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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
421

The implications of fibulin-5 on elastin assembly and its role in the elastic fiber /

Ferron, Florence Joelle. January 2007 (has links)
The extracellular matrix (ECM) is the material found surrounding the cells in a tissue. One component of the ECM is the elastic fiber, which confers the property of elasticity to its environment. Organs such as the lung, skin and major blood vessels have an abundance of elastic fibers so that they are able to expand and recoil. Elastic fibers are composed of two main components; elastin and microfibrils. Microfibrils are composed primarily of fibrillin-1 and provide a scaffold unto which tropoelastin monomers assemble. Elastic fibers interact with many other proteins in the ECM, one of which is fibulin-5. Based on the severe elastic fiber defects observed in the fibulin-5 null mouse, it was established that fibulin-5 plays an essential role in elastic fiber development. This role may be in the deposition of tropoelastin onto microfibrils and/or in stabilizing the elastic fibers in the extracellular matrix. In the present study, the relationship between fibulin-5 and the elastic fiber was investigated through a number of in vivo and in vitro experiments. To test the hypothesis that fibulin-5 requires the presence of elastin to assemble in the ECM, full-length recombinant fibulin-5 (rF5) was purified from transfected cells and used to make a fibulin-5 antibody. Solid-phase binding assays using rF5 showed that fibulin-5 binds tropoelastin at two sites; the initial portion of the C-terminus and the first calcium-binding epidermal growth factor-like domain at the N-terminus. Immunofluorescence staining of elastin null mouse embryonic fibroblast cultures revealed that fibulin-5 does not require elastin to be present in the ECM in order to assemble. Subsequently, solid-phase binding assays showed that fibulin-5 can bind to the N-terminus of fibrillin-1. To determine if fibulin-5 could exist independent of elastin and/or fibrillin-1 in vivo, an immunohistochemical analysis was conducted on heart, liver, lung, colon, spleen, testis and kidney. All three proteins were co-localized in all organs except in the kidney, where fibrillin-1 was found to independently stain the capillary tufts of the renal corpuscles and renal tubules. Thus, fibulin-5 may be co-regulated with elastin and is not present on elastin-independent microfibrils. Additionally, novel locations of elastic fibers were uncovered in the heart, liver, colon, spleen and testis. Overall, this study provides important insights as to the role of fibulin-5 in elastic fiber structure and assembly and also reveals the complexity in understanding the pathogenesis of diseases involving elastic fiber proteins.
422

Enzymatic degradation of bovine serum albumin nanoparticles for drug delivery

Singh, Harsh 06 1900 (has links)
Coacervation is a mild process for developing protein NPs. Bovine serum albumin (BSA) NPs formed via this technique were stabilized using poly-L-Lysine (PLL); short interfering ribonucleic acid (siRNA) was used as a model drug for encapsulation. Specific and non-specific degradation of these coated and uncoated BSA NPs were carried using matrix metalloproteinase-2 (MMP-2) and trypsin, respectively. The particles were characterized with atomic force microscopy, zeta-potential, and photon correlation spectroscopy measurements. There was a significant increase in the zeta potential of BSA NPs upon coating. Trypsin digested the uncoated and coated BSA NPs and resulted in higher BSA release from the particles. However, MMP-2 treatment did not result in higher release of BSA from coated NPs despite the cleavability of coated polymer by MMP-2. This study described a method for obtaining BSA NPs in a controllable size range. Such particles showed degradability in the presence of trypsin and could be promising for targeted drug delivery applications. / Chemical Engineering
423

Aspects of random matrix theory: concentration and subsequence problems

Xu, Hua 17 November 2008 (has links)
The present work studies some aspects of random matrix theory. Its first part is devoted to the asymptotics of random matrices with infinitely divisible, in particular heavy-tailed, entries. Its second part focuses on relations between limiting law in subsequence problems and spectra of random matrices.
424

A T-Matrix Approach to Heavy Quark Interaction with Thermal Gluons in a Quark Gluon Plasma

Huggins, Kyle 2012 August 1900 (has links)
The interactions of heavy quarks within the Quark Gluon Plasma (QGP) are interpreted utilizing an elastic, thermodynamic, 2-body T-matrix in order to calculate drag coefficients of heavy-quark systems derived from a Fokker-Planck equation. A spacelike momentum constraint is employed and produces an effective, color dependent potential with the addition of relativistic factors motivated by the appropriate Feynman diagrams. Hard Thermal Loop (HTL) corrections are interpreted in the context of a finite temperature quark-gluon system, allowing a non-perturbative determination of the gluon's contribution to the drag coefficient. An enhancement of the relaxation rate of ~2 is observed at low momenta, leading to an enhancement of the overall relaxation rate of 20%, while the high-p limit approaches a perturbative level. The importance of a nonperturbative treatment of the QGP to reproduce the dynamical drag coefficient is illustrated.
425

Patterns in correlation matrices arising in wine-tasting and other experiments.

