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Abstract

Beginning with some observations about the periodic and
nonperiodic
structures commonly adopted by elements in the periodic table, I will
introduce a definition ("objective structures") of a mathematically
small but physically well represented class of molecular structures.
This definition will be seen to have an intimate relation to the
invariance of the equations of quantum mechanics. The resulting
framework can be used to design various multiscale methods, and gives a
new perspective on some of the fundamental solutions in continuum
mechanics for solids and fluids. Open mathematical problems will be
highlighted.