Moreover, we introduce the parabolic cylinder function with matrix parameters in the present article and analyse its asymptotic behaviour.
The representation of this solution uses parabolic cylinder functions with matrix parameters.
The Weber matrix differential equation provides us with an example for the use of parabolic cylinder functions with matrix parameters.
Lu established Pioncare's inequality in ; we can similarly derive the following lemma by replacing the C-C ball [B.sub.R] with the parabolic cylinder [Q.sub.R].
Take the suitable parabolic cylinder [Q.sub.R/2]([[xi].sub.'0], [t'.sub.0]) to cover ([epsilon], T) x [OMEGA] such that [Q.sub.4R] ([[xi].sub.'0], [t'.sub.0]) [subset] [Q.sub.T]; the result is obtained.
The proof is complete by using suitable parabolic cylinder [Q.sub.R/2]([[xi].sub.'0], [t'.sub.0]) to cover ([epsilon], T) x [OMEGA] such that [Q.sub.4R]([[xi]'.sub.0], [t'.sub.0]) [subset] [Q.sub.T].
(43) are pertained to the type of ordinary differential equations for the parabolic cylinder functions.
They are expressible via products of the parabolic cylinder functions (47).
Besides, all the solutions expressible via the parabolic cylinder functions satisfy the conservation of energy law (56), as well, for arbitrary [alpha] = -(2n + 1)/2, n [greater than or equal to] 0.
Concentrated Solar Power technologies, on the other hand, and in particular tower and parabolic cylinder
mirror power stations, have been designed exclusively for larger plants since their first commercial use in United States in the 1980s.
A parabolic cylinder
is the simplest parabolic tube.
In 1912 Shuman built 37-45 kW pumping plant in Egypt where he used long parabolic cylinders
to focus sunlight onto a long absorbing tube .