Quantum-Mechanical Dualities on the Torus

On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e., independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments suggest that the notion of a quantum may not be universal. Transformations between observers that do not agree on the notion of an elementary quantum are called dualities. Classical phase spaces admitting more than one complex-differentiable structure thus provide a natural framework to study dualities in quantum mechanics. As an example we quantise a classical mechanics whose phase space is a torus and prove explicitly that it exhibits dualities.Comment: New examples added, some precisions mad

Arte, matemática e Pibid: explorando as obras de Vinicius de Moraes e Kandinsky

Anais do II Seminário Seminário Estadual PIBID do Paraná: tecendo saberes / organizado por Dulcyene Maria Ribeiro e Catarina Costa Fernandes — Foz do Iguaçu: Unioeste; Unila, 2014O projeto envolvendo Arte e Matemática contando com a colaboração de pibidianos (acadêmicos bolsistas do Programa Institucional de Iniciação à Docência) surgiu em função da comemoração do centenário de Vinicius de Moraes em 2013. Inicialmente, os alunos conheceram a obra do pintor Kandinsky que utiliza muitas formas geométricas em suas telas. Após, solicitamos que reproduzissem telas semelhantes (com mesmo estilo do pintor) inspiradas na música “Aquarela” de Vinicius de Moraes. Desta forma, homenageando dois grandes vultos da Arte, o ensino da geometria se apresentou de forma mais agradável, divertida e estétic

Influence of a walking aid on temporal and spatial parameters of gait in healthy adults

This is the post-print version of the final paper published in PM&R. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2014 Elsevier B.V.Objective - To determine the effect of using a walking aid on temporal and spatial parameters of gait when used for balance versus support on the dominant and nondominant hand side. Design - Repeated measures observational study design. Setting - University gymnasium. Participants - Twenty-seven healthy male and female adults of mean ± standard deviation age 44.74 ± 10.00 years. Methods - Five walking conditions (C) were completed by all participants on the GAITRite pressure mat. Normal walking (C1), walking with a cane in the dominant hand (C2) and nondominant hand (C3) as if using for balance, walking with a cane in the dominant hand (C4) and nondominant hand (C5) while allowing approximately 10% of the body weight through the cane. Main Outcome Measurements - Temporal measurements (swing time, stance time, single limb support time, double limb support time) as percentage of a gait cycle and the base of support for the left and the right foot for all 5 walking conditions. Results - A significant difference (P < .001) was observed between C1, C2, and C3 in percentage swing time and percentage stance time of the ipsilateral side, and in percentage single limb support time of the contralateral side. The double limb support time was significantly different (P ≤ .04) for both ipsilateral and contralateral sides. Comparisons among C1, C4, and C5 demonstrated significance (P < .001) for all variables. Post hoc analysis showed significance between C1 and C4, and C1 and C5 for all variables except percentage stance time of the ipsilateral side and percentage single limb support of the contralateral side. Conclusions - In healthy adults, use of a cane for balance modifies swing and stance parameters of the ipsilateral side and does not affect the base of support formed by the feet. When used for support, the cane alters the swing and stance parameters, and also the base of support formed by the feet

A global analysis of worker protest in digital labour platforms

This paper presents findings from the Leeds Index of Platform Labour Protest, a database of platform worker protest events around the world in four platform sectors: ride-hailing, food delivery, courier services and grocery delivery for the period January 2017 to July 2020. The findings show that the single most important cause of platform worker protest is pay, followed by employment status, and health and safety

Labour protests during the pandemic: The case of hospital and retail workers in 90 countries

With a novel methodology searching news events from world’s largest news agencies via the online GDELT project, this report documents protest of key workers against their working conditions during the COVID-19 pandemic in 90 countries

Changes in Black Carbon Deposition to Antarctica from Two Ice Core Records, A.D. 1850-2000

Continuous flow analysis was based on a steady sample flow and in-line detection of BC and other chemical substances as described in McConnell et al. (2007). In the cold room, previously cut one meter ice core sticks of 3x3cm, are melted continuously on a heated melter head specifically designed to eliminate contamination from the atmosphere or by the external parts of the ice. The melted ice from the most inner part of the ice stick is continuously pumped by a peristaltic pump and carried to a clean lab by Teflon lines. The recorded signal is continuous, integrating a sample volume of about 0.05 mL, for which the temporal resolution depends on the speed of melting, ice density and snow accumulation rate at the ice core drilling site. For annual accumulation derived from the WAIS and Law Dome ice cores, we assumed ~3.1 cm water equivalent uncertainty in each year's accumulation from short scale spatial variability (glaciological noise) which was determined from several measurements of annual accumulation in multiple parallel ice cores notably from the WAIS Divide ice core site (Banta et al., 2008) and from South Pole site (McConnell et al., 1997; McConnell et al., 2000). Refractory black carbon (rBC) concentrations were determined using the same method as in (Bisiaux et al., 2011) and adapted to continuous flow measurements as described by (McConnell et al., 2007). The technique uses a single particle intracavity laser induced incandescence photometer (SP2, Droplet Measurement Technologies, Boulder, Colorado) coupled to an ultrasonic nebulizer/desolvation (CETAC UT5000) Flow Injection Analysis (FIA). All analyses, sample preparation etc, were performed in a class 100 cleanroom using anti contamination "clean techniques". The samples were not acidified

Editing and reading early modern mathematical texts in the digital age

The advent of digital technology has brought a world of new possibilities for editors of historical texts. Though much has been written about conventions for digital editing, relatively little attention has been paid to the particular question of how best to deal with texts with heavily mathematical content. This essay outlines some ways of encoding mathematics in digital form, and then discusses three recent digital editions of collections of early modern mathematical manuscripts

The Bayesian boom: good thing or bad?

A series of high-profile critiques of Bayesian models of cognition have recently sparked controversy. These critiques question the contribution of rational, normative considerations in the study of cognition. The present article takes central claims from these critiques and evaluates them in light of specific models. Closer consideration of actual examples of Bayesian treatments of different cognitive phenomena allows one to defuse these critiques showing that they cannot be sustained across the diversity of applications of the Bayesian framework for cognitive modeling. More generally, there is nothing in the Bayesian framework that would inherently give rise to the deficits that these critiques perceive, suggesting they have been framed at the wrong level of generality. At the same time, the examples are used to demonstrate the different ways in which consideration of rationality uniquely benefits both theory and practice in the study of cognition