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The boundary conditions and the conditions of continuity are satisfied directly by using a Fourier expansion collocation method which has been given by Nagaya.
The target pressure waveform is divided into an early systolic upstroke, determined by the water hammer equation, and a diastolic decay equal to that in the peripheral arterial tree, interposed by a late systolic portion described by a second-order polynomial constrained by conditions of continuity and conservation of mean arterial pressure.
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The condition of continuity between the inner annular support and the plate is satisfied exactly.
The close-form frequency function that yields the eigenvalues of the plate is extracted by considering the condition of continuity in displacement and slope between the regions and by considering the simply supported boundary condition of the plate.
We employed an analysis method in which the impact force assumes an exponential function for the basic equation of the one-dimensional elastic vibration corresponding to the longitudinal vibration of the bar and the lateral vibration of the beam, and in which the force satisfies the condition of continuity of the displacement.
However, such change is not easy to occur because stress should satisfy the condition of continuity.
It is possible to remove the heavy condition of continuity of the self-mapping f in Theorem 2.5.
Remark 2.3 (i) By considering the condition of continuity of F in Corollary 2.4, we obtain Theorem 3 in [4].
for all, controlled by a product of different powers of norms, where and real numbers, and retained the condition of continuity of in for each fixed.
The condition of continuity given by (15) ensures the continuity of first order derivatives of the spline (s x,tau)) at interior points.
In what follows, we replace the condition of continuity of the operator by the condition of α-regularity of the space.
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