The Similarity Boundary of a Self-Similar Set

A general theory of self-similarity II: recognition

This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the standard simplices (self-similar by barycentric subdivision) and solutions of iterated function systems. Perhaps surprisingly, every compact metrizable space is self-similar in at least one way. From this follow the classical results on the role of the Cantor set among compact metrizable spaces.

Similarity solutions of mixed convection boundary-layer flows in a porous medium

The similarity differential equation $f'''+ff''+βf'(f'-1)=0$ with $β\textgreater{}0$ is considered. This differential equation appears in the study of mixed convection boundary-layer flows over a vertical surface embedded in a porous medium. In order to prove the existence of solutions satisfying the boundary conditions $f(0)=a\geq0$, $f'(0)=b\geq0$ and $f'(+\infty)=0$ or $1$, we use shooting and consider the initial value problem consisting of the differential equation and the initial conditions $f(0)=a$, $f'(0)=b$ and $f''(0)=c$. For $0\textless{}β\leq1$, we prove that there exists a unique …

气泡的自相似性

Self-similarity of bubbles

本文研究与圆周微分同胚相关的分形集气泡（Arnold舌的复类似物），证明了其近似自相似性。

Graphs, groups and self-similarity

We study a family of C*-algebras generalizing both Katsura algebras and certain algebras introduced by Nekrashevych in terms of self-similar groups.