相关论文: Calculus, fractals, and analysis on metric spaces

Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

In this work, we introduce a class of fractal subsets of $[0,1]$ corresponding to the aperiodically ordered metallic means sequences. We find simple formulas for the fractal dimension for these fractals.

This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…

We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.

This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

Some aspects of Cauchy integrals on sets with dimension larger than 1 are briefly discussed.

This paper develops a technical and practical reinterpretation of the real interval [a,b] under the paradigm of fractal countability. Instead of assuming the continuum as a completed uncountable totality, we model [a,b] as a layered…

The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.

There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.

This article discusses the notion of convergence of sequences of iterated function systems. The technique of iterated function systems is one of the several methods to construct objects with fractal nature, and the fractals obtained with…

We explore a novel link between two seemingly disparate mathematical concepts: Egyptian fractions and fractals. By examining the decomposition of rationals into sums of distinct unit fractions, a practice rooted in ancient Egyptian…

This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…

The special case of closed subsets of C^n is briefly discussed.

Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…

Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study…

Given strong local Dirichlet forms and $\mathbb{R}^N$-valued functions on a metrizable space, we introduce the concepts of geodesic distance and intrinsic distance on the basis of these objects. They are defined in a geometric and an…

Analysis on fractals is a growing field, with hints of potential for widespread applicability across all of STEM. One of the most heavily researched type of fractals are the nested fractals, fractal shapes defined by virtue of being made of…

In this manuscript, fractal and fuzzy calculus are summarized. Fuzzy calculus in terms of fractal limit, continuity, its derivative, and integral are formulated. The fractal fuzzy calculus is a new framework that includes fractal fuzzy…