Related papers: Complex base numeral systems
IFS fractals - the attractors of Iterated Function Systems - have motivated plenty of research to date, partly due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design…
Root systems are sets with remarkable symmetries and therefore they appear in many situations in mathematics. Among others, denominator formulae of root systems are very beautiful and mysterious equations which have several meanings from a…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the…
The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
Let G be a graph with a perfect matching. A complete forcing set of G is a subset of edges of G to which the restriction of every perfect matching is a forcing set of it. The complete forcing number of G is the minimum cardinality of…
This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will…
The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
In this paper we present a uniform way to derive families of maps from the corresponding differential equations describing systems which experience periodic kicks. The families depend on a single parameter - the order of a differential…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
The aim of this book is to show that the use of f-analytic families of finite type cycles (cycles having finitely many irreducible components, but not compact in general) in a given complex space may be useful in complex geometry, despite…
Conditions are given which imply that analytic iterated function systems (IFS's) in the complex plane have uniformly perfect attractor sets. In particular, it is shown that the attractor set of a finitely generated conformal IFS is…
In our previous work, On the localization of Hutchinson-Barnsley fractals, Chaos Solitons Fractals, 173 (2023), 113-674, we presented a method for finding a finite family of closed balls whose union contains the attractor of a given…
Let P be a polygon with rational vertices in the plane. We show that for any finite odd-sized collection of translates of P, the area of the set of points lying in an odd number of these translates is bounded away from 0 by a constant…
For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the…
We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension.…
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…
The incomplete statistics for complex systems is characterized by a so called incompleteness parameter $\omega$ which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the…