A 3-D invertible map generating a 4-loop solenoid attractor is presented. The attractor of the "standard" 4-solenoid turns out to be "fat" that is, fractal dimensionality exceeds topological dimensionality by more than unity. If a fourth variable that is weakly damped is added to this 3-variable map, a new type of attractor is generated. In a cross section it is a continuous nowheredifTerentiab...

In this paper we work with invertible skew pairings for weak bialgebras in a symmetric monoidal category where every idempotent morphism splits. We prove that kind of induces examples distributive laws and therefore they provide wreath products. Also will show define weakly comonoidal mutually inverse pairs and, by the results proved G. Böhm J. Gómez-Torrecillas, obtain products become respect ...

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate n. Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimat...

We introduce the notion of weakly (strongly) infinite real rank for unital C∗-algebras. It is shown that a compact space X is weakly (strongly) infine-dimensional if and only if C(X) has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group C∗-algebra C∗ (F∞) of the free group on countable number of generators ha...

| Many scientists believe that all pulse-coupled neural networks are toy models that are far away from the biological reality. We show here, however, that a huge class of biophysically detailed and biologically plausible neu-ral network models can be transformed into a canonical pulse-coupled form by a piece-wise continuous, possibly non-invertible, change of variables. Such transformations exi...