Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Calculus of variations on time scales and applications to economics

We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. Afterwards, we prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems. Next we investigate the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange equations in integral form, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. In the end, two main issues of application of time scales in economic, with interesting results, are presented. In the former case we consider a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness. The model which describes firm activities is studied in two different ways: using classical discretizations; and applying discrete versions of our result on time scales. In the end we compare the cost functional values obtained from those two approaches. The latter problem is more complex and relates to rate of inflation, p, and rate of unemployment, u, which inflict a social loss. Using known relations between p, u, and the expected rate of inflation π, we rewrite the social loss function as a function of π. We present this model in the time scale framework and find an optimal path π that minimizes the total social loss over a given time interval.

Single-electron multiple-valued memory using ultra-small floating gate metal-oxide-semiconductor field effect transistor

This paper proposes a novel single-electron multiple-valued memory. It is a metal-oxide-semiconductor field effect transistor (MOS)-type memory with multiple separate control gates and floating gate layer, which consists of nano-crystal grains. The electron can tunnel among the grains (floating gates) and between the floating gate layer and the MOS channel. The memory can realize operations of 'write', 'store' and 'erase' of multiple-valued signals exceeding three values by controlling the single electron tunneling behavior. We use Monte Carlo method to simulate the operation of single-electron four-valued memory. The simulation results show that it can operate well at room temperature.

Building on the past for the future : assessment for learning as a field of exchange

Standardised testing does not recognise the creativity and skills of marginalised youth. This paper presents the development of an innovative approach to assessment designed for the re-engagement of at risk youth who have left formal schooling and are now in an alternative education institution. An electronic portfolio system (EPS) has been developed to capture, record and build on the broad range of students’ cultural and social capital. The assessment as a field of exchange model draws on categories from sociological fields of capital and reconceptualises an eportfolio and social networking hybrid system as a sociocultural zone of learning and development. The EPS, and assessment for learning more generally, are conceptualised as social fields for the exchange of capital (Bourdieu 1977, 1990). The research is underpinned by a sociocultural theoretical perspective that focuses on how students and teachers at the Flexible Learning Centre (FLC) develop and learn, within the zone of proximal development (Vygotsky, 1978). The EPS is seen to be highly effective in the engagement and social interaction between students, teachers and institutions. It is argued throughout this paper that the EPS provides a structurally identifiable space, an arena of social activity, or a field of exchange. The students, teachers and the FLC within this field are producing cultural capital exchanges. The term efield (exchange field) has been coined to refer to this constructed abstract space. Initial results from the trial show a general tendency towards engagement with the EPS and potential for the attainment of socially valued cultural capital in the form of school credentials.

Breaching the standardised assessment boundary : assessment for learning as a field of exchange

The introduction of the Australian curriculum, the use of standardised testing (e.g. NAPLAN) and the My School website are couched in a context of accountability. This circumstance has stimulated and in some cases renewed a range of boundaries in Australian Education. The consequences that arise from standardised testing have accentuated the boundaries produced by social reproduction in education which has led to an increase in the numbers of students disengaging from mainstream education and applying for enrolment at the Edmund Rice Education Australia Flexible Learning Centre Network (EREAFLCN). Boundaries are created for many young people who are denied access to credentials and certification as a result of being excluded from or in some way disengaging from standardised education and testing. Young people who participate at the EREAFLCN arrive with a variety of forms of cultural capital that are not valued in current education and employment fields. This is not to say that these young people’s different forms of cultural capital have no value, but rather that such funds of knowledge, repertoires and cultural capital are not valued by the majority of powerful agents in educational and employment fields. How then can the qualitative value of traditionally unorthodox - yet often intricate, ingenious, and astute - versions of cultural capital evident in the habitus of many young people be made to count, be recognised, be valuated? Can a process of educational assessment be a field of capital exchange and a space which breaches boundaries through a valuating process? This paper reports on the development of an innovative approach to assessment in an alternative education institution designed for the re-engagement of ‘at risk’ youth who have left formal schooling. A case study approach has been used to document the engagement of six young people, with an educational approach described as assessment for learning as a field of exchange across two sites in the EREAFLCN. In order to capture the broad range of students’ cultural and social capital, an electronic portfolio system (EPS) is under trial. The model draws on categories from sociological models of capital and reconceptualises the eportfolio as a sociocultural zone of learning and development. Results from the trial show a general tendency towards engagement with the EPS and potential for the attainment of socially valued cultural capital in the form of school credentials. In this way restrictive boundaries can be breached and a more equitable outcome achieved for many young Australians.