Brien, Christopher J. January 1980 (has links)
There are two distinct areas of research on which the work in this thesis impinges. They are methods for the analysis of patterns in correlation matrices and the analysis of taster performance in wine-tasting experiments in which the wines are scored. For the analysis patterns in correlation matrices, least squares procedures are developed to examine patterns under certain equal correlation hypotheses. The procedures are applied to the z-transforms of the elements of correlation matrices that can be based on either a single group of variables, or variables that can be cross-indexed by two factors such as the multitrait-multimethod matrices given by Campbell and Fiske (1959). The procedures are of the analysis of variance type, being investigative in the sense that, in the event that the correlation matrix is judged to depart from the hypothesised pattern, alternative models to be pursued further are indicated. The associated statistics are calculated directly from closed-form expressions, rather that requiring the iterative solution of some estimation function as is the case with some alternative methods. The procedures are used to analyse the data from a number of wine-tasting and other experiments. The results obtained are shown to be similar, in many instances, to those obtained with maximum likelihood procedures applied to variance-covariance matrices; in other instances, large differences occur between the methods. The test for the hypothesis of equal correlation between all variables developed here is also shown to give similar answers to Lawley’s (1963) test for the hypothesis, in a number of cases. For the analysis of taster performance in wine-tasting experiments in which the wines are scored, the method of examining patterns in correlation matrices can be applied to multitaster and multitaster-multisession correlation matrices. Certain conditions to be fulfilled by multitaster-multisession matrices are specified; the extent to which they are met in a particular experiment can be ascertained from the results of these analyses. The data from several wine-tasting experiments are analysed and the results provide further substantive evidence of the lack of agreement and differences in reliability that can occur between tasters in such experiments. As the technique is applied to data from a single experiment, it can be used, particularly when session replicates are included, to select tasters on the basis of their performance in the experiment under consideration – a highly desirable approach. Four duplicate-evaluation wine-tasting experiments, that were aimed at determining the effect of several treatments on wine quality, fit into this category and so are analysed in more detail. A group of less heterogeneous tasters is selected, where possible, for each of the experiments using the results of the analysis of the multitaster-multisession correlation matrices. Compared with other techniques for selecting tasters on the basis of their results in a wine-tasting experiment, the analysis of multitaster-multisession correlation matrices has the advantages that both reliability and agreement are measured and that the measures are correlation coefficients. However, even the subsets of selected tasters do not behave in a manner that would justify a single analysis for mean differences for each subset. Because this is likely to be a common phenomenon, it is recommended that wine-tasting experiments be designed to include session replicates and the scores of each taster be analysed for mean differences separately. The results of the analysis of the multitaster-multisession matrix can then be used to determine the confidence to be attached to the results of individual tasters in drawing inferences from the experiment. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=721471 / Thesis (M.Ag.Sci.) - University of Adelaide, Dept. of Biometry, 1980
426

Ratings transitions and total return

Arnold, Bruce Robert, Banking & Finance, Australian School of Business, UNSW January 2009 (has links)
The expected yield to maturity on a defaultable obligation equals the nominal yield less expected default losses. However, in a mark-to-market world, one doesn't have the luxury of reporting one's performance on the basis of yield to maturity. Total return is calculated for an arbitrary holding period, and must reflect any mark-to-market gains or losses as at the close of the period-gains or losses that can be triggered by the bond's upgrade or downgrade. Thus to estimate expected total return, one must estimate not only expected default losses, but also the impact on capital price of expected ratings transitions. This paper begins with the observation that a bond which is blessed by more favourable transition characteristics is likely to produce a higher total return, and poses the question of how that benefit can be quantified. How much is it worth? To answer the question, I start by specifying a formal bond-pricing model reflective of ratings transitions. I survey various statistical methods and past research efforts to identify the ratings-transition matrix which best parametrises the model, and propose a novel test for selecting between competing matrices. Using this approach, I replicate several important studies of ratings transitions. I also use it to examine new published and unpublished data, testing for (and finding) ratings path-dependency, and otherwise exploring the effect of ratings changes on different bond sectors. I then turn to the question of whether it is possible to estimate bond-specific transition probabilities, and propose a way to do so. I combine these efforts into the specifications for a pricing model capable of answering the question: How much is it worth?
427

Changing power balance in matrix organizations.

