In this thesis, we introduce the theory of locally nilpotent derivations and use it to compute certain ring invariants. We prove some results about quasi-extensions of derivations and use them to show that certain rings are non-rigid. Our main result states that if k is a field of characteristic zero, C is an affine k-domain and B = C[T,Y] / < T^nY - f(T) >, where n >= 2 and f(T) \in C[T] is such that delta^2(f(0)) != 0 for all nonzero locally nilpotent derivations delta of C, then ML(B) != k. This shows in particular that the ring B is not a polynomial ring over k.

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An (associative) algebra is a vector space over a field equipped with an associative, bilinear multiplication. By use of a new bilinear operation, any associative algebra morphs into a nonassociative abstract Lie algebra, where the new product in terms of the given associative product, is the commutator. The crux of this paper is to investigate the commutator as it pertains to the general linear group and its subalgebras. This forces us to examine properties of ring theory under the lens of linear algebra, as we determine subalgebras, ideals, and solvability as decomposed into an extension of abelian ideals, and nilpotency, as decomposed into the lower central series and eventual zero subspace. The map sending the Lie algebra L to a derivation of L is called the adjoint representation, where a given Lie algebra is nilpotent if and only if the adjoint is nilpotent. Our goal is to prove Engel's Theorem, which states that if all elements of L are ad-nilpotent, then L is nilpotent.

A recent result of Salvetti and Settepanella gives, for a complexified real arrangement, an explicit description of a minimal CW decomposition as well as an explicit algebraic complex which computes local system homology. We apply their techniques to discriminantal arrangements in two dimensional complex space and calculate the boundary maps which will give local system homology groups given any choice of local system. This calculation generalizes several known results; examples are given related to Milnor fibrations, solutions of KZ equations, and the LKB representation of the braid group. Another algebraic object associated to a hyperplane arrangement is the module of derivations. We analyze the behavior of the derivation module for an affine arrangement over an infinite field and relate its derivation module to that of its cone. In the case of an arrangement fibration, we analyze the relationship between the derivation module of the total space arrangement and those of the base and fiber arrangements. In particular, subject to certain restrictions, we establish freeness of the total space arrangement given freeness of the base and fiber arrangements.

Background: Primary subarachnoid hemorrhage (1°SAH) is an important disease that causes significant morbidity and mortality. The sparse Canadian epidemiologic literature on 1° SAH is outdated and relies on diagnostic coding for case ascertainment which misses true cases and incorrectly labels non-cases. Objectives: Primary objective was to identify all patients with 1° SAH presenting to the Ottawa Hospital (TOH) between July 1, 2002 and June 30, 2011 by deriving and validating a search algorithm using an enriched administrative database. Secondary objectives included: 1) determine incidence and case-fatality rates (CFR) of 1° SAH at TOH; and 3) derive and validate a method to identify 1° SAH using routinely collected administrative data. Methods: A cohort of 1° SAH patients were identified with a case-defining algorithm that was derived and validated using a combination of cerebrospinal fluid analysis results and text-search algorithms of both cranial imaging and post-mortem reports. The incidence of 1° SAH was calculated using the total number of hospital encounters over the same time period. CFR was calculated by linking to vital statistic data of hospitalized patients at discharge. An optimal1° SAH prediction model was derived and validated using binomial recursive partitioning built with independent variables obtained from routinely collected administrative data. Results: Using the case-defining algorithm, 831 patients were identified with a 1° SAH over the study period. Hospital incidence of 1° SAH was 17.2 events per 10,000 inpatient encounters (or 0.17% of encounters) with a case-fatality rate of 18.1%. A validated SAH prediction model based on administrative data using a recursive partitioning model had a sensitivity of 96.5% (95% CI 93.9-98.0), a specificity of 99.8% (95%CI 99.6-99.9), and a +LR of 483 (95% CI 254-879). This results in a post-test probability of disease of 45%. Conclusion: We identified almost all cases of 1° SAH at our hospital using an enriched administrative data. Accurately identifying such patients with routinely collected health administrative data is possible, providing important opportunities to examine and study this patient population. Further studies, involving multiple centres are needed to reproduce these results.

