Chitosan, which is an abundant biopolymer, with sulfonic acid groups was used as an efficient, environmentally friendly heterogeneous catalyst for the esterification of free fatty acids with methanol into their more fatty acid methyl ester. Sulfonic acid catalysts supported on chitosan have been studied in the esterification of palmitic acid with methanol at 60 C. The sulfonic acid groups were introduced onto ...
Transesterification of glycerol with methyl acetate was carried out over resins, poly(vinyl alcohol) (PVA) and chitosan (CH) with sulfonic acid groups at 70º C. The products of glycerol transesterification are monoacetin, diacetin and triacetin. It was observed that the catalytic activity increases with the amount of sulfonic acid groups on materials. The CH material showed the highest catalytic activity of all...
Using linearization principle and tools from chronological calculus one establishes a criteria for stabilization of, usually unstable, equilibrium position of Double Inverted Pendula when subject an arbitrary fast oscillation. Both, planar and spherical cases are considered.
Dissertação de mestrado em Matemática Computacional ; O problema que consiste em minimizar uma função não linear sem restrições nas variáveis é há muito estudado. Existem vários métodos para o resolver, sendo o de Newton o método clássico e o mais conhecido. Devido às falhas deste método várias modificações têm sido sugeridas. Neste trabalho estuda-se uma modificação específica ao método de Newton que se desi...
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