Saleh A. Al-Suhaibani and Mohammed F. Wahby
In Saudi Arabia, the cultivated area was doubled four times in the last 12 years. That was mainly attributed by the introduction of farm machines on a large scale. As a result, the total amount of energy input to agriculture was increased.
The objective of this study was to determine the amount of energy needed for each field operation of wheat production in the central region in the Kingdom. A survey of 49 wheat farms was made. The collected information were analyzed to determine the amount of energy needed for field operation, the total amount of energy per unit area, and the energy index (output energy from wheat to fuel energy).
The results of this study showed that the amount of energy per unit weight of produced wheat was in the acceptable level, also the energy index was high.
The amount of energy per unit area was higher than that of other studies by more than double. That was mainly due to over tilling the soil by the chisel and the moldboard plows at the same season, and also because of the mismatching and improper operation of farm machines and tractors. It is recommended that further study of tillage systems, proper selection of farm machines and tractors, and the suitable training of farm operators would be needed for the wheat production farms.
Boubaker- Khaled Sadallah
We continue our study of the heat equation with Cauchy- Dirichlet conditions in the non convex polygonal domain Ω, described by the time variable t and one space variable x.
The second member f of the heat equation is in L²(Ω), the space of functions the squares of which are integrable in Ω. We look for the solution u in a non symmetric Sobolev space H^(r,2r) (Ω) defined as an interpolation space between H^(1,2) (Ω) and L²(Ω) where H^(1,2) (Ω) = {u ϵ L² (Ω): u'₁, u'ₓ, u"ₓ, ϵ L² (Ω)}.
It is known (Sadallah 1976, 1983) that u is smooth (i.e. belongs to H^(1,2) (Ω)) when the domain Ω is convex, but in general, this does not hold in a non convex polygon. The First Part of this work (Sadallah 1989) was devoted to the special case in which Ω is a non convex domain and is the product of two rectangles. It had been proved there, that for all f in L²(Ω) there exist two functions v, w, such that u= v+w where v ϵ H^(1,2) (Ω) and w not an element of H^(1,2) (Ω), Our main result was:
The singularity w ϵ H^(r,2r) (Ω) iff r <3/4.
In this second part, we prove that the same result remains unchanged in the general case (i.e. when Ω is not necessary product of two rectangles).
The proof uses the First Part of this work and some other results of the author (Sadallah 1976) as well as the interpolation theory.