Suppose that m,n ∈ N and that A : R → R is a linear operator. It is shown here that if k, r ∈ N satisfy k < r 6 rank(A) then there exists a subset σ ⊆ {1, . . . ,m} with |σ| = k such that the restriction of A to R ⊆ R is invertible, and moreover the operator norm of the inverse A−1 : A(R) → R is at most a constant multiple of the quantity √ mr/((r − k) ∑m i=r si(A) 2), where s1(A) > . . . > sm(...

In cryptosystem theory, it is well-known that a logical mapping that returns the same value that was used as its argument can be inverted with a zero failure probability in linear time. In this paper, however, I show that such a mapping, while trivially assigning a logical state to itself, comes up against an impassable entropy wall such that its computational path is undone inside the threshol...

In this study, we examine the quasi-balanced dynamics of Hurricane Bonnie (1998) using the invertibility principle of Ertel's potential vorticity (PV). Given an atmospheric flow that is dynamically balanced, the conservative property of PV (in the absence of heating and friction) may be exploited to obtain a simple interpretation of all relevant dynamical information. Previous studies have show...

A new method to decide the invertibility of a given high-dimensional function over a domain is presented. The problem arises in the field of verified solution of differential algebraic equations (DAEs) related to the need to perform projections of certain constraint manifolds over large domains. The question of invertibility is reduced to a verified linear algebra problem involving first partia...

The change of variable theorem is proved under the sole hypothesis of differentiability of the transformation. Specifically, it is shown under this hypothesis that the transformed integral equals the given one over every measurable subset on which the transformation is injective; that countably many of these subsets cover the domain of invertibility; and that its complement – the domain of non-...

This paper considers structural nonparametric random utility models for continuous choice variables. It provides sufficient conditions on random preferences to yield reducedform systems of nonparametric stochastic demand functions that allow global invertibility between demands and random utility components. Invertibility is essential for global identification of structural consumer demand mode...

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...