rane (Suprane, Baxter Healthcare, Puerto Rico, USA) in the Dräger vaporizer (Dräger D-vapor, Dräger Medical GmbH, Lübeck, Germany) had turned yellow while filling the vaporizer (Fig. 1). We immediately changed the vaporizer. Yellow discoloration of desflurane occurs relatively infrequently and is not widely known; however, this was the second incident in our hospital. The yellowing of desfluran...

The conformal loop ensembles CLEκ, defined for 8/3 ≤ κ ≤ 8, are random collections of loops in a planar domain which are conjectured scaling limits of the O(n) loop models. We calculate the distribution of the conformal radii of the nested loops surrounding a deterministic point. Our results agree with predictions made by Cardy and Ziff and by Kenyon and Wilson for the O(n) model. We also compu...

As a fundamental research object, the minimum edge dominating set (MEDS) problem is of both theoretical and practical interest. However, determining size MEDS number all MEDSs in general graph NP-hard, it thus makes sense to find special graphs for which can be exactly solved. In this paper, we study analytically pseudofractal scale-free web Sierpiński gasket with same vertices edges. For graph...

We studied oscillatory behavior of critical amplitudes for the Gaussian model on a hierarchical structure presented by a modified Sierpinski gasket lattice. This model is known to display nonstandard critical behavior on the lattice under study. The leading singular behavior of the correlation length xi near the critical coupling K=K(c) is modulated by a function which is periodic in ln/ln(K(c)...

The spectral dimension and the Hausdorff dimension of the Sierpiński gasket are known to be different. Kigami proved that the Hausdorff dimension dh with respect to the harmonic metric is less than or equal to the spectral dimension and conjectured equality. We give estimates of dh which are strictly less than the spectral dimension and therefore disprove this conjecture. 1. Sierpiński gasket a...

In this paper we get a power estimate from above of the probability that Buffon’s needle will land within distance 3 of Sierpinski’s gasket of Hausdorff dimension 1. In comparison with the case of 1/4 corner Cantor set considered in Nazarov, Peres, and the second author [14]: we still need the technique of [14] for splitting the directions to good and bad ones, but the case of Sierpinski gasket...

Introduction to Fractal Geometry .................................................................. 1 1. A few Random Quotes ......................................................................... 1 2. Introduction ....................................................................................... 1 3. Types of fractals ........................................................................

Given an undirected graph, finding a minimum 2-edge connected spanning subgraph is NP-hard. We solve the problem for silicate network, brother cell and sierpiński gasket rhombus.