The set of conditions for the coefficients of these LC-RK-schemes could be derived explicitly for arbitrary order N. From an efficiency viewpoint the LC-RK 3rd order methods in combination with upwind 3rd or 5th order or the LC-RK 4th order scheme with 4th order centered difference advection are a good choice.
Moreover, some exact rogue wave solutions are derived explicitly.
For some special cases, surface wave velocities are derived explicitly.
Set to the last movement of Schubert's Ninth Symphony and arrayed in costumes that alluded to ballet tradition with their stiff, platelike tutus, this is choreography derived explicitly from classroom steps.
Silicate speciation equilibria are described by relationships derived explicitly from high-resolution 29Si NMR data, and an autocatalytic polymerisation step provides good agreement with the observed kinetics of geopolymerisation.
The BET-specific surface areas were not quoted explicitly but could be derived from the data in the respective figures (50 and 6.5 m/g, respectively; specifications presumably supplied by the particle manufacturer).
The HBSAC working group requested that the number of Hospital Groups (K) be derived from the data itself, not explicitly predetermined prior to the clustering process nor modified after clustering is completed.
The y-Axis is not stored explicitly since it can be derived from the cross product of ( overrightarrow{x}times overrightarrow{z} ).
Because the original PREVASC clinical studies did not explicitly study the effects of unifaceted prevention, this had to be derived from the clinical data.
The trajectory of these solutions is defined explicitly by x = − l 2 t + ϕ 1 + r k 2, which can be derived from ζ + ϕ 1 + r = 0.
Because the energy model is derived from explicitly mechanistic (i.e., energetic) first principles, it is sensitive to many potential features of DNA sequence that allow or inhibit local nucleosome formation.
