We consider on X × R a differential equation of the type LXu = P ∂t)u, where P ∂t) is a second order differential operator in tϵ R. Using the Radon transform on X we relate Huygens' principle for the solutions u to this equation, to the corresponding question for the solutions v to the equation LAv = (P ∂t) + R v on a maximal flat subspace A, where R is a certain explicit constant.
holds, where λ is a certain positive constant.
Nonetheless, it is known that a significant subclass of \ \textbf{NP}\ -complete problems possess polynomial time approximation algorithms -- i.e. algorithms which are guaranteed to find a solution which is within a certain constant factor of optimality.
We then insert k c, N − 1 into k N, p obtaining: k N, p = 1 k 0, p ∑ c M cp 1 k c, 0 ∑ p ′ M cp ′ k N − 2, p ′, k N, p = ∑ p ′ k N − 2, p ′ ∑ c M cp M cp ′ k 0, p k c, 0. and rewrite this as: k N, p = ∑ p ′ M ˜ p p ′ k N − 2, p ′, where: M ˜ p p ′ = ∑ c M cp M cp ′ k 0, p k c, 0. We note in the last formulation k N, p is satisfied when k N, p = k N − 2, p and this is equal to a certain constant a.
Kwong and Wong [7] showed that BVP (1.1) with (1.4) has at least one positive solution if (bar{f}_{0}< L_{theta}) and (underline{f}_{infty}>L_{theta}), where (L_{theta}) is a certain but not specified constant related to the associated linear operator.
When the speed of the moving endpoint is less than a certain constant which is less than the characteristic speed, we obtain exact controllability for this equation.
For constant angular velocity, Miyamoto [2] have found that there exists an equilibrium solution if the angular velocity is less than a certain constant and there is no equilibrium for large velocity.
Skid resistance of a road is typically measured with a locked wheel trailer procedure where the trailer is pulled at a certain constant speed while the braking system of the test tire is actuated to lock the tire on a wet road surface.
