About Topological Groups and the Baire Property in Remainders

Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - Изследвани са прирасти със свойството на Бер на топологични групи.

On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials

In 1917 Pell (1) and Gordon used sylvester2, Sylvester’s little known and hardly ever used matrix of 1853, to compute(2) the coefficients of a Sturmian remainder — obtained in applying in Q[x], Sturm’s algorithm on two polynomials f, g ∈ Z[x] of degree n — in terms of the determinants (3) of the corresponding submatrices of sylvester2. Thus, they solved a problem that had eluded both J. J. Sylvester, in 1853, and E. B. Van Vleck, in 1900. (4) In this paper we extend the work by Pell and Gordon and show how to compute (2) the coefficients of an Euclidean remainder — obtained in finding in Q[x], the greatest common divisor of f, g ∈ Z[x] of degree n — in terms of the determinants (5) of the corresponding submatrices of sylvester1, Sylvester’s widely known and used matrix of 1840. (1) See the link http://en.wikipedia.org/wiki/Anna_Johnson_Pell_Wheeler for her biography (2) Both for complete and incomplete sequences, as defined in the sequel. (3) Also known as modified subresultants. (4) Using determinants Sylvester and Van Vleck were able to compute the coefficients of Sturmian remainders only for the case of complete sequences. (5) Also known as (proper) subresultants.

Series representations of the remainders in the expansions for certain functions with applications

We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1)2/(et+1) , sech t and coth t and establish simple bounds for these remainders when t>0t>0 . Several applications of these expansions are given which enable us to deduce some inequalities and completely monotonic functions associated with the ratio of two gamma functions. In addition, we derive a (presumably new) quadratic recurrence relation for the Bernoulli numbers Bn.

Parents’ choice of early childhood education service in Hong Kong : a pilot study

The introduction of a voucher scheme for early childhood education in Hong Kong has resulted in significant changes in the field. This paper reports data from a pilot study that aimed at gaining a deeper understanding of how parents chose early childhood education service following the introduction of a voucher scheme in Hong Kong. Eight-six Chinese parents with children aged three participated in interviews and focus group discussions. This group of parents had just gone through the process of selecting a kindergarten or nursery for their child for the school year of 2007-2008. Parents from a range of socioeconomic circumstances and educational levels who had selected non-profit kindergartens and nurseries in public and private housing estates participated. Results showed that what parents looked in their choice of service matched closely with how they defined quality. As evidenced in the study, parents’ changing views on quality shared a great deal of resemblance with the specific notion of quality being heavily promoted by recent reform policy. The findings pointed to the complex interactions of policy, choice and practices of early childhood education. The new voucher scheme is intensifying the governing of the self and the field, the impact of which can be worrying.

The phenomenology of utopia : reimagining the political

This thesis argues that the end of Soviet Marxism and a bipolar global political imaginary at the dissolution of the short Twentieth Century poses an obstacle for anti-systemic political action. Such a blockage of alternate political imaginaries can be discerned by reading the work of Francis Fukuyama and "Endism" as performative invocations of the closure of political alternatives, and thus as an ideological proclamation which enables and constrains forms of social action. It is contended that the search through dialectical thought for a competing universal to posit against "liberal democracy" is a fruitless one, because it reinscribes the terms of teleological theories of history which work to effect closure. Rather, constructing a phenomenological analytic of the political conjuncture, the thesis suggests that the figure of messianism without a Messiah is central to a deconstructive reframing of the possibilities of political action - a reframing attentive to the rhetorical tone of texts. The project of recovering the political is viewed through a phenomenological lens. An agonistic political distinction must be made so as to memorialise the remainders and ghosts of progress, and thus to gesture towards an indeconstructible justice which would serve as a horizon for the articulation of an empty universal. This project is furthered by a return to a certain phenomenology inspired by Cornelius Castoriadis, Claude Lefort, Maurice Merleau-Ponty and Ernesto Laclau. The thesis provides a reading of Jacques Derrida and Walter Benjamin as thinkers of a minor universalism, a non-prescriptive utopia, and places their work in the context of new understandings of religion and the political as quasi-transcendentals which can be utilised to think through the aporias of political time in order to grasp shards of meaning. Derrida and Chantal Mouffe's deconstructive critique and supplement to Carl Schmitt's concept of the political is read as suggestive of a reframing of political thought which would leave the political question open and thus enable the articulation of social imaginary significations able to inscribe meaning in the field of political action. Thus, the thesis gestures towards a form of thought which enables rather than constrains action under the sign of justice.

