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.

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.

Borders, belonging, beyond: New curriculum history

For Iain Chambers, understanding the redefinition of social life and hence of social theories is not aided by splitting the analytical register simply between global and local. This is especially problematic if global is taken to mean the dispersal of an already-dominant or privileged version of the local within wider coordinates that ensure the continuation of forms of representation and frames of reference that are familiar and over-exposed. The chapters in New Curriculum History take up the challenge posed by Chambers, collectively confronting the dread of a rationality confronted with what exceeds and slips its grasp. Finding purchase and continually slipping away from the strictures of the taken-for-granted and of fixity, New Curriculum History embodies the dueling reverberations of its non-localizable domains – in some ways, a shaping by its pasts and in others, contributions irreducible to dominant narratives about the field of education and “its” histories...

Non-reductive Physicalism, Irreducibility of the Mental and the Problem of Mental Causation : A study of Donald Davidson's and Georg Henrik von Wright's positions in the philosophy of mind

In this study I consider what kind of perspective on the mind body problem is taken and can be taken by a philosophical position called non-reductive physicalism. Many positions fall under this label. The form of non-reductive physicalism which I discuss is in essential respects the position taken by Donald Davidson (1917-2003) and Georg Henrik von Wright (1916-2003). I defend their positions and discuss the unrecognized similarities between their views. Non-reductive physicalism combines two theses: (a) Everything that exists is physical; (b) Mental phenomena cannot be reduced to the states of the brain. This means that according to non-reductive physicalism the mental aspect of humans (be it a soul, mind, or spirit) is an irreducible part of the human condition. Also Davidson and von Wright claim that, in some important sense, the mental aspect of a human being does not reduce to the physical aspect, that there is a gap between these aspects that cannot be closed. I claim that their arguments for this conclusion are convincing. I also argue that whereas von Wright and Davidson give interesting arguments for the irreducibility of the mental, their physicalism is unwarranted. These philosophers do not give good reasons for believing that reality is thoroughly physical. Notwithstanding the materialistic consensus in the contemporary philosophy of mind the ontology of mind is still an uncharted territory where real breakthroughs are not to be expected until a radically new ontological position is developed. The third main claim of this work is that the problem of mental causation cannot be solved from the Davidsonian - von Wrightian perspective. The problem of mental causation is the problem of how mental phenomena like beliefs can cause physical movements of the body. As I see it, the essential point of non-reductive physicalism - the irreducibility of the mental - and the problem of mental causation are closely related. If mental phenomena do not reduce to causally effective states of the brain, then what justifies the belief that mental phenomena have causal powers? If mental causes do not reduce to physical causes, then how to tell when - or whether - the mental causes in terms of which human actions are explained are actually effective? I argue that this - how to decide when mental causes really are effective - is the real problem of mental causation. The motivation to explore and defend a non-reductive position stems from the belief that reductive physicalism leads to serious ethical problems. My claim is that Davidson's and von Wright's ultimate reason to defend a non-reductive view comes back to their belief that a reductive understanding of human nature would be a narrow and possibly harmful perspective. The final conclusion of my thesis is that von Wright's and Davidson's positions provide a starting point from which the current scientistic philosophy of mind can be critically further explored in the future.

Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation [script D]alpha of the para-Bose system is obtained as the direct sum Dbeta[direct-sum]Dbeta+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation [script D]alpha, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

A cryptographic system based on finite field transforms

In this paper, we develop a cipher system based on finite field transforms. In this system, blocks of the input character-string are enciphered using congruence or modular transformations with respect to either primes or irreducible polynomials over a finite field. The polynomial system is shown to be clearly superior to the prime system for conventional cryptographic work.

Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.