As an analog model of general relativity, optics on some two-dimensional (2D) curved surfaces has received increasing attention in the past decade. Here, light Huygens–Fresnel principle, we propose a theoretical frame to study propagation along arbitrary geodesics any 2D surfaces. This theory not only enables us solve enigma “infinite intensity” that existed previously at artificial singulariti...

Abstract Recent applications of digital photogrammetry in forestry have highlighted its utility as a viable mensuration technique. However, tropical regions little research has been done on the accuracy this approach for stem volume calculation. In study, performance Structure from Motion estimating individual tree relation to traditional approaches was evaluated. We selected 30 trees five sava...

We study first-passage properties for a particle that diffuses either inside or outside of generalized paraboloids, defined by y = a(x1 + · · ·+ xd−1) where p > 1, with absorbing boundaries. When the particle is inside the paraboloid, the survival probability S(t) generically decays as a stretched exponential, lnS ∼ −t(p−1)/(p+1), independent of the spatial dimension. For a particle outside the...

For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear adjoint restriction estimates. As corollaries, we first extend the ranges of exponents for the classical linear or bilinear adjoint restriction conjectures for such functions and verify the linear adjoint restriction conjecture for the paraboloid. We also interpret the r...