Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation

2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.

How employees with different national identities experience a geocentric organizational culture of a global corporation: A phenomenological study

A global corporation values both profitability and social acceptance; its units mutually negotiate governance and represent a highly interdependent network where centers of excellence and high-potential employees are identified regardless of geographic locations. These companies try to build geocentric, or “world oriented” (Marquardt, 1999, p. 20), organizational cultures. Such culture “transcends cultural differences and establishes ‘beacons’ – values and attitudes – that are comprehensive and compelling” (Kets de Vries & Florent-Treacy, 2002, p. 299) for all employees, regardless of their national origins. Creating a geocentric organizational culture involves transforming each employee’s mindset, beliefs, and behaviors so that he/she can become “a world citizen in spite of having a national identity” (Marquardt, 1999, p. 47). The purpose of this phenomenological study was to explore how employees with different national identities experience a geocentric organizational culture of a global corporation. Phenomenological research aims to understand “how people experience some phenomenon—how they perceive it, describe it, feel about it, judge it, remember it, make sense of it, and talk about it with others” (Patton, 2002, p. 104). Twelve participants were selected using criteria, convenience, and snow-ball sampling strategies. A semi-structured interview guide was used to collect data. Data were analyzed inductively, using Moustakas’s (1994) Modification of the Stevick-Colaizzi-Keen Method of Analysis of Phenomenological Data. The participants in this study experienced a geocentric organizational culture of a global corporation as on in which they felt connected, valued, and growing personally and professionally. The participants felt connected to the companies via business goals and social responsibility. The participants felt valued by the company because their creativity was welcomed and they could contribute to the corporation certain unique knowledge of the culture and language of their native countries. The participants felt growing personally and professionally due to the professional development opportunities, cross-cultural awareness, and perspective consciousness. Based on the findings from this study, a model of a geocentric organizational culture of a global corporation: An employee perspective is proposed. Implications for research and practice conclude this study.

A polynomial algorithm for the three-machine open shop with a bottleneck machine

Abstract not available

Learning to construct our identities over the life course: a study with lesbian, gay, bisexual and transgender adults in Scotland

To date, adult educational research has had a limited focus on lesbian, gay, bisexual and transgendered (LGBT) adults and the learning processes in which they engage across the life course. Adopting a biographical and life history methodology, this study aimed to critically explore the potentially distinctive nature and impact of how, when and where LGBT adults learn to construct their identities over their lives. In-depth, semi-structured interviews, dialogue and discussion with LGBT individuals and groups provided rich narratives that reflect shifting, diverse and multiple ways of identifying and living as LGBT. Participants engage in learning in unique ways that play a significant role in the construction and expression of such identities, that in turn influence how, when and where learning happens. Framed largely by complex heteronormative forces, learning can have a negative, distortive impact that deeply troubles any balanced, positive sense of being LGBT, leading to self- censoring, alienation and in some cases, hopelessness. However, learning is also more positively experiential, critically reflective, inventive and queer in nature. This can transform how participants understand their sexual identities and the lifewide spaces in which they learn, engendering agency and resilience. Intersectional perspectives reveal learning that participants struggle with, but can reconcile the disjuncture between evolving LGBT and other myriad identities as parents, Christians, teachers, nurses, academics, activists and retirees. The study’s main contributions lie in three areas. A focus on LGBT experience can contribute to the creation of new opportunities to develop intergenerational learning processes. The study also extends the possibilities for greater criticality in older adult education theory, research and practice, based on the continued, rich learning in which participants engage post-work and in later life. Combined with this, there is scope to further explore the nature of ‘life-deep learning’ for other societal groups, brought by combined religious, moral, ideological and social learning that guides action, beliefs, values, and expression of identity. The LGBT adults in this study demonstrate engagement in distinct forms of life-deep learning to navigate social and moral opprobrium. From this they gain hope, self-respect, empathy with others, and deeper self-knowledge.

Coping with uncertainty:gender and leadership identities in UK corporate life

Within corporate contexts, senior leaders must construct credible leadership identities if they are to demonstrate effectiveness in achieving business goals. This is a particular challenge for women, who have struggled historically to gain senior leadership positions. This chapter explores the identity struggles experienced by Karen, a woman Human Resources director within a management meeting as she delivers bad news about ‘company restructuring’ to her colleagues. Using Feminist Poststructuralist Discourse Analysis (FPDA), I show how this leader struggles to maintain a professionally competent identity as she negotiates the bad news. The analysis reveals that despite the demands of her role, Karen demonstrates extraordinary linguistic competence in managing her team within a turbulent business world that continues to remain inhospitable to female leaders.