Leaving a legacy : bequest giving in Australia

This article considers what drives donors to leave charitable bequests. Building on theories of charitable bequest giving, we consider two types of motivations for leaving a bequest: attitudinal and structural motivations. Using unique Australian data, we show that a strong belief in the efficacy of charitable organisations has a significant positive effect on the likelihood of leaving a bequest, as does past giving behaviour and having no children. As bequests constitute an important income stream for charitable organisations, this research can help fundraisers better target their marketing strategies towards those most likely to plan their estates and motivate these people to make bequests.

Measuring performance of municipal real estate : softening the impact of financial crisis to local governments

Asset management in local government is an emerging discipline and over a decade has become a crucial aspect towards a more efficient and effective organisation. One crucial feature in the public asset management is performance measurement toward the public real estates. This measurement critically at the important component of public wealth and seeks to apply a standard of economic efficiency and effective organisational management especially in such global financial crisis condition. This paper aims to identify global economic crisis effect and proposes alternative solution for local governments to softening the impact of the crisis to the local governments organisation. This study found that the most suitable solution for local government to solve the global economic crisis in Indonesia is application of performance measurement in its asset management. Thus, it is important to develop performance measurement system in local government asset management process. This study provides suggestions from published documents and literatures. The paper also discusses the elements of public real estate performance measurement. The measurement of performance has become an essential component of the strategic thinking of assets owners and managers. Without having a formal measurement system for performance, it is difficult to plan, control and improve local government real estate management system. A close look at best practices in public sectors reveals that in most cases these practices were transferred from private sector reals estate management under the direction of real estate experts retained by government. One of the most significant advances in government property performance measurement resulted from recognition that the methodology used by private sector, non real estate corporations for managing their real property offered a valuable prototype for local governments. In general, there are two approaches most frequently used to measure performance of public organisations. Those are subjective and objective measures. Finally, findings from this study provides useful input for the local government policy makers, scholars and asset management practitioners to establish a public real estate performance measurement system toward more efficient and effective local governments in managing their assets as well as increasing public services quality in order to soften the impact of global financial crisis.

Offending Youth : Crime, Sex and Justice

Rates of female delinquency, especially for violent crimes, are increasing in most common law countries. At the same time the growth in cyber-bullying, especially among girls, appears to be a related global phenomenon. While the gender gap in delinquency is narrowing in Australia, United States, Canada and the United Kingdom, boys continue to dominate the youth who commit crime and have a virtual monopoly over sexually violent crimes. Indigenous youth continue to be vastly over-represented in the juvenile justice system in every Australian jurisdiction. The Indigenisation of delinquency is a persistent problem in other countries such as Canada and New Zealand. Young people who gather in public places are susceptible to being perceived as somehow threatening or riotous, attracting more than their share of public order policing. Professional football has been marred by repeated scandals involving sexual assault, violence and drunkenness. Given the cultural significance of footballers as role models to thousands, if not millions, of young men around the world, it is vitally important to address this problem. Offending Youth explores these key contemporary patterns of delinquency, the response to these by the juvenile justice agencies and moreover what can be done to address these problems. The book also analyses the major policy and legislative changes from the nineteenth to twenty first centuries, chiefly the shift the penal welfarism to diversion and restorative justice. Using original cases studied by Carrington twenty years ago, Offending Youth illustrates how penal welfarism criminalised young people from socially marginal backgrounds, especially Aboriginal children, children from single parent families, family-less children, state wards and young people living in poverty or in housing commission estates. A number of inquiries in Australia and the United Kingdom have since established that children committed to these institutions, supposedly for their own good, experienced systemic physical, sexual and psychological abuse during their institutionalisation. The book is dedicated to the survivors of these institutions who only now are receiving official recognition of the injustices they suffered. The underlying philosophy of juvenile justice has fundamentally shifted away from penal welfarism to embrace positive policy responses to juvenile crime, such as youth conferencing, cautions, warnings, restorative justice, circle sentencing and diversion examined in the concluding chapter. Offending Youth is aimed at a broad readership including policy makers, juvenile justice professionals, youth workers, families, teachers, politicians as well as students and academics in criminology, policing, gender studies, masculinity studies, Indigenous studies, justice studies, youth studies and the sociology of youth and deviance more generally.-- [from publisher website]