The process of language development is quite complex, it occurs under the interactions between diachronic derivation and synchronic derivation. This paper examines the development of Chinese language through the scope of disposal construction to provide evidence that diachronic and synchronic derivations could affect the development of a language simultaneously. From the progression of disposal prepositions in Mandarin based on historical documents, we can observe how diachronic derivation took place. Also, through diachronic derivation, it is safe to say that the earlier sentence structures can have an impact on later sentence structures. By comparing the disposal constructions between Mandarin and Min dialect, the syntactic characteristics and limitations present the possibility of synchronic derivation, which is the result of language contact. The findings of this paper demonstrates the features of language contact through the borrowing of disposal prepositions, and the similarities and differences between the syntax of disposal sentence structure of Mandarin and Min dialect.

The generation of wind energy deliberately becomes a significant part of generated electrical power in developed nations. Factors like fluctuation in natural wind speed and the use of power electronics present issues related power quality in wind turbine application. Following to the fact that there have been remarkable increase of wind energy in the electrical energy production worldwide, the effect on power quality and power system stability caused by wind power is considered significant, and hence the evaluation of this effect is crucial and obligatory. In order to examine and evaluate the characteristics of power quality of grid-integration of wind power in a persistent and authentic manner, several guidelines were introduced and established. One of the widely used guideline to define power quality of wind turbine is IEC standard 61400-21. Moreover, power system operator demands wind turbines to tolerate a certain voltage dip in some countries. The wind turbines concepts such as doubly-fed induction generator wind turbine and the direct driven wind turbine wind turbine with a permanent magnet synchronous generator are considered as the most promising concepts among other wind turbine types since they can operate in wide range of wind speed. The major goal of this PhD work is to examine the power quality character aspects of these wind turbine concepts. The power quality problems were calculated according to that devised by IEC- 61400-21 and then compared afterwards. The research includes the evaluation of the following power quality characteristics: voltage dip response, current harmonics distortion, control of active and reactive power and voltage flicker. Besides the IEC-standard 61400-21, the study also looks into the short-circuit current and fault-ride through with specifications provided by some grid codes, as power system stability is greatly influenced by these aspects. In order to achieve the research's goal, a reliable dynamic model of wind turbine system and control are required. Thus a complete model for both wind turbines systems was developed in PSCAD/EMTDC simulation-program which is the fanatical power system analysis tool, which can achieve a complete simulation of the system dynamic behaviour from the wind turbine. Two controllers are adopted for wind turbine system, converter control and pitch angle control. The converter controlled by a vector control in order to regulate the active and the reactive power whereas the pitch control scheme is put to function to limit the aerodynamic power in high wind speed. The ability of providing adequate state steady and dynamic performances are what wind turbine assures, as examined by simulation results, and via this, problems related to power quality caused by integrating wind turbines to the grid can be studied by wind turbine model.

The freedom to operate (FTO) and the costs of acquiring and protecting intellectual property (IP) has become a major concern among both private and public plant breeders, especially in the IP intensive transgenic crops. Despite the developments in biotechnology, crop breeding still remains a sequential process where the best new varieties build on the successful varieties of the past. Given this breeding process, if FTO reduces the ability of breeders to access the best germplasm this could slow the rate of global crop improvement in both transgenic and non-transgenic crops. This potential problem has led many agricultural science leaders to raise concern about the possibility of an anti-commons developing because of growing freedom to operate issues.<p>One of the solutions that is proposed for the growing FTO issue in plant breeding is the development of open source research platforms similar to those that led to the development of the Linux computer operating system. With an open source research process anyone is able to use the research platform to develop commercial products but any improvements made to the research platform become part of the platform for future users. The proponents of this approach, such as CAMBIA, argue that it will maintain access to critical intellectual property and allow optimal sharing of knowledge to take place.<p>In this paper we examine the intellectual property rights associated with crop germplasm and varieties in Canada. We show that the breeder rights that are built into many current systems of breeder rights systems create a de facto open source system. This system allows breeders to use previously released varieties as breeding material for their own breeding programs allowing them to improve their own germplasm base. Once this is done, and a new variety is released from the program, it then becomes available for other breeders to use in the same manner. Few would argue that this system has not had a long history of success.<p>As a counterfactual we consider the case where provisions of the UPOV 1991 act are used to give plant breeders the rights to not only protect their current varieties from being illegally copied but would also give them claim over any future varieties developed that use their variety as breeding material. In the factual, a three stage model has two public sector breeders seeking to maximize the benefits of their varieties over a heterogeneous group of iii farmers. In the first stage of the model the breeders decide the optimum amount of germplasm to share between each other. The second stage of the model requires the breeders to decide the optimal level of yield it should set as a plant breeding target. In the final stage farmers make an adoption choice basing their decision on the variety that best suits their farm. Backward induction is then used to solve both of the models. Applying the results of this simulation to the wheat plant breeding system in western Canada, shows that such a revised breeders rights system would quickly lead to a large number of potential owners for each variety released, which would then increase transactions costs and eventually lead to an anti-commons or FTO issue. In the case where there are no intellectual property rights on varieties breeders are able to produce a variety that more farmers will adopt because breeders costs will be lower due to germplasm sharing. Once intellectual property rights are introduced into the system, breeders choose to reduce the amount of variety sharing, which then reduces the number of farmers who would adopt the new variety, thus decreasing the benefits for farmers. Given this outcome, jurisdictions that implement the provisions of UPOV 1991 which may hinder FTO, may find benefits from developing other legal measures to maintain an open source type access to germplasm.

