Search results for "Affine"

Covering and differentiation

1995

Equidistribution and Counting of Rational Points in Completed Function Fields

2019

Let K be a (global) function field over Fq of genus g, let v be a (normalised discrete) valuation of K, let Kv be the associated completion of K, and let Rv be the affine function ring associated with v.

On the Efficiency of Affine Invariant Multivariate Rank Tests

1998

AbstractIn this paper the asymptotic Pitman efficiencies of the affine invariant multivariate analogues of the rank tests based on the generalized median of Oja are considered. Formulae for asymptotic relative efficiencies are found and, under multivariate normal and multivariatetdistributions, relative efficiencies with respect to Hotelling'sT2test are calculated.

Design, Control, and Analysis of Nonlinear Circuits with Tunnel Diode with Piecewise Affine Dynamics

2019

Statistical geometric affinity in human brain electric activity

2007

10 pages, 9 figures.-- PACS nrs.: 87.19.La; 05.45.Tp.-- ISI Article Identifier: 000246890100105

Uncalibrated Reconstruction: An Adaptation to Structured Light Vision

2003

Abstract Euclidean reconstruction from two uncalibrated stereoscopic views is achievable from the knowledge of geometrical constraints about the environment. Unfortunately, these constraints may be quite difficult to obtain. In this paper, we propose an approach based on structured lighting, which has the advantage of providing geometrical constraints independent of the scene geometry. Moreover, the use of structured light provides a unique solution to the tricky correspondence problem present in stereovision. The projection matrices are first computed by using a canonical representation, and a projective reconstruction is performed. Then, several constraints are generated from the image an…

Characterization of ellipsoids through an overdetermined boundary value problem of Monge–Ampère type

2014

Abstract The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.

Singular systems in dimension 3: Cuspidal case and tangent elliptic flat case

2007

We study two singular systems in R3. The first one is affine in control and we achieve weighted blowings-up to prove that singular trajectories exist and that they are not locally time optimal. The second one is linear in control. The characteristic vector field in sub-Riemannian geometry is generically singular at isolated points in dimension 3. We define a case with symmetries, which we call flat, and we parametrize the sub-Riemannian sphere. This sphere is subanalytic.

Shape optimization for monge-ampére equations via domain derivative

2011

In this note we prove that, if $\Omega$ is a smooth, strictly convex, open set in $R^n$ $(n \ge 2)$ with given measure, the $L^1$ norm of the convex solution to the Dirichlet problem $\det D^2 u=1$ in $\Omega$, $u=0$ on $\partial\Omega$, is minimum whenever $\Omega$ is an ellipsoid.

New isoperimetric estimates for solutions to Monge - Ampère equations

2009

Abstract We prove some sharp estimates for solutions to Dirichlet problems relative to Monge–Ampere equations. Among them we show that the eigenvalue of the Dirichlet problem, when computed on convex domains with fixed measure, is maximal on ellipsoids. This result falls in the class of affine isoperimetric inequalities and shows that the eigenvalue of the Monge–Ampere operator behaves just the contrary of the first eigenvalue of the Laplace operator.