Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

Physiological quality, content and activity of antioxidants in soybean seeds artificially aged.

ABSTRACT - The objective of this study was to evaluate physiological quality, content, and activity of antioxidants, in soybean seeds subjected to accelerated aging during different periods. Seeds of cultivars BRS 258, BRS 262 and BRS 268, subjected to accelerated aging during 12, 24, 36 and 48 hours and non-aged seeds were used. After each aging period, the seed were evaluated by tests of: germination; first count and tetrazolium. The total of phenolic compounds, total flavonoides, total of isoflavones, and activity for eliminating ABTS°+ radicals were quantified. There were differences among cultivars according to vigor and viability only after seeds were aged. Cultivars BRS 158 and BRS 268 have shown better seed physiological quality in each aging period; however, not presenting higher amounts of isoflavones and efficiency in removing free radicals. For all cultivars, the values for total of phenolic compounds, as well as total of flavonoids have shown quadratic positive behavior; the values for isoflavones remained constant and the vigor and viability showed contrary trend to activity of antioxidant agents. RESUMO: Qualidade fisiológica, conteúdo e atividade de antioxidantes presentes em sementes de soja envelhecidas artificialmente. O objetivo deste trabalho foi avaliar a qualidade fisiológica, o conteúdo e a atividade de agentes antioxidantes presentes em sementes de soja envelhecidas durante diferentes períodos. Foram utilizadas sementes das cultivares BRS 258, BRS 262 e BRS 268, envelhecidas durante 12, 24, 36 e 48 h e sementes não envelhecidas. Após cada período de envelhecimento, as sementes foram avaliadas pelo testes de: germinação; primeira contagem e tetrazólio. Foram quantificados: compostos fenólicos totais; flavonóides totais; total de isoflavonas e atividade eliminadora do radical ABTS°+. Houve diferença entre as cultivares em relação ao vigor e viabilidade somente quando foram envelhecidas. BRS 158 e BRS 268 apresentaram melhor qualidade fisiológica de sementes em cada período de envelhecimento, porém, não apresentaram maior quantidade de isoflavonas e eficiência no sequestro dos radicais livres. Para todas as cultivares, os valores de compostos fenólicos totais, assim como os flavonóides totais, apresentaram comportamento quadrático positivo; os valores das isoflavonas permaneceram constantes e o vigor e a viabilidade apresentaram tendência contrária à atividade dos agentes antioxidantes

Can You Hear us Now? Voices from the Margin: Using Indigenous Methodologies in Geographic Research

Indigenous methodologies are an alternative way of thinking about research processes. Although these methodologies vary according to the ways in which different Indigenous communities express their own unique knowledge systems, they do have common traits. This article argues that research on Indigenous issues should be carried out in a manner which is respectful and ethically sound from an Indigenous perspective. This naturally challenges Western research paradigms, yet it also affords opportunities to contribute to the body of knowledge about Indigenous peoples. It is further argued that providing a mechanism for Indigenous peoples to participate in and direct these research agendas ensures that their communal needs are met, and that geographers then learn how to build ethical research relationships with them. Indigenous methodologies do not privilege Indigenous researchers because of their Indigeneity, since there are many ‘insider’ views, and these are thus suitable for both Indigenous and non-Indigenous researchers. However, there is a difference between research done within an Indigenous context using Western methodologies and research done using Indig- enous methodologies which integrates Indigenous voices. This paper will discuss those differences while presenting a historical context of research on Indigenous peoples, providing further insights into what Indigenous methodologies entail, and proposing ways in which the academy can create space for this discourse

Muscle architecture and passive lengthening properties of the gastrocnemius medialis and Achilles tendon in children who idiopathically toe-walk

Children who idiopathically toe-walk (ITW) habitually operate at greater plantarflexion angles and thus, at shorter muscle-tendon unit (MTU) lengths than typically developing (TD) children. Therefore, it is often assumed that habitual use of the gastrocnemius muscle in this way will cause remodelling of the muscle-tendon architecture compared to TD children. However, the gastrocnemius muscle architecture of children who ITW has never been measured. It is essential that we gain a better understanding of these muscle-tendon properties, to ensure that appropriate clinical interventions can be provided for these children. Five children who ITW (age 8 ± 2 years) and 14 TD children (age 10 ± 2 years) participated in this study. Ultrasound was combined with isokinetic dynamometry and surface electromyography, to measure muscle architecture at common positions and passive lengthening properties of the gastrocnemius muscle and tendon across full range of motion. Regardless of which common condition groups were compared under, both the absolute and normalised to MTU muscle belly and fascicle lengths were always longer, and the Achilles tendon length was always shorter in children who ITW than TD children (p 0.05); however, passive joint stiffness was greater in children who ITW at maximum dorsiflexion (p = 0.001) and at a joint moment common to all participants (p = 0.029). Consequently, the findings of this pilot study indicate a remodelling of the relative MTU that does not support the concept that children who ITW commonly experience muscle shortening. Therefore, greater consideration of the muscle and tendon properties are required when prescribing clinical interventions that aim to lengthen the MTU, and treatments may be better targeted at the Achilles tendon in children who ITW