The freedom to operate (FTO) and the costs of acquiring and protecting intellectual property (IP) has become a major concern among both private and public plant breeders, especially in the IP intensive transgenic crops. Despite the developments in biotechnology, crop breeding still remains a sequential process where the best new varieties build on the successful varieties of the past. Given this breeding process, if FTO reduces the ability of breeders to access the best germplasm this could slow the rate of global crop improvement in both transgenic and non-transgenic crops. This potential problem has led many agricultural science leaders to raise concern about the possibility of an anti-commons developing because of growing freedom to operate issues.<p>One of the solutions that is proposed for the growing FTO issue in plant breeding is the development of open source research platforms similar to those that led to the development of the Linux computer operating system. With an open source research process anyone is able to use the research platform to develop commercial products but any improvements made to the research platform become part of the platform for future users. The proponents of this approach, such as CAMBIA, argue that it will maintain access to critical intellectual property and allow optimal sharing of knowledge to take place.<p>In this paper we examine the intellectual property rights associated with crop germplasm and varieties in Canada. We show that the breeder rights that are built into many current systems of breeder rights systems create a de facto open source system. This system allows breeders to use previously released varieties as breeding material for their own breeding programs allowing them to improve their own germplasm base. Once this is done, and a new variety is released from the program, it then becomes available for other breeders to use in the same manner. Few would argue that this system has not had a long history of success.<p>As a counterfactual we consider the case where provisions of the UPOV 1991 act are used to give plant breeders the rights to not only protect their current varieties from being illegally copied but would also give them claim over any future varieties developed that use their variety as breeding material. In the factual, a three stage model has two public sector breeders seeking to maximize the benefits of their varieties over a heterogeneous group of iii farmers. In the first stage of the model the breeders decide the optimum amount of germplasm to share between each other. The second stage of the model requires the breeders to decide the optimal level of yield it should set as a plant breeding target. In the final stage farmers make an adoption choice basing their decision on the variety that best suits their farm. Backward induction is then used to solve both of the models. Applying the results of this simulation to the wheat plant breeding system in western Canada, shows that such a revised breeders rights system would quickly lead to a large number of potential owners for each variety released, which would then increase transactions costs and eventually lead to an anti-commons or FTO issue. In the case where there are no intellectual property rights on varieties breeders are able to produce a variety that more farmers will adopt because breeders costs will be lower due to germplasm sharing. Once intellectual property rights are introduced into the system, breeders choose to reduce the amount of variety sharing, which then reduces the number of farmers who would adopt the new variety, thus decreasing the benefits for farmers. Given this outcome, jurisdictions that implement the provisions of UPOV 1991 which may hinder FTO, may find benefits from developing other legal measures to maintain an open source type access to germplasm.

In this thesis, we describe the Jordan isomorphisms and Jordan derivations on prime rings of characteristic 2. We prove that every Jordan isomorphism of M_{n}(F),n >= 3 is either an isomorphism or an antiisomorphism if n is odd, and it is not true if n is even. We also describe the Jordan isomorphisms and Jordan derivations on M_{2}(GF(2)).