Explanation in mathematical conversations:An empirical investigation

Analysis of online mathematics forums can help reveal how explanation is used by mathematicians; we contend that this use of explanation may help to provide an informal conceptualization of simplicity. We extracted six conjectures from recent philosophical work on the occurrence and characteristics of explanation in mathematics. We then tested these conjectures against a corpus derived from online mathematical discussions. To this end, we employed two techniques, one based on indicator terms, the other on a random sample of comments lacking such indicators. Our findings suggest that explanation is widespread in mathematical practice and that it occurs not only in proofs but also in other mathematical contexts. Our work also provides further evidence for the utility of empirical methods in addressing philosophical problems

Arsenic-phosphorus interactions in the soil-plant-microbe system: dynamics of uptake, suppression and toxicity to plants

High arsenic (As) concentrations in the soil, water and plant systems can pose a direct health risk to humans and ecosystems. Phosphate (Pi) ions strongly influence As availability in soil, its uptake and toxicity to plants. Better understanding of As(V)-Pi interactions in soils and plants will facilitate a potential remediation strategy for As contaminated soils, reducing As uptake by crop plants and toxicity to human populations via manipulation of soil Pi content. However, the As(V)-Pi interactions in soil-plant systems are complex, leading to contradictory findings among different studies. Therefore, this review investigates the role of soil type, soil properties, minerals, Pi levels in soil and plant, Pi transporters, mycorrhizal association and microbial activities on As-Pi interactions in soils and hydroponics, and uptake by plants, elucidate the key mechanisms, identify key knowledge gaps and recommend new research directions. Although Pi suppresses As uptake by plants in hydroponic systems, in soils it could either increase or decrease As availability and toxicity to plants depending on the soil types, properties and charge characteristics. In soil, As(V) availability is typically increased by the addition of Pi. At the root surface, the Pi transport system has high affinity for Pi over As(V). However, Pi concentration in plant influences the As transport from roots to shoots. Mycorrhizal association may reduce As uptake via a physiological shift to the mycorrhizal uptake pathway, which has a greater affinity for Pi over As(V) than the root epidermal uptake pathway

Towards a 300 WP p-Type HIP-MWT-Module - Simulation, Experimental Results and Costs

In this work we are aiming at the goal of fabricating a cost-effective HIP-MWT module exceeding 300W. In order to accomplish this goal HIP-MWT (high-performance metal wrap through) silicon solar cells [1, 2] are fabricated on industrial PERC (passivated emitter and rear cell) precursors. Simulation of the optimal metallization layout for MWT based on measured parameters show cell efficiencies up to 21.5%. The consequentially fabricated HIP-MWT solar cells reach maximum efficiencies of 21.4%. The in parallel processed H-pattern reference cells reach maximum efficiencies of 21.2%. The cell efficiencies show a reduced advantage for MWT than in similar experiments, which is due to the tapered busbars of the reference cells allowing nearly the same short circuit currents. Anyhow, combined with a module interconnection based on back contact foils a cell-to-module (CTM) loss of 2 % is demonstrated which allows module power over 300 WP. Due to a power advantage of about 15W in comparison to H-pattern modules the cost of ownership calculation shows a cost advantage of the HIP-MWT module of 3.2 %. Simulation, experimental results and cost calculation show an advantage for HIP-MWT technology over the H-pattern reference leading to the conclusion that MWT is a more cost-effective concept