We consider the inverse boundary value problem of determining the potential q in the equation ∆u + qu = 0 in Ω ⊂ Rn, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension n ≥ 3 for potentials that are piecewise linear on a given partition of Ω. No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation ∆u+ kcu = 0...

In this paper, we devise a computational approach for designing polyphase sequences with two key properties; (i) a phase argument which is piecewise linear, and (ii) an impulse-like autocorrelation. The proposed approach relies on fast Fourier transform (FFT) operations and thus can be used efficiently to design sequences with a large length or alphabet size. Moreover, using the suggested metho...

We derive Sobolev-type inner products with respect to which hat functions on arbitrary triangulations of domains in R are orthogonal. Compared with linear interpolation, the resulting approximation schemes yield superior accuracy at little extra cost.

This note revisits a paper from Velan and Florian [Velan and Florian(2002)] dealing with the entropy condition in traffic flow models. It aims to clarify the application of this condition for non-differentiable fundamental diagrams and then to correct some misunderstandings that appear in the above-mentioned paper. Notably, this note clearly exhibits that the non-smoothness of the fundamental d...

This paper presents an algorithm for finding a piecewise linear band which bounds given two-dimensional data. The band is of constant height, and the distance between adjacent slope discontinuities in opposite directions is restricted by two user-specified parameters.

We present a method for the computation of reachable sets of uncertain linear systems. The main innovation of the method consists in the use of zonotopes for reachable set representation. Zonotopes are special polytopes with several interesting properties : they can be encoded efficiently, they are closed under linear transformations and Minkowski sum. The resulting method has been used to trea...

In this paper, an approximate solution of sensitivity matrix of required velocity with final velocity constraint is derived using a piecewise linear gravity assumption. The total flight time is also fixed for the problem. Simulation results show the accuracy of the method. Increasing the midway points for linearization, increases the accuracy of the solution, which this, in turn, depends on the...

In this paper we conjecture that the piecewise linear map f(x) = px1I[0,1/p)(x)+ (sx − s/p)1I[1/p,1](x), p > 1, 0 < s < 1 which has an expanding, onto branch and a contracting branch is eventually piecewise expanding. We give a partial proof of the conjecture, in particular for values of p and s such that d− ln(p(1−s)+s) ln s e 6 = d− ln p ln s e.

We extend results from Part I about estimating gradient errors elementwise a posteriori, given there for quadratic and higher elements, to the piecewise linear case. The key to our new result is to consider certain technical estimates for differences in the error, e(x1)− e(x2), rather than for e(x) itself. We also give a posteriori estimators for second derivatives on each element.