We study classical solutions of the vector O(3) sigma model in (2 + 1) dimensions, spontaneously broken to O(2) × Z2. The model possesses Skyrmion-type solutions as well as stable domain walls which connect different vacua. We show that different types of waves can propagate on the wall, including waves carrying a topological charge. The domain wall can also absorb Skyrmions and, under appropri...

This work is concerned with the development of inverse-type inequalities for piecewise polynomial functions and, in particular, functions belonging to hp-finite element spaces. The cases of positive and negative Sobolev norms are considered for both continuous and discontinuous finite element functions.The inequalities are explicit both in the local polynomial degree and the local mesh size.The...

It is observed that exchanging two values of a function over F2n , its differential uniformity and nonlinearity change only a little. Using this idea, we find permutations of differential 4-uniform over F26 whose number of the pairs of input and output differences with differential 4-uniform is 54, less than 63, which provides a solution for an open problem proposed by Berger et al. [1]. Moreov...

Let f : X → X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We find several criteria for transitivity of noncompact connected Lie group extensions. As a consequence, we find transitive extensions for any finitedimensional connected Lie group extension. If, in addition, the group is perfect and has an open set of elements that generate a compact subgroup, we find open ...

Providing each simplex in C(S) with the standard euclidean metric of side-length 1 equips the complex of curves with the structure of a geodesic metric space whose isometry group is just M̃g,m (except for the twice punctured torus). However, this metric space is not locally compact. Masur and Minsky [MM1] showed that nevertheless the geometry of C(S) can be understood quite explicitly. Namely, C...