Connected Hopf algebras of finite Gelfand-Kirillov dimension

Following the seminal work of Zhuang, connected Hopf algebras of finite GK-dimension over algebraically closed fields of characteristic zero have been the subject of several recent papers. This thesis is concerned with continuing this line of research and promoting connected Hopf algebras as a natural, intricate and interesting class of algebras. We begin by discussing the theory of connected Hopf algebras which are either commutative or cocommutative, and then proceed to review the modern theory of arbitrary connected Hopf algebras of finite GK-dimension initiated by Zhuang. We next focus on the (left) coideal subalgebras of connected Hopf algebras of finite GK-dimension. They are shown to be deformations of commutative polynomial algebras. A number of homological properties follow immediately from this fact. Further properties are described, examples are considered and invariants are constructed. A connected Hopf algebra is said to be "primitively thick" if the difference between its GK-dimension and the vector-space dimension of its primitive space is precisely one . Building on the results of Wang, Zhang and Zhuang,, we describe a method of constructing such a Hopf algebra, and as a result obtain a host of new examples of such objects. Moreover, we prove that such a Hopf algebra can never be isomorphic to the enveloping algebra of a semisimple Lie algebra, nor can a semisimple Lie algebra appear as its primitive space. It has been asked in the literature whether connected Hopf algebras of finite GK-dimension are always isomorphic as algebras to enveloping algebras of Lie algebras. We provide a negative answer to this question by constructing a counterexample of GK-dimension 5. Substantial progress was made in determining the order of the antipode of a finite dimensional pointed Hopf algebra by Taft and Wilson in the 1970s. Our final main result is to show that the proof of their result can be generalised to give an analogous result for arbitrary pointed Hopf algebras.

The challenges of participatory research with ‘tech-savvy’ youth

This paper focuses on participatory research and how it can be understood and employed when researching children and youth. The aim of this paper is to provide a theoretically and empirically grounded discussion of participatory research methodologies with respect to investigating the dynamic and evolving phenomenon of young people growing up in networked societies. Initially, we review the nature of participatory research and how other researchers have endeavoured to involve young people (children and youth) in their research projects. Our review of these approaches aims to elucidate what we see as recurring and emerging issues with respect to the methodological design of involving young people as co-researchers. In the light of these issues and in keeping with our aim, we offer a case study of our own research project that seeks to understand the ways in which high school students use new media and network ICT systems (Internet, mobile phone applications, social networking sites) to construct identities, form social relations, and engage in creative practices as part of their everyday lives. The article concludes by offering an assessment of our tripartite model of participatory research that may benefit other researchers who share a similar interest in youth and new media.

Certainties and uncertainties : ethics and professional identities of early childhood educators

This study is an inquiry into the professional identity constructions of early childhood educators, where identity is conceptualised as social and contextual. Through a genealogical analysis of narratives of four Queensland early childhood teachers, the thesis renders as problematic universal and fixed notions of what it is to be an early childhood professional. The data are the four teachers’ professional life history narratives recounted through a series of conversational interviews with each participant. As they spoke about professionalism and ethics, these teachers struggled to locate themselves as professionals, as they drew on a number of dominant discourses available to them. These dominant discourses were located and mapped through analysis of the participants’ talk about relationships with parents, colleagues and authorities. Genealogical analysis enabled multiple readings of the ways in which the participants’ talk held together certainties and uncertainties, as they recounted their experiences and spoke of early childhood expertise, relational engagement and ethics. The thesis concludes with suggestions for ways to support early childhood teachers and pre-service teachers to both engage with and resist normative processes and expectations of professional identity construction. In so doing, multiple and contextual opportunities can be made available when it comes to being professional and ‘doing’ ethics. The thesis makes an argument for new possibilities for thinking and speaking professional identities that include both certainty and uncertainty, comfort and discomfort, and these seemingly oppositional terms are held together in tension, with an insistence that both are necessary and true. The use of provocations offers tools through which pre-service teachers, teachers and teacher educators can access new positions associated with certainties and uncertainties in professional identities. These new positions call for work that supports experiences of ‘de-comfort’ – that is, experiences that encourage early childhood educators to step away from the comfort zones that can become part of expertise, professional relationships and ethics embedded within normative representations of what it is to be an early childhood professional.

