Environmental observations are usually sampled in irregularly spaced points even though the information we need must be, in most cases, continuous and representative of continuous phenomena. To create the thematic map, the stochastic approach is often the best interpolating method to apply. One of the advantages of the application of this theory consists in making available not only a predictio...

We prove surjectivity of the comparison map from continuous bounded cohomology to continuous cohomology for Hermitian Lie groups with finite center. For general semisimple Lie groups with finite center, the same argument shows that the image of the comparison map contains all the even degree primitive elements. Our proof uses a Hirzebruch type proportionality principle in combination with Gromo...

We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The wavelet transform of a signal is an L2-function on an appropriately chosen group while the Wigner function is defined on a coadjoint orbit of the group and serves ...

We present the “Parametrized Self-Organizing Map” (PSOM) as a method for 3D object recognition and pose estimation. The PSOM can be seen as a continuous extension of the standard SelfOrganizing Map which generalizes the discrete set of reference vectors to a continuous manifold. In the context of visual learning, manifolds based on PSOMs can be used to represent the appearance of various object...

A result by Franzová and Smı́tal shows that a continuous map of the interval into itself is chaotic if and only if its topological sequence entropy relative to a suitable increasing sequence of nonnegative integers is positive. In the present paper we prove that for any increasing sequence of nonnegative integers there exists a chaotic continuous map with zero topological sequence entropy relati...

For any affine variety equipped with coordinates, there is a surjective, continuous map from its Berkovich space to its tropicalisation. Exploiting torus actions, we develop techniques for finding an explicit, continuous section of this map. In particular, we prove that such a section exists for linear spaces, Grassmannians of planes (reproving a result due to Cueto, Häbich, and Werner), matrix...

Let (X, d) be a compact metric space, f : X 7→ X be a continuous map with the specification property, and φ : X 7→ R be a continuous function. We prove a variational principle for topological pressure (in the sense of Pesin and Pitskel) for non-compact sets of the form { x ∈ X : lim n→∞ 1 n n−1 ∑ i=0 φ(f (x)) = α } . Analogous results were previously known for topological entropy. As an applica...

where φp(s)=|s|p−2s, p > 1, ∆u(k− 1)=u(k)−u(k−1), T∈{1,2, . . .}, N+={0,1, . . . ,T}, and u :N+ →R. Throughout this paper, we will assume f :N × (0,∞)→R is continuous. As a result, our nonlinearity f (k,u) may be singular at u= 0 and may change sign. Remark 1.1. Recall a map f :N × (0,∞)→R is continuous if it is continuous as a map of the topological space N × (0,∞) into the topological space R...

It is well known that the absolute value map on the self-adjoint operators on an infinite dimensional Hilbert spaces is not Lipschitz continuous, although Lipschitz continuity holds on certain subsets of operators. In this note, we provide an elementary proof that the absolute value map is Lipschitz continuous on the set of all operators which are bounded below in norm by any fixed positive con...

For a continuous map / of the circle to itself, let P(f) denote the set of positive integers n such that / has a periodic point of (least) period n. Results are obtained which specify those sets, which occur as P(f), for some continuous map/ of the circle to itself having a fixed point. These results extend a theorem of Sarkovskii on maps of the interval to maps of the circle which have a fixed...