Individuals in a mass market environment: Australian bequest donors seek better communication from charities

Swelling social need and competing calls on government funds have heightened the philanthropic dollar’s value. Yet, Australia is not regarded as having a robust giving culture: while 86% of adults give, a mere 16% plan their giving with those who do donating four times as much as spontaneous givers (Giving Australia, 2005). Traditionally, the prime planned giving example is a charitable bequest, a revenue stream not prevalent here (Baker, 2007). In fact, Baker’s Victorian probate data shows under 5% of estates provide a charitable bequest and just over 1% of estate assets is bequeathed. The UK, in contrast, sources 30% and the US 10% of charitable income through bequests (NCVO, 2004; Sargeant, Wymer and Hilton,2006). Australian charities could boost bequest giving. Understanding the donor market, which has or may remember them in their will is critical. This paper reports donor perceptions of Australian charities’ bequest communication/ marketing. The data forms part of a wider study of Australian donors’ bequest attitudes and behaviour. Charities spend heavily on bequest promotion, from advertising to personal selling to public relations and promotion. Infrastructure funds are scarce so guidance on what works for donors is important. Guy and Patton (1988) made their classic call for a nonprofit marketing perspective and identify the need for charities to better understand the motivations and behaviour of their supporters. In similar vein, this study aims to improve the way nonprofits and givers interact; and ultimately, enhance the giving experience and thus multiply planned giving participation. Academically, it offers insights to Australian bequest motivations and attitudes not studied empirically before.

Concerns about the rollout of broadband : a legal consideration of Australia’s NBN greenfield policy

This paper examines the Australian federal government’s proposal that developers take the primary role for deploying the National Broadband Network (‘NBN’) in greenfield estates. It identifies issues facing the NBN’s implementation and concerns raised by industry. A failure to address these concerns may lessen industry support as well as adversely impact on consumers as NBN implementation costs are passed onto them. The author identifies the need for NBN legislation to clearly establish what is a ‘greenfield estate’; how and when exemptions from implementation obligations will apply; and that NBN services must be treated the same as any other utility service.

Property, planning and purpose : legal concerns facing broadband rollout in Australia

The Australian government, and opposition, are committed to facilitating high-speed broadband provision. In April 2009 the (then) Labor government announced a proposal to facilitate provision by mandating “…the use of fibre optic infrastructure … in greenfield estates ….” Separately, the installation of (usually overhead) cables commenced in select brownfield areas throughout Australia. In the lead up to the 2010 federal election, the broadband policy focus of the (then) federal opposition was to enabling private investment rather than direct investment by government itself. High-speed broadband is essential for Australia’s economic future. Whether implementation is undertaken by government, government owned corporations or private investors, will impact on the processes to be followed. Who does what, also will determine the rights available to land owners. The next stage, of necessity, will involve the establishment of procedures to require the retrofitting of existing urban environments. This clearly will have major property, property rights and valuation impacts. As Horan (2000) observed “…preserving... unique characteristics … of…regions requires a compromise between economic ambitions and social, cultural, and environmental values”. The uncertainty following the federal election, and the influence of independants with individual agendas; presents unique challenges for broadband implementation. This paper seeks to identify the processes to be followed by various potential broadband investors as they work to establish a ubiquitous network. It overviews current legislative regimes and examines concerns raised by stakeholders in various government reviews. It concludes by plotting a clear way forward to the future, with particular regard to property rights and usage.

