The Abelian equations of the tenth degree irreducible in a given domain of rationality,

Thesis (Ph. D.)--University of California, 1912.

Irreducible cyclic presentations of the trivial group

We produce families of irreducible cyclic presentations of the trivial group. These families comprehensively answer questions about such presentations asked by Dunwoody and by Edjvet, Hammond, and Thomas. Our theorems are purely theoretical, but their derivation is based on practical computations. We explain how we chose the computations and how we deduced the theorems.

Irreducible 2-fold cycle systems

In this paper, it is shown that for any pair of integers (m, n) with 4 ≤ m ≤ n, if there exists an m-cycle system of order n, then there exists an irreducible 2-fold m-cycle system of order n, except when (m, n) = (5,5). A similar result has already been established for the case of 3-cycles. © 2005 Wiley Periodicals, Inc.

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.

Invariance under type morphisms: the bayesian Nash equilibrium

Ely and Peski (2006) and Friedenberg and Meier (2010) provide examples when changing the type space behind a game, taking a "bigger" type space, induces changes of Bayesian Nash Equilibria, in other words, the Bayesian Nash Equilibrium is not invariant under type morphisms. In this paper we introduce the notion of strong type morphism. Strong type morphisms are stronger than ordinary and conditional type morphisms (Ely and Peski, 2006), and we show that Bayesian Nash Equilibria are not invariant under strong type morphisms either. We present our results in a very simple, finite setting, and conclude that there is no chance to get reasonable assumptions for Bayesian Nash Equilibria to be invariant under any kind of reasonable type morphisms.

The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F )

The real-quaternionic indicator, also called the $\delta$ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely related to the Frobenius-Schur indicator, which we call the $\varepsilon$ indicator. The Frobenius-Schur indicator $\varepsilon(\pi)$ is known to be given by a particular value of the central character. We would like a similar result for the $\delta$ indicator. When $G$ is compact, $\delta(\pi)$ and $\varepsilon(\pi)$ coincide. In general, they are not necessarily the same. In this thesis, we will give a relation between the two indicators when $G$ is a real reductive algebraic group. This relation also leads to a formula for $\delta(\pi)$ in terms of the central character. For the second part, we consider the construction of the local Langlands correspondence of $GL(2,F)$ when $F$ is a non-Archimedean local field with odd residual characteristics. By re-examining the construction, we provide new proofs to some important properties of the correspondence. Namely, the construction is independent of the choice of additive character in the theta correspondence.

Hypercapitalism:Political economy, electric identity, and authorial alienation

Hypercapitalism, with its "knowledge economy", is the form of capitalism under which thought itself is produced, commodified, and exchanged within the globally integrated system of communication technologies. As such, hypercapitalism may be seen as not so much a revolution, but rather an evolution: the progressively thorough, inexorable totalisation of social relations by Capital. The study on which this paper is based synthesises the sociological perspectives of Marx (1970, 1844/1975, 1846/1972, 1976, 1978, 1981) and Adorno (1951/1974, 1991; Horkheimer & Adorno, 1944/1998), and the Critical Discourse perspectives of Fairclough (1989, 1992) and Lemke (1995) to argue that alienated thought and language are the fundamental, irreducible commodity-forms of Cybersociety’s knowledge economy.

The Effective and The Evocative : A Spectrum of Creative Practice Research

In the expanding literature on creative practice research, art and design are often described as a unified field. They are bracketed together (art-and-design), referred to as interchangeable terms (art/design), and nested together, as if the practices of one domain encompass the other. However it is possible to establish substantial differences in research approaches. In this chapter we argue that core distinctions arise out of the goals of the research, intentions invested in the resulting “artefacts” (creative works, products, events), and the knowledge claims made for the research outcomes. Moreover, these fundamental differences give rise to a number of contingent attributes of the research such as the forming contexts, methodological approaches, and ways of evidencing and reporting new knowledge. We do not strictly ascribe these differences to disciplinary contexts. Rather, we use the terms effective practice research and evocative practice research to describe the spirit of the two distinctive research paradigms we identify. In short, effective practice research (often pursued in design fields) seeks a solution (or resolution) to a problem identified with a particular community, and it produces an artefact that addresses this problem by effecting change (making a situation, product or process more efficient or effective in some way). On the other hand, evocative practice research (often pursued by creative arts fields) is driven by individual pre-occupations, cultural concerns or human experience more broadly. It produces artefacts that evoke affect and resonance, and are poetically irreducible in meaning. We cite recent examples of creative research projects that illustrate the distinctions we identify. We then go on to describe projects that integrate these modes of research. In this way, we map out a creative research spectrum, with distinct poles as well as multiple hybrid possibilities. The hybrid projects we reference are not presented as evidence an undifferentiated field. Instead, we argue that they integrate research modes in deliberate, purposeful and distinctive ways: employing effective practice research methods in the production of evocative artefacts or harnessing evocative (as well as effective) research paradigms to effect change.

