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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.