Duncan F. Gregory,William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction

This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on ‘algebraical geometry’ and ‘geometrical algebra’ in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the ‘abstract algebra’ and ‘abstract geometry’ of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to ‘algebraical geometry’ and ‘geometrical algebra’ of the second generation of ‘scientific’ symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s–1840s.     

Enhanced performance of nano-sized SiC reinforced Al metal matrix nanocomposites synthesized through microwave sintering and hot extrusion techniques

In the present study, nano-sized SiC (0, 0.3, 0.5, 1.0 and 1.5 vol%) reinforced aluminum (Al) metal matrix composites were fabricated by microwave sintering and hot extrusion techniques. The structural (XRD, SEM), mechanical (nanoindentation, compression, tensile) and thermal properties (co-efficient of thermal expansion- CTE) of the developed Al-SiC nanocomposites were studied. The SEM/EDS mapping images show a homogeneous distribution of SiC nanoparticles into the Al matrix. A significant increase in the strength (compressive and tensile) of the Al-SiC nanocomposites with the addition of SiC content is observed. However, it is noticed that the ductility of Al-SiC nanocomposites decreases with increasing volume fraction of SiC. The thermal analysis indicates that CTE of Al-SiC nanocomposites decreases with the progressive addition of hard SiC nanoparticles. Overall, hot extruded Al 1.5 vol% SiC nanocomposites exhibited the best mechanical and thermal performance as compared to the other developed Al-SiC nanocomposites.     

Development and pathologies of the arterial wall

Arteries consist of an inner single layer of endothelial cells surrounded by layers of smooth muscle and an outer adventitia. The majority of vascular developmental studies focus on the construction of endothelial networks through the process of angiogenesis. Although many devastating vascular diseases involve abnormalities in components of the smooth muscle and adventitia (i.e., the vascular wall), the morphogenesis of these layers has received relatively less attention. Here, we briefly review key elements underlying endothelial layer formation and then focus on vascular wall development, specifically on smooth muscle cell origins and differentiation, patterning of the vascular wall, and the role of extracellular matrix and adventitial progenitor cells. Finally, we discuss select human diseases characterized by marked vascular wall abnormalities. We propose that continuing to apply approaches from developmental biology to the study of vascular disease will stimulate important advancements in elucidating disease mechanism and devising novel therapeutic strategies.     

Melatonin transport into mitochondria

Melatonin is a well-known, nighttime-produced indole found in bacteria, eukaryotic unicellulars, animals or vascular plants. In vertebrates, melatonin is the major product of the pineal gland, which accounts for its increase in serum during the dark phase, but it is also produced by many other organs and cell types. Such a wide distribution is consistent with its multiple and well-described functions which include from the circadian regulation and adaptation to seasonal variations to immunomodulatory and oncostatic actions in different types of tumors. The discovery of its antioxidant properties in the early 1990s opened a new field of potential protective functions in multiple tissues. A special mention should be made regarding the nervous system, where the indole is considered a major neuroprotector. Furthermore, mitochondria appear as one of the most important targets for the indole’s protective actions. Melatonin’s mechanisms of action vary from the direct molecular interaction with free radicals (free radical scavenger) to the binding to membrane (MLT1A and MLT1B) or nuclear receptors (RZR/RORα). Receptor binding has been associated with some, but not all of the indole functions reported to date. Recently, two new mechanisms of cellular uptake involving the facilitative glucose transporters GLUT/SLC2A and the proton-driven oligopeptide transporter PEPT1/2 have been reported. Here we discuss the potential importance that these newly discovered transport systems could have in determining the actions of melatonin, particularly in the mitochondria. We also argue the relative importance of passive diffusion vs active transport in different parts of the cell.     

Historical review and redescription of three poorly known species of the catfish genus Trichomycterus from south-eastern Brazil (Siluriformes: Trichomycteridae)

ABSTRACT

This study is primarily directed to the most poorly known species of the genus Trichomycterus, comprising five nominal species (T. florensis, T. immaculatus, T. nigricans, T. paquequerensis and T. santaeritae) endemic to south-eastern Brazil. One of them, T. nigricans, is the type species of the genus, involved in taxonomic problems for over 150 years. A detailed historical review, accompanied by examination of type specimens and recent collections, revealed that the correct type locality of T. nigricans is in the vicinity of Rio de Janeiro, not Santa Catarina as commonly appears in the literature; specimens previously misidentified as T. nigricans from Santa Catarina belong to a possibly undescribed species of the genus Cambeva; T. paquequerensis is a synonym of T. immaculatus, and T. florensis is a synonym of T. santaeritae; and the hypothesis that T. santaeritae is closely related to the Amazon Sarcoglanidinae is refuted. The three valid species are redescribed. These species are members of a clade also including T. caipora that is highly supported by molecular data, diagnosed by a pronounced posterior maxillary process and caudal fin emarginate at least in larger specimens. A subclade comprising T. caipora, T. nigricans and T. santaeritae is diagnosed by a long maxilla and a bifid anterior extremity of hypobranchial 3.