Which Women are More Likely to be Abused? Public Housing, Cohabitation and Separated/Divorced Women.

Data collected at Canadian public housing estates in eastern Ontario are used here to analyze two hypotheses. Overall these women report more violence than do otherwise situated women in other general surveys. More specifically, complex theoretical models were designed to generate two hypotheses for further analysis: First, that separated/divorced women are more likely to be abused within public housing than married women. Second, that cohabiting women will report violence victimization at a higher rate than separated, divorced, or married women. Some support for both hypotheses were found, and the theoretical models are used to discuss these findings.

Identity verification in conveyancing : the failure of current legislative and regulatory measures, and recommendations for change

"Defrauding land titles systems impacts upon us all. Those who deal in land include ordinary citizens, big business, small business, governments, not-for-profit organisation, deceased estates...Fraud here touches almost everybody." the thesis presented in this paper is that the current and disparate steps taken by jurisdictions to alleviate land fraud associated with identity-based crimes are inadequate. The centrepiece of the analysis is the consideration of two scenarios that have recently occurred. One is the typical scenario where a spouse forges the partner's signature to obtain a mortgage from a financial institution. The second is atypical. It involves a sophisticated overseas fraud duping many stakeholders involved in the conveyancing process. After outlining these scenarios, we will examine how identity verification requirements of the United Kingdom, Ontario, the Australian states, and New Zealand would have been applied to these two frauds. Our conclusion is that even though some jurisdictions may have prevented the frauds from occurring, the current requirements are inadequate. We use the lessons learnt to propose what we consider core principles for identity verification in land transactions.

Front interactions in a three-component system

The three-component reaction-diffusion system introduced in [C. P. Schenk et al., Phys. Rev. Lett., 78 (1997), pp. 3781–3784] has become a paradigm model in pattern formation. It exhibits a rich variety of dynamics of fronts, pulses, and spots. The front and pulse interactions range in type from weak, in which the localized structures interact only through their exponentially small tails, to strong interactions, in which they annihilate or collide and in which all components are far from equilibrium in the domains between the localized structures. Intermediate to these two extremes sits the semistrong interaction regime, in which the activator component of the front is near equilibrium in the intervals between adjacent fronts but both inhibitor components are far from equilibrium there, and hence their concentration profiles drive the front evolution. In this paper, we focus on dynamically evolving N-front solutions in the semistrong regime. The primary result is use of a renormalization group method to rigorously derive the system of N coupled ODEs that governs the positions of the fronts. The operators associated with the linearization about the N-front solutions have N small eigenvalues, and the N-front solutions may be decomposed into a component in the space spanned by the associated eigenfunctions and a component projected onto the complement of this space. This decomposition is carried out iteratively at a sequence of times. The former projections yield the ODEs for the front positions, while the latter projections are associated with remainders that we show stay small in a suitable norm during each iteration of the renormalization group method. Our results also help extend the application of the renormalization group method from the weak interaction regime for which it was initially developed to the semistrong interaction regime. The second set of results that we present is a detailed analysis of this system of ODEs, providing a classification of the possible front interactions in the cases of $N=1,2,3,4$, as well as how front solutions interact with the stationary pulse solutions studied earlier in [A. Doelman, P. van Heijster, and T. J. Kaper, J. Dynam. Differential Equations, 21 (2009), pp. 73–115; P. van Heijster, A. Doelman, and T. J. Kaper, Phys. D, 237 (2008), pp. 3335–3368]. Moreover, we present some results on the general case of N-front interactions.