The closed-form expressions correctly reduce to simpler forms for film-substrate systems without residual stresses, and further include the special case of spontaneous delamination under the presence of a critical residual stress only.
Furthermore, our results can reduce to simple closed-form under reasonable special case for modern urban cellular networks.
For this case, the expressions of coverage probability reduce to simple closed-form, which can provide clear insight into the performance analysis of each user.
The solution is shown to reduce to the simpler limiting form for a single resistance system under conditions such that either the micropore or macropore resistance is dominant.
The course uses examples from biology as an integrating theme, principles from physics and mathematics to reduce complex problems to simpler forms, and computer simulation to allow students to develop their intuition about the behavior of the dynamical systems that control the physical and biological universe.
His progression to more simplified forms can be seen in the portrait heads Baudelaire (1911) and Maggy (1911), which were virtually reduced to simple geometric shapes.
But his art can't be reduced to simple pathology.
Obviously, Jeffrey conditioning reduces to simple conditioning when q = 1.
In the case of constant population size, g = 1 and τi approaches ∞, and thus the model reduces to a simpler form, denoted as L0.
The equations of motion for these moments can be straightforwardly obtained from the master equation to this order, leading to a set of coupled but solvable ordinary differential equations: (23) where, (25) Note that the matrices and vectors in the above equations have been reduced to a simpler form by the application of a few row operations.
The interactions between care facilities, educational facilities, and other professionals or structures are most often absent or reduced to their simplest forms.
