spaces can be derived from the stability of analogues that use unbroken spaces. This technique is used to provide a complete error analysis of DPG methods for Maxwell equations with perfect electric boundary ...


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


Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces, Sean A. Broughton 2016 Rose-Hulman Institute of Technology

Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

Two Riemann surfaces S1 and S2 with conformal G-actions have topologically equivalent actions if there is a homeomorphism h : S1 -> S2 which intertwines the actions. A weaker equivalence may be defined by comparing the representations of G on the spaces of holomorphic q-differentials Hq(S1) and Hq(S2). In this note we study the differences between topological equivalence and Hq equivalence of prime cyclic actions, where S1/G and S2/G have genus zero.


The Next Linear Collider Test Accelerator, R. D. Ruth, C. Adolphsen, K. Bane, R. F. Boyce, D. L. Burke, R. Calin, G. Caryotakis, R. Cassel, Stephen L. Clark, H. Deruyter, K. Fant, R. Fuller, S. Heifets, H. Hoag, R. Humphrey, S. Kheifets, R. Koontz, N. M. Kroll, R. T. Lavine, G. A. Loew, A. Menegat, R. H. Miller, C. Nantista, J. M. Patterson, C. Pearson, R. Phillips, J. Rifkin, J. Spencer, S. Tantawi, K. A. Thompson, A. Vlieks, V. Vylet, J. W. Wang, P. B. Wilson, A. Yeremian, B. Youngman 2016 Missouri University of Science and Technology

The Next Linear Collider Test Accelerator, R. D. Ruth, C. Adolphsen, K. Bane, R. F. Boyce, D. L. Burke, R. Calin, G. Caryotakis, R. Cassel, Stephen L. Clark, H. Deruyter, K. Fant, R. Fuller, S. Heifets, H. Hoag, R. Humphrey, S. Kheifets, R. Koontz, N. M. Kroll, R. T. Lavine, G. A. Loew, A. Menegat, R. H. Miller, C. Nantista, J. M. Patterson, C. Pearson, R. Phillips, J. Rifkin, J. Spencer, S. Tantawi, K. A. Thompson, A. Vlieks, V. Vylet, J. W. Wang, P. B. Wilson, A. Yeremian, B. Youngman

Stephen L. Clark

During the past several years, there has been tremendous progress on the development of the RF system and accelerating structures for a Next Linear Collider (NLC). Developments include high-power klystrons, RF pulse compression systems and damped/detuned accelerator structures to reduce wakefields. In order to integrate these separate development efforts into an actual X-band accelerator capable of accelerating the electron beams necessary for an NLC, we are building an NLC Test Accelerator (NLCTA). The goal of the NLCTA is to bring together all elements of the entire accelerating system by constructing and reliably operating an engineered model of a high-gradient ...


Tid And See Testing Results Of Altera Cyclone Field Programmable Gate Array, Stephen L. Clark, K. Avery, R. Parker 2016 Missouri University of Science and Technology

Tid And See Testing Results Of Altera Cyclone Field Programmable Gate Array, Stephen L. Clark, K. Avery, R. Parker

Stephen L. Clark

Total ionizing dose (TID) and single event effects testing was performed on Altera Cyclone FPGAs. The devices exhibit slight performance degradation to a TID of 1 Mrad (Si), but also exhibited single event latchup at a low LET.


On Self-Adjoint And J-Self-Adjoint Dirac-Type Operators: A Case Study, Stephen L. Clark, Fritz Gesztesy 2016 Missouri University of Science and Technology

On Self-Adjoint And J-Self-Adjoint Dirac-Type Operators: A Case Study, Stephen L. Clark, Fritz Gesztesy

Stephen L. Clark

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schrödinger equation, of relevance to nonlinear optics. In addition to a study of Dirac and Hamiltonian systems, we also introduce the concept of Weyl-Titchmarsh half-line m-coefficients (and 2 × 2 matrix-valued M-matrices) in the non-self-adjoint context and derive some of their basic properties. We conclude with an illustrative example showing that crossing spectral arcs in the non-self-adjoint context imply the blowup of the norm of spectral projections in the limit where the crossing point is ...


Elimination Of Supply Harmonics, Stephen L. Clark, P. Famouri, W. L. Cooley 2016 Missouri University of Science and Technology

Elimination Of Supply Harmonics, Stephen L. Clark, P. Famouri, W. L. Cooley

Stephen L. Clark

The price of the extensive use of power electronic devices is becoming clear: increasing harmonic "pollution." The greater amount of harmonics being introduced into power distribution systems is of concern to both power consumers and power companies. First, a brief look is taken at background information which describes harmonic sources, effects, and characteristics. Then the evolution of the harmonics elimination approaches of current compensation and active filtering are discussed to give some insight into the directions that research is taking.


