We study transfer operators associated to piecewise monotone interval transformations and show that the essential spectrum is large whenever Banach space bounds $L^\infty$ transformation fails be Markov. Constructing a family of spaces we lower bound on spectral radius optimal. Indeed, these realise an as close desired theoretical best possible case.

In seismic images, the opaque oscillatory nature of the ever present sedimentary layers often hide the boundaries between sedimentary packages, such as faults or river channels. Interpreters painstakingly identify these boundaries by inspecting individual planes of the image volume. Discontinuity attribute maps computed from image volumes depict these boundaries and greatly simplify and acceler...

Discontinuity meshing has greatly enhanced the visual and numerical accuracy of radiosity solutions. However, its computational expense means that it cannot be used in dynamic interactive environments with current hardware. Techniques are proposed which allow the discontinuity information to be reused as the environment changes. These techniques complement existing dynamic radiosity methods whi...

Information and communication technologies (ICT) are now an integral part of our environment and are among the most important drivers for innovation in many industry sectors. Whether complex control technologies in the field of machine tools, fly-by-wire systems in the aircraft industry or intelligent components in modern cars, everyday life without ICT is no longer conceivable. Moreover, the c...

We propose a new primal-dual framework for representation, capture, processing, and display of piecewise smooth surfaces, where the dual space is the space of oriented 3D lines, or rays, as opposed to the traditional dual space of planes. An image capture process detects points on a depth discontinuity sweep from a camera moving with respect to an object, or from a static camera and a moving ob...

Non{strictly-hyperbolic and mixed-type conservation laws pose a challenge to computational methods. Speciically, the computation of transitional shock waves, which are dependent on the parabolic regularization of the conservation laws, is sensitive to the numerical viscosity. In this paper, we propose a front tracking algorithm that treats transitional shock waves correctly. The algorithm inclu...

Reconstruction of surface discontinuities from unorganized 3D points is a difficult problem. Both the polygonization and surface fitting approaches to surface reconstruction face the same chicken-and-egg problem: to correctly reconstruct surface discontinuities, the points that lie on the same side of the discontinuities should be used to reconstruct the surfaces to form the discontinuities. Ho...

In this paper we propose a novel high resolution scheme for scalar nonlinear hyperbolic conservation laws. The aim of high resolution schemes is to provide at least second order accuracy in smooth regions and produce sharp solutions near the discontinuities. We prove that the proposed scheme that is derived by utilizing an appropriate flux limiter is nonlinear stable in the sense of total varia...

Various problems in continuum mechanics or artificial intelligence can be modelled by integral functionals depending on second order derivatives of competing functions and on closed sets where discontinuities for either such functions or their first derivatives are allowed. The existence of minimizers for such functionals is shown together with some information about their regularity.