We analyze surface patches with a corner that is rounded in the sense partial derivatives at point are antiparallel. Sufficient conditions for $G^1$ smoothness given, which, up to certain degenerate case, also necessary. Further, we investigate curvature integrability and present examples

We prove the absence of non-scattering energies for potentials in the plane having a corner of angle smaller than π. This extends the earlier result of Bl̊asten, Päivärinta and Sylvester who considered rectangular corners. In three dimensions, we prove a similar result for any potential with a circular conic corner whose opening angle is outside a countable subset of (0, π).

This paper presents an effective technique to monitor and predict the open circuit voltage (OCV) for lead-acid battery cells. The underlying principal of the technique described in this paper employs one simple equation to predict the equilibrated cell voltage after a small rest period. The technique was tested and analyzed using results obtained from experiments conducted at the Yuasa Battery ...

In Exact Real Arithmetic, real numbers are represented as potentially infinite streams of information units, called digits. In this paper, we work in the framework of Linear Fractional Transformations (LFT’s, also known as Möbius transformations) that provide an elegant approach to real number arithmetic (Gosper 1972, Vuillemin 1990, Nielsen and Kornerup 1995, Potts and Edalat 1996, Edalat and ...

When corners are embedded in a luminance gradient, their perceived salience varies linearly with corner angle (Troncoso et al., 2005). Here we hypothesize that this relationship may hold true for all corners, not just corner gradients. To test this hypothesis, we developed a novel variant of the flicker-augmented contrast illusion (Anstis and Ho, 1998) that employs solid (non-gradient) corners ...

An approach for estimating 3D head orientation in a monocular image sequence is proposed. The approach employs recently developed image-based parameterized tracking for face and face features to locate the area in which a sub-pixel parameter-ized shape estimation of the eye's boundary is performed. This involves tracking of ve points (four at the eye corners and the fth is the tip of the nose)....

We study the asymptotic behavior at small diffusivity of the solutions, u, to a convection-diffusion equation in a rectangular domain Ω. The diffusive equation is supplemented with a Dirichlet boundary condition, which is smooth along the edges and continuous at the corners. To resolve the discrepancy, on ∂Ω, between uε and the corresponding limit solution, u, we propose asymptotic expansions o...