The Laplace transform is a tool of a key importance regarding solving and analyzing of fractional differential equations in the continuous (see, e.g., [1, 2]), as well as in the discrete case (see, e.g., [7] and [14]).
"A trauma cast out of time, experienced continuously, if unconsciously, instead of as a discrete event".
For each model (lambda _{k}^{(c)}), as in the discrete case, we define a vector of observations, U (k,c).
That is, as in the discrete case, there is a resolution of the identity I = \int_\Omega |\phi_y\rangle\, \langle\phi_y|\,dy where the operator-valued integral is again understood in the weak sense.
where denotes differential entropy, is submodular as in the discrete case.
In particular, we believe that the zero analysis of Q instead of Q ˜ should be involved here similarly as in the discrete case.
In [20], we have critically examined this approach and have shown that, just as in the discrete case, there exist integrable ultradiscrete systems with unconfined singularities but also nonintegrable systems with confined singularities.
Also we offer some applications, for example, criteria for strong (non-) oscillation and Kneser-type criteria, comparison with existing results (our theorems turn out to be new even in the discrete case as well as in many other situations), and comments with examples.
In the discrete case a trajectory can be represented as a sequence of symbols of this kind (it is basically a list of states).
Energy remains well conserved in the discrete case as well.
Concerning the conditional oscillation of Euler type linear and half-linear equations, several results are known in the discrete case as well.
