This article addresses the invertibility problem for switched nonlinear systems affine in controls. The problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state. We extend the concept of switch-singular pairs, introduced recently, to nonlinear systems and develop a formula for checking if the given state and output form a switch-singul...

This paper presents a new wavelet family for lossless image compression by re-factoring the channel representation of the update-then-predict lifting wavelet, introduced by Claypoole, Davis, Sweldens and Baraniuk, into lifting steps. We name the new wavelet family as invertible update-then-predict integer lifting wavelets (IUPILWs for short). To build IUPILWs, we investigate some central issues...

We construct discrete analogs of multidimensional singular integral operators and study their invertibility. Moreover, we give a comparison between continual case. the theory periodic Riemann problem also, because it is needed for studying invertibility so-called paired equations. For more general case pseudo-differential operators, solvability equations in Sobolev–Slobodetskii spaces. Some res...

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...