“I am a secondary teacher and I teach history and SOSE” : negotiating pre-service teacher identities in times of curriculum change

Secondary social education in Australia is set to change with the new national history curriculum but integrated social education will continue in the middle years of schooling. Competing discourses of disciplinary and integrated social education approaches create new challenges for pre-service teachers as identification with a teaching area is an important aspect of developing a broader teacher identity. Feedback on a compulsory, final year curriculum studies unit revealed the majority of secondary pre-service teachers identified with at least one social science discipline. However, only a small number listed the integrated social education curriculum of Studies of Society and Environment (SOSE), even though SOSE was an essential part of their brief. More complex identities were revealed in post-teaching practice interviews. In times of curriculum change, attention to pre-service teachers’ disciplinary knowledge is critical in developing a stable subject identity.

Digital media literacy : connecting young people’s identities, creative production and learning about video games

This chapter outlines examples of classroom activities that aim to make connections between young people’s everyday experiences with video games and the formal high school curriculum. These classroom activities were developed within the emerging field of digital media literacy. Digital media literacy combines elements of ‘traditional’ approaches to media education with elements of technology and information education (Buckingham, 2007; Warschauer, 2006). It is an educational field that has gained significant attention in recent years. For example, digital media literacy has become a significant objective for media policy makers in response to the increased social and cultural roles of new media technologies and controversies associated with young people’s largely unregulated online participation. Media regulators, educational institutions and independent organizations1 in the United States, Canada, the United Kingdom and Australia have developed digital media literacy initiatives that aim to provide advice to parents, teachers and young people.

Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Digital kids, analogue students : a mixed methods study of students' engagement with a school-based Web 2.0 learning innovation

