Open Access. Powered by Scholars. Published by Universities.®
Harmonic Analysis and Representation Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Institution
- Publication
- Publication Type
Articles 1 - 4 of 4
Full-Text Articles in Harmonic Analysis and Representation
Characterization Of The Drilling Via The Vibration Augmenter Of Rotary-Drills And Sound Signal Processing Of Impacted Pipe As A Potential Water Height Assessment Tool, Nicholas Morris
STAR Program Research Presentations
The focus of the internship has been on two topics: a) Characterize the drilling performance of a novel percussive augmenter – this drill was developed by the JPL’s Advanced Technologies Group and its performance was characterized; and b) Examine the feasibility of striking a pipe as a means of assessing the water height inside the pipe. The purpose of this investigation is to examine the possibility of using a simple method of applying impacts to a pipe wall and determining the water height from the sonic characteristic differences including damping, resonance frequencies, etc. Due to multiple variables that are relevant …
Stability Of Multiwavelet Frames With Different Matrix Dilations And Matrix Translations, F. A. Shah, Sunita Goyal
Stability Of Multiwavelet Frames With Different Matrix Dilations And Matrix Translations, F. A. Shah, Sunita Goyal
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study the stability of multiwavelet frames with different matrix dilations and matrix translations by means of operator theory and show that these frames remain stable over some kinds of perturbations of the basic generators.
On The Lp-Error Of Approximation Of Bivariate Functions By Harmonic Splines, Yuliya Babenko, Tatyana Leskevich
On The Lp-Error Of Approximation Of Bivariate Functions By Harmonic Splines, Yuliya Babenko, Tatyana Leskevich
Faculty Articles
Interpolation by various types of splines is the standard procedure in many applications. In this paper we discuss harmonic spline “interpolation” (on the lines of a grid) as an alternative to polynomial spline interpolation (at vertices of a grid). We will discuss some advantages and drawbacks of this approach and present the asymptotics of the Lp-error for adaptive approximation by harmonic splines.
Supercharacters, Exponential Sums, And The Uncertainty Principle, J.L. Brumbaugh '13, Madeleine Bulkow '14, Patrick S. Fleming, Luis Alberto Garcia '14, Stephan Ramon Garcia, Gizem Karaali, Matt Michal '15, Andrew P. Turner '14
Supercharacters, Exponential Sums, And The Uncertainty Principle, J.L. Brumbaugh '13, Madeleine Bulkow '14, Patrick S. Fleming, Luis Alberto Garcia '14, Stephan Ramon Garcia, Gizem Karaali, Matt Michal '15, Andrew P. Turner '14
Pomona Faculty Publications and Research
The theory of supercharacters, which generalizes classical character theory, was recently introduced by P. Diaconis and I.M. Isaacs, building upon earlier work of C. Andre. We study supercharacter theories on $(Z/nZ)^d$ induced by the actions of certain matrix groups, demonstrating that a variety of exponential sums of interest in number theory (e.g., Gauss, Ramanujan, and Kloosterman sums) arise in this manner. We develop a generalization of the discrete Fourier transform, in which supercharacters play the role of the Fourier exponential basis. We provide a corresponding uncertainty principle and compute the associated constants in several cases.