The evaluation of scientific research is crucial for both the academic community and society as a whole. Numerous bibliometric indices have been proposed for the ranking of research performance, mainly on an ad hoc basis. We introduce the novel class of Scientific Research Measures (SRMs) to rank scientists' research performance and provide a rigorous theoretical foundation for these measures. In contrast to many bibliometric indices, SRMs take into account the whole citation curve of the scientist, offer appealing structural properties, allow a finer ranking of scientists, correspond to specific features of different disciplines, research areas and seniorities, and include several bibliometric indices as special cases. Thus SRMs result in more accurate rankings than ad hoc bibliometric indices. We also introduce the further general class of Dual SRMs that reflect the value of journals and permit the ranking of research institutions based on theoretically sound criteria, which has been a central theme in the scientific community over recent decades. An empirical application to the citation curves of 173 finance scholars shows that SRMs can be easily calibrated to actual citation curves and generate different authors' rankings than those produced by seven traditional bibliometric indices.