Nessa dissertação, apresentamos os Teoremas de Dualidade de Cohen e Montgomery, [4]. Discutimos também a construção de um contexto de Morita para uma álgebra graduada por um grupo finito. Como aplicação dos resultados desenvolvidos no texto, estudamos a relação entre o radical de Jacobson e o radical de Jacobson graduado de álgebras graduadas, apresentando a solução de Cohen e Montgomery para uma conjectura de Bergman. / In this work, we will present the Cohen and Montgomery's Duality Theorems, [4]. We also discuss the construction of a Morita context to an algebra graded by a nite group. As an application of the results developed in the text, we studied the relations between the Jacobson radical and the graded Jacobson radical of graded algebras, presenting to Cohen and Montgomery's solution for a Bergman's conjecture.

Nessa dissertação, apresentamos os Teoremas de Dualidade de Cohen e Montgomery, [4]. Discutimos também a construção de um contexto de Morita para uma álgebra graduada por um grupo finito. Como aplicação dos resultados desenvolvidos no texto, estudamos a relação entre o radical de Jacobson e o radical de Jacobson graduado de álgebras graduadas, apresentando a solução de Cohen e Montgomery para uma conjectura de Bergman. / In this work, we will present the Cohen and Montgomery's Duality Theorems, [4]. We also discuss the construction of a Morita context to an algebra graded by a nite group. As an application of the results developed in the text, we studied the relations between the Jacobson radical and the graded Jacobson radical of graded algebras, presenting to Cohen and Montgomery's solution for a Bergman's conjecture.

This thesis is concerned with a process which has become commonly used. Producing radical cations specifically for observation at reduced temperatures within the X-band electron spin resonance spectrometer cavity. Gamma irradiation is used to cause electron addition and electron loss centres in a CCl3F matrix. These damage centres can be passed to solutes by the processes outlined below:- [equation] Various functional groups have been investigated. A variety of groups have been chosen to attempt to show a great many of the effects, which cause a molecule to produce interesting e.s.r. spectra. Effects ranging from the 'solvent adducts' investigated in Chapter 2, to the Breit-Rabi distortions encountered by the cations of dialkyl mercurials. Attempts have also been made to clarify one or two areas of radical cation chemistry which have caused contention in the current literature. Such areas are those outlined in Chapters 3, 4 and 5 with ester groupings and Chapter 7 with oxirane cations.

Nessa dissertação, apresentamos os Teoremas de Dualidade de Cohen e Montgomery, [4]. Discutimos também a construção de um contexto de Morita para uma álgebra graduada por um grupo finito. Como aplicação dos resultados desenvolvidos no texto, estudamos a relação entre o radical de Jacobson e o radical de Jacobson graduado de álgebras graduadas, apresentando a solução de Cohen e Montgomery para uma conjectura de Bergman. / In this work, we will present the Cohen and Montgomery's Duality Theorems, [4]. We also discuss the construction of a Morita context to an algebra graded by a nite group. As an application of the results developed in the text, we studied the relations between the Jacobson radical and the graded Jacobson radical of graded algebras, presenting to Cohen and Montgomery's solution for a Bergman's conjecture.

M.Sc. (Mathematics) / Please refer to full text to view abstract

M.Sc. (Mathematics) / Please refer to full text to view abstract

Radical SAM enzymes are ancient, essential enzymes. They perform radical chemical reactions in virtually all living organisms and are involved in producing antibiotics, generating greenhouse gases, human health, and likely many other essential roles that have yet to be established. A wide variety of reactions have been characterized from this group of enzymes, including hydrogen abstractions, the transferring of methylthio groups, complex cyclization and rearrangement reactions, and others. However, many radical SAM enzymes have yet to be identified or characterized. There have been great leaps forward in the amount of enzyme sequences that are available in public databases, but experiments to investigate what chemical reactions the enzymes perform take a great deal of time. In our work, we utilize Hidden Markov Models to identify possible radical SAM enzymes and predict their possible functions through BLAST alignments and homology modelling. We also explore their distribution across the tree of life and determine how it is correlated with organism oxygen tolerances, because the core iron-sulfur cluster is oxygen sensitive. Trends in the abundances of radical SAM enzymes depending on oxygen tolerances were more apparent in prokaryotes than in eukaryotes. Although eukaryotes tend to have fewer radical SAM enzymes than prokaryotes, we were able to analyze uncharacterized radical SAM enzymes from both an aerobic eukaryote (Entamoeba histolytica) and a eukaryote capable of oxygenic photosynthesis (Gossypium barbadense), and predict the reactions they catalyze. This work sets the stage for the functional characterization of these essential yet elusive enzymes in future laboratory experiments. / Master of Science in Life Sciences / Radical SAM enzymes are ancient, essential enzymes that perform chemical reactions in virtually all living organisms. We do know that they are involved in producing antibiotics, human health, and generating greenhouse gases. We also know that there are many radical SAM enzymes whose functions remain a mystery. There have been great leaps forward in the amount of enzyme sequences that are available in public databases, but experiments to investigate what chemical reactions enzymes perform take a great deal of time. The experiments are especially difficult for radical SAM enzymes because the oxygen we breathe can break the enzymes down in a laboratory. In our work, we utilize computational techniques to identify possible radical SAM enzymes and predict what reactions they might catalyze. Because these enzymes are vulnerable to oxygen in laboratory environments, we also explore whether organisms that breathe oxygen have fewer of these enzymes than organisms that perform anaerobic respiration instead. We found that does seem to be the case in microbes like bacteria and archaea, but the results were not as consistent for eukaryotes. We then chose radical SAM enzymes we had identified from both an aerobic eukaryote (Entamoeba histolytica) and a eukaryote capable of producing oxygen (Gossypium barbadense), and predicted the reactions they catalyze. This work sets the stage for the functional characterization of these essential yet elusive enzymes in future laboratory experiments.

