This paper analyzes the task of optoacoustic imaging of the objects located under the surface covering them. In this paper, we suggest the algorithm of the surface eliminating based on the fact that the intensity of the image as a function of the spatial point should change slowly inside the local objects, and will suffer a discontinuity of the spatial gradients on their boundaries. The algorit...

Let Lu := ∇ · (a(x)∇u) = −δ(x − y) in R 3 , 0 < c 1 ≤ a(x) ≤ c 2 , a(x) is a piecewise-smooth function with the discontinuity surface S which is smooth. It is proved that in a neighborhood of S the behavior of the function u is given by the formula:

This paper concerns the construction of a discontinuous parametric curve or surface from a finite set of points and tangent conditions. The method is adapted from the theory of the discrete smoothing variational splines to introduce a discontinuity set and some tangent conditions. Such method is justified by a convergence result.

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind elds. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind elds with MCMC sampling.

We present two-dimensional hydrodynamic models of thermally driven winds from highly irradiated, closein extra-solar planets. We adopt a very simple treatment of the radiative heating processes at the base of the wind, and instead focus on the differences between the properties of outflows in multidimensions in comparison to spherically symmetric models computed with the same methods. For hot (...

In the paper we derive new necessary optimality conditions for optimal control of differential equations systems with discontinuous right hand side. The main attention is paid to a situation when an optimal trajectory slides on the discontinuity surface. The new conditions, derived in the paper, are essential and do not follow from any known necessary conditions for such systems.

When a flow suffers a discontinuity in its vector field at some switching surface, the flow can cross through or slide along the surface. Sliding can be understood as the flow along an invariant manifold inside a switching layer. It turns out that the usual method for finding sliding modes – the Filippov convex combination or Utkin equivalent control – results in a degeneracy in the switching l...

This paper describes a robust method for crease detection and curvature estimation on large, noisy triangle meshes. We assume that these meshes are approximations of piecewise-smooth surfaces derived from range or medical imaging systems and thus may exhibit measurement or even registration noise. The proposed algorithm, which we call normal vector voting, uses an ensemble of triangles in the g...