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Definition of the Lorentz factor γ. The Lorentz factor or Lorentz term (also known as the gamma factor [1]) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in several equations in special relativity, and it arises in ...
The curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people, although this is not rigorously true for a finite population (see below). It is often used to represent income distribution , where it shows for the bottom x % of households, what percentage ( y %) of the total income they have.
A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 / 3 . The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz.
A plot of Lorenz' strange attractor for values ρ=28, σ = 10, β = 8/3. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other.
The Lorentz factor γ retains its definition for a boost in any direction, since it depends only on the magnitude of the relative velocity. The definition β = v/c with magnitude 0 ≤ β < 1 is also used by some authors.
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.
Another important factor of common development of graph theory and topology came from the use of the techniques of modern algebra. The first example of such a use comes from the work of the physicist Gustav Kirchhoff , who published in 1845 his Kirchhoff's circuit laws for calculating the voltage and current in electric circuits .
The two basic qualitative notions of "size" of a function are: how tall is the graph of the function, and how spread out is it. The Lorentz norms provide tighter control over both qualities than the L p {\displaystyle L^{p}} norms, by exponentially rescaling the measure in both the range ( p {\displaystyle p} ) and the domain ( q {\displaystyle ...