No description available.

No description available.

No description available.

<p>The 2-D INADEQUATE experiment is a useful experiment for determining carbon structures of organic molecules known for having low signal-to-noise ratios. A non-linear optimization method for solving low-signal spectra resulting from this experiment is introduced to compensate. The method relies on the peak locations defined by the INADEQUATE experiment to create boxes around these areas and measure the signal in each. By measuring pairs of these boxes and applying penalty functions that represent a priori information, we are able to quickly and reliably solve spectra with an acquisition time under a quarter of that required by traditional methods. Examples are shown using the spectrum of sucrose. The concept of a non-uniform Fourier transform and its potential advantages are introduced. The possible application of this type of transform to the INADEQUATE experiment and the previously explained optimization program is detailed.</p> / Master of Applied Science (MASc)

<p>The central theme of this thesis is to develop methods of financial mathematics to understand the dynamics of a firm's capital structure through observations of market prices of liquid securities written on the firm. Just as stock prices are a direct measure of a firm's equity, other liquidly traded products such as options and credit default swaps (CDS) should also be indicators of aspects of a firm's capital structure. We interpret the prices of these securities as the market's revelation of a firm's financial status. In order not to enter into the complexity of balance sheet anatomy, we postulate a balance sheet as simple as Asset = Equity + Debt. Using mathematical models based on the principles of arbitrage pricing theory, we demonstrate that this reduced picture is rich enough to reproduce CDS term structures and implied volatility surfaces that are consistent with market observations. Therefore, reverse engineering applied to market observations provides concise and crucial information of the capital structure.</p> <p>Our investigations into capital structure modeling gives rise to an innovative pricing formula for spread options. Existing methods of pricing spread options are not entirely satisfactory beyond the log-normal model and we introduce a new formula for general spread option pricing based on Fourier analysis of the payoff function. Our development, including a flexible and general error analysis, proves the effectiveness of a fast Fourier transform implementation of the formula for the computation of spread option prices and Greeks. It is found to be easy to implement, stable, and applicable in a wide variety of asset pricing models.</p> / Doctor of Philosophy (PhD)

Fiber-optic systems represent the backbone of the communication networks, carrying most of the world’s data traffic. The main bottleneck in today’s fiber-optic communication systems has roots in the inherent nonlinearity of the fiber. Hence, developing new transmission schemes that are compatible with the nonlinear behavior of the optical fiber has become necessary. To utilize the full transmission capacity of an optical fiber, this thesis investigates two different techniques---compensation-based method and nonlinear Fourier transform (NFT). For the purpose of suppressing the nonlinear distortion in real time, an optical back propagation (OBP) technique using Raman pumped dispersion compensating fibers (DCF). OBP, as an all-optical signal processing technique, can compensate for both intra- and inter-channel nonlinear impairments in real time in point-to-point systems as well as in optical networks. The proposed inline OBP module consists of an optical phase conjugator (OPC), amplifiers and a Raman pumped DCF. In order to suppress the nonlinear effects of the transmission fiber, the power in the OBP fiber should increase exponentially with distance. This can be approximately achieved by using Raman pumping of the backpropagation fiber. Simulation results show that this technique provides 7.7 dB performance improvement in Q-factor over conventional systems. The second part of this thesis is dedicated to the NFT as a promising framework to exploit the inherent nonlinearity of optical fiber rather than treating it as an undesirable effect and using perturbation and approximation-based methods to mitigate it. A novel multistage perturbation technique to realize the NFT as a cascade of linear discrete Fourier transforms is developed. The linear Fourier transform can be easily implemented in the optical domain using a time lens or discrete photonic components, which can be implemented in silicon photonics. The proposed technique provides a promising way to implement NFT in the optical domain, which will fully utilize the potential of NFT for wavelength-division multiplexed fiber-optic systems in the optical domain. Moreover, a nonlinear frequency-division multiplexed (NFDM) transmission scheme with midpoint OPC is investigated. The proposed mid-OPC NFDM system offers a degree of freedom to have a flexible power normalization factor, P_n to minimize the signal-noise mixing in NFT processing for a specific launch power, resulting in significant system performance improvement up to 5.6 dB in Q-factor over conventional NFDM systems. Another advantage of the proposed scheme is that the mid-OPC NFDM system extends the transmission reach without having to increase the guard interval, which leads to higher spectral efficiency. / Thesis / Doctor of Philosophy (PhD)

No description available.

No description available.

This work examines the use of supercritical fluid extraction (SFE)as a sample introduction technique for supercritical fluid chromatography (SFC) and Fourier transform infrared spectrometry (FT-IR). In order to study the effects of a supercritical mobile phase on the resulting IR spectra, carbon dioxide was compared to xenon as a supercritical fluid mobile phase for flow cell SFC/FT-IR. A packed capillary column (30 cm x 320 μm, Deltabond® Cyano, 5 μm particle) was employed for the chromatographic portion of the study. Various samples were tested, such as an ethoxylated alcohol mixture and a unique polarity mix. The roles of temperature and density on the IR spectra were also examined as each was independently varied for the analysis of five different probe compounds. Comparisons of spectra produced in supercritical CO₂ and xenon each matched well with the Nicolet vapor phase library. CO₂ spectra matched the vapor phase spectra equally as well as did the xenon spectra, despite the fact that CO₂ spectra have blanked regions where the mobile phase absorbs in the IR. Following this study, SFE was coupled directly to FT-IR to produce the novel method of on-line SFE/FT-IR. This technique was optimized for the analysis of n-tetracosane, yielding a detection limit of 74 ng. The method was later applied to the quantitative and qualitative analysis of fiber finishes from textile matrices with equivalent success. Finish was extracted directly from the fiber or textile surface and passed through the IR flow cell as an analyte "plug". In this way, the entire finish was quickly quantified, and if desired, qualitatively analyzed as well, without need of prior chromatographic separation. The method required no organic solvent and was proven to be fairly reproducible for four fiber finish types tested. Lastly, supercritica1 fluid extraction (SFE) was examined and optimized as a sample introduction technique for on-line SFE/SFC. Trapping and recovery of analytes in SFE/SFC were studied under varying conditions using a currently marketed system. The system was replumbed using a 12 cm x 100 μm fused silica capillary (100% methyl, d_f = 0.25 μm) for trapping and increased solute focusing. These changes nearly doubled the total analyte recovery (as based on FID peak areas) and lowered the overall system recovery RSDs from 30 % to 4 %. / Ph. D.

Chemical and physical changes occur during the processing of toughened thermosetting resins. A number of properties are related to the type and sequence of these changes. There is a need for the development of in-situ real-time sensors to follow these changes. Once these sensors are developed, they can be used to preferentially select networks and/or morphologies by feedback-controlled "intelligent" processing. A practical, durable, inexpensive Fourier Transform NearInfrared (FTNIR) fiber optic sensor was developed and the cure of a model toughened cyanate as well as a commercial paste adhesive was followed with this sensor In the near-infrared. The design was suitable for many applications. A mold was designed to incorporate the fiber sensor for composite applications. The growth of the normalized triazine (crosslink) peak appeared to follow second order kinetics. The normalized peak reflected chemical as well as physical changes. Analysis of the individual peaks showed significant physical effects. Conversion based on triazine concentration did not follow second order kinetics. / Ph. D.