When can scientific publications have a dedication?
(Mathematics:) I have dedicated a few journal articles "to the memory of" recently deceased colleagues (one in a "special issue journal" for this purpose, but others in regular journal issues). I just included the dedication in the submitted paper, and no-one complained about or commented on it, and it appeared in the published version. 

Regarding placement: The place of the dedication seems to depend on the journal style; in most cases I encountered it was between the author list and the abstract. 

Actually, the first time I dedicated a paper I put the dedication into the acknowledgment section, the (copy) editor then moved it to the proper place. From that time on, I placed the dedications there myself, using in LaTeX (amsart class) the command \dedicatory{Dedicated to the memory of N. N. (1930--2010)}. So far all journals left the dedications there; apart form one who moved it to an own section between the abstract and the acknowledgment section.