One can define a map to singular homology by sending a critical point to the singular chain associated to the unstable manifold associated to that point; inversely, a singular chain is sent to the limiting critical points reached by flowing the chain using the gradient vector field.
22.
This space is spanned by two vectors, the difference of energy gradient vectors of the two intersecting electronic states ( the " g vector " ), and the non-adiabatic coupling vector between these two states ( the " h vector " ).
23.
Given that " S " is convex, it is minimized when its gradient vector is zero ( This follows by definition : if the gradient vector is not zero, there is a direction in which we can move to minimize it further-see maxima and minima . ) The elements of the gradient vector are the partial derivatives of " S " with respect to the parameters:
24.
Given that " S " is convex, it is minimized when its gradient vector is zero ( This follows by definition : if the gradient vector is not zero, there is a direction in which we can move to minimize it further-see maxima and minima . ) The elements of the gradient vector are the partial derivatives of " S " with respect to the parameters:
25.
Given that " S " is convex, it is minimized when its gradient vector is zero ( This follows by definition : if the gradient vector is not zero, there is a direction in which we can move to minimize it further-see maxima and minima . ) The elements of the gradient vector are the partial derivatives of " S " with respect to the parameters:
26.
The economical cost of the " Badr-B " is not publicly known but it is estimated to be more costly than the first satellite, " Al-13 with a total mass of 70 kg . " Badr-B " was launched in a sun-synchronous orbit of 1050 km with an earth orbital period of 106 minutes . " Badr-B " is a cube with side dimensions of 510 mm x 510 mm x 465 mm and a gravity gradient vector system to stabilize the satellite to its mission control centre.
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