We use the existence of localized eigenfunctions of the Laplacian on the Sierpiński gasket (SG) to formulate and prove analogues of the strong Szegö limit theorem in this fractal setting. Furthermore, we recast some of our results in terms of equally distributed sequences.

The Hofstadter butterfly, a quantum fractal made up of integers describing quantum Hall states, is shown to be related to an integral Apollonian gasket with D3 symmetry. This mapping unfolds as the self-similar butterfly landscape is found to describe a close packing of (Ford) circles that represent rational flux values and is characterized in terms of an old ((300BC) problem of mutually tangen...

Graphs S[n, k] are introduced as the graphs obtained from the Sierpiński graphs S(n, k) by contracting edges that lie in no triangle. The family S[n, k] is a previously studied class of Sierpiński gasket graphs Sn. Several properties of graphs S[n, k] are studied in particular, hamiltonicity and chromatic number.

The Sierpiński fractal or Sierpiński gasket Σ is a familiar object studied by specialists in dynamical systems and probability. In this paper, we consider a graph Sn derived from the first n iterations of the process that leads to Σ, and study some of its properties, including its cycle structure, domination number and pebbling number. Various open questions are posed.

An approach based on the method of virtual elements is used to solve contact problem for a thin shell revolution lying rigid foundation. In this case, surface base has shape inconsistent with shell. The makes it possible determine area and pressure from unknown in two coordinate directions. Since not known advance, structurally nonlinear. A isotropic described by classical theory Kirchhoff–Love...

We study the holographic quantum error correcting code properties of a Sierpinski Triangle-shaped boundary subregion in $AdS_4/CFT_3$. Due to existing no-go theorems topological correction regarding fractal noise, this gives codes specific advantage over codes. then further argue that shape gasket $AdS_5/CFT_4$ does not possess these properties.

We compute the complexity of two infinite families of finite graphs: the Sierpiński graphs, which are finite approximations of the well-known Sierpiński gasket, and the Schreier graphs of the Hanoi Towers group H(3) acting on the rooted ternary tree. For both of them, we study the weighted generating functions of the spanning trees, associated with several natural labellings of the edge sets.

From 1982 until 1991, a series of studies was performed to evaluate the airborne concentration of chrysotile asbestos associated with replacing gaskets and packing materials. These studies were conducted by the senior author in response to concerns raised by a report from the Navy in 1978 on asbestos exposures associated with gasket work. A series of studies was conducted because results of tho...