We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a  direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is sho...

Making use of noncommutative motives we relate exceptional collections (and more generally semi-orthogonal decompositions) to motivic decompositions. On one hand we prove that the Chow motive M(X )Q of every smooth and proper Deligne-Mumford stack X , whose bounded derived category D(X ) of coherent schemes admits a full exceptional collection, decomposes into a direct sum of tensor powers of t...

Given general quasi-differential expressions , each of order n with complex coefficients and their formal adjoint are on the interval [a,b) respectively, we give a characterization all regularly solvable operators adjoints generated by ordinary expression in direct sum Hilbert spaces . The domains these described terms boundary conditions involving -solutions equations intervals [ap,bp). This i...