Differential equations with four or more singular points only infrequently have a solution which can be given explicitly as a series whose coefficients are known, or have an explicit integral representation.
32.
Thus, having an integral representation for an " L "-function by no means indicates its analytic properties are resolved : there may be serious analytic issues remaining.
33.
The price of a path integral representation is that the unitarity of a theory is no longer self-evident, but it can be proven by changing variables to some canonical representation.
34.
This integral representation of the velocity can be viewed as a reduction in dimensionality : from the three-dimensional partial differential equation to a two-dimensional integral equation for unknown densities.
35.
Recall that for evolution PDE's the second step of the Fokas method involves the derivation of an integral representation, defined in the complex plane which depends a all boundary values.
36.
For example, by employing either the classical Green's representation formula, or by performing the spectral analysis of the associated Lax pair ., we find the following novel integral representation:
37.
In its infancy, the firm provided a number of integral representations, including litigation defending Thomas Edison's ownership of the creation of the lightbulb and the original incorporation of IBM in the 1920s.
38.
The notation adopted in the following description of the integral representation formula is the one used by and by : the notations used in the original works and in other references, though equivalent, are significantly different.
39.
The interpretation of the integral representation over the " proper time " ? is that the two point function is the sum over all random walk paths that link position 0 to position x over time ?.
40.
This method, which is based on the synthesis, as opposed to the separation of variables [ 6, unifies and extends several classical branches of mathematics, form the usual transforms to the formulation of Ehrenpreis type integral representations.
