Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Changes in the geographical distribution of plant species and climatic variables on the West Cornwall peninsula (South West UK)

Recent climate change has had a major impact on biodiversity and has altered the geographical distribution of vascular plant species. This trend is visible globally; however, more local and regional scale research is needed to improve understanding of the patterns of change and to develop appropriate conservation strategies that can minimise cultural, health, and economic losses at finer scales. Here we describe a method to manually geo-reference botanical records from a historical herbarium to track changes in the geographical distributions of plant species in West Cornwall (South West England) using both historical (pre-1900) and contemporary (post-1900) distribution records. We also assess the use of Ellenberg and climate indicator values as markers of responses to climate and environmental change. Using these techniques we detect a loss in 19 plant species, with 6 species losing more than 50% of their previous range. Statistical analysis showed that Ellenberg (light, moisture, nitrogen) and climate indicator values (mean January temperature, mean July temperature and mean precipitation) could be used as environmental change indicators. Significantly higher percentages of area lost were detected in species with lower January temperatures, July temperatures, light, and nitrogen values, as well as higher annual precipitation and moisture values. This study highlights the importance of historical records in examining the changes in plant species’ geographical distributions. We present a method for manual geo-referencing of such records, and demonstrate how using Ellenberg and climate indicator values as environmental and climate change indicators can contribute towards directing appropriate conservation strategies

Principle of Least Action

A history of the principle of least action from Leibniz to Lagrang