Two local adaptative nonlinear lters for image denoising are described and compared to other methods. The rst one is a median lter computed over a connected neighborhood that ts the local conformation of level lines. The second one deals with the size of grains in image. Both lters depend on a single parameter, the area A, are morphological and associated with smooth as well as unsmooth xed poi...

IN THIS SUPPLEMENT, we give two examples showing that the assumptions of bounded out-degree and L-connectedness are crucial. Our approach in constructing equilibria will be to prescribe the initial moves of the agents and then extend this to an equilibrium strategy profile. Define the set of times and histories agents have to respond to as H = {(i t a) : i ∈ V t ∈ N0 a ∈ [0 1] × {0 1}|N(i)|·t}....

We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computer-free proof of the original Feigenbaum observation of the universal parameter scaling laws. We use the Hyperbolicity Theorem to prove Milnor’s conjectures on self-similarity and “hairiness” of the Mandelbrot set near the corresponding parame...

This paper studies the dynamics of the family λ sin z for some values of λ. First we give a description of the Fatou set for values of λ inside the unit disc. Then for values of λ on the unit circle of parabolic type (λ = exp(i2πθ), θ = p/q, (p, q) = 1), we prove that if q is even, there is one q-cycle of Fatou components, if q is odd, there are two q cycles of Fatou components. Moreover the Fa...

In the beginning of article we show some consequences of the regularity axiom. In the second part we introduce the successor of a set and the notions of transitivity and connectedness wrt membership relation. Then we define ordinal numbers as transitive and connected sets, and we prove some theorems of them and of their sets. Lastly we introduce the concept of a transfinite sequence and we show...

“...I is this passion for beautiful colors that makes us paint as we do... and not the love of the ‘dot,’ as foolish people say,” wrote painter Paul Signac in his journal (1). He was defending the art movement started by his good friend and fellow artist George Seurat and built upon by Signac himself, Camille Pissarro, and others. This movement, divisionism or pointillism, was Seurat’s artistic...

We define direct sums and a corresponding notion of con-nectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric functions on a probability space; there are natural definitions of direct sums and connectedness for such functions, and there is a perfect correspondence with the...

In [2] o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally definable spaces, for which we introduce homology and homotopy functors. We also study the concept of connectedness in ∨ -definable groups – which are examples of locally definable spaces. We s...