Rational formulae of a much simpler description than these graphic formulae are generally employed.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 1" by Various
In order to compare Planck's formula graphically with Wien's, the distribution curves corresponding to both formulae are plotted in fig.
"Encyclopaedia Britannica, 11th Edition, Volume 13, Slice 2" by Various
We can use this formula to deﬁne the τ k by induction, the graphical interpretation is directly satisﬁed.
Combinatorial aspects of matrix models
For this, we have to determine the Poisson brackets of the associated Wilson loop observables, which can be done either by expressing the curves in terms of the dual generators mi , aj , bj and using (98) or via the graphical procedure in Sect. 3.2 and formula (101).
Dual generators of the fundamental group and the moduli space of flat connections
This is an inference problem in the graphical model associated to the formula.
A review of the Statistical Mechanics approach to Random Optimization Problems
We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems.
Duality of real and quaternionic random matrices
Using the graphical Weingarten formula (Theorem 4.4), we obtain the following theorem, which contains the main result of this section.
Random graph states, maximal flow and Fuss-Catalan distributions