On The Erdos-Straus Conjecture,
2011
Columbus State University
On The Erdos-Straus Conjecture, Eugen J. Ionascu
Faculty Bibliography
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessarily distinct, so that 4 n = 1 a + 1 b + 1 c (see [3]). In this paper we prove an extension of Mordell’s theorem and formulate a conjecture which is stronger than Erdos’ conjecture.
Regular Tetrahedra Whose Vertices Have Integer Coordinates,
2011
Columbus State University
Regular Tetrahedra Whose Vertices Have Integer Coordinates, Eugen J. Ionascu
Faculty Bibliography
In this paper we introduce theoretical arguments for constructing a procedure that allows one to find the number of all regular tetrahedra that have coordinates in the set {0, 1, ..., n}. The terms of this sequence are twice the values of the sequence A103158 in the Online Encyclopedia of Integer Sequences [16]. These results lead to the consideration of an infinite graph having fractal nature which is tightly connected to the set of orthogonal 3-by-3 matrices with rational coefficients. The vertices of this graph are the primitive integer solutions of the Diophantine equation a 2 + b 2 + …
Making Algebra More Accessible: How Steep Can It Be For Teachers?,
2011
Towson University
Making Algebra More Accessible: How Steep Can It Be For Teachers?, Diana Cheng, Polina Sabinin
Mathematics Faculty Publications
Teacher educators need to support middle grades teachers in developing mathematical knowledge for teaching algebraic concepts. In particular, teachers should become familiar with possible introductions and sequencing to the concept of slope, and common middle school students’ limited conceptions about measuring the steepness of an incline. Steepness can be expressed directly in terms of an angle or indirectly as a slope. Encouraging middle school students to find a measure of steepness using a ratio may help support students’ transition to multiplicative thinking. This mixed – methods study explores middle school students’ responses in solving a comparison problem involving the steepness …
Extending A Mips Simulator For Fpga Support,
2011
Otterbein University
Extending A Mips Simulator For Fpga Support, Pete Sanderson
Mathematics Faculty Scholarship
This project enriches computer organization education by providing another avenue for execution of MIPS code. The initial and existing avenue is the MARS simulator for MIPS code, a well-established open source product for educational environments, in use at universities and colleges worldwide (http://www.cs.missouristate.edu/MARS). The new avenue is a special adaptation of MIPS circuitry on a Field Programmable Gate Array (FPGA) platform. FPGAs such as the Altera DE2 are very attractive in an educational environment because of their flexibility, re-use, and low cost. The FPGA MIPS circuit includes VGA graphical output for real-time display of the MIPS machine state, including registers, …
Balanced Pod For Model Reduction Of Linear Pde Systems: Convergence Theory,
2011
Missouri University of Science and Technology
Balanced Pod For Model Reduction Of Linear Pde Systems: Convergence Theory, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We consider convergence analysis for a model reduction algorithm for a class of linear infinite dimensional systems. The algorithm computes an approximate balanced truncation of the system using solution snapshots of specific linear infinite dimensional differential equations. The algorithm is related to the proper orthogonal decomposition, and it was first proposed for systems of ordinary differential equations by Rowley (Int. J. Bifurc. Chaos Appl. Sci. Eng. 15(3), 997-1013, 2005). For the convergence analysis, we consider the algorithm in terms of the Hankel operator of the system, rather than the product of the system Gramians as originally proposed by Rowley. For …
Balanced Pod For Linear Pde Robust Control Computations,
2011
Missouri University of Science and Technology
Balanced Pod For Linear Pde Robust Control Computations, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also "nearby" systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale nite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Convergence theory is given, and numerical results are presented …
A Model Based Feedback Controller For Wing-Twist Via Piezoceramic Actuation,
2011
Missouri University of Science and Technology
A Model Based Feedback Controller For Wing-Twist Via Piezoceramic Actuation, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
In this paper we present a model for a rubber plate with piezoceramic actuators to represent a bioinspired flexible wing. Using a Galerkin based finite element approximation to the system, we compute a linear quadratic based tracking control for piezoelectric actuators placed along both leading and trailing edges. Using these piezoceramic devices, we demonstrate the effectiveness of model based feedback control in achieving a desired wing tip position; this modified shape is analogous to aircraft roll moment generation via wing twist.
Convergent Snapshot Algorithms For Infinite-Dimensional Lyapunov Equations,
2011
Missouri University of Science and Technology
Convergent Snapshot Algorithms For Infinite-Dimensional Lyapunov Equations, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We consider two algorithms to approximate the solution Z of a class of stable operator Lyapunov equations of the form AZ + ZA* + BB* = 0. The algorithms utilize time snapshots of solutions of certain linear infinite-dimensional differential equations to construct the approximations. Matrix approximations of the operators a and B are not required and the algorithms are applicable as long as the rank of B is relatively small. The first algorithm produces an optimal low-rank approximate solution using proper orthogonal decomposition. The second algorithm approximates the product of the solution with a few vectors and can be implemented …
Sub-Supersolution Method In Variational Inequalities With Multivalued Operators Given By Integrals,
2011
Missouri University of Science and Technology
Sub-Supersolution Method In Variational Inequalities With Multivalued Operators Given By Integrals, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
Tangential Extremal Principles For Finite And Infinite Systems Of Sets, I: Basic Theory,
2011
Wayne State University
Tangential Extremal Principles For Finite And Infinite Systems Of Sets, I: Basic Theory, Boris S. Mordukhovich, Hung M. Phan
Mathematics Research Reports
In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to infinite systems of sets. The first part of the paper concerns the basic theory of tangential extremal principles while the second part presents applications to problems of semi-infinite programming and multiobjective optimization.
