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The financial trader and analyst Bill Williams [5] believes that this complexity is built up from self-similar patterns of trader behavior.
In our case, self-similar objects are convex bodies in n-dimensional spaces, for example, in the three-dimensional Euclidean space.
There exists a unique solution of Cauchy problem (1) in the self-similar form [v.sub.m](t, x) = [t.sup.-1/3] [f.sub.m]([xt.sup.-1/3]), such that
In this experiment, we have considered the azimuthal angles of the shower tracks belonging to four overlapping pseudorapidity intervals centered around [c.sub.r], from the same interaction to analyse the fluctuation and to identify the clustering pattern from a complex network perspective, and attempted to detect whether the azimuthal fluctuation is also self-similar in nature and follows scaling laws.
Besides isometries, there are symmetries called the self-similar solutions of space-time which are more restrictive.
The spreading rate is given by the gradient of the best-fit line for the [r.sub.1/2] plot in the self-similar region.
D = log (number of self-similar pieces)/log (scale factor)
The layout of the paper is as follows: Section 2 estimates brain plasma parameters and set up a set of two-fluid Vlasov-Maxwell equations; Section 3 derives a set of nonlinear, self-similar differential equations for the excitation and propagation of EEG waves; Section 4 exposes the data-fit modeling of the solitary EEG waves under different conditions.
First, we recall that Carrillo and Ferreira [1] considered self-similar solutions for equation (1.1).
Following the self-similar model, at a distance exceeding several diameters of the thruster's nozzle, the plume has Gaussian density profile, a constant axial velocity, and a linearly increasing radial velocity [15].
(i) The Q-sequence is built out of apparently self-similar "sausages."
The mathematical models of self-similar hierarchies of cities can be expressed as a set of exponential functions and power functions.