RESUMO
We prove the existence of free objects in certain subcategories of Banach lattices, including p-convex Banach lattices, Banach lattices with upper p-estimates, and AM-spaces. From this we immediately deduce that projectively universal objects exist in each of these subcategories, extending results of Leung, Li, Oikhberg and Tursi (Israel J. Math. 2019). In the p-convex and AM-space cases, we are able to explicitly identify the norms of the free Banach lattices, and we conclude by investigating the structure of these norms in connection with nonlinear p-summing maps.
RESUMO
A new matrix-integral part of the new DNA microarray instrumentation DNA analyzer (DNASER) is introduced based on a novel DNA patterning on the solid support surface. Such patterning found the way to modify a glass surface for a precise positioning of small droplets of aqueous DNA solutions, without special robots (arrayers), within the boundaries of the modified regions. The physically heterogeneous surface consists of highly hydrophilic spots surrounded by a highly hydrophobic area leading to the surface patterning needed for a DNA microarray: a matrix of hydrophilic spots properly activated for immobilization of oligonucleotides has been fabricated on absolutely passive hydrophobic surface. The optimal efficiency of the above functionalitation technology of a glass-substrate in obtaining DNA microarray was confirmed by the Cy3-dCTP-labeled DNA sample, as shown by charge-coupled device images of the DNASER previously described.