Sporopollenin is a physically robust and chemically resilient biopolymer that comprises the outermost layer of pollen walls and is the first line of defense against harsh environmental conditions. The unique physicochemical properties of sporopollenin increasingly motivate the extraction of sporopollenin exine capsules (SECs) from pollen walls as a renewable source of organic microcapsules for ...

We present a short and self-contained proof of Jin’s theorem about the piecewise syndeticity of difference sets which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. An explicit bound to the number of shifts that are needed to cover a thick set is provided. Precisely, we prove the following:...