A zero of a piecewise smooth function f is said to be nondegenerate if the function is Fr echet diierentiable at that point. Using this concept, we describe the usual nondegeneracy notions in the settings of nonlinear (vertical, horizontal, mixed) complementarity problems and the variational inequality problem corresponding to a polyhedral convex set. Some properties of nondegenerate zeros of p...

We consider piecewise monotone maps of the interval with zero entropy or no periodic points. First, we give a rigid model for these maps: the interval translations mappings, possibly with ips. It follows, e.g., that the complexity of a piecewise monotone map of the interval is at most polynomial if and only if this map has a nite number of periodic points up to monotone equivalence. Second, we ...

Let (X,B, μ, T ) be a measure-preserving system. The well-known Poincare recurrence theorem asserts for any A ∈ B with μ(A) > 0, there exist infinitely many n ∈ N such that μ(A ∩ TA) > 0. For a subset S of N, we say S is syndetic if there exists a constant C > 0 such that S ∩ [x, x + C] 6= ∅ for any sufficiently large x, i.e., S has bound gaps. In [5], Khintchine proved that for any A ∈ B with ...

Our achievements on the theoretical front will be very poor indeed if...we close our eyes to problems and can only memorize isolated conclusions or principles... A mathematical discipline is alive and well if it has many exciting open problems of different levels of difficulty. This section's goal is to show that this is the case with Ergodic Ramsey Theory. To warm up we shall start with some r...

The presence of positive Lyapunov exponents in a dynamical system is often taken to be equivalent to the chaotic behavior of that system. We construct a Bernoulli toral linked twist map which has positive Lyapunov exponents and local stable and unstable manifolds defined only on a set of measure zero. This is a deterministic dynamical system with the strongest stochastic property, yet it has po...

For the evaluation of the usability of interaction devices it is important to take the cognitive resources into account that a user needs to perform particular tasks. These aspects are dealt with mainly by usability testing and heuristics in a rather late stage in the design process. Although these approaches are important, they have also serious drawbacks. They do not support rigorous reasonin...

In this work, the issue of estimation reachable sets in continuous bimodal piecewise affine systems is studied. A new method proposed, framework ellipsoidal bounding, using quadratic Lyapunov functions. Although can be seen as a special class hybrid systems, reachability methods developed for might inappropriately complex dynamics. This work goes direction exploiting dynamical structure system ...

Nowadays it is widely recognised that in the design of software it is important to take human factors into consideration. The cognitive aspects of human computer interaction form an important and interesting part of these factors. There exist several approaches to incorporate knowledge on these aspects into the design cycle. They range from using a list of general heuristics based on previous e...