The physical properties of hydrochloric acid and deuterium chloride were derived through the use of the harmonic oscillator and rigid rotor quantum mechanical models. By first obtaining angular momentum quantum values for HCl and DCl through Fourier Transform Infrared Spectroscopy, these two systems could be summed and processed with additional...
The black and white pattern formed when an individual word is
printed on a page was analyzed by the Fourier transform. The Fourier
transform produces a sequence of sinusodial functions, usually called
spatial frequencies, whose amplitudes depend upon the particular
pattern analyzed. These amplitudes were examined to determine if the...
Broadband absorption spectroscopy, by way of FTIR, was used to investigate the vapor cloud of a single millimeter sized liquid droplet suspended by a syringe as it evaporates at standard conditions. Single beam data were collected every 8 seconds resulting in a time-resolved record. Species concentrations were tracked using their...
Liquid transportation fuels require costly and time-consuming tests to characterize metrics, such as Research Octane Number (RON) for gasoline. If fuel sale restrictions requiring use of standard Cooperative Fuel Research (CFR) testing procedures do not apply, these tests may be avoided by using multivariate statistical models to predict RON and...
Using a plastic bottle, we explore the capabilities of a reflective phase-only Spatial Light Modulator (SLM) in removing wavefront aberrations using a Zernike polynomial phase mask, with the modulators phase depth limited to 0.8π radians. Wavefront aberrations, which can be modeled with Zernike polynomials, distort image transmission through various optical...
The gravitational anomalies of simple bodies (sphere, cylinder, and fault) were used to develop methods for analyzing gravity data in the frequency domain. The Fourier transforms of the functional representations of the theoretical gravitational anomalies of these bodies were obtained. Mathematical formulations were made between the transform versus frequency relationships...
Signal Temporal logic(STL) provides a convenient framework to describe various system properties over time. While there has been extensive research on verification and control synthesis from STL requirements, a lot of them revolve around the time-domain analysis. So, there are still some questions properly unaddressed like what is the frequency...
The generalized Hankel transforms are studied in the
first part of this thesis; these include the Watson transforms
as a special case. For the validity of the reciprocal
relations, a necessary and sufficient condition on
the kernel is proved. The proof involves first changing
the variables so that all the...