The unit ball of the complex P(3H)

Let H be a two-dimensional complex Hilbert space and P(3H) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, P(3H), from which we deduce that the unit sphere of P(3H) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of P(3H) remains extreme as considered as an element of L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H) and give a characterization of its smooth points.

The management of radial scars of the breast - does core biopsy help?

Purpose: To compare the effectiveness of fine needle aspiration cytology (FNAC) with core biopsy (CB) in the pre-operative diagnosis of radial scar (RS) of the breast.

Patients and methods: A retrospective analysis was made of all radial scars diagnosed on surgical histology over an 8-year period. Comparison was made between the results of different preoperative needle biopsy techniques and surgical histology findings.

Results: Forty of 47 patients with a preoperative radiological diagnosis of radial scar were included in this analysis. Thirty-eight patients had impalpable lesions diagnosed on mammography and two presented with a palpable lump. FNAC (n=17) was inadequate in 47% of patients, missed two co-existing carcinomas found in this group, and gave a false positive or suspicious result for malignancy in 4 patients. CB (n=23) suggested a RS in 15 patients, but only diagnosed 4 out of 7 co-existing carcinomas found in this group.

Conclusion: CB is more accurate than FNAC in the diagnosis of RS. However, these data demonstrate that CB may offer little to assist in the management of patients with RS. In summary, this paper advocates the use of CB in any lesion with a radiological suspicion of carcinoma and diagnostic excision of all lesions thought to be typical of RS on mammography.

Characteristics of shadowed fading in off–body communications channels at 2.45 GHz

In this paper, a number of off-body channels which are susceptible to shadowing caused by the human body are investigated. In particular, the recently proposed shadowed κ–μ fading model is fitted to data obtained from field trials performed in low multipath conditions at 2.45 GHz. It is shown that this model provides a significantly improved fit to off-body channels which are subject to shadowing when compared to other fading models such as lognormal, Nakagami-m and Rice which are commonly applied to model fading in body centric communications channels.

Out of the Shadows: A one day investigation of the politics of architecture explored through the lens of post-conflict, Belfast

This booklet covers the itinerary and some of the findings of a day-long visit to Belfast on the 7th November 2014 by Peter Oborn; Vice President International of the Royal Institute of British Architects. His visit was in response to a motion submitted to the RIBA council (19.05.2014) calling for the suspension of the Israeli Association of United Architects from the International Union of Architects. Despite members of council speaking against the motion it was carried; 23 members voting for, 16 against, and 10 abstentions. Subsequently the RIBA came under considerable pressure to consider its position in such critical contexts. This visit to Belfast was part of a wider fact-finding mission and evidence taking. At its heart was the question: 'Is it appropriate for the institute (RIBA) to engage with communities facing civil conflict and/or natural disaster and, if so, how it can do so most effectively.' The visit was facilitated by Ruth Morrow, Professor of Architecture, School of Planning, Architecture & Civil Engineering, Queen's University Belfast, and Martin Hare, Royal Society of Ulster Architects (RSUA) president.

Space-time monitoring of prescribed burnt soils performance – an effective tool for forest management

Among the most important measures to prevent wild forest fires is the use of prescribed and controlled burning actions in order to reduce the availability of fuel mass. However, the impact of these activities on soil physical and chemical properties varies according to the type of both soil and vegetation and is not fully understood. Therefore, soil monitoring campaigns are often used to measure these impacts. In this paper we have successfully used three statistical data treatments - the Kolmogorov-Smirnov test followed by the ANOVA and the Kruskall-Wallis tests – to investigate the variability among the soil pH, soil moisture, soil organic matter and soil iron variables for different monitoring times and sampling procedures.

A minor theory of the transit of materiality into discourse, Via Campesina.

In this thesis I explore how the material properties of plant seed enter the political discourses of the international peasant coalition the Via Campesina and coalition member the National Fanners Union of Canada (NFU), querying how this process might be employed as a resource for a transformative eco-social politics. I employ several post-structural theoretical constructs, configuring them together as a "minor theory". This minor theory provides the basis for a "minor" reading of three sets of Via Campesina and NFU texts. The aim of these readings is to track the movement of seed from a local agricultural concern to a transitive political one, across both the material and discursive registers. In surfacing the presence of the seed's physical properties in the three texts, I highlight the distinctions between the constraining seed of corporate industrial agriculture, and the social and agroecological opportunities resulting from what I call a "Seed Event".

James VI of Scotland Letter, 1579

This letter authorizes William Hamilton of Portmollart to repair to Edinburgh notwithstanding the acts discharging the Hamiltons from being within six miles of the King’s person. James VI and James I (June 19, 1566 – March 27, 1625) was King of Scots as James VI from July 24th, 1567 and King of England and Ireland as James I from the union of the English and Scottish crowns on March 24, 1603 after the passing of Elizabeth I.

Characterization of the unfolding of a weak focus and modulus of analytic classification

La thèse présente une description géométrique d’un germe de famille générique déployant un champ de vecteurs réel analytique avec un foyer faible à l’origine et son complexifié : le feuilletage holomorphe singulier associé. On montre que deux germes de telles familles sont orbitalement analytiquement équivalents si et seulement si les germes de familles de difféomorphismes déployant la complexification de leurs fonctions de retour de Poincaré sont conjuguées par une conjugaison analytique réelle. Le “caractère réel” de la famille correspond à sa Z2-équivariance dans R^4, et cela s’exprime comme l’invariance du plan réel sous le flot du système laquelle, à son tour, entraîne que l’expansion asymptotique de la fonction de Poincaré est réelle quand le paramètre est réel. Le pullback du plan réel après éclatement par la projection monoidal standard intersecte le feuilletage en une bande de Möbius réelle. La technique d’éclatement des singularités permet aussi de donner une réponse à la question de la “réalisation” d’un germe de famille déployant un germe de difféomorphisme avec un point fixe de multiplicateur égal à −1 et de codimension un comme application de semi-monodromie d’une famille générique déployant un foyer faible d’ordre un. Afin d’étudier l’espace des orbites de l’application de Poincaré, nous utilisons le point de vue de Glutsyuk, puisque la dynamique est linéarisable auprès des points singuliers : pour les valeurs réels du paramètre, notre démarche, classique, utilise une méthode géométrique, soit un changement de coordonée (coordonée “déroulante”) dans lequel la dynamique devient beaucoup plus simple. Mais le prix à payer est que la géométrie locale du plan complexe ambiante devient une surface de Riemann, sur laquelle deux notions de translation sont définies. Après avoir pris le quotient par le relèvement de la dynamique nous obtenons l’espace des orbites, ce qui s’avère être l’union de trois tores complexes plus les points singuliers (l’espace résultant est non-Hausdorff). Les translations, le caractère réel de l’application de Poincaré et le fait que cette application est un carré relient les différentes composantes du “module de Glutsyuk”. Cette propriété implique donc le fait qu’une seule composante de l’invariant Glutsyuk est indépendante.