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Two-frequency beats of a non-dispersive transverse wave. Since the wave is non-dispersive, phase and group velocities are equal. For an ideal string, the dispersion relation can be written as =, where T is the tension force in the string, and μ is the string's mass per unit length. As for the case of electromagnetic waves in vacuum, ideal ...
In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems.
He confirmed the distribution of the spacings between non-trivial zeros using detailed numerical calculations and demonstrated that Montgomery's conjecture would be true and that the distribution would agree with the distribution of spacings of GUE random matrix eigenvalues using Cray X-MP.
The smallest asymmetric non-trivial graphs have 6 vertices. [1] The smallest asymmetric regular graphs have ten vertices; there exist 10-vertex asymmetric graphs that are 4-regular and 5-regular. [2] [3] One of the five smallest asymmetric cubic graphs [4] is the twelve-vertex Frucht graph discovered in 1939. [5]
This distribution is a common alternative to the asymptotic power-law distribution because it naturally captures finite-size effects. The Tweedie distributions are a family of statistical models characterized by closure under additive and reproductive convolution as well as under scale transformation. Consequently, these models all express a ...
In the mid-1990s, in the study of dynamics of spin glass models, a generalization of the fluctuation–dissipation theorem was discovered that holds for asymptotic non-stationary states, where the temperature appearing in the equilibrium relation is substituted by an effective temperature with a non-trivial dependence on the time scales. [9]
A disconnected graph is not an expander, since the boundary of a connected component is empty. Every connected graph is an expander; however, different connected graphs have different expansion parameters. The complete graph has the best expansion property, but it has largest possible degree. Informally, a graph is a good expander if it has low ...
If the relationship between values of and values of ¯ is linear (which is certainly true when there are only two possibilities for x) this will give the same result as the square of Pearson's correlation coefficient; otherwise the correlation ratio will be larger in magnitude. It can therefore be used for judging non-linear relationships.