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Groebner bases have many applications in mathematics, science, and engineering. This dissertation deals with the algorithmic aspects of computing these bases. The dissertation begins with a brief introduction of fundamental concepts about Groebner bases. Following this a discussion of various implementation issues are discussed. Much of the practical difficulties of using Groebner basis algorithms and techniques stems from the high computational complexity. It is shown that the algorithmic complexity of computing a Groebner basis primarily stems from the calculation of normal forms. This is established by studying run profiles of various computations. This leads to two options of making Groebner basis techniques more practical. They are to reduce the complexity by developing new algorithms (heuristics) or reduce running time of normal form calculations by introducing concurrency. The later approach is taken in the remainder of the dissertation where a multithreaded normal form algorithm is presented and discussed. It is shown with a simple example that the new algorithm demonstrates a speedup and scalability. The algorithm also has the advantage of being completion strategy independent. We conclude with an outline of future research involving the new algorithm.

The aim of this study was to investigate what empathy means to Swedish social workers and to discover in which ways empathy may be used within social work practice in Sweden. The phenomenon of empathy has already been investigated in several areas such as; social science, psychology and neuroscience and it remains as a growing subject in academic research. In this study, the subject of empathy was investigated within the context of Swedish social work practice. A qualitative study was conducted by using the methodology of a phenomenological approach. The research questions were formed to obtain substantial information about the description of empathy, as well as to discover how empathy has been used by a sample of Swedish social workers when working with people from vulnerable groups. The chosen theory in this study was symbolic interactionism and it was employed in the analysis along with different previous research. The results in this study indicated that the respondents found it important to show empathy towards the clients as a part of being a professional social worker. Empathy still appeared to be a contextually dependent phenomenon and the positive outcomes of showing empathy may be affected negatively due to distressful factors.    Key words: social work, empathy, symbolic interactionism

This educational study on narrative and symbolic art and its impact on me as artist, researcher, and teacher and ultimately how the use of narrative and symbolism impacts student learning was conducted throughout the school year 2013-2014 in the environment of both my home and my classroom in a south metro Atlanta high school. The research is based on my reflections of my artistic processes, my research of family history, and my observations as I introduced narrative and symbolic art in the classroom. The findings of the study reveal that the roles of artist, teacher, and researcher are significantly interrelated and enhance one another; I also believe that my students’ learning was impacted. While students are at first assigned narrative and symbolic art projects, many begin to extrapolate that art is more meaningful to them when it has a story to tell or includes symbolism with which they associate importance.

We study compensation functions for an infinite-to-one factor code $\pi : X \to Y$ where $X$ is a shift of finite type. The $p$-Dini condition is given as a way of measuring the smoothness of a continuous function, with $1$-Dini corresponding to functions with summable variation. Two types of compensation functions are defined in terms of this condition. Given a fully-supported invariant measure $\nu$ on $Y$, we show that the relative equilibrium states of a $1$-Dini function $f$ over $\nu$ are themselves fully supported, and have positive relative entropy. We then show that there exists a compensation function which is $p$-Dini for all $p > 1$ which has relative equilibrium states supported on a finite-to-one subfactor. / Graduate / 0405 / antoniol@uvic.ca

This thesis holds that the application of the archaeological method, developed by the French philosopher Michel Foucault, to the field of anthropology reveals a hitherto hidden primitive episteme. Such a project represents a rejection of a search for a fundamental Truth, available through the traditional figures of rationality, either vertically in history or horizontally across cultures. The form of reason posited by this project does not have a constant and universal occurrence but is given in the discontinuous figures of the episteme. The quest for a single manifestation of the conditions of validity in reason is replaced by a study of the conditions of possibility of the truths, discourses and institutions of a primitive peoples. The conditions of possibility for the emergence of the elements of primitive knowledge and practices are available through the application of the explanatory unities of the archaeological method. These unities replace the traditional explanatory role of the subject, with all of its psychological baggage, which has a central role in modern theories of rationality. The subject-knowledge link that dominates traditional anthropological analyses is replaced by a powerknowledge link that postulates the two axes of discursive and non-discursive concerns. The discursive axis is concerned with the objects, concepts, statements and discursive formations of primitive knowledge while the non-discursive axis is concerned with the systems of power that propagate and sustain those discourses. These two axes constitute the nature of the archaeology employed in this study. This thesis is sustained by both negative and positive evidence. The negative evidence takes the form of an antisubjectivist thrust where the subject-dependent explanatory unities of the tradition are replaced by the positivistic elements of archaeology. The positive evidence primarily takes the form of a detailed analysis of the presence of the guiding codes of the episteme amongst the Trobriand Islanders that give rise to their primitive knowledge and practices. In this area, I make extensive use of Malinowski's ethnographic observations for their breath of detail and application without employing his subject-dependent psychobiological conclusions. Further, I am proposing a transformative position such that orality becomes a feature of the episteme rather than its condition of possibility. The guiding codes of the Trobriand episteme take the form of enclosed oppositional figures that are everywhere related to space. The Trobriand episteme provides the conditions for the emergence of primitive discourses and orders the experiences of the Trobrianders. The guiding figures of the episteme are based in a form of complementary opposition, causation as vitality and a dogma of topological space that give rise to primitive knowledge which is a form of divination. A significant part of this dissertation is taken up with an examination of the detail and limitation of these figures where ideas from Levy-Bruhl, Hallpike, and others are employed to produce the most appropriate configuration for my project. A particular form of language as the manipulation of real signs, rather than ideational signs, has its possibility in this configuration which has consequences for the type of knowledge produced. The form of knowledge appropriate to the presence of such a model of language is magic. Writing has no possibility for emerging in this episteme and, therefore, there are significant consequences for the type of knowledge that can be maintained and propagated in a context which must utilise static tradition to the detriment of reflection. An archaeological analysis of the Trobriand Islanders, focusing on discourses on sex and marriage, the nature of tabooed sexual acts, economic relations arising out of marriage and the role of the polygamous chief, the nature of love-magic and magic in general, reveals a shared possibility for all of these discursive realms in the figures of the episteme. These discourses are regulated by the presence of a fundamental opposition between a brother and his sister. This opposition forms the motif for primitive problematizations and constitutes a vulnerable boundary which is the appropriate focus of taboos relating to sex and food, amongst others. This primitive episteme characterises the unity of the experiences of the Trobrianders. This experience is discontinuous with our own and does not involve a role for the individual ego. This project represents a worthwhile contribution to an understanding of human experience and knowledge in general which does not seek to reduce the natural diversity of man to just the monotonous experience of modern man. In conclusion, I tentatively speculate about the appropriateness of the Trobriand figures for primitive experience in general.

This thesis presents a new algorithm for computing the Hermite form of a polynomial matrix. Given a nonsingular n by n matrix A filled with degree d polynomials with coefficients from a field, the algorithm computes the Hermite form of A in expected number of field operations similar to that of matrix multiplication. The algorithm is randomized of the Las Vegas type.

Typescript. / Thesis (Ph. D.)--University of Hawaii at Manoa, 1977. / Bibliography: leaves 172-175. / Microfiche. / vii, 175 leaves ill

Thesis (Ph. D.)--University of Hawaii at Manoa, 1996. / Includes bibliographical references (leaves 140-144). / Microfiche. / x, 144 leaves, bound ill. 29 cm