Let ABC be a triangle with incentre I, circumcentre O, orthocentre H, centroid G and symmedian point K. In standard notation, the triangle ABC has sides a, b, c, semiperimeter s, circumradius R and inradius r. Euler’s well-known result that the incentre I is always within the orthocentroidal disc DGH, the disc with diameter GH, is probably the first result about the location of the incentre in some disc formed by triangle centres. Investigating the location of the incentre I in other discs, in [1] we proved that the incentre is interior to the Brocard disc DOK, that is, the disc with diameter OK. The disc is named after the French military meteorologist and geometer Henri Brocard (1845-1922), known in triangle geometry for the Brocard points and the Brocard angle (see [2]).

This paper investigates the effect of taxation of polluting products and redistribution on pollution, income and welfare inequalities. We consider a two-sector Ramsey model with a green and a polluting good, two types of households and a subsistence level of consumption for the polluting good. The environmental tax is always effective in reducing pollution regardless of the level of subsistence consumption. However, this level, together with the redistribution rate, matters at the individual level as it shapes the impact of the environmental policy on individual consumption and welfare. Looking at the stability properties of the economy, a high subsistence level of polluting consumption leads to instability or indeterminacy of the steady state, while the environmental externality reduces the scope for indeterminacy. Increasing the tax rate and redistributing more to the worker affect the occurrence of indeterminacy and instability. Considering the subsistence level of consumption and the level of redistribution among households are of importance as it determines the effects of environmental tax policy in the long term and the stability of the economy in the short term.

Given the centrality of immediate revelation to early Quaker theology, modern historians have often assumed that the first Quakers disregarded tradition. However, this article demonstrates that the early Friends frequently made historical arguments, both to launch and rebut polemical assaults. The Quakers did not, therefore, turn to history as the movement became increasingly conservative or respectable. Instead, they consistently claimed to be the true heirs of John Foxe’s Protestant martyrs. By maintaining that their movement represented the culmination of the tradition celebrated in the Acts and monuments, they were deeply engaged in the historiographical contests which constituted ‘England’s second Reformation’.

The aim of this study was to evaluate the kinetics of local and systemic immune cell populations in mammary secretions and blood samples from cows free of intramammary infections (IMI) and chronically infected with Staphylococcus aureus during active involution. Cows in late lactation that were either uninfected or with chronic S. aureus IMI were included in this study. The percentages of CD14+ cells in blood samples were significantly higher in S. aureus-infected animals than in uninfected animals at days 7 and 21 post-drying-off. However, the percentages of these cells in the mammary secretions from S. aureus-infected quarters were significantly lower compared with those of the uninfected quarters in all evaluated periods. The percentages of CD4+ cells were similar between uninfected animals and S. aureus-infected animals at all involution times in both blood and mammary secretion samples. The percentages of CD8+ cells decreased significantly in mammary secretions of S. aureus-infected quarters compared with those of the uninfected quarters at all involution stages. The percentages of CD21+ cells decreased in blood samples of S. aureus-infected animals compared with uninfected animals at day 21. In secretion samples, the percentages of CD21+ cells decreased in S. aureus-infected quarters at day 7 compared with those of the uninfected quarters. In conclusion, chronic S. aureus IMI induces a significant increase in the number of CD14+ cells in the blood circulation; however, these cells do not appear to migrate to the mammary secretion being potentially retained in the tissue. Although CD4+ and CD8+ lymphocytes did not vary between S. aureus-infected and uninfected animals throughout involution, the decrease in CD8+ cells in mammary secretion from S. aureus-infected animals suggests that these cells are retained in the mammary tissue, fulfilling their specific functions to eliminate intracellularly infected cells. The low number of CD21+ lymphocytes in mammary secretions of infected animals would reduce the humoral defence potential of the gland.

We introduce the super Alternative Daugavet property (super ADP), which lies strictly between the Daugavet property (DP) and the ADP. A Banach space X has the super ADP if for every element x in the unit sphere and every relatively weakly open subset W of the unit ball intersecting the unit sphere, there are an element $y\in W$ and a modulus one scalar θ such that $\|x+\theta y\|$ is almost two. Spaces with the DP satisfy this condition, and it implies the ADP. We first provide examples of super ADP spaces that fail the DP. We show that the norm of a super ADP space is rough, hence the space cannot be Asplund, and we also prove that the space fails the point of continuity property (particularly, the Radon–Nikodým property). In particular, we get examples of spaces with the ADP that fail the super ADP. For a better understanding of the differences between the super ADP, the DP and the ADP, we consider the localizations of these properties and prove that they behave rather differently. As a consequence, we provide characterizations of the super ADP for spaces of vector-valued continuous functions and of vector-valued integrable functions.

The crime of rape has been postulated as an unlawful violation of an individual’s rights or interests. However, this article argues that sexual violence against women in Thailand was traditionally viewed as a breach of an interpersonal hierarchy. It was not until the modern criminalization of rape that lawyers attempted to identify the victim’s individual rights as the essence of the crime. By examining the legal techniques employed by these lawyers in drafting, implementing, and adjudicating the crime, the article contends that the voices and demands of female subjects of rape have been silenced or misplaced. The article will offer studies of legal techniques used by lawyers from various institutions in articulating rape and constructing its subjects from the 19th century to the present. This jurisprudence provides context for the current debate on sexual violence in Thailand and makes it possible to critically reassess the right-based conceptualization of rape law.

I show that a neat expression emerges for the number of spheres in each shell of an octahedron composed of close packed spheres, and that from this expression we can compute the value of the packing density for an infinite array of such spheres.

In this research work, a low-profile elliptical microstrip antenna has been designed with a recessed ground structure. A portion of the ground below the substrate has been cut out for the implementation of the recessed ground. Due to the recessed ground, the gain and bandwidth of the conventional antenna are increased along with the shifting of the resonant band toward high-frequency range. First-time theoretical analysis of the recessed ground is performed using a 2-D capacitance model to understand the effect of its dimensions on the dielectric constant of the antenna and the amount of shifting of the primary resonant frequency. A comprehensive parametric study of the dimension of the recessed ground was carried out to optimize the performance of the antenna. The conventional antenna without recessed ground generates a resonant frequency of 2.35 GHz with a resonant band of 2.28–2.4 GHz (S11≤−10dB) and a gain of −1.35 dB. After using optimum rectangular recessed ground, the resonant frequency of the conventional antenna is shifted to 2.58 GHz, occupying the 2.49–2.69 GHz frequency band with 0.5 dB gain. Therefore, the proposed antenna with recessed ground covers the 2.5–2.69 GHz WiMAX application band with enhanced gain and bandwidth.

This article explores the history and development of British manifestations of a Black diasporic anti-colonial anti-fascist political tradition that stretches across the twentieth century. It centers the experiences and reflections of Black activists and intellectuals in Britain, exploring their efforts to theorize about fascism as a manifestation of white supremacy. The article explores what we can learn about British society and political culture by returning to the overlooked and excluded experiences of Black British activists and intellectuals—in particular, their theoretical and physical encounters with what they called British “fascism” from the 1930s to the 1970s. Journeying from interwar anti-colonial Marxist political writing, Black periodicals in the 1950s and 1960s, to the publications of the British Black Power movement, the article ultimately argues that these encounters confront historians of modern Britain with a different and generative way of thinking about British racism and British fascism in relational terms.