Saracoglu, Nursen Emine January 2009 (has links)
Modern organizations require new structural forms to cope with uncertainties arising from the challenges of global competition and rapid technological and environmental changes (Clarke and Clegg, 1998). One of the most important developments in the area of planned change has been on how to work with large systems so as to initiate and sustain change over time. It was from such contexts that the matrix concept emerged. During the 1950s the term matrix emerged in the United States aerospace industry and, as it has developed through the years, the term has come to be accepted in both business and academic circles. In the 1960s the matrix was sought as a fundamental alternative for dealing with unique management problems of coordination, communication and control (Davis and Lawrence, 1977). In the 1970s and 1980s interest in matrix organizational structures peaked. Since that time, research and literature on the matrix has diminished; contrarily, organizations continue to adopt the matrix as a viable alternative to deal with their increasingly complex business environment. In the recent past, some of the companies that applied a complex global matrix structure have included Asea Brown Boveri (ABB), Zurich (1991); Brown & Root (BR), UK (1999); Hatch (1999) – Formerly BHPE and Kaiser mergers; IMC (1999); Parsons Brinckerhoff (PB), (1999); and Sinclair Knight and Merz (SKM), (2002). These companies have used matrix structures to achieve worldwide economies of scale, combined with local flexibility and responsiveness. The purpose of this study was to investigate the validity of political theories of organizations in major international companies that have implemented matrix structure, with a focus that includes identifying: i. The key factors behind the strategic decision to change the corporate organization in international companies to a matrix structure. ii. The weaknesses and strengths of these matrix structures for subsequent organizational performance. iii. The effects of transition to matrix structure on organizational performance. iv. The factors used to maintain a power balance between divisions. v. A model that seeks to diminish or reduce matrix structure weaknesses to increase organizational effectiveness. The research was conducted in the form of a questionnaire survey and semistructured interviews. To illustrate the implementation of the matrix structure that occurred in a real world environment, SKM has been researched as an intensive case study. Preface As a professional engineer I have had opportunities to be involved with major projects in various international organizations. I have also had opportunities to observe organizations and to analyse their operations by exploring existing procedures and manuals. It was noticeable that the overall success of the projects relied very much on organizational decision making. This observation led my paradigm shift from projects to organizational studies and to the idea of conducting research that aims to investigate the weaknesses and strengths of matrix structures for organizational performance. Introduction Thesis structure This thesis presents a detailed account of the research activities undertaken by Nursen Saracoglu and the outcomes of that research. The purpose of this research is to investigate the validity of political theories of organizations in major international companies that have implemented matrix structure. Data has been collected using a combination of methods, including questionnaires, semistructured interviews, and direct examination of library catalogues and databases. The structure of this thesis is designed as follows: Chapter 1 introduces, and describes the background to the research project. The theories that provide a background to the various factors involved in organizations choosing to change to matrix structures, and the resulting positive and negative effects on the organization, are presented in this chapter. Chapters 2 reviews and analyses the literature review that has been conducted to focus, especially, on how changes to the structure and design of power in matrix organizations can have important implications and consequences. The literature review looks in detail at different organizational theories, particularly theories on power within organizations, which have a bearing on the effect of a matrix structure on an organization. Each theory is critiqued in terms of its relevance to matrix structure analysis. Strategic Contingencies Theory (SCT) and Resource Dependency Theory (RDT) best explain the effect of different levels of power inside a matrix structure. Chapter 3 details the research design and methodology. This chapter describes the advantages and disadvantages of quantitative and qualitative approaches and presents the rationale of selecting research methodology. The participating organization, SKM, is described in terms of its history and its matrix structure is outlined. Chapter 4 illustrates the results of research that defines potential areas of concern associated with matrix structures. The discussion mainly centres on the methods used to analyse the data and then focuses on the different dependent and independent variables derived from the data that are used in the analysis for correlation purposes. The aim of this chapter is to explain the various statistics used to analyse the data and to list the variables that came up as a result of answers to questionnaire. These variables are then analysed against each other in order to develop a sense of the effectiveness of the matrix structure in SKM. In Chapter 5 the qualitative data was examined using the responses obtained from interviews with the top managers of SKM. This chapter aims to identify the themes that have emerged from these interview responses and present them in order of most to least common within each area of research, illustrated with comments from some of the respondents. Chapter 6 discusses the survey and interview results in order to exploit quantitative findings to identify patterning in qualitative data. In parallel with SCT and RDT, the relationship between power and performance in matrix organizations is presented. The new concepts that emerged based on the research findings are introduced and discussed according to the relevance to the research objectives. Chapter 7 This chapter concludes the research and presents research limitations, boundaries, the contribution to the body of knowledge and a summary of future research opportunities. The case studies give a sense of how various elements of Matrix structure that outlined in this research were actually applied by other particular organizations are exhibited in Appendix A.
428