Methanogenesis is the biological production of methane and is utilized by methanogenic archaea (methanogens) to generate energy. This process is responsible for 70% of total atmospheric methane, a potent greenhouse gas and an important energy source (natural gas). In the future, reversing methanogenesis in an engineered methanogenic strain could be realized to efficiently convert natural gas into liquid fuels. Methyl coenzyme M reductase (Mcr) catalyzes the final reaction of methanogenesis in methanogens and the first reaction in the anaerobic oxidation of methane (AOM) carried out by the anaerobic methanotrophs (ANME). Cofactor F₄₃₀, a unique nickel-containing tetrapyrrole, serves as the prosthetic group and catalytic component of Mcr. Recently, multiple F₄₃₀ variants have been discovered in several methanogenic species, including Methanococcus maripaludis, Methanosarcina acetivorans, and Methanocaldococcus jannaschii. A novel variant reported here has an exact mass of 1008.3478, a similar absorption spectrum as unmodified F₄₃₀, and associates with purified Mcr from M. acetivorans. Based on the exact mass, this molecule is likely modified with a mercaptopropamide moiety. In some conditions, this modified F₄₃₀ comprises 30-50% of the total F₄₃₀ pool. We also report upon our work to identify the sulfur insertion enzyme required to produce methylthio-F₄₃₀ that functions with Mcr in ANME-1. We hypothesized that the insertion of the methylthio moiety is likely catalyzed by a methylthiotransferase (MTTase) homolog present in ANME. However, purified ANME MTTase does not appear to catalyze this reaction, and instead catalyzes the methylthiolation of N6-threonylcarbamoyladenosine (t6A) in tRNA. / Master of Science in Life Sciences / Methanogens are a unique but diverse group of microorganisms that produce methane to generate their energetic needs. The byproduct of their metabolism is methane gas, most of which escapes into the atmosphere. Methanogens produce 70% of Earth's atmospheric methane, which is a gas that has contributed to 20% of global warming since the start of the industrial era. However, methane, which makes up the majority of natural gas, is also an important source of energy, and natural gas generates 40% of the United States' electricity. An issue with natural gas is, as a gas, it readily leaks out in the extraction and transport process. A solution to this is to convert the gas into liquids, which do not display these negatives. It is possible, through a better understanding of how methanogens work, we could produce a methanogen strain that can efficiently convert methane into liquid fuels. The last methane-generating step in methanogenic metabolism uses a protein known as methyl-coenzyme M reductase (Mcr). To do this, Mcr uses a small molecule known as cofactor F₄₃₀. Recently, variants of the standard F₄₃₀ structure have been described, in both methanogens as well as another microbial group known as the anaerobic methanotrophs (ANME). ANME generate their energy through reversing methanogenic metabolism. The work here involves studying why and how methanogens and ANME make F₄₃₀ variants. The hope is this work will reveal either different functionalities of cofactor F₄₃₀ not previously known, or that they influence Mcr catalysis, potentially in the reverse (methane degradation) direction.