Elimination Of Supply Harmonics: An Evolution Of Current Compensation And Active Filtering Methods, Stephen L. Clark, P. Famouri, W. L. Cooley 2016 Missouri University of Science and Technology

Elimination Of Supply Harmonics: An Evolution Of Current Compensation And Active Filtering Methods, Stephen L. Clark, P. Famouri, W. L. Cooley

Stephen L. Clark

The price of the extensive use of power electronic devices is becoming clear: increasing harmonic "pollution." This survey takes a brief look at background information related to harmonics, including their sources, effects, and characteristics. Then, the evolution of the harmonics elimination approaches of current compensation and active filtering, which are becoming more feasible due to research and technological improvements, are discussed in order to give some insight into the directions that research is taking.


Signal Velocity In Oscillator Networks, Carlos E. Cantos, J.J. P. Veerman, David K. Hammond 2016 Portland State University

Signal Velocity In Oscillator Networks, Carlos E. Cantos, J.J. P. Veerman, David K. Hammond

J.J.P. Veerman

We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. We first derive necessary and sufficient conditions for asymptotic stability, then derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocities c+>0 and c−f(x−c ...


Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, J.J. P. Veerman, Jovan Petrovic 2016 Portland State University

Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, J.J. P. Veerman, Jovan Petrovic

J.J.P. Veerman

Coherent state transfer is an important requirement in the construction of quantum computer hardware. The state transfer can be realized by linear next-neighbour-coupled finite chains. Starting from the commensurability of chain eigenvalues as the general condition of periodic dynamics, we find chains that support full periodic state revivals. For short chains, exact solutions are found analytically by solving the inverse eigenvalue problem to obtain the coupling coefficients between chain elements. We apply the solutions to design optical waveguide arrays and perform numerical simulations of light propagation thorough realistic waveguide structures. Applications of the presented method to the realization of a ...


Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J.J. P. Veerman 2016 Portland State University

Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J.J. P. Veerman

J.J.P. Veerman

The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped harmonic oscillators in R with completely decentralized nearest neighbor interaction. We then use the theory to establish that in a certain range of the parameters transients grow linearly in the number of agents (and faster outside that range). Finally, in the regime where this linear growth occurs we give the constant of proportionality as a function of the signal velocities ...


Nine Faculty Members Earn Tenure, Andrew Lazowski 2016 Selected Works

Nine Faculty Members Earn Tenure, Andrew Lazowski

Andrew Lazowski

Sacred Heart University reaffirmed its commitment to academic excellence when the Board of Trustees awarded tenure to nine faculty members recently.
The newly tenured faculty members, who all received promotions from assistant professor to associate professor, are:
 
Anita August - English
Pamela Buck - English
Grace Guo - Management
Andrew Lazowski - Mathematics
Kerry Milner - Nursing
Amanda Moras - Sociology
Julianna Stockton - Mathematics
Barabara Tarasovich - Accounting
David Taylor - Marketing


Kemeny's Constant And An Analogue Of Braess' Paradox For Trees, Steve Kirkland, Ze Zeng 2016 University of Manitoba

Kemeny's Constant And An Analogue Of Braess' Paradox For Trees, Steve Kirkland, Ze Zeng

Electronic Journal of Linear Algebra

Given an irreducible stochastic matrix M, Kemeny’s constant K(M) measures the expected time for the corresponding Markov chain to transition from any given initial state to a randomly chosen final state. A combinatorially based expression for K(M) is provided in terms of the weights of certain directed forests in a directed graph associated with M, yielding a particularly simple expression in the special case that M is the transition matrix for a random walk on a tree. An analogue of Braess’ paradox is investigated, whereby inserting an edge into an undirected graph can increase the value of ...


On The Matrix Square Root Via Geometric Optimization, Suvrit Sra 2016 Massachusetts Institute of Technology

On The Matrix Square Root Via Geometric Optimization, Suvrit Sra

Electronic Journal of Linear Algebra

This paper is triggered by the preprint [P. Jain, C. Jin, S.M. Kakade, and P. Netrapalli. Computing matrix squareroot via non convex local search. Preprint, arXiv:1507.05854, 2015.], which analyzes gradient-descent for computing the square root of a positive definite matrix. Contrary to claims of Jain et al., the author’s experiments reveal that Newton-like methods compute matrix square roots rapidly and reliably, even for highly ill-conditioned matrices and without requiring com-mutativity. The author observes that gradient-descent converges very slowly primarily due to tiny step-sizes and ill-conditioning. The paper derives an alternative first-order method based on geodesic convexity ...


On A Desert Island With Unit Sticks, Continued Fractions And Lagrange, Victor J. Ricchezza, H. L. Vacher 2016 University of South Florida

On A Desert Island With Unit Sticks, Continued Fractions And Lagrange, Victor J. Ricchezza, H. L. Vacher

Numeracy

GLY 4866, Computational Geology, provides an opportunity, welcomed by our faculty, to teach quantitative literacy to geology majors at USF. The course continues to evolve although the second author has been teaching it for some 20 years. This paper describes our experiences with a new lab activity that we are developing on the core issue of measurement and units. The activity is inspired by a passage in the 2008 publication of lectures that Joseph Louis Lagrange delivered at the Ecole Normale in 1795. The activity envisions that young scientists are faced with the need to determine the dimensions of a ...


Digital Commons powered by bepress