Towards general capabilities through technology : assessment for learning as a field of exchange

The introduction of the Australian curriculum, the use of standardised testing (e.g. NAPLAN) and the My School website have stimulated and in some cases renewed a range of boundaries for young people in Australian Education. Standardised testing has accentuated social reproduction in education with an increase in the numbers of students disengaging from mainstream education and applying for enrolment at the Edmund Rice Education Australia Flexible Learning Centre Network (EREAFLCN). Many young people are denied access to credentials and certification as they become excluded from standardised education and testing. The creativity and skills of marginalised youth are often evidence of general capabilities and yet do not appear to be recognised in mainstream educational institutions when standardised approaches are adopted. Young people who participate at the EREAFLCN arrive with a variety of forms of cultural capital, frequently utilising general capabilities, which are not able to be valued in current education and employment fields. This is not to say that these young people‟s different forms of cultural capital have no value, but rather that such funds of knowledge, repertoires and cultural capital are not valued by the majority of powerful agents in educational and employment fields. How then can the inherent value of traditionally unorthodox - yet often intricate, ingenious, and astute-versions of cultural capital evident in the habitus of many young people be made to count, be recognised, be valuated?Can a process of educational assessment be a field of capital exchange and a space which crosses boundaries through a valuating process? This paper reports on the development of an innovative approach to assessment in an alternative education institution designed for the re engagement of „at risk‟ youth who have left formal schooling. A case study approach has been used to document the engagement of six young people, with an educational approach described as assessment for learning as a field of exchange across two sites in the EREAFLCN. In order to capture the broad range of students‟ cultural and social capital, an electronic portfolio system (EPS) is under trial. The model draws on categories from sociological models of capital and reconceptualises the eportfolio as a sociocultural zone of learning and development. Results from the trial show a general tendency towards engagement with the EPS and potential for the attainment of socially valued cultural capital in the form of school credentials. In this way restrictive boundaries can be breached and a more equitable outcome achieved for many young Australians.

Turning histories into futures : assessment for learning as a field of exchange

Standardised testing does not recognise the creativity and skills of marginalised youth. Young people who come to the Edmund Rice Education Australia Flexible Learning Centre Network (EREAFLCN) in Australia arrive with forms of cultural capital that are not valued in the field of education and employment. This is not to say that young people‟s different modes of cultural capital have no value, but rather that such funds of knowledge, repertoires and cultural capital are not valued by the powerful agents in educational and employment fields. The forms of cultural capital which are valued by these institutions are measurable in certain structured formats which are largely inaccessible for what is seen in Australia to be a growing segment of the community. How then can the inherent value of traditionally unorthodox - yet often intricate, adroit, ingenious, and astute - versions of cultural capital evident in the habitus of many young people be made to count, be recognised, be valuated? Can a process of educational assessment be used as a marketplace, a field of capital exchange? This paper reports on the development of an innovative approach to assessment in an alternative education institution designed for the re-engagement of „at risk‟ youth who have left formal schooling. In order to capture the broad range of students‟ cultural and social capital, an electronic portfolio system (EPS) is under trial. The model draws on categories from sociological models of capital and reconceptualises the eportfolio as a sociocultural zone of learning and development. Initial results from the trial show a general tendency towards engagement with the EPS and potential for the attainment of socially valued cultural capital in the form of school credentials.

Rural dispositions of floating children within the field of Beijing schools: can disadvantaged rural habitus turn into recognised cultural capital?

The rapid pace of urbanisation in China has seen a massive increase in the movement of the rural population to work and live in urban regions. In this large-scale migration context, the educational, health, and psychological problems of floating children are becoming increasingly visible. Different from extant studies, we focus our investigation on the rural dispositions of floating children through interviews with leaders, teachers, and students in four schools in Beijing. Drawing on Bourdieu’s key notions of habitus, capital, and field, our study indicates that the rural habitus of floating children can differentiate these children from their urban peers. This habitus can be marginalised and stigmatised in certain fields but can be recognised and valued as capital in other fields. Our paper offers some implications for research and practice in relation to the schooling of floating children.

Applying the principles of interpretive field research: An example of an IS case study on shared services

All sound research commence with the selection of a research paradigm. The chosen research paradigm is significant in shaping the researcher’s perspectives of the world and it is a vital step in any study’s’ research design. There are different paradigms that IS researchers can choose from; amongst which the interpretive paradigm is growing in acceptance.. Though interpretive research has emerged as an important strand in Information Systems (IS), guidelines on how to conduct interpretive research and how to evaluate them have been scarce. Klein and Myers presented seven principles with examples for each from three case examples. While these principles are much valued, there is a lack of support for novice researchers on how to embed these principles in an overall research design, which could help with the aid of a detailed example that has done so. Thus, this paper aims to address this gap, and presents how Klein and Myers’s principles were applied within an example study that investigated shared services in the Malaysian Higher Education context. The example study adopted the interpretive paradigm as the most suited approach that fitted their research questions and goals. More details about the selection and adoption of the Klein and Myers’s guidelines in the context of the shared services research case study are presented in the paper.

