The topics include a measure-theoretic result for approximation by Delone sets, self-similar
tilings of fractal blow-ups, dimensions of limit sets of Kleinian groups, an overview of complex fractal dimensions: from fractal strings to fractal drums and back, and eigenvalues of the Laplacian on domains with fractal boundary.
Outside, in nature we may see many fractals pattern such us the twigs linked to the tree or snowflakes, these reinforce the properties of being self-similar
. No matter how complex is the whole situation, the fractal patterns are recursive since it is built from many repetitions of the same process.
Another assumption within the synthetic control arm approach is that disease progressions are at best case linear, and at worst case, self-similar
within disease states.
The combinatorial model, called "the plaid model," has a self-similar
structure that blends geometry and elementary number theory.
Calculation of the numerical value of r can be performed based on the definition of fractional dimension, as a property of self-similar
objects (fractional dimension is a dimension in the form of a fraction, for example, 23900/10000).
Fractals have 'self-similar
' structure on a variety of size scales.
Next we prove the existence of the self-similar
solutions [v.sub.m](t, x) = [t.sup.-1/3] [f.sub.m]([xt.sup.-1/3]).
The evidences of self-similar
characteristics in high-energy interactions have connections to the idea of fractality.
Sharif and Aziz [12, 13] studied kinematic self-similar
solutions of plane and cylindrically symmetric space-time for the perfect fluid and dust.
When we look at landscapes that have a natural fractal pattern [fractals are infinitely complex patterns that are self-similar
across different scales]--natural shapes like tree limbs, clouds, ripples on the water, or coastlines--our brains produce more alpha waves, which signify a wakefully relaxed state.