We propose four fractal point processes (FPPs) as novel approaches to modeling and analyzing various types of self-similar traac: the fractal renewal process (FRP), the superposition of several fractal renewal processes (Sup-FRP), the fractal-shot-noise-driven Poisson process (FSNDP), and the fractal-binomial-noise-driven Poisson process (FBNDP). These models fall into two classes depending on ...

Although quintessence cosmologies seem to explain the amount of cosmological constant today, the required conditions are severe. For example, an extremely slowly varying and light scalar field that rolls toward the vanishing vacuum energy state is needed, which must satisfy the required initial conditions so that the energy density in matter is comparable to the energy density stored in quintes...

We investigate the detailed dynamics of a truncated αω dynamo model with a dynamic α effect. We find the presence of multiple attractors, including two chaotic attractors with a fractal basin boundary which merge to form a single attractor as the control parameter is increased. By considering phase portraits and the scaling of averaged times of transitions between the two attractors, we demonst...

Dube proved some undecidability on self-affine fractals. In this paper, we obtain the decidability for self-similar fractal of Dube’s type. In fact, we prove that the following problems are decidable to test if the Hausdorff dimension of a given Dube’s self-similar set is equal to its similarity dimension, and to test if a given Dube’s self-similar set satisfies the strong separation condition.

Integrations in fixed N-body realisations of smooth density distributions corresponding to a chaotic galactic potential can be used to derive reliable estimates of the largest (finite time) Lyapunov exponent χS associated with an orbit in the smooth potential generated from the same initial condition, even though the N -body orbit is typically characterised by an N -body exponent χN χS. This ca...

This paper presents a design of Rectangular Fractal microstrip patch antenna using Iteration Methods by cutting different slots on rectangular microstrip antenna and experimentally studied on IE3D software This design is achieved by using three stages of iteration and a Probe feed This design has been studied in 3 iterations The radiation pattern of the proposed fractal shaped antennas maintain...

We discuss correlation properties of a general mass density field introducing a classification of structures based on their complexity. Standard cosmological models for primordial mass fluctuations are characterized by a sort of large-scale stochastic order, that we call super-homogeneity to highlight the fact that mass fluctuations increase as a function of scale in the slowest possible way fo...

In this paper we find a critical condition for nonempty intersection of a limsup random fractal and an independent fractal percolation set defined on the boundary of a spherically symmetric tree. We then use a codimension argument to derive a formula for the Hausdorff dimension of limsup random fractals.

Application of fractal-scaling analysis methods to the investigation of thermal radio radiation in the millimeter radio waves range and with presence of artificial perturbations of ionosphere has been considered in this work.

Abstract Aiming to evaluate cortical bone microarchitecture and osteonal morphology after irradiation, twelve male New Zealand rabbits were used. The animals divided: control group (no radiation-NIr); 3 irradiated groups, sacrificed after: 7 (Ir7d); 14 (Ir14d) 21 (Ir21d) days. A single radiation dose of 30 Gy was Computed microtomography analyzed the microarchitecture: thickness (CtTh), volume ...