Changing power balance in matrix organizations.

Saracoglu, Nursen Emine January 2009 (has links)
Modern organizations require new structural forms to cope with uncertainties arising from the challenges of global competition and rapid technological and environmental changes (Clarke and Clegg, 1998). One of the most important developments in the area of planned change has been on how to work with large systems so as to initiate and sustain change over time. It was from such contexts that the matrix concept emerged. During the 1950s the term matrix emerged in the United States aerospace industry and, as it has developed through the years, the term has come to be accepted in both business and academic circles. In the 1960s the matrix was sought as a fundamental alternative for dealing with unique management problems of coordination, communication and control (Davis and Lawrence, 1977). In the 1970s and 1980s interest in matrix organizational structures peaked. Since that time, research and literature on the matrix has diminished; contrarily, organizations continue to adopt the matrix as a viable alternative to deal with their increasingly complex business environment. In the recent past, some of the companies that applied a complex global matrix structure have included Asea Brown Boveri (ABB), Zurich (1991); Brown & Root (BR), UK (1999); Hatch (1999) – Formerly BHPE and Kaiser mergers; IMC (1999); Parsons Brinckerhoff (PB), (1999); and Sinclair Knight and Merz (SKM), (2002). These companies have used matrix structures to achieve worldwide economies of scale, combined with local flexibility and responsiveness. The purpose of this study was to investigate the validity of political theories of organizations in major international companies that have implemented matrix structure, with a focus that includes identifying: i. The key factors behind the strategic decision to change the corporate organization in international companies to a matrix structure. ii. The weaknesses and strengths of these matrix structures for subsequent organizational performance. iii. The effects of transition to matrix structure on organizational performance. iv. The factors used to maintain a power balance between divisions. v. A model that seeks to diminish or reduce matrix structure weaknesses to increase organizational effectiveness. The research was conducted in the form of a questionnaire survey and semistructured interviews. To illustrate the implementation of the matrix structure that occurred in a real world environment, SKM has been researched as an intensive case study. Preface As a professional engineer I have had opportunities to be involved with major projects in various international organizations. I have also had opportunities to observe organizations and to analyse their operations by exploring existing procedures and manuals. It was noticeable that the overall success of the projects relied very much on organizational decision making. This observation led my paradigm shift from projects to organizational studies and to the idea of conducting research that aims to investigate the weaknesses and strengths of matrix structures for organizational performance. Introduction Thesis structure This thesis presents a detailed account of the research activities undertaken by Nursen Saracoglu and the outcomes of that research. The purpose of this research is to investigate the validity of political theories of organizations in major international companies that have implemented matrix structure. Data has been collected using a combination of methods, including questionnaires, semistructured interviews, and direct examination of library catalogues and databases. The structure of this thesis is designed as follows: Chapter 1 introduces, and describes the background to the research project. The theories that provide a background to the various factors involved in organizations choosing to change to matrix structures, and the resulting positive and negative effects on the organization, are presented in this chapter. Chapters 2 reviews and analyses the literature review that has been conducted to focus, especially, on how changes to the structure and design of power in matrix organizations can have important implications and consequences. The literature review looks in detail at different organizational theories, particularly theories on power within organizations, which have a bearing on the effect of a matrix structure on an organization. Each theory is critiqued in terms of its relevance to matrix structure analysis. Strategic Contingencies Theory (SCT) and Resource Dependency Theory (RDT) best explain the effect of different levels of power inside a matrix structure. Chapter 3 details the research design and methodology. This chapter describes the advantages and disadvantages of quantitative and qualitative approaches and presents the rationale of selecting research methodology. The participating organization, SKM, is described in terms of its history and its matrix structure is outlined. Chapter 4 illustrates the results of research that defines potential areas of concern associated with matrix structures. The discussion mainly centres on the methods used to analyse the data and then focuses on the different dependent and independent variables derived from the data that are used in the analysis for correlation purposes. The aim of this chapter is to explain the various statistics used to analyse the data and to list the variables that came up as a result of answers to questionnaire. These variables are then analysed against each other in order to develop a sense of the effectiveness of the matrix structure in SKM. In Chapter 5 the qualitative data was examined using the responses obtained from interviews with the top managers of SKM. This chapter aims to identify the themes that have emerged from these interview responses and present them in order of most to least common within each area of research, illustrated with comments from some of the respondents. Chapter 6 discusses the survey and interview results in order to exploit quantitative findings to identify patterning in qualitative data. In parallel with SCT and RDT, the relationship between power and performance in matrix organizations is presented. The new concepts that emerged based on the research findings are introduced and discussed according to the relevance to the research objectives. Chapter 7 This chapter concludes the research and presents research limitations, boundaries, the contribution to the body of knowledge and a summary of future research opportunities. The case studies give a sense of how various elements of Matrix structure that outlined in this research were actually applied by other particular organizations are exhibited in Appendix A.
429

