On the principal frequency of a convex membrane and related problems
Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra
Generalizing earlier results about the set of idempotents in a Banach algebra, or of self-adjoint idempotents in a -algebra, we announce constructions of nice connecting paths in the connected components of the set of elements in a Banach algebra, or of self-adjoint elements in a -algebra, that satisfy a given polynomial equation, without multiple roots. In particular, we prove that in the Banach algebra case every such non-central element lies on a complex line, all of whose points satisfy the...
Unilateral tilings of the plane with squares of three sizes.
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