We consider the problem of detecting edges—jump discontinuities in piecewise smooth functions from their N -degree spectral content, which is assumed to be corrupted by noise. There are three scales involved: the “smoothness” scale of order 1/N , the noise scale of order √ η, and the O(1) scale of the jump discontinuities. We use concentration factors which are adjusted to the standard deviatio...

We present a novel deconvolution approach to accurately restore piecewise smooth signals from blurred data. The first stage uses Higher Order Total Variation restorations to obtain an estimate of the location of jump discontinuities from the blurred data. In the second stage the estimated jump locations are used to determine the local orders of a Variable Order Total Variation restoration. The ...

We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...

Abstract. In a flow of two immiscible incompressible viscous fluids, jump discontinuities of flow quantities appear at the two-fluid interface. The immersed interface method can accurately and efficiently simulate the flow without smearing the sharp interface by incorporating necessary jump conditions into a numerical scheme. In this paper, we systematically derive the principal jump conditions...

We prove the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these disco...

Convergence of a sequence of deterministic functions in the Skorohod topology d…‰0;?†† implies convergence of the jumps. For processes with independent additive increments the ®xed discontinuities converge. In this paper it will be shown that this is not true for processes with independent max-increments. The limit in d…‰0;?†† of a sequence of stochastically continuous extremal processes may ha...

For a nondecreasing score function having finitely many jump-discontinuities. a representation of M-estimators with the second order asymptotic distribution is established. and the result is also extended to one-step versions of M-estimators.

we propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. some asymptotic properties of the proposed estimator based on block thresholding are investigated. it is found that the estimators achieve optimal minimax convergence rates over large class...

We study the involution of the real line, induced by Dyer’s outer automorphism of PGL(2,Z). It is continuous at irrationals with jump discontinuities at rationals. We prove that its derivative exists almost everywhere and vanishes almost everywhere.