common light stabilizer for a family

We consider the problem on the existence of a common stabilizer for a finite family of continuous linear scalar nonstationary plants. To solve the problem, we suggest to use a topological approach based on finding a common light stabilizer in the form of a convex combination of stabilizers for the individual plants and on an application of well-known assertions about the properties of sets on simplices.

A green synthesis of size-controllable, uniform gold nanospheres is reported. The size of the gold particles can be selectively tuned from nanometer to submicrometer regimes with narrow size distribution through pH adjustment of the solution. Based on the employed green chemical reduction method, soluble starch is used as both reducing agent and light stabilizer. Soluble starch is generally a very weak reducing agent. However, under an alkaline condition, its reducing efficiency is enhanced by the concomitant generation of reducing species as the starch molecules are alkaline degraded. The in situ generated reducing species nucleate and grow gold nanoparticles. The growth mechanism of gold particles is systematically investigated and proposed. The synthesized gold colloid is very stable and can be kept over 4 months without precipitation, aggregation, or any significant changes. Moreover, all processes of this method are simple and environmentally friendly, and no complex instrument is needed.