This second branch of algebraic graph theory is related to the first, since the symmetry properties of a graph are reflected in its spectrum.
12.
Spectroscopic features are analyzed and described with respect to the symmetry properties of the, " inter alia ", vibrational or electronic states.
13.
Knowledge of the symmetry properties of the ground and excited states allows one to predict the numbers and intensities of absorptions in vibrational and electronic spectra.
14.
A general approach to solve DEs uses the symmetry property of differential equations, the continuous infinitesimal transformations of solutions to solutions ( Lie theory ).
15.
A general approach to solving PDE's uses the symmetry property of differential equations, the continuous infinitesimal transformations of solutions to solutions ( Lie theory ).
16.
The similarity parameter is connected to basic symmetry properties of the collisionless Vlasov equation and is thus the relativistic plasma analog of the Reynolds number in fluid mechanics.
17.
Fast algorithms to calculate the forward and inverse Zernike transform use symmetry properties of trigonometric functions, separability of radial and azimuthal parts of Zernike polynomials, and their rotational symmetries.
18.
The following illustrates how local gauge invariance can be " motivated " heuristically starting from global symmetry properties, and how it leads to an interaction between originally non-interacting fields.
19.
The rarer seven-membered and higher ring systems may also show the same symmetry property, as can linked and fused aromatic ring systems such as biphenyls, naphthalenes and isoindoles.
20.
They will obey the usual symmetry properties; for example, the curvature of the connection will be anti-symmetric in the last two indexes, and will satisfy the second Bianchi identity.