Aggregate quality of service computation for composite services

This paper addresses the problem of computing the aggregate QoS of a composite service given the QoS of the services participating in the composition. Previous solutions to this problem are restricted to composite services with well-structured orchestration models. Yet, in existing languages such as WS-BPEL and BPMN, orchestration models may be unstructured. This paper lifts this limitation by providing equations to compute the aggregate QoS for general types of irreducible unstructured regions in orchestration models. In conjunction with existing algorithms for decomposing business process models into single-entry-single-exit regions, these functions allow us to cover a larger set of orchestration models than existing QoS aggregation techniques.

Producing the NAPLAN Machine: A Schizoanalytic Cartography

Everything revolves around desiring-machines and the production of desire… Schizoanalysis merely asks what are the machinic, social and technical indices on a socius that open to desiring-machines (Deleuze & Guattari, 1983, pp. 380-381). Achievement tests like NAPLAN are fairly recent, yet common, education policy initiatives in much of the Western world. They intersect with, use and change pre-existing logics of education, teaching and learning. There has been much written about the form and function of these tests, the ‘stakes’ involved and the effects of their practice. This paper adopts a different “angle of vision” to ask what ‘opens’ education to these regimes of testing(Roy, 2008)? This paper builds on previous analyses of NAPLAN as a modulating machine, or a machine characterised by the increased intensity of connections and couplings. One affect can be “an existential disquiet” as “disciplinary subjects attempt to force coherence onto a disintegrating narrative of self”(Thompson & Cook, 2012, p. 576). Desire operates at all levels of the education assemblage, however our argument is that achievement testing manifests desire as ‘lack’; seen in the desire for improved results, the desire for increased control, the desire for freedom, the desire for acceptance to name a few. For Deleuze and Guattari desire is irreducible to lack, instead desire is productive. As a productive assemblage, education machines operationalise and produce through desire; “Desire is a machine, and the object of the desire is another machine connected to it”(Deleuze & Guattari, 1983, p. 26). This intersection is complexified by the strata at which they occur, the molar and molecular connections and flows they make possible. Our argument is that when attention is paid to the macro and micro connections, the machines built and disassembled as a result of high-stakes testing, a map is constructed that outlines possibilities, desires and blockages within the education assemblage. This schizoanalytic cartography suggests a new analysis of these ‘axioms’ of testing and accountability. It follows the flows and disruptions made possible as different or altered connections are made and as new machines are brought online. Thinking of education machinically requires recognising that “every machine functions as a break in the flow in relation to the machine to which it is connected, but at the same time is also a flow itself, or the production of flow, in relation to the machine connected to it”(Deleuze & Guattari, 1983, p. 37). Through its potential to map desire, desire-production and the production of desire within those assemblages that have come to dominate our understanding of what is possible, Deleuze and Guattari’s method of schizoanalysis provides a provocative lens for grappling with the question of what one can do, and what lines of flight are possible.

Disorganizing educational tropes: Conceptions of dis/ability and curriculum

A study examined the politics of dis/ability and curriculum. Data were obtained from a review of the new disability studies literature, focusing on the areas of history, sociology, anthropology, and critical legal theory. The results indicate that this new literature challenges popular psychoeducational models that assume disability as an objective medical, individual, and pathological deficiency, effectively restricting the systematic study of dis/ability as relational, external, shifting, and socially constituted. The findings suggest ways in which perceptions of “school problems” have to be adjusted to understand how the constant refiguration of normativities in everyday activities creates perceptions of disability-negative ontologies, generates experiences that incite efforts to modify those perceptions in multiple ways, and produces unintended effects from well-intended approaches that in the end remain irreducible to simplistic definitions for the one “ethical” or “politically correct” strategy.