The Segal-Bargmann Transform on Classical Matrix Lie Groups

We study the complex-time Segal-Bargmann transform $\mathbf{B}_{s,\tau}^{K_N}$ on a compact type Lie group $K_N$, where $K_N$ is one of the following classical matrix Lie groups: the special orthogonal group $\mathrm{SO}(N,\mathbb{R})$, the special unitary group $\mathrm{SU}(N)$, or the compact symplectic group $\mathrm{Sp}(N)$. Our work complements and extends the results of Driver, Hall, and Kemp on the Segal-Bargman transform for the unitary group $\mathrm{U}(N)$. We provide an effective method of computing the action of the Segal-Bargmann transform on \emph{trace polynomials}, which comprise a subspace of smooth functions on $K_N$ extending the polynomial functional calculus. Using these results, we show that as $N\to\infty$, the finite-dimensional transform $\mathbf{B}_{s,\tau}^{K_N}$ has a meaningful limit $\mathscr{G}_{s,\tau}^{(\beta)}$ (where $\beta$ is a parameter associated with $\mathrm{SO}(N,\mathbb{R})$, $\mathrm{SU}(N)$, or $\mathrm{Sp}(N)$), which can be identified as an operator on the space of complex Laurent polynomials

An Assessment of Normalized Difference Skin Index Robustness in Aquatic Environments

The Normalized Difference Skin Index (NDSI) is a numeric value generated from two wavelengths of the electromagnetic spectrum, a feature that can be utilized for a dismount detection system. Skin is a major anatomical trait of human beings, furthermore, the most exposed trait to the elements. An aspect of a person\u27s skin is typically uncovered, such as their face or hands. If skin pixels are detected in a spectral image, we can confidently conclude a person is present in the scene. There has been successful research on the use of spectral imagery for NDSI skin detection in ideal conditions [35]. However, in efforts to achieve an operational dismount detection system, the robustness of NDSI has to be explored for more austere conditions. The focus of this thesis is on aquatic environments. Water in aquatic environments poses a challenging problem in the spectral domain because of its absorptive characteristic in several regions of the electromagnetic spectrum, known as water absorption bands [13, 15]. In these particular bands, spectral information becomes occluded from the dominance of water. Unfortunately, the two NDSI wavelengths exist in close proximity with these bands. Experiments were devised to emulate scenarios that may arise between skin and water in a pixel of a hyperspectral image. With a mixed pixel of skin with water in the background, the spread of NDSI values were within a range defined by previous research until 64% or less of the pixel constituted skin. With a mixed pixel of skin with water droplets, the evaluated amount of water had negligible impact on NDSI. A mixed pixel of skin under a thin layer of water rendered NDSI useless with a shallow depth of 5 mm; water layers prove to be extremely detrimental to NDSI. Also, the temporal factor of water absorption by skin was assessed. Within the evaluated durations, up to 6300 s, the results showed negligible impact on NDSI

Models of high rank for weakly scattered theories

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.Includes bibliographical references (leaves 32-33).The Scott rank of a countable structure A, denoted sr(A), was observed by Nadel to be at most wA + 1, where wA4 is the least ordinal not recursive in A. Let T be weakly scattered and L(a,T) be E2-admissible. We give a sufficient condition, the B,-hypothesis, under which T has model A with w4A = a and sr(A) = a + 1. Given the B,-hypothesis, an iterated forcing argument is used to obtain a generic Ta D T such that Th has a model with the desired properties.by Alice Shih Ying Chan.Ph.D

Distillation of Biocrude Oil Converted from Biowaste via Hydrothermal Liquefaction

Modern dependence on petroleum-based fuels contributes to the production of greenhouse gases and is not sustainable in the long run. One way to combat this issue is to develop alternative fuel sources such as biofuels derived from algae and food waste. Our study of biofuel converted from wet biowaste such as food waste and algae focused on the possibility of biofuel replacing commercial fuels. To create the biofuel products, a plug-flow reactor was used to convert wet biowaste at a temperature of 260'C for 20 minutes via hydrothermal liquefaction (HTL). The HTL process transformed the food processing waste (e.g. salad dressing waste) into biocrude oil that was then distilled. Distillation separates the biocrude oil into various fractions of biofuels with different boiling points and other characteristics. The fractional distillation process involved heating the biocrude oil to temperatures between 250'C and 300'C for one distillation cycle of 8 to 9 hours. When the heat was applied, the liquid biocrude oil was vaporized, and then the vapor was condensed slowly by cooling water. The newly formed condensate consisted of various fractions of biofuel separated by density and boiling point. Analyzing the distillates with Fourier-Transform Infrared Spectroscopy (FTIR) provided the chemical functionalities of the biofuel products. This study indicates biofuels distilled from wet biowaste can be used in place of current commercial fuel products. More study is suggested to improve the distillation efficiency.Ope

The effectiveness of using a bilingualized dictionary for determining noun countability and article selection

This article discusses the use of a bilingualized dictionary, namely Oxford Advanced Learner's English–Chinese Dictionary 8 (OALECD8), by advanced Hong Kong Cantonese ESL learn-ers in the determination of noun countability and associated article use. A homogenous group of 30 English majors in a local university participated in the study, which consisted of a noun countabil-ity and article selection task without and with the use of the dictionary. The results show that although bilingualized dictionaries are useful in helping learners determine noun countability and associated article use, learners often misinterpret dictionary information and model on inappro-priate structures, resulting in article errors and/or wrong countability judgments. Chinese transla-tions are also sometimes sources of errors. The results of the study provide lexicographers with signposts to the selection of noun information to be included in a learner's dictionary. More explicit information about noun countability and related article use should be provided in a more user-friendly arrangement. ESL teachers are also advised to engage advanced learners in analyses uncovering the different syntactic requirements of equivalent vocabulary items in the target and source languages when using a bilingualized dictionary. Keywords: English Noun Countability, English Article System, Article Selection, Bilingualized Dictionaries, Learners' Dictionaries, Cantonese Esl Learners, Second Language Acquisition, Effectiveness Of Dictionaries 

A tale of two repositories: linking the local and the global

Apresentação efectuada na Conferência Iberoamericana sobre Publicações Eletrónicas no Contexto da Comunicação Científica (CIPECC2006), 1, Brasília, Brasil, 25 - 28 Abril 2006.Overview of Institutional Repositories. Comparative study: University of Minho (Portugal) - University of Toronto (Canada)