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Physical Sciences and Mathematics Commons™

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Mathematics

Selected Works

Selected Works

2004

Articles 1 - 19 of 19

Full-Text Articles in Physical Sciences and Mathematics

Wavelet Estimation Of Partially Linear Models, Xiao-Wen Chang, Leming Qu Jul 2004

Wavelet Estimation Of Partially Linear Models, Xiao-Wen Chang, Leming Qu

Leming Qu

A wavelet approach is presented for estimating a partially linear model (PLM). We find an estimator of the PLM by minimizing the square of the l2 norm of the residual vector while penalizing the l1 norm of the wavelet coefficients of the nonparametric component. This approach, an extension of the wavelet approach for nonparametric regression problems, avoids the restrictive smoothness requirements for the nonparametric function of the traditional smoothing approaches for PLM, such as smoothing spline, kernel and piecewise polynomial methods. To solve the optimization problem, an efficient descent algorithm with an exact line search is presented. Simulation …

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Group Actions In Number Theory, Tyler J. Evans Jul 2004

Group Actions In Number Theory, Tyler J. Evans

Tyler Evans

Students having had a semester course in abstract algebra are
exposed to the elegant way in which one can use the theory of finite
cyclic groups to derive familiar results from Number Theory.
We present 3 examples suitable for a second semester course in
algebra.
Each uses the notion of the action of a group on a set.
This work was done with Ben Holt, who, at the time, was an HSU
undergraduate student taking second semester algebra

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Bounding The Firing Synchronization Problem On A Ring, André Berthiaume, Todd Bittner, Ljubomir Perković, Amber Settle, Janos Simon Jun 2004

Bounding The Firing Synchronization Problem On A Ring, André Berthiaume, Todd Bittner, Ljubomir Perković, Amber Settle, Janos Simon

Amber Settle

In this paper we improve the upper and lower bounds on the complexity of solutions to the firing synchronization problem on a ring. In this variant of the firing synchronization problem the goal is to synchronize a ring of identical finite automata. Initially, all automata are in the same state except for one automaton that is designated as the initiator for the synchronization. The goal is to define the set of states and the transition function for the automata so that all machines enter a special fire state for the first time and simultaneously during the final round of the …

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Application Of A Mickens Finite-Difference Scheme To The Cylindrical Bratu-Gelfand Problem, Ron Buckmire Apr 2004

Application Of A Mickens Finite-Difference Scheme To The Cylindrical Bratu-Gelfand Problem, Ron Buckmire

Ron Buckmire

No abstract provided.

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On The Edge Set Of Graphs Of Lattice Paths, Lara Pudwell, Steven Klee, Rick Gillman Dec 2003

On The Edge Set Of Graphs Of Lattice Paths, Lara Pudwell, Steven Klee, Rick Gillman

Lara K. Pudwell

No abstract provided.

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On Cross Numbers Of Minimal Zero Sequences In Certain Cyclic Groups, Lara Pudwell, Scott Chapman, Paul Baginski, Kathryn Mcdonald Dec 2003

On Cross Numbers Of Minimal Zero Sequences In Certain Cyclic Groups, Lara Pudwell, Scott Chapman, Paul Baginski, Kathryn Mcdonald

Lara K. Pudwell

No abstract provided.

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Hands-On Geometry, S. Sportsman, Shannon Driskell Dec 2003

Hands-On Geometry, S. Sportsman, Shannon Driskell

Shannon O.S. Driskell

Sportsman, S. (Co-PI), & Driskell, S. (Co-PI), Improving Teacher Quality State Grants Program, Ohio Board of Regents, $90,246

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Fixed Point Theorems, Karen Saxe, Karine Moe Dec 2003

Fixed Point Theorems, Karen Saxe, Karine Moe

Karen Saxe

No abstract provided.

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Biorthogonal Spline Type Wavelets, Tian-Xiao He Dec 2003

Biorthogonal Spline Type Wavelets, Tian-Xiao He

Tian-Xiao He

Let ¢ be an orthonormal scaling function with approximation degree p - 1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by fn = f * Bn (n = 1, 2, ... ) possess higher approximation order, p+n-1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function system. As an application of the method supplied in this paper, one can easily construct a sequence of pairs of biorthogonal spline type scaling functions from one pair of biorthogonal scaling functions or …

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Students’ Problem-Solving Strategies With Fractions, Shannon Driskell Dec 2003

Students’ Problem-Solving Strategies With Fractions, Shannon Driskell

Shannon O.S. Driskell

Driskell, S. (PI), University of Dayton Research Council Seed Grant, $4,000

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Pseudospectral Iterated Method For Differential Equations With Delay Terms, Jodi Mead, Barbara Zubik-Kowal Dec 2003

Pseudospectral Iterated Method For Differential Equations With Delay Terms, Jodi Mead, Barbara Zubik-Kowal

Jodi Mead

New efficient numerical methods for hyperbolic and parabolic partial differential equations with delay terms are investigated. These equations model a development of cancer cells in human bodies. Our goal is to study numerical methods which can be applied in a parallel computing environment. We apply our new numerical method to the delay partial differential equations and analyse the error of the method. Numerical experiments confirm our theoretical results.

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Almost Alternating Harmonic Series, Ramin Naimi, Curtis Fesit Dec 2003

Almost Alternating Harmonic Series, Ramin Naimi, Curtis Fesit

Ramin Naimi

No abstract provided.

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Inverse Eigenproblems And Associated Approximation Problems For Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench Dec 2003

Inverse Eigenproblems And Associated Approximation Problems For Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench

William F. Trench

No abstract provided.

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Hermitian, Hermitian R-Symmetric, And Hermitian R-Skew Symmetric Procrustes Problems, William F. Trench Dec 2003

Hermitian, Hermitian R-Symmetric, And Hermitian R-Skew Symmetric Procrustes Problems, William F. Trench

William F. Trench

No abstract provided.

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Minimization Problems For (R,S)-Symmetric And (R,S)-Skew Symmetric Matrices, William F. Trench Dec 2003

Minimization Problems For (R,S)-Symmetric And (R,S)-Skew Symmetric Matrices, William F. Trench

William F. Trench

No abstract provided.

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Simplification And Strengthening Of Weyl's Definition Of Asymptotic Equal Distribution Of Two Families Of Finite Sets, William F. Trench Dec 2003

Simplification And Strengthening Of Weyl's Definition Of Asymptotic Equal Distribution Of Two Families Of Finite Sets, William F. Trench

William F. Trench

No abstract provided.

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An Elementary Note On Asymptotic Properties Of Toeplitz And Multilevel Toeplitz Matrices, William F. Trench Dec 2003

An Elementary Note On Asymptotic Properties Of Toeplitz And Multilevel Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.

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On Multivariate Abel-Gontscharoff Interpolation, Tian-Xiao He Dec 2003

On Multivariate Abel-Gontscharoff Interpolation, Tian-Xiao He

Tian-Xiao He

By using Gould's annihilation coefficients, we obtain an explicit fundamental polynomials of Multivariate Abel-Gontscharoff Interpolation and its remainder expression.

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Using Dynamic Information In The Supply Network, Jeffrey Barker Dec 2003

Using Dynamic Information In The Supply Network, Jeffrey Barker

Jeffrey Barker

No abstract provided.

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