For a lively exposition of this theorem and its connection to the Riemann Hypothesis see [5]. In this note, we propose a method that will establish explicit upper bounds for σ(n)/en log log n. Our main observation is that the least number violating the inequality (2) should be a superabundant number. A positive integer n is said to be superabundant if σ(m)/m < σ(n)/n for all m < n. The first 20...

This work reports the use of cross-linkers in bio-based blends from hydroxypropyl-modified lignin (TcC) and a polyamide (PA1010) for possible as carbon fibre precursors, which, while minimising their effects on melt processing into filaments, assist cross-linking components during subsequent thermal stabilisation stage. Cross-linkers included highly sterically hindered aliphatic hydrocarbon (Pe...

Nutrition labels on food items provide valuable information to consumers. To ensure authenticity, the Food and Drug Administration (FDA) checks the reported values on the nutrition labels. This Application Note shows a total sugar analysis method for commercially available maple syrup using the Agilent 1260 Infinity Binary LC system coupled with the Agilent 1260 Infinity Refractive Index Detect...

The purifi cation of a valuable product or product library after a long and complex synthesis is a very important process. The Agilent Automated Purifi cation Software introduces an Open-Access-based solution for isolating substances, with automated focused gradient to simplify the preand post-purifi cation steps. This Technical Overview describes the easy steps to follow, from crude sample ana...