Theory Of "Art" : Qualitative In Nature And Quaintintative In Practice,
2011
Marshall University
Theory Of "Art" : Qualitative In Nature And Quaintintative In Practice, Richard Merritt
Theses, Dissertations and Capstones
The primary focus of this work is to discuss the mechanical action of the Marshall Differential Analyzer ("ART") in a mathematical context. Differential Analyzers are primarily used to calculate the solutions to Differential Equations. A full account of the uses of Marshall's Differential Analyzer is given. Furthermore, a pure mathematical justification of how the machine integrates (mechanical integration) is provided via an application of the Riemann Integral. Many simple example problems are detailed ultimately leading up to the calculation of nonlinear problems, more specifically, a nonlinear oscillator.
Solutions To Dynamic Equations On Varying Times Scales,
2011
Marshall University
Solutions To Dynamic Equations On Varying Times Scales, Sher B. Chhetri
Theses, Dissertations and Capstones
Note: The mathematical symbols could not be represented. See the abstract in the thesis for complete text.
Infinitesimal Time Scale Calculus,
2011
Marshall University
Infinitesimal Time Scale Calculus, Tom Cuchta
Theses, Dissertations and Capstones
Calculus has historically been fragmented into multiple distinct theories such as differential calculus, difference calculus, quantum calculus, and many others. These theories are all about the concept of what it means to "change", but in various contexts. Time scales calculus (introduced by Stefan Hilger in 1988) is a synthesis and extension of all the various calculi into a single theory. Calculus was originally approached with "infinitely small numbers" which fell out of use because the use of these numbers could not be justified. In 1960, Abraham Robinson introduced hyperreal numbers, a justification for their use, and therefore the original approach …
Predictors Of Student Outcomes In Developmental Math At A Public Community And Technical College,
2011
Shawnee State University
Predictors Of Student Outcomes In Developmental Math At A Public Community And Technical College, Linda Darlene Hunt
Theses, Dissertations and Capstones
With the wide range of abilities of community college students, proper course placement is crucial. Therefore, having better predictors of success can help improve placement of students for their achievement. This study analyzed student predictors, instructor predictors, and classroom predictors in relation to student final exam score and student final grade in Elementary Algebra and Intermediate Algebra classes. Student predictors included gender, ACT math score, SAT math score, community college enrollment, math pretest score, and ASC grade. Instructor predictors included gender, employment status, Mozart music use, and ALEKS software use. Classroom predictors included time of day, number of class meetings …
Numerical Calculation Of Lyapunov Exponents For Three-Dimensional Systems Of Ordinary Differential Equations,
2011
Marshall University
Numerical Calculation Of Lyapunov Exponents For Three-Dimensional Systems Of Ordinary Differential Equations, Clyde-Emmanuel Estorninho Meador
Theses, Dissertations and Capstones
We consider two algorithms for the computation of Lyapunov exponents for systems of ordinary dierential equations: orbit separation and continuous Gram-Schmidt orthonormal-ization. We also consider two Runge-Kutta methods for the solution of ordinary dierential equations. These algorithms and methods are applied to four three-dimensional systems of ordinary dierential equations, and the results are discussed.
Linear Systems Of Fractional Nabla Difference Equations,
2011
Western Kentucky University
Linear Systems Of Fractional Nabla Difference Equations, Ferhan M. Atici, Paul W. Eloe
Mathematics Faculty Publications
In this paper we shall consider a linear system of fractional nabla difference equations with constant coefficients. We shall construct the fundamental matrix for the homogeneous system and the causal Green’s function for the nonhomogeneous system. We employ transform methods and series methods, and we illustrate analogies with classical first-order differential or difference equations. We shall close the paper with an asymptotic result that follows from the analysis of a half-order nabla difference equation.
Research In Mathematics Educational Technology: Current Trends And Future Demands,
2011
University of Dayton
Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee
Mathematics Faculty Publications
This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, …
Global Stability Of Complex-Valued Neural Networks On Time Scales,
2011
Missouri University of Science and Technology
Global Stability Of Complex-Valued Neural Networks On Time Scales, Martin Bohner, V. Sree Hari Rao, Suman Sanyal
Mathematics and Statistics Faculty Research & Creative Works
In this paper, activation dynamics of complex-valued neural networks are studied on general time scales. Besides presenting conditions guaranteeing the existence of a unique equilibrium pattern, its global exponential stability is discussed. Some numerical examples for different time scales are given in order to highlight the results. © 2011 Foundation for Scientific Research and Technological Innovation.
On The Equivariant Cohomology Of Rotation Groups And Stiefel Manifolds,
2011
Whittier College
On The Equivariant Cohomology Of Rotation Groups And Stiefel Manifolds, William Kronholm
Mathematics
In this paper, we compute the RO(Z/2)-graded equivariant cohomology of rotation groups and Stiefel manifolds with particular involutions.
Topological Symmetry Groups Of K4r+3,
2011
Claremont Graduate University
Topological Symmetry Groups Of K4r+3, Dwayne Chambers '12, Erica Flapan, John D. O'Brien
Pomona Faculty Publications and Research
We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the topological symmetry group of an embedding of a complete graph of the form K4r+3^in S³.
