We prove for any μ = μ < θ < λ, λ large enough (just strongly inaccessible Mahlo) the consistency of 2 = λ → [θ]23 and even 2 μ = λ → [θ]2σ,2 for σ < μ. The new point is that possibly θ > μ. Typed 5/92 (20 , k 2 -Mahlo,λ → [א2]23; some on models) I thank Alice Leonhardt for the beautiful typing. Latest Revision 2012/Oct/24 Revised and Expanded 5/94 based on lectures, Summer ’94, Jerusalem. Part...

It is possible for one to define fractals as those sets which have non-integral Hausdorff Dimension. This paper defines Hausdorff Dimension and rigorously introduces the necessary theory to prove that one such set is indeed a fractal. The first chapter includes a proof of Banach’s Fixed Point Theorem. The Hausdorff Metric is defined and it is mentioned how one produces ‘generators’ for creating...

We prove that all Sierpi\'nski carpets in the plane are non-removable for (quasi)conformal maps. More precisely, we show any two $S,S'\subset \hat{\mathbb{C}}$ there exists a homeomorphism $f\colon \hat{\mathbb{C}}\to is conformal $\hat{\mathbb{C}}\setminus S$ and it maps $S$ onto $S'$. The proof topological utilizes ideas of characterization Whyburn. As corollary, obtain partial answer to ques...

Abstract— Fractal based CBIR is based on the self similarity fundamentals of fractals. Mathematical and natural fractals are the shapes whose roughness and fragmentation neither tend to vanish, nor fluctuate, but remain essentially unchanged as one zooms in continually and examination is refined. Since an image can be characterized by its fractal code, a fractal code can therefore be used as a ...

In this paper, the upper bounds of the Hausdorff measure of the generalized Sierpinski gasket is estimated by using genetic algorithm, which is inspired by evolution.

For a number of years the author was fascinated by the following six lines of QBasic code, which produce an image (Figure 1) reminiscent of the Sierpinski triangle.

In this paper we modify the method of Nazarov, Peres, and Volberg [14] to get an estimate from above of the Buffon needle probability of the nth partially constructed Sierpinski gasket of Hausdorff dimension 1.