Let (alpha>0) and f be defined in a suitable domain.
Let (x t) in R) be defined in a suitable q-geometric set (A=[0,a]_{q}), (D_{q}x t)in C_{q}[0,q]) (where (C_{q}[0,a]) is the space of all continuous functions on the interval ([0, a])).
The POAF criteria had to be defined in the report, and only patients who were observed for POAF over at least 3 days were considered suitable for analysis.
Definition 1.3 The generalized Bernoulli polynomials B n [ m − 1, α ] ( x ), m ∈ N, are defined, in a suitable neighborhood of t = 0, by means of the generating function ( t m e t − ∑ l = 0 m − 1 t l l ! ) α ⋅ e x t = ∑ n = 0 ∞ B n [ m − 1, α ] ( x ) t n n !. (1.5).
Definition 1.5 For complex numbers α ∈ C, natural numbers m ∈ N, the generalized Euler polynomials E n [ m − 1, α ] ( x ) are defined, in a suitable neighborhood of t = 0, by means of the generating function ( 2 m e t + ∑ l = 0 m − 1 t l l ! ) α ⋅ e x t = ∑ n = 0 ∞ E n [ m − 1, α ] ( x ) t n n !. (1.7).
Definition 1.4 For arbitrary real or complex parameters λ and the natural numbers m, α ∈ N, the generalized Bernoulli polynomials B n [ m − 1, α ] ( x ) are defined, in a suitable neighborhood of t = 0, by means of the generating function ( t m λ e t − ∑ l = 0 m − 1 t l l ! ) α ⋅ e x t = ∑ n = 0 ∞ B n [ m − 1, α ] ( x ; λ ) t n n !. (1.6).
Definition 1.6 For arbitrary real or complex parameters λ, α and natural numbers m ∈ N, the generalized Euler polynomials E n [ m − 1, α ] ( x ) are defined, in a suitable neighborhood of t = 0, by means of the generating function ( 2 m λ e t + ∑ l = 0 m − 1 t l l ! ) α ⋅ e x t = ∑ n = 0 ∞ E n [ m − 1, α ] ( x ; λ ) t n n !. (1.8).
However, all types of PCM present their specific problems and therefore requirements are defined in order to select the most suitable PCMs.
Other Poisson-based similarity measures are defined in [8], which however are not suitable for the generation of RCGs since, in practice, large number of genes turn out to have the same coexpression with any given gene, so as to make the definition of small RCGs problematic.
Once the CTV(s) have been defined, in external beam radiation treatment, a suitable arrangement of radiation beam(s) must be selected to achieve an acceptable dose distribution.
