In a recent article, we showed that trigonometric shearlets are able to detect directional step discontinuities along edges of periodic characteristic functions. this paper, extend these results bivariate functions which have jump in higher order derivatives edges. prove suitable upper and lower bounds for the shearlet coefficients, need generalize about localization- orientation-dependent deca...

We obtain sufficient conditions, easily verifiable, for the existence and uniqueness of piecewise smooth solutions of a linear two-point boundaryvalue problem with general interface conditions. The coefficients of the differential equation may have jump discontinuities at the interface point. As an example, the conditions obtained are applied to a problem with typical interface such as perfect ...

The creation and propagation of jump discontinuities in the solutions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {xi}~= 1, of jump discontinuities. Let S be the smallest closed set which satisfies: (i) S is a union of forward characteristics. (ii) S contains all the forward characteristics from the points {xi}~= 1" (iii) if two fo...

We propose a new edge detection method that is effective on multivariate irregular data in any domain. The method is based on a local polynomial annihilation technique and can be characterized by its convergence to zero for any value away from discontinuities. The method is numerically cost efficient and entirely independent of any specific shape or complexity of boundaries. Application of the ...

Abstract Consider a balance law where the flux depends explicitly on space variable. At jump discontinuities, modeling considerations may impose defect in conservation of some quantities, thus leading to non conservative products. Below, we deduce evolution smooth case from conditions at discontinuities. Moreover, resulting framework enjoys well posedness and solutions are uniquely characterize...

In this work, a class of new finite-element methods, called immersed-interface finite-element methods, is developed to solve elliptic interface problems with nonhomogeneous jump conditions. Simple non–body-fitted meshes are used. A single function that satisfies the same nonhomogeneous jump conditions is constructed using a level-set representation of the interface. With such a function, the di...

Motivated by recent work on studying massive imaging data in various neuroimaging studies, we propose a novel spatially varying coefficient model (SVCM) to capture the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) with a set of covariates. Two stylized features of neuorimaging data are the presence of multiple piecewise smooth regions with unkno...

In [1] and some following publications, Tadmor and Gelb took up a well known property of conjugate Fourier series in 1-d, namely the property to detect jump discontinuities in given spectral data. In fact, this property of conjugate series is known for quite a long time. The research in papers around the year 1910 shows that there were also other means of detecting jumps observed and analysed. ...

We study hyperbolic maps depending on a parameter ε. Each of them has an invariant Cantor set. As ε tends to zero, the map approaches the boundary of hyperbolicity. We analyze the asymptotics of scaling function of the invariant Cantor set as ε goes to zero. We show that there is a limiting scaling function of the limiting map and this scaling function has dense jump discontinuities because the...