Handling Non - Invertibility : Theories and

Handling Non - Invertibility :

5 Existing research provides no systematic, limited information procedure for handling 6 non-invertibility, despite the well-known inference problem it causes as well as its 7 presence in many types of dynamic systems. Non-invertibility means that structural 8 shocks cannot be recovered from a history of observed variables. It can arise from 9 a form of delayed responses due to, among other thi...

Invertibility of retarded response functions for Laplace transformable potentials: Application to one-body reduced density matrix functional theory.

A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time dependence of the potentials should be Laplace transformable and the initial state should be a ground state, though it might be degenerate. This theorem provides a rigorous foundation for all density-functional-like theories in the time-dependent linear response regime. Especial...

A Survey of Invertibility and Spectrum Preserving Linear Maps

Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.

Finite Type Link Invariants and the Non-invertibility of Links

We show that a variation of Milnor’s μ̄-invariants, the so-called Campbell-Hausdorff invariants introduced recently by Stefan Papadima, are of finite type. This implies, in particular, that finite type link invariants can detect the non-invertibility of a link with more than one components and they are thus stronger than quantum invariants. It is still open whether finite type knot invariants (V...