The fractal necklaces in R^d (d>1) introduced this paper are a class of connected sets generated by the so-called necklace IFSs, for which lot basic topology questions interesting. We give two subclasses and prove that every these classes has no cut points. Also, we stable self-similar R^2 points, whilst an analog self-affine is false.

Recently, Guibas et al. 10 studied deformable necklaces – flexible chains of balls, called beads, in which only adjacent balls can intersect. In this paper, we investigate the problem of covering a necklace by cylinders. We consider several problems under different optimization criteria. We show that optimal cylindrical cover of a necklace with n beads in R by k cylinders can be computed in pol...

We give an explicit description of the rigidification $\infty$-operad as a simplicial operad. This is based on notion dendroidal necklace, extending work Dugger and Spivak from categorical context to operadic context, although with different framework, which relates constructions involving necklaces standard factorization maps in category trees.

Total embedding distributions have been known for only a few classes of graphs. In this paper the total embedding distributions of the cacti and the necklaces are obtained. Furthermore we obtain the total embedding distributions of all graphs with maximum genus 1 by using the method of this paper.

Here we report that silver nanoparticle necklaces can be readily formed by treatment of colloidal silica with ammoniacal silver complex solution followed by washing, deposition and ageing. We investigate the morphology of the produced materials and elucidate the key variables that influence this promising new approach to one-dimensional nanostructuring.

We demonstrate that the regular ring-shaped arrays of Gaussian beams, or optical necklaces, can be generated using diffraction on a stack of dielectric wedges. A condition for self-similarity and structural stability of the beams has been derived and shows good comparison with experimental data. © 2008 Elsevier B.V. All rights reserved. PACS: 41.85.Ja; 41.85.Ct

A vanishing cause can lead to a large response in quantum systems which undergo cyclic deformations that pinch a point of level crossing. We call such behavior homeopathic. We illustrate this behavior by studying charge circulation in quantum models of necklaces of atoms driven by a running wave of small amplitude.