Search results for "infinity"

Asymptotic paths for subsolutions of quasilinear elliptic equations

1988

Letu be an entire lower semicontinuous subsolution to the quasilinear elliptic equation divA(x,∇u)=0 in ℝn. It is shown that ifu is not bounded above, then there exists a path going to infinity along whichu tends to infinity. The result extends works of Talpur, Fuglede, and others. Growth aspects of subsolutions are also studied.

Cosmic censorship conjecture in some matching spherical collapsing metrics

2017

A physically plausible Lema{\^{\i}}tre-Tolman-Bondi collapse in the marginally bound case is considered. By "physically plausible" we mean that the corresponding metric is ${\cal C}^1$ matched at the collapsing star surface and further that its {\em intrinsic} energy is, as due, stationary and finite. It is proved for this Lema{\^{\i}}tre-Tolman-Bondi collapse, for some parameter values, that its intrinsic central singularity is globally naked, thus violating the cosmic censorship conjecture with, for each direction, one photon, or perhaps a pencil of photons, leaving the singularity and reaching the null infinity. Our result is discussed in relation to some other cases in the current liter…

On the uniqueness of the space-time energy in General Relativity. The illuminating case of the Schwarzschild metric

2013

The case of asymptotic Minkowskian space-times is considered. A special class of asymptotic rectilinear coordinates at the spatial infinity, related to a specific system of free falling observers, is chosen. This choice is applied in particular to the Schwarzschild metric, obtaining a vanishing energy for this space-time. This result is compared with the result of some known theorems on the uniqueness of the energy of any asymptotic Minkowskian space, showing that there is no contradiction between both results, the differences becoming from the use of coordinates with different operational meanings. The suitability of Gauss coordinates when defining an {\em intrinsic} energy is considered a…

Pseudoscalar Transition Form Factors from Rational Approximants

2014

The $\pi^0$, $\eta$, and $\eta^\prime$ transition form factors in the space-like region are analyzed at low and intermediate energies in a model-independent way through the use of rational approximants. Slope and curvature parameters as well as their values at infinity are extracted from experimental data. These results are suited for constraining hadronic models such as the ones used for the hadronic light-by-light scattering piece of the anomalous magnetic moment of the muon, and for the mixing parameters of the $\eta - \eta^\prime$ system.

Bifurcations of Links of Periodic Orbits in Mathieu Systems

2000

We prove that orbits escape from infinity, and that therefore the sphere S can be considered as its phase space. If the parameter δ is large enough, the system is non-singular MorseSmale, and its periodic orbits define a Hopf link. As δ decreases, the system undergoes some bifurcations that we describe geometrically. We relate the bifurcation orbits to periodic orbits continued from the linear Mathieu equation.

Waveguides. Radiation Principle. Scattering Matrices

2021

Chapter 2 exposes a mathematical model of a waveguide with several cylindrical ends going to infinity, basic notions and mathematical results (with complete proofs) needed in successive chapters: waves, continuous spectrum eigenfunctions, intrinsic radiation principle, and scattering matrices.

Lau rings: In-register incoherent superposition of radial self-images

1989

Abstract We describe an optical method for obtaining in-register, incoherent superposition of self-images, with radial symmetry. That is, the Lau effect is implemented, either at infinity or at finite distances, in the form of bright and dark rings of high visibility. This is applied for visualizing radially phase structures, with good-signal-to-noise ratio.

A New Set of Quartic Trivariate Polynomial Equations for Stratified Camera Self-calibration under Zero-Skew and Constant Parameters Assumptions

2012

This paper deals with the problem of self-calibrating a moving camera with constant parameters. We propose a new set of quartic trivariate polynomial equations in the unknown coordinates of the plane at infinity derived under the no-skew assumption. Our new equations allow to further enforce the constancy of the principal point across all images while retrieving the plane at infinity. Six such polynomials, four of which are independent, are obtained for each triplet of images. The proposed equations can be solved along with the so-called modulus constraints and allow to improve the performance of existing methods.

C0-semigroups norm continuous at infinity

1996

Harnack's inequality for p-harmonic functions via stochastic games

2013

We give a proof of asymptotic Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Lipsc...