This major assumption is made primarily to facilitate exact analytical solutions, and it is discussed at length in the Introduction, both in the context of real materials which exhibit large angles of internal friction, and in the context of using the solutions derived here as the leading term in a regular perturbation solution involving powers of 1−sinφ.
The display orientation-dependent stock per facing (g_{ib_i}) is derived here as follows: As the shelf depth does not allow case packs to be put behind each other regardless of a crosswise or lengthwise positioning, the stock per facing is given by the quantity per carton.
An important conclusion derived here is as follows: when M5 stands on an actin filament and faces the advancing direction, the motor domains do not grasp the top surface of the actin filament but grasp the right flank of the filament, as shown in Figure 8b.
The lunar topography models derived here have an improved accuracy.
The pattern derived here provides inference for (a) fire acting as an increasing aggregation & spatial autocorrelation force, (b) tree survival under fire regimes is potentially facilitated by forming patches of trees and (c) scale-dependent facilitation and competition coexisting within the same ecosystem with finer scale facilitation and coarser scale competition.
The improved projection method removes some of the numerical issues with the previously derived (here referred to as traditional) projection method.
The solutions derived here can serve as benchmark solutions for certain classes of anisotropic micropolar medium, and also can be used as an approximate solution for a micropolar medium with general material properties without any constraint conditions.
The analytical solution as derived here helps understanding the complex collision process and can be applied for the evaluation of integration methods or in the context of an event-driven discrete element method.
The special thermodynamic properties of the binding of flexible molecules, as derived here, show that the probability of the bioactive conformations in solution can determine the likelihood of binding.
In particular, the normal form as derived here reveals the presence of phase shift symmetry and is seen to simplify the identification of degenerate Hopf bifurcation occurring in the system.
