相关论文: Fractality, Self-Similarity and Complex Dimensions
We give a generalization of Lagarias' formula for diffraction by ideal crystals, and we apply it to the lattice case, in preparation for addressing the problem of quasicrystals and complex dimensions posed by Lapidus and van Frankenhuijsen…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
The local theory of complex dimensions for real and $p$-adic fractal strings describes oscillations that are intrinsic to the geometry, dynamics and spectrum of archimedean and nonarchimedean fractal strings. We aim to develop a global…
We establish pointwise and distributional fractal tube formulas for a large class of relative fractal drums in Euclidean spaces of arbitrary dimensions. A relative fractal drum (or RFD, in short) is an ordered pair $(A,\Omega)$ of subsets…
There are many research papers dealing with fractal dimension of real-valued fractal functions in the recent literature. The main focus of the present paper is to study fractal dimension of complex-valued functions. This paper also…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for fractal drums in larger dimensions. To…
The fractal and self-similarity properties are revealed in many complex networks. In order to show the influence of different part in the complex networks to the information dimension, we have proposed a new information dimension based on…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
We study possibilities for semantic and syntactic rigidity, i.e., the rigidity with respect to automorphism group and with respect to definable closure. Variations of rigidity and their degrees are studied in general case, for special…
This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…
We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial Fredholm module if and only if the fractal is not…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
A representation of frequency of strings of length K in complete genomes of many organisms in a square has led to seemingly self-similar patterns when K increases. These patterns are caused by under-represented strings with a certain…
In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called \textit{periodic…
Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…
We investigate the homological behaviour of compactly generated triangulated categories under separable extensions. We show that homological invariants (finiteness of global dimension, gorensteinness and regularity) are preserved under such…