Polar Multiplicities and Euler obstruction of the stable types in weighted homogeneous map germs from C-n to C-3 n >= 3

In this article we show that for corank 1, quasi-homogeneous and finitely determined map germs f : (C-n, 0)-> (C-3, 0), n >= 3 one can obtain formulae for the polar multiplicities defined on the following stable types of f, f(Delta(f) and f(Sigma(n-2,1)(f), in terms of the weights and degrees of f. As a consequence we show how to compute the Euler obstruction of such stable types, also in terms of the weights and degrees of f.

Finite determinacy and Whitney equisingularity of map germs from C(n) to C(2n-1)

We show that a holomorphic map germ f : (C(n), 0) -> (C(2n-1), 0) is finitely determined if and only if the double point scheme D(f) is a reduced curve. If n >= 3, we have that mu(D(2)(f)) = 2 mu(D(2)(f)/S(2))+C(f)-1, where D(2)(f) is the lifting of the double point curve in (C(n) x C(n), 0), mu(X) denotes the Milnor number of X and C(f) is the number of cross-caps that appear in a stable deformation of f. Moreover, we consider an unfolding F(t, x) = (t, f(t)(x)) of f and show that if F is mu-constant, then it is excellent in the sense of Gaffney. Finally, we find a minimal set of invariants whose constancy in the family f(t) is equivalent to the Whitney equisingularity of F. We also give an example of an unfolding which is topologically trivial, but it is not Whitney equisingular.

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.

Regulatory multiplicities in telecommunications reforms in Indonesia and China

Telecommunications is a key component in any country's economic infrastructure, requiring a vast amount of capital injection and ongoing technical support and innovation. Many developing countries experience handicaps in accessing capital and sustaining the required technical capability in their industralisation process. Therefore, attracting both capital investments and expertise by attuning the developing country's economic policies and legal environment to meet investors' expectations is a priority. Privatisation has been seen as a triumph by international institutions such as the World Bank, and a major requirement for developing economies to industrialise. However from a regulatory perspective, this process is far from straightforward. Implementing economic policies requires a number of regulations and regulatory instruments to be in place. Apart from the need for an independent regulator, regulatory outcomes are often dependent on the willingness of various stakeholders to comply with the course of actions undertaken by authorities. This article examines the factors steering the processes and changes in the telecommunication reforms of Indonesia and China.

Combining Cartesian and polar coordinates in IBVS

Image-based visual servo (IBVS) is a simple, efficient and robust technique for vision-based control. Although technically a local method in practice it demonstrates almost global convergence. However IBVS performs very poorly for cases that involve large rotations about the optical axis. It is well known that re-parameterizing the problem by using polar, instead of Cartesian coordinates, of feature points overcomes this limitation. First, simulation and experimental results are presented to show the complementarity of these two parameter-izations. We then describe a new hybrid visual servo strategy based on combining polar and Cartesian image Jacobians. © 2009 IEEE.

Reduction of functionalized graphite oxides by trioctylphosphine in non-polar organic solvents

Graphene, functionalized with oleylamine (OA) and soluble in non-polar organic solvents, was produced on a large scale with a high yield by combining the Hummers process for graphite oxidation, an amine-coupling process to make OA-functionalized graphite oxide (OA-GO), and a novel reduction process using trioctylphosphine (TOP). TOP acts as both a reducing agent and an aggregation-prevention surfactant in the reduction of OA-GO in 1,2-dichlorobenzene (DCB). The reduction of OA-GO is confirmed by X-ray photoelectron spectroscopy, Fourier-transform infrared spectroscopy, X-ray diffraction, thermogravimetric analysis, and Raman spectroscopy. The exfoliation of GO, OA GO, and OA-functionalized graphene (OA-G) is verified by atomic force microscopy. The conductivity of TOP-reduced OA G, which is deduced from the current–voltage characteristics of a vacuum-filtered thin film, shows that the reduction of functionalized GO by TOP is as effective as the reduction of GO by hydrazine.

