Counting singularities via fitting ideals

The stable singularities of differential map germs constitute the main source of studying the geometric and topological behavior of these maps. In particular, one interesting problem is to find formulae which allow us to count the isolated stable singularities which appear in the discriminant of a stable deformation of a finitely determined map germ. Mond and Pellikaan showed how the Fitting ideals are related to such singularities and obtain a formula to count the number of ordinary triple points in map germs from C-2 to C-3, in terms of the Fitting ideals associated with the discriminant. In this article we consider map germs from (Cn+m, 0) to (C-m, 0), and obtain results to count the number of isolated singularities by means of the dimension of some associated algebras to the Fitting ideals. First in Corollary 4.5 we provide a way to compute the total sum of these singularities. In Proposition 4.9, for m = 3 we show how to compute the number of ordinary triple points. In Corollary 4.10 and with f of co-rank one, we show a way to compute the number of points formed by the intersection between a germ of a cuspidal edge and a germ of a plane. Furthermore, we show in some examples how to calculate the number of isolated singularities using these results.

Stable singularities of co-rank one quasi homogeneous map germs from (ℂn+1, 0) to (ℂn, 0), n = 2, 3

In this article, we investigate the geometry of quasi homogeneous corank one finitely determined map germs from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. We give a complete description, in terms of the weights and degrees, of the invariants that are associated to all stable singularities which appear in the discriminant of such map germs. The first class of invariants which we study are the isolated singularities, called 0-stable singularities because they are the 0-dimensional singularities. First, we give a formula to compute the number of An points which appear in any stable deformation of a quasi homogeneous co-rank one map germ from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. To get such a formula, we apply the Hilbert's syzygy theorem to determine the graded free resolution given by the syzygy modules of the associated iterated Jacobian ideal. Then we show how to obtain the other 0-stable singularities, these isolated singularities are formed by multiple points and here we use the relation among them and the Fitting ideals of the discriminant. For n = 2, there exists only the germ of double points set and for n = 3 there are the triple points, named points A1,1,1 and the normal crossing between a germ of a cuspidal edge and a germ of a plane, named A2,1. For n = 3, there appear also the one-dimensional singularities, which are of two types: germs of cuspidal edges or germs of double points curves. For these singularities, we show how to compute the polar multiplicities and also the local Euler obstruction at the origin in terms of the weights and degrees. © 2013 Pushpa Publishing House.

Patterns of fitting cosmetically tinted contact lenses

Cosmetically tinted soft contact lenses are an attractive option for contact lens wearers. Data that we have gathered from annual contact lens fitting surveys demonstrate that those wearing tinted lenses are more likely to be female (4.6% of all soft lenses fitted vs. 1.6% for males; p < 0.0001) and younger (27 11 years vs. 33 13 years for those wearing non-tinted lenses; p < 0.0001). Tinted lenses tend to be worn more on a part-time basis and are replaced less frequently than non-tinted lenses. The decline in fitting tinted lenses over the past 12 years may be due to (a) the current limited availability of tinted lenses in silicone hydrogel materials and daily disposable replacement frequencies, which together represent a significant majority (78%) of new soft lenses fits today, (b) growing concerns among lens wearers and practitioners relating to the risks of complications associated with the wearing of tinted lenses, and (c) reduced promotion of such lenses by the contact lens industry.

Twenty first century trends in silicone hydrogel contact lens fitting : an international perspective

Silicone hydrogel contact lenses were introduced into the market in 1999. To assess prescribing trends of this lens type since then, up to 1000 survey forms were sent to contact lens fitters in Australia, Canada, Japan, the Netherlands, Norway, the UK and the USA each year between 2000 and 2008. Practitioners were asked to record data relating to the first 10 contact lens fits or refits performed after receiving the survey form. Analysis of returned forms revealed a rapid increase in the prescribing of silicone hydrogel lenses over the survey period. In 2008, silicone hydrogel lenses represented 36% of all soft lenses prescribed. The categorization of the majority of lenses prescribed as ‘refits’ is primarily attributed to the mass conversion of lens wearers from hydrogel to silicone hydrogel lenses. Silicone hydrogels may soon represent the majority of soft contact lenses prescribed.

