In several space dimensions, scalar shock waves between two constant states are not necessarily planar. We describe them in detail. Then we prove their asymptotic stability L 1 -distance, assuming that they uniformly non-characteristic. Our result is conditional for a general flux, while unconditional the multi-D Burgers equation.

Keywords: Image segmentation Level set model Chan–Vese model Lee–Seo model Energy minimization Unconditional stability a b s t r a c t In this paper, we propose a new level set-based model and an unconditionally stable numerical method for bimodal image segmentation. Our model is based on the Lee–Seo active contour model. The numerical scheme is semi-implicit and solved by an analytical method....

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. Then we prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a quotient...

Reputation formation is a key to understanding indirect reciprocity. In particular, the way to assign reputation to each individual, namely a norm that describes who is good and who is bad, greatly affects the possibility of sustained cooperation in the population. Previously, we have exhaustively studied reputation dynamics that are able to maintain a high level of cooperation at the ESS. Howe...

We prove a general result on complemented unconditional basic sequences in Banach lattices and apply it to give some new examples of spaces with unique unconditional basis. We show that Tsirelson space and certain Nakano spaces have unique unconditional bases. We also construct an example of a space with a unique unconditional basis with a complemented subspace failing to have a unique uncondit...

Let X he a Banach space with an unconditional finite-dimensional Schauder decomposition (En). We consider the general problem of characterizing conditions under which one can construct an unconditional basis for X by forming an unconditional basis for each En. For example, we show that if sup,, dim En < c~ and X has Gordon-Lewis local unconditional s t ructure then X has an unconditional basis ...

A new approach is described for generating exactly energy–momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System mode...