No description available.

by Au Yun-Nam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 133-137). / Introduction --- p.iv / Chapter 1 --- Preliminaries --- p.1 / Chapter 1.1 --- Some Semigroup Properties --- p.1 / Chapter 1.2 --- General Properties of Semigroup Algebras --- p.5 / Chapter 1.3 --- Group Algebras --- p.7 / Chapter 1.3.1 --- Some Basic Properties of Groups --- p.7 / Chapter 1.3.2 --- General Properties of Group Algebras --- p.8 / Chapter 1.3.3 --- Δ-Method for Group Algebras --- p.10 / Chapter 1.4 --- Graded Algebras --- p.12 / Chapter 1.5 --- Crossed Products and Smash Products --- p.14 / Chapter 2 --- Radicals of Graded Rings --- p.17 / Chapter 2.1 --- Jacobson Radical of Crossed Products --- p.17 / Chapter 2.2 --- Graded Radicals and Reflected Radicals --- p.18 / Chapter 2.3 --- Radicals of Group-graded Rings --- p.24 / Chapter 2.4 --- Algebras Graded by Semilattices --- p.26 / Chapter 2.5 --- Algebras Graded by Bands --- p.27 / Chapter 2.5.1 --- Hereditary Radicals of Band-graded Rings --- p.27 / Chapter 2.5.2 --- Special Band-graded Rings --- p.30 / Chapter 3 --- Radicals of Semigroup Algebras --- p.34 / Chapter 3.1 --- Radicals of Polynomial Rings --- p.34 / Chapter 3.2 --- Radicals of Commutative Semigroup Algebras --- p.36 / Chapter 3.2.1 --- Commutative Cancellative Semigroups --- p.37 / Chapter 3.2.2 --- General Commutative Semigroups --- p.39 / Chapter 3.2.3 --- The Nilness and Semiprimitivity of Commutative Semigroup Algebras --- p.45 / Chapter 3.3 --- Radicals of Cancellative Semigroup Algebras --- p.48 / Chapter 3.3.1 --- Group of Fractions of Cancellative Semigroups --- p.48 / Chapter 3.3.2 --- Jacobson Radical of Cancellative Semigroup Algebras --- p.54 / Chapter 3.3.3 --- Subsemigroups of Polycyclic-by-Finite Groups --- p.57 / Chapter 3.3.4 --- Nilpotent Semigroups --- p.59 / Chapter 3.4 --- Radicals of Algebras of Matrix type --- p.62 / Chapter 3.4.1 --- Properties of Rees Algebras --- p.62 / Chapter 3.4.2 --- Algebras Graded by Elementary Rees Matrix Semigroups --- p.65 / Chapter 3.5 --- Radicals of Inverse Semigroup Algebras --- p.68 / Chapter 3.5.1 --- Properties of Inverse Semigroup Algebras --- p.69 / Chapter 3.5.2 --- Radical of Algebras of Clifford Semigroups --- p.72 / Chapter 3.5.3 --- Semiprimitivity Problems of Inverse Semigroup Algebras --- p.73 / Chapter 3.6 --- Other Semigroup Algebras --- p.76 / Chapter 3.6.1 --- Completely Regular Semigroup Algebras --- p.76 / Chapter 3.6.2 --- Separative Semigroup Algebras --- p.77 / Chapter 3.7 --- Radicals of Pi-semigroup Algebras --- p.80 / Chapter 3.7.1 --- PI-Algebras --- p.80 / Chapter 3.7.2 --- Permutational Property and Algebras of Permutative Semigroups --- p.80 / Chapter 3.7.3 --- Radicals of PI-algebras --- p.82 / Chapter 4 --- Finiteness Conditions on Semigroup Algebras --- p.85 / Chapter 4.1 --- Introduction --- p.85 / Chapter 4.1.1 --- Preliminaries --- p.85 / Chapter 4.1.2 --- Semilattice Graded Rings --- p.86 / Chapter 4.1.3 --- Group Graded Rings --- p.88 / Chapter 4.1.4 --- Groupoid Graded Rings --- p.89 / Chapter 4.1.5 --- Semigroup Graded PI-Algebras --- p.91 / Chapter 4.1.6 --- Application to Semigroup Algebras --- p.92 / Chapter 4.2 --- Semiprime and Goldie Rings --- p.92 / Chapter 4.3 --- Noetherian Semigroup Algebras --- p.99 / Chapter 4.4 --- Descending Chain Conditions --- p.107 / Chapter 4.4.1 --- Artinian Semigroup Graded Rings --- p.107 / Chapter 4.4.2 --- Semilocal Semigroup Algebras --- p.109 / Chapter 5 --- Dimensions and Second Layer Condition on Semigroup Algebras --- p.119 / Chapter 5.1 --- Dimensions --- p.119 / Chapter 5.1.1 --- Gelfand-Kirillov Dimension --- p.119 / Chapter 5.1.2 --- Classical Krull and Krull Dimensions --- p.121 / Chapter 5.2 --- The Growth and the Rank of Semigroups --- p.123 / Chapter 5.3 --- Dimensions on Semigroup Algebras --- p.124 / Chapter 5.4 --- Second Layer Condition --- p.128 / Notations and Abbreviations --- p.132 / Bibliography --- p.133