Changing power balance in matrix organizations.

Saracoglu, Nursen Emine January 2009 (has links)
Modern organizations require new structural forms to cope with uncertainties arising from the challenges of global competition and rapid technological and environmental changes (Clarke and Clegg, 1998). One of the most important developments in the area of planned change has been on how to work with large systems so as to initiate and sustain change over time. It was from such contexts that the matrix concept emerged. During the 1950s the term matrix emerged in the United States aerospace industry and, as it has developed through the years, the term has come to be accepted in both business and academic circles. In the 1960s the matrix was sought as a fundamental alternative for dealing with unique management problems of coordination, communication and control (Davis and Lawrence, 1977). In the 1970s and 1980s interest in matrix organizational structures peaked. Since that time, research and literature on the matrix has diminished; contrarily, organizations continue to adopt the matrix as a viable alternative to deal with their increasingly complex business environment. In the recent past, some of the companies that applied a complex global matrix structure have included Asea Brown Boveri (ABB), Zurich (1991); Brown & Root (BR), UK (1999); Hatch (1999) – Formerly BHPE and Kaiser mergers; IMC (1999); Parsons Brinckerhoff (PB), (1999); and Sinclair Knight and Merz (SKM), (2002). These companies have used matrix structures to achieve worldwide economies of scale, combined with local flexibility and responsiveness. The purpose of this study was to investigate the validity of political theories of organizations in major international companies that have implemented matrix structure, with a focus that includes identifying: i. The key factors behind the strategic decision to change the corporate organization in international companies to a matrix structure. ii. The weaknesses and strengths of these matrix structures for subsequent organizational performance. iii. The effects of transition to matrix structure on organizational performance. iv. The factors used to maintain a power balance between divisions. v. A model that seeks to diminish or reduce matrix structure weaknesses to increase organizational effectiveness. The research was conducted in the form of a questionnaire survey and semistructured interviews. To illustrate the implementation of the matrix structure that occurred in a real world environment, SKM has been researched as an intensive case study. Preface As a professional engineer I have had opportunities to be involved with major projects in various international organizations. I have also had opportunities to observe organizations and to analyse their operations by exploring existing procedures and manuals. It was noticeable that the overall success of the projects relied very much on organizational decision making. This observation led my paradigm shift from projects to organizational studies and to the idea of conducting research that aims to investigate the weaknesses and strengths of matrix structures for organizational performance. Introduction Thesis structure This thesis presents a detailed account of the research activities undertaken by Nursen Saracoglu and the outcomes of that research. The purpose of this research is to investigate the validity of political theories of organizations in major international companies that have implemented matrix structure. Data has been collected using a combination of methods, including questionnaires, semistructured interviews, and direct examination of library catalogues and databases. The structure of this thesis is designed as follows: Chapter 1 introduces, and describes the background to the research project. The theories that provide a background to the various factors involved in organizations choosing to change to matrix structures, and the resulting positive and negative effects on the organization, are presented in this chapter. Chapters 2 reviews and analyses the literature review that has been conducted to focus, especially, on how changes to the structure and design of power in matrix organizations can have important implications and consequences. The literature review looks in detail at different organizational theories, particularly theories on power within organizations, which have a bearing on the effect of a matrix structure on an organization. Each theory is critiqued in terms of its relevance to matrix structure analysis. Strategic Contingencies Theory (SCT) and Resource Dependency Theory (RDT) best explain the effect of different levels of power inside a matrix structure. Chapter 3 details the research design and methodology. This chapter describes the advantages and disadvantages of quantitative and qualitative approaches and presents the rationale of selecting research methodology. The participating organization, SKM, is described in terms of its history and its matrix structure is outlined. Chapter 4 illustrates the results of research that defines potential areas of concern associated with matrix structures. The discussion mainly centres on the methods used to analyse the data and then focuses on the different dependent and independent variables derived from the data that are used in the analysis for correlation purposes. The aim of this chapter is to explain the various statistics used to analyse the data and to list the variables that came up as a result of answers to questionnaire. These variables are then analysed against each other in order to develop a sense of the effectiveness of the matrix structure in SKM. In Chapter 5 the qualitative data was examined using the responses obtained from interviews with the top managers of SKM. This chapter aims to identify the themes that have emerged from these interview responses and present them in order of most to least common within each area of research, illustrated with comments from some of the respondents. Chapter 6 discusses the survey and interview results in order to exploit quantitative findings to identify patterning in qualitative data. In parallel with SCT and RDT, the relationship between power and performance in matrix organizations is presented. The new concepts that emerged based on the research findings are introduced and discussed according to the relevance to the research objectives. Chapter 7 This chapter concludes the research and presents research limitations, boundaries, the contribution to the body of knowledge and a summary of future research opportunities. The case studies give a sense of how various elements of Matrix structure that outlined in this research were actually applied by other particular organizations are exhibited in Appendix A.
430

