Analysis of directional higher order jump discontinuities with trigonometric shearlets

Unilateral Boundary Value Problems with Jump Discontinuities

Using the critical point theory of Szulkin (1986), we study elliptic problems with unilateral boundary conditions and discontinuous nonlinearities. We do not use the method of upper and lower solutions. We prove two existence theorems: one when the right-hand side is nondecreasing and the other when it is nonincreasing. 1. Introduction. In this paper, using the critical-point theory of Szulkin ...

Spatially Varying Coefficient Model for Neuroimaging Data with Jump Discontinuities.

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...

Higher order Fourier analysis

WKB analysis of higher order

WKB analysis of higher order Painlevé equations with a large parameter. II. — Structure theorem for instanton-type solutions of (P J) m (J = I, 34, II-2 or IV) near a simple P-turning point of the first kind

Detecting Strength and Location of Jump Discontinuities in Numerical Data

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. ...