Retracing the Roots and Ideals of Confucian Principles of Governance: the Art of Regulating Governance without Legal Rules in Chinese Societies

Confucius was and still is one of the most eminent Chinese philosophers. Such is the importance of Confucius’s teachings; it had influenced all aspects of social life in Chinese societies. In the post-Enron, post-Worldcom, and post-Global Financial Crisis era there are raising doubts in the mantra of the so-called conventional wisdom about law and economic order. Whilst many recent publications offered solutions to those problems like advocating for more laws, rules or reforms in regulatory institutions to enhance the regulation of corporate governance. What Confucius advocated was a non-legal, social mode of regulation based on moral ideals that should be embedded into the minds of every person. Whilst this is an ancient concept from primitive societies, its relevance and merits could be seen in modern Chinese societies like Hong Kong. In essence, Confucian principles of governance build on relational and paternalistic order based on moral ideals.

Fitting airport privatisation to purpose : aligning governance, time and management focus

Where airports were once the sole responsibility of their governments, liberalisation of economies has seen administrative interests in airport spaces divested increasingly towards market led authority. Extant literature suggests that actions in decision spaces can be described under broad idealised forms of governance. However in looking at a sample of 18 different airports it is apparent that these classic models are insufficient to appreciate the contextual complexity of each case. Issues of institutional arrangements, privatisation, and management focus are reviewed against existing governance modes to produce a model for informing privatisation decisions, based on the contextual needs of the individual airport and region. Expanding governance modes to include emergent airport arrangements both contribute to the existing literature, and provides a framework to assist policy makers and those charged with the operation of airports to design effective governance models. In progressing this framework, contributions are made to government decision makers for the development of new, or review of existing strategies for privatisation, while the private sector can identify the intent and expectations of privatisation initiatives to make better informed decisions.

3D ellipsoid fitting for multi-view gait recognition

Gait recognition approaches continue to struggle with challenges including view-invariance, low-resolution data, robustness to unconstrained environments, and fluctuating gait patterns due to subjects carrying goods or wearing different clothes. Although computationally expensive, model based techniques offer promise over appearance based techniques for these challenges as they gather gait features and interpret gait dynamics in skeleton form. In this paper, we propose a fast 3D ellipsoidal-based gait recognition algorithm using a 3D voxel model derived from multi-view silhouette images. This approach directly solves the limitations of view dependency and self-occlusion in existing ellipse fitting model-based approaches. Voxel models are segmented into four components (left and right legs, above and below the knee), and ellipsoids are fitted to each region using eigenvalue decomposition. Features derived from the ellipsoid parameters are modeled using a Fourier representation to retain the temporal dynamic pattern for classification. We demonstrate the proposed approach using the CMU MoBo database and show that an improvement of 15-20% can be achieved over a 2D ellipse fitting baseline.

Fitting in : a pervasive new graduate nurse need

Aim: This qualitative study aims to provide insight into how Australian New Graduate Nurses (NGNs) experienced their transition to acute care nursing practice. Method: Nine NGNs each participated in three in-depth interviews conducted across their first year of practice. Constant comparative analysis was used to identify the emergent themes. Findings: The desire to fit in (establishment of secure social bonds) with ward staff is an important element of NGN transition experiences. Fitting in was about feeling one's self to be part of a social group, and participants made it clear that their perceptions of their success in establishing secure and meaningful social bonds in each new ward was extremely important for their sense of being as NGNs. Current NGN Transition Programmes (NGNTPs) involve multiple ward rotations, increasing the demand for the NGN to fit in. Thus participants were engaged in a deeply personal transition experience that was not necessarily aligned with multiple ward rotations. Conclusions: Although NGNTPs have the word “transition” in their title, it may be that current programmes are more focussed on organisations’ desire to “orient” NGNs to working within the acute care setting than facilitating personal transitions to practice. Further investigation of the impact of NGNTPs on NGNs and the associated multiple ward rotations is required.