The phrase "analytical description is" is correct and usable in written English.
It can be used when discussing the nature or characteristics of an analytical description in various contexts, such as academic writing or technical documentation.
Example: "The analytical description is essential for understanding the underlying patterns in the data."
Alternatives: "analytical account is" or "analytical explanation is".
By using a Wiener-Hopf approach, an analytical description is derived of the scattered field of a harmonic sound wave coming out of an open ended annular duct (a semi-infinite cylinder inside of which, coaxially, is a doubly infinite hub), submerged in a subsonic, coaxial, uniform mean flow.
For the sake of generality, we consider an AR process of order R, whose analytical description is given by mathbf{H}_{t} = sum_{r=1}^{mathit{R}} a_{r} mathbf{H}_{t-r} + mathbf{V}_{t}, (5).
Either the utilization of Minimum Mean Squared Error (MMSE) equalizers is not supported (as recommended for MIMO HSDPA) [17, 25], multiple-stream operation is not covered [13], the mandatory precoding (e.g., for D-TxAA) is missing [24], or no full analytical description is derived to be available for system-level evaluations [12, 13].
Fig 1 shows the anatomical locations of the ten ROIs (details and a more analytical description is given in the Supporting file S2).
This analytical description is exact in the case of infinitely "soft" learning and infinite number of cells.
Once the mapping with the analytical description is performed, the coarse-grained particle wall interaction is fully consistent with the particle particle coarse-grained description.
Analytical description are presented for non-linear heterogeneous conversion of a porous solid particle reacting with a surrounding gas.
Reasonably good agreement with respect to the mean effectiveness factor is produced when the analytical/semi-analytical description is applied to the respective pellet size distributions.
As such cards are commonly installed on most desktop computers, we expect that this will prove useful in many cases where simple analytical descriptions are not available or appropriate, e.g. in complex geometries or where short gradient pulse approximations do not hold, or for the analysis of diffusion-weighted MRI in complex tissues such as the lungs and brain.
Based on the energy balance, an analytical model with improved boundary layer description is proposed to predict maximum spreading of droplet following impact on porous surfaces when the effect of heat transfer is negligible.
The method is applied to the one-dimensional model of a heat source with time delay placed in a low-Mach-number compressible flow, for which an analytical description can be derived from first principles.
