A structured light system provides a dense sampling of 3D coordinates from visible surfaces in a scene. This paper compares several methods for determining the principle frame, Gaussian curvature, and mean curvature at each visible surface point from this data. The principle frame, etc, parameterize a model which completely characterizes the local surface geometry. Given the local surface model...

Recently the area of tropical geometry has introduced the concept of the tropical elliptic group law associated with a tropical elliptic curve. This gives rise to a notion of the tropical QRT mapping. We compute the explicit tropically birational expressions that define the tropical QRTmapping for some arbitrary set of parameters. We consider this a new integrable ultradiscrete system. This als...

A structured light system provides a dense sampling of 3D coordinates from visible surfaces in a scene. This paper compares several methods for determining the principle frame, Gaussian curvature, and mean curvature at each visible surface point from this data. The principle frame, etc, parameterize a model which completely characterizes the local surface geometry. Given the local surface model...

Let (R;G) be a pair consisting of an elliptic root system R with a marking G. Assume that the attached elliptic Dynkin diagram (R;G) is simply-laced (see Sect. 2). We associate three Lie algebras, explained in 1), 2) and 3) below, to the elliptic root system, and show that all three are isomorphic. The isomorphism class is called the elliptic algebra. 1) The rst one is the subalgebra e g(R) gen...

Two distinct redistribution grids - adaptation techniques, spring analogy and elliptic grid generator are applied to two-dimensional steady, inviscid, shocked flows, and the ability of each technique is examined and compared. Euler equations are solved base on Roe's Reimann solver approach to simulate supersonic flow around a sphere, transonic flow about an airfoil and supersonic flow in a symm...

We start from an interpretation of the BC2-symmetric “Type I” (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation, and give an extension to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding elliptic beta integral and transformation formula in a new way, ...

the paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. attention goes to the number of limit cycles produced by the period annulus under perturbations. by using the appropriate p...

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

In axiomatizing their study of Frobenius distributions [5], Lang and Trotter introduce the notion of an adelic Galois representation of elliptic type, and they ask in passing whether every such representation arises from an elliptic curve (see pp. 5 and 19 of [5]). Formulated in the language of `-adic representations [7], their question is as follows. Put G = Gal(Q/Q), let p denote a prime, and...