In this paper an example is given of a C2 map g from the circle onto itself, which permits an ß-explosion. It is shown that topological entropy (considered as a map from C2(Sl, S1) to the nonnegative real numbers) is continuous at g.

The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...

|Many of the properties of the well-known Koho-nen map algorithm are not easily derivable from its discrete formulation. For instance, the \projection" implemented by the map from a high dimensional input space to a lower dimensional map space must be properly regarded as a projection from a smooth manifold to a lattice and, in this framework , some of its property are not easily identiied. Thi...

Suppose that the inverse image of the zero vector by a continuous map f : R → R has an isolated point P . The existence of a continuous map g which approximates f but is nonvanishing near P is equivalent to a topological property we call “locally inessential,” generalizing the notion of index zero for vector fields, the q = n case. For dimensions n, q where πn−1(Sq−1) is trivial, every isolated...

Automatic disorder recognition in speech can be very helpful for the therapist while monitoring therapy progress of the patients with disordered speech. In this article we focus on prolongations. We analyze the signal using Continuous Wavelet Transform with 18 bark scales, we divide the result into vectors (using windowing) and then we pass such vectors into Kohonen network. Quite large search ...

The attracting set and the inverse limit set are important objects associated to a self-map on a set. We call stable set of the self-map the projection of the inverse limit set. It is included in the attracting set, but is not equal in the general case. Here we determine whether or not the equality holds in several particular cases, among which are the case of a dense range continuous function ...

The attracting set and the inverse limit set are important objects associated to a self-map on a set. We call stable set of the self-map the projection of the inverse limit set. It is included in the attracting set, but is not equal in the general case. Here we determine whether or not the equality holds in several particular cases, among which are the case of a dense range continuous function ...

We study a two-dimensional, two-band double-exchange model for eg electrons coupled to Jahn-Teller distortions in the presence of quenched disorder using a recently developed Monte Carlo technique. In the absence of disorder the half-filled system at low temperatures is an orbitally ordered ferromagnetic insulator with a staggered pattern of Jahn-Teller distortions. We examine the finite-temper...

any (continuous) map N → M between stably parallelizable compact n-manifolds, n 6= 1, 2, 3, 7, is realizable in R, i.e. the composition of f with an embedding M ⊂ R is C-approximable by embeddings. It has been long believed that any degree 2 map S → S, obtained by capping off at infinity a time-symmetric (e.g. Shapiro’s) sphere eversion S×I → R, was non-realizable in R. We show that there exist...

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...