Off-axis field approximations for ion traps with apertures

In recent work (Int. J. Mass Spec., vol. 282, pp. 112–122) we have considered the effect of apertures on the fields inside rf traps at points on the trap axis. We now complement and complete that work by considering off-axis fields in axially symmetric (referred to as “3D”) and in two dimensional (“2D”) ion traps whose electrodes have apertures, i.e., holes in 3D and slits in 2D. Our approximation has two parts. The first, EnoAperture, is the field obtained numerically for the trap under study with apertures artificially closed. We have used the boundary element method (BEM) for obtaining this field. The second part, EdueToAperture, is an analytical expression for the field contribution of the aperture. In EdueToAperture, aperture size is a free parameter. A key element in our approximation is the electrostatic field near an infinite thin plate with an aperture, and with different constant-valued far field intensities on either side. Compact expressions for this field can be found using separation of variables, wherein the choice of coordinate system is crucial. This field is, in turn, used four times within our trap-specific approximation. The off-axis field expressions for the 3D geometries were tested on the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT), and the corresponding expressions for the 2D geometries were tested on the linear ion trap (LIT) and the rectilinear ion trap (RIT). For each geometry, we have considered apertures which are 10%, 30%, and 50% of the trap dimension. We have found that our analytical correction term EdueToAperture, though based on a classical small-aperture approximation, gives good results even for relatively large apertures.

Many-Valued Logic and Qualitative Modelling of Electrical Circuits

Lee M.H., Many-Valued Logic and Qualitative Modelling of Electrical Circuits, in Proc. QR?2000, 14th Int. Workshop on Qualitative Reasoning, Morelia, Mexico June 3rd - 7th 2000.

SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.

Unitary SK1 of unitary and graded division algebras

The reduced unitary Whitehead group $\SK$ of a graded division algebra equipped with a unitary involution (i.e., an involution of the second kind) and graded by a torsion-free abelian group is studied. It is shown that calculations in the graded setting are much simpler than their nongraded counterparts. The bridge to the non-graded case is established by proving that the unitary $\SK$ of a tame valued division algebra wih a unitary involution over a henselian field coincides with the unitary $\SK$ of its associated graded division algebra. As a consequence, the graded approach allows us not only to recover results available in the literature with substantially easier proofs, but also to calculate the unitary $\SK$ for much wider classes of division algebras over henselian fields.

Many valued algebraic structures as measures of comparison

This thesis studies the properties and usability of operators called t-norms, t-conorms, uninorms, as well as many valued implications and equivalences. Into these operators, weights and a generalized mean are embedded for aggregation, and they are used for comparison tasks and for this reason they are referred to as comparison measures. The thesis illustrates how these operators can be weighted with a differential evolution and aggregated with a generalized mean, and the kinds of measures of comparison that can be achieved from this procedure. New operators suitable for comparison measures are suggested. These operators are combination measures based on the use of t-norms and t-conorms, the generalized 3_-uninorm and pseudo equivalence measures based on S-type implications. The empirical part of this thesis demonstrates how these new comparison measures work in the field of classification, for example, in the classification of medical data. The second application area is from the field of sports medicine and it represents an expert system for defining an athlete's aerobic and anaerobic thresholds. The core of this thesis offers definitions for comparison measures and illustrates that there is no actual difference in the results achieved in comparison tasks, by the use of comparison measures based on distance, versus comparison measures based on many valued logical structures. The approach has been highly practical in this thesis and all usage of the measures has been validated mainly by practical testing. In general, many different types of operators suitable for comparison tasks have been presented in fuzzy logic literature and there has been little or no experimental work with these operators.

Educating for professional capability in the field of information technology: integrating industry-based learning with the academic curriculum

In response to the forces of globalisation, societies and organisations have had to adapt and even proactively transform themselves. Universities, as knowledge-based organisations, have recognised that there are now many other important sites of knowledge construction and use. The apparent monopoly over valued forms of knowledge making and knowledge certification is disappearing. Universities have had to recognise the value of practical working knowledge developed in workplace settings beyond university domains, and promote the value of academic forms of knowledge making to the practical concerns of everyday learning. It is within this broader systems view that professional curriculum development undertaken by universities needs to be examined.

University educational planning responds to these external forces in ways that are drawing together formal academic capability/competence and practice-based capability/competence. Both forms of academic and practice-based knowledge and knowing are being equally valued and related one to the other. University planning in turn gives impetus to the development of new forms of professional education curricula. This paper presents a contemporary case of a designed professional curriculum in the field of information technology that situates workplace learning as a central element in the education of Information Technology (IT)/Information Systems (IS) professionals.

The key dimensions of the learning environment of Deakin University’s BIT (Hons) program are considered with a view to identifying areas of strong integration between the worlds of academic and workplace learning from the perspectives of major stakeholders. The dynamic interplay between forms of theorising and practising is seen as critical in educating students for professional capability in their chosen field. From this analysis, an applied research agenda, relating to desired forms of professional learning in higher education, is outlined, with specific reference to the information and communication technology professions.