The inquiry documented in this thesis is located at the nexus of technological innovation and traditional schooling. As we enter the second decade of a new century, few would argue against the increasingly urgent need to integrate digital literacies with traditional academic knowledge. Yet, despite substantial investments from governments and businesses, the adoption and diffusion of contemporary digital tools in formal schooling remain sluggish. To date, research on technology adoption in schools tends to take a deficit perspective of schools and teachers, with the lack of resources and teacher ‘technophobia’ most commonly cited as barriers to digital uptake. Corresponding interventions that focus on increasing funding and upskilling teachers, however, have made little difference to adoption trends in the last decade. Empirical evidence that explicates the cultural and pedagogical complexities of innovation diffusion within long-established conventions of mainstream schooling, particularly from the standpoint of students, is wanting. To address this knowledge gap, this thesis inquires into how students evaluate and account for the constraints and affordances of contemporary digital tools when they engage with them as part of their conventional schooling. It documents the attempted integration of a student-led Web 2.0 learning initiative, known as the Student Media Centre (SMC), into the schooling practices of a long-established, high-performing independent senior boys’ school in urban Australia. The study employed an ‘explanatory’ two-phase research design (Creswell, 2003) that combined complementary quantitative and qualitative methods to achieve both breadth of measurement and richness of characterisation. In the initial quantitative phase, a self-reported questionnaire was administered to the senior school student population to determine adoption trends and predictors of SMC usage (N=481). Measurement constructs included individual learning dispositions (learning and performance goals, cognitive playfulness and personal innovativeness), as well as social and technological variables (peer support, perceived usefulness and ease of use). Incremental predictive models of SMC usage were conducted using Classification and Regression Tree (CART) modelling: (i) individual-level predictors, (ii) individual and social predictors, and (iii) individual, social and technological predictors. Peer support emerged as the best predictor of SMC usage. Other salient predictors include perceived ease of use and usefulness, cognitive playfulness and learning goals. On the whole, an overwhelming proportion of students reported low usage levels, low perceived usefulness and a lack of peer support for engaging with the digital learning initiative. The small minority of frequent users reported having high levels of peer support and robust learning goal orientations, rather than being predominantly driven by performance goals. These findings indicate that tensions around social validation, digital learning and academic performance pressures influence students’ engagement with the Web 2.0 learning initiative. The qualitative phase that followed provided insights into these tensions by shifting the analytics from individual attitudes and behaviours to shared social and cultural reasoning practices that explain students’ engagement with the innovation. Six indepth focus groups, comprising 60 students with different levels of SMC usage, were conducted, audio-recorded and transcribed. Textual data were analysed using Membership Categorisation Analysis. Students’ accounts converged around a key proposition. The Web 2.0 learning initiative was useful-in-principle but useless-in-practice. While students endorsed the usefulness of the SMC for enhancing multimodal engagement, extending peer-topeer networks and acquiring real-world skills, they also called attention to a number of constraints that obfuscated the realisation of these design affordances in practice. These constraints were cast in terms of three binary formulations of social and cultural imperatives at play within the school: (i) ‘cool/uncool’, (ii) ‘dominant staff/compliant student’, and (iii) ‘digital learning/academic performance’. The first formulation foregrounds the social stigma of the SMC among peers and its resultant lack of positive network benefits. The second relates to students’ perception of the school culture as authoritarian and punitive with adverse effects on the very student agency required to drive the innovation. The third points to academic performance pressures in a crowded curriculum with tight timelines. Taken together, findings from both phases of the study provide the following key insights. First, students endorsed the learning affordances of contemporary digital tools such as the SMC for enhancing their current schooling practices. For the majority of students, however, these learning affordances were overshadowed by the performative demands of schooling, both social and academic. The student participants saw engagement with the SMC in-school as distinct from, even oppositional to, the conventional social and academic performance indicators of schooling, namely (i) being ‘cool’ (or at least ‘not uncool’), (ii) sufficiently ‘compliant’, and (iii) achieving good academic grades. Their reasoned response therefore, was simply to resist engagement with the digital learning innovation. Second, a small minority of students seemed dispositionally inclined to negotiate the learning affordances and performance constraints of digital learning and traditional schooling more effectively than others. These students were able to engage more frequently and meaningfully with the SMC in school. Their ability to adapt and traverse seemingly incommensurate social and institutional identities and norms is theorised as cultural agility – a dispositional construct that comprises personal innovativeness, cognitive playfulness and learning goals orientation. The logic then is ‘both and’ rather than ‘either or’ for these individuals with a capacity to accommodate both learning and performance in school, whether in terms of digital engagement and academic excellence, or successful brokerage across multiple social identities and institutional affiliations within the school. In sum, this study takes us beyond the familiar terrain of deficit discourses that tend to blame institutional conservatism, lack of resourcing and teacher resistance for low uptake of digital technologies in schools. It does so by providing an empirical base for the development of a ‘third way’ of theorising technological and pedagogical innovation in schools, one which is more informed by students as critical stakeholders and thus more relevant to the lived culture within the school, and its complex relationship to students’ lives outside of school. It is in this relationship that we find an explanation for how these individuals can, at the one time, be digital kids and analogue students.

Modeling videokeratoscopic height data with spherical harmonics

Purpose: All currently considered parametric models used for decomposing videokeratoscopy height data are viewercentered and hence describe what the operator sees rather than what the surface is. The purpose of this study was to ascertain the applicability of an object-centered representation to modeling of corneal surfaces. Methods: A three-dimensional surface decomposition into a series of spherical harmonics is considered and compared with the traditional Zernike polynomial expansion for a range of videokeratoscopic height data. Results: Spherical harmonic decomposition led to significantly better fits to corneal surfaces (in terms of the root mean square error values) than the corresponding Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters, and model orders. Conclusions: Spherical harmonic decomposition is a viable alternative to Zernike polynomial decomposition. It achieves better fits to videokeratoscopic height data and has the advantage of an object-centered representation that could be particularly suited to the analysis of multiple corneal measurements.

Youth identities : time, space and social exclusion : exploring youth policy and practice in Sheffield, 1999-2003

The type and quality of youth identities ascribed to young people living in residual housing areas present opportunities for action as well as structural constraints. In this book three ethnographies, based on a youth work practitioner's observations, interviews and participation in local networks, identify young people's resistant identities. Through an analysis of social exclusion, youth policies and interviews with young people, youth workers and their managers, the book outlines a contingent network of relationships that hinder informal learning. Globalisation, individualisation, welfare/education reform and the rise of cultural social movements act upon youth identities and steer youth policies to subordinate the notion of informal group learning. Drawing on Castells' and Touraine's sociological models of identity, the book explores youth as a category of time and residual housing areas as a category of space, as they pertain to local dynamics of social exclusion.

Modeling corneal surfaces with three-dimensional basis functions

Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.