This method consists of the construction of a basis of solutions for different values of this parameter.
It is easy to check that x0 t), x1 t), x2 t), and x3 t) form a basis of solutions of L[x] = 0.
Note that our basis of solutions for the velocity are divergence free, and thus the pressure disappears in this formulation.
where m = - k 2. It is easy to check that x0 t), x1 t), x2 t), and x3 t) form a basis of solutions of L[x] = 0.
Equation (2.1) is disconjugate on a compact interval if and only if there exists a basis of solutions such that (2.2). on.
By the discussion in the proof of Theorem 3.2, it follows that these four solutions are linearly independent on ℐ and so they form a basis of solutions for (3.2).
Since λ i ≠ λ j with i ≠ j, it can easily be shown that these four solutions, { ϕ j, ψ j } j = 1 2, of (3.2) are linearly independent on ℐ and so forms a basis of solutions for (3.2).
Then, a survey on the technology available to design these types of PSs is given, together with the most suitable circuit topologies and guidelines for the design, on the basis of solutions adopted in existing experiments.
Applying the similar method to prove case 1 in Theorem 2.4, we conclude that x 0 ( t ) = e - 3 π 2 t cos π 2 t, x 1 ( t ) = e - 3 π 2 t sin π 2 t, x 2 ( t ) = e - 3 π 2 t cos π 2 t, x 3 ( t ) = e - 3 π 2 t sin π 2 t. form a basis of solutions of L[x] = 0.