Finite reducible matrix algebras

Brown, Scott January 2006 (has links)
[Truncated abstract] A matrix is said to be cyclic if its characteristic polynomial is equal to its minimal polynomial. Cyclic matrices play an important role in some algorithms for matrix group computation, such as the Cyclic Meataxe of Neumann and Praeger. In 1999, Wall and Fulman independently proved that the proportion of cyclic matrices in general linear groups over a finite field of fixed order q has limit [formula] as the dimension approaches infinity. First we study cyclic matrices in maximal reducible matrix groups, that is, the stabilisers in general linear groups of proper nontrivial subspaces. We modify Wall’s generating function approach to determine the limiting proportion of cyclic matrices in maximal reducible matrix groups, as the dimension of the underlying vector space increases while that of the invariant subspace remains fixed. This proportion is found to be [formula] note the change of the exponent of q in the leading term of the expansion. Moreover, we exhibit in each maximal reducible matrix group a family of noncyclic matrices whose proportion is [formula]. Maximal completely reducible matrix groups are the stabilisers in a general linear group of a nontrivial decomposition U1⊕U2 of the underlying vector space. We take a similar approach to determine the limiting proportion of cyclic matrices in maximal completely reducible matrix groups, as the dimension of the underlying vector space increases while the dimension of U1 remains fixed. This limiting proportion is [formula]. ... We prove that this proportion is[formula] provided the dimension of the fixed subspace is at least two and the size q of the field is at least three. This is also the limiting proportion as the dimension increases for separable matrices in maximal completely reducible matrix groups. We focus on algorithmic applications towards the end of the thesis. We develop modifications of the Cyclic Irreducibility Test - a Las Vegas algorithm designed to find the invariant subspace for a given maximal reducible matrix algebra, and a Monte Carlo algorithm which is given an arbitrary matrix algebra as input and returns an invariant subspace if one exists, a statement saying the algebra is irreducible, or a statement saying that the algebra is neither irreducible nor maximal reducible. The last response has an upper bound on the probability of incorrectness.

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