Ruptures in the production of girlhood : teenage flows and multiplicities [Abstract]

This paper examines the paradoxical and ubiquitous nature of Butler’s heterosexual matrix, and opens it up to an alternative Deleuzian analysis. Drawing on stories and art works produced in a collective biography workshop on girls and sexuality this paper extends previous work on the subversion of the heterosexual matrix undertaken by Renold and Ringrose (2008). The paper moves, as they do, from a molar to a molecular analysis, but extends that work by re-thinking the girl/subject in terms of Deleuze and Guattari’s endlessly transforming multiplicities where “the self is only a threshold, a door, a becoming between two multiplicities” (Deleuze and Guattari, 1987: 249)

Ruptures in the heterosexual matrix through teenage flows and multiplicities

This article analyzes a series of stories and artworks that were produced in a collective biography workshop. It explores Judith Butler’s concept of the heterosexual matrix combined with a Deleuzian theoretical framework. The article begins with an overview of Butler’s concept of the heterosexual matrix and her theorizations on how it might be disrupted. It then suggests how a Deleuzian framework offers other tools for analyzing these ruptures at the micro level of girls’ everyday interactions.

The cooling steam of the Polar Express : historical origins, properties and implications of performance capture

As the first academically rigorous interrogation of the generation of performance within the global frame of the motion capture volume, this research presents a historical contextualisation and develops and tests a set of first principles through an original series of theoretically informed, practical exercises to guide those working in the emergent space of performance capture. It contributes a new understanding of the framing of performance in The Omniscient Frame, and initiates and positions performance capture as a new and distinct interdisciplinary discourse in the fields of theatre, animation, performance studies and film.

Combining passive sampling and toxicity testing for evaluation of mixtures of polar organic chemicals in sewage treatment plant effluent

Effluent from sewage treatment plants has been associated with a range of pollutant effects. Depending on the influent composition and treatment processes the effluent may contain a myriad of different chemicals which makes monitoring very complex. In this study we aimed to monitor relatively polar organic pollutant mixtures using a combination of passive sampling techniques and a set of biochemistry based assays covering acute bacterial toxicity (Microtox™), phytotoxicity (Max-I-PAM assay) and genotoxicity (umuC assay). The study showed that all of the assays were able to detect effects in the samples and allowed a comparison of the two plants as well as a comparison between the two sampling periods. Distinct improvements in water quality were observed in one of the plants as result of an upgrade to a UV disinfection system, which improved from 24× sample enrichment required to induce a 50% response in the Microtox™ assay to 84×, from 30× sample enrichment to induce a 50% reduction in photosynthetic yield to 125×, and the genotoxicity observed in the first sampling period was eliminated. Thus we propose that biochemical assay techniques in combination with time integrated passive sampling can substantially contribute to the monitoring of polar organic toxicants in STP effluents.

Ruptures in the heterosexual matrix through teenage flows and multiplicities

Feminist research on girlhood has drawn extensively on Butler's conceptual work in order to theorise the normative forces of heterosexuality in the everyday construction of gender. This chapter explores girlhood by drawing on memories and artwork generated in a collective biography workshop held in Australian on the topic of girlhood and sexuality. We are interested in thinking through Butler's notion of the heterosexual matrix. Following Renold and Ringrose (2008) we do so with the help of Deleuze and Guattari, who invite us to think about difference as differenciation or continuous becoming, where difference is an evolutionary multiplicity.

Comparison of Rectangular and Polar Quantizers in Digital Holography

Complex amplitude encoded in any digital hologram must undergo quantization, usually in either polar or rectangular format . In this paper these two schemes are compared under the constraints and conditions inherent in digital holography . For Fourier transform holograms when the spectrum is levelled through phase coding, the rectangular format is shown to be optimal . In the absence of phase coding, and also if the amplitude spectrum has a large dynamic range, the polar format may be preferable .