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...

We propose a test for invertibility or fundamentalness of structural vector autoregressive moving average models generated by non-Gaussian independent shocks. We prove that in these models the Wold innovations are serially dependent if and only if the structural shocks are non-fundamental. This simple but powerful characterization suggests an empirical strategy to assess invertibility. We propo...

Operators of Wiener-Hopf plus Hankel type have been receiving an increasing attention in the last years (see [1, 2, 4, 6, 10, 12–16]). Some of the interest in their study arises directly from concrete applications where these kind of operators appear. This is the case in problems of wave diffraction by some particular rectangular geometries which originate specific boundary-transmission value p...

In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the L2 norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non–interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formula...

We recall the classical tree-cotree technique in magnetostatics. (1) extend it frame of high-order finite elements general domains. (2) focus on its connection with question invertibility final algebraic system arising from a edge element discretization magnetostatic problem formulated terms magnetic vector potential. With same purpose invertibility, we analyse another classically used conditio...

The invertibility of the rules of a sequent calculus is important for guiding proof search and can be used in some formalised proofs of Cut admissibility. We present sufficient conditions for when a rule is invertible with respect to a calculus. We illustrate the conditions with examples. It must be noted we give purely syntactic criteria; no guarantees are given as to the suitability of the ru...

We discuss the consequences of the possibility that Vassiliev invariants do not detect knot invertibility as well as the fact that quantum Lie group invariants are known not to do so. On the other hand, finite group invariants, such as the set of homomorphisms from the knot group to M11, can detect knot invertibility. For many natural classes of knot invariants, including Vassiliev invariants a...

A linear algebraic framework for the analysis of synthesis-type problems for discrete-time nonlinear systems in introduced. This is an extension of a similar tool for continuous-time systems which established important connections between many algorithms associated with right-invertibility, left-invertibility and dynamic decoupling, as well as between these algorithms and an approach based upon...