Under certain continuity conditions, we estimate upper and lower box dimensions of the graph a function defined on Sierpiński gasket. We also give an bound for Hausdorff dimension having finite energy. Further, introduce two sets definitions bounded variation show that fractal continuous is [Formula: see text] prove class all functions closed under arithmetic operations. Furthermore, every almo...

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed.

This work studies the problem of GPU thread mapping for a Sierpiński gasket fractal embedded in a discrete Euclidean space of n × n. A block-space map λ : Z2E 7→ Z 2 F is proposed, from Euclidean parallel space E to embedded fractal space F, that maps in O(log 2 log 2 (n)) time and uses no more than O(n) threads with H ≈ 1.58... being the Hausdorff dimension, making it parallel space efficient....

For the Laplacian ∆ defined on a p.c.f. self-similar fractal, we give an explicit formula for the resolvent kernel of the Laplacian with Dirichlet boundary conditions, and also with Neumann boundary conditions. That is, we construct a symmetric function G(λ) which solves (λI − ∆)−1 f (x) = ∫ G(λ)(x, y) f (y) dμ(y). The method is similar to Kigami’s construction of the Green kernel in [Kig01, §3...