His intervention extended to the issues and interests of this problem.
The physical engineering quantities of interest in this problem are the skin friction coefficients in the x - and z -directions and the local Nusselt number, Nu x which are defined as follows: C f x = − 2 μ ( ∂ u / ∂ y ) y = 0 ρ U w 2 = − 2 Re x − 1 / 2 f ″ ( 0 ), C f z = 2 μ ( ∂ w / ∂ y ) y = 0 ρ U w 2 = 2 Re x − 1 / 2 g ′ ( 0 ), Nu x = x q w κ ( T w − T ∞ ), (15).
The physical quantities of interest in this problem are the local skin-friction coefficient C f, Nusselt number Nu x and the local Sherwood number Sh x, which are defined as C f x = τ w y = 0 ρ U 0 2 e 2 x l, N u x = - x T w - T ∞ ∂ T ∂ y y = 0, S h x = - x C w - C ∞ ∂ C ∂ y y = 0, 2 Re C f x = f ″ 0, N u x / 2 R e x = - x 2 l θ ′ 0, S h x / 2 R e x = - x 2 l g ′ ( 0 ), (11).
The main driver of the interest towards this problem is represented by the series of international benchmarking initiatives organized in the last four years that allowed dozens of research groups to propose innovative methodologies for HEp-2 cells' staining pattern classification.
The estimated receiver positions are also of much interest in this problem and are not simply a by-product in improving pairwise distance estimates.
The main interest of this kind of problems is the presence of the singular potential (frac{1}{|x|^{s}}), (0leq sleq p), (frac{1}{|x|^{s}}) relating to the Hardy inequality.
Besides being of considerable theoretical interest, this problem has applications in computer vision and graphics---for instance, in determining lighting and bidirectional reflectance distribution functions (BRDFs), in rendering environment maps, and in image-based rendering.
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