Search results for " Mathematica"

Volume growth and parabolicity

2001

Analytische Geometrie nach Prof. Dr. F. Schur

1892

Mappings of finite distortion : size of the branch set

2018

Abstract We study the branch set of a mapping between subsets of ℝ n {\mathbb{R}^{n}} , i.e., the set where a given mapping is not defining a local homeomorphism. We construct several sharp examples showing that the branch set or its image can have positive measure.

TANGENTIAL DEFORMATIONS ON FIBRED POISSON MANIFOLDS

2005

In a recent article, Cattaneo, Felder and Tomassini explained how the notion of formality can be used to construct flat Fedosov connections on formal vector bundles on a Poisson manifold $M$ and thus a star product on $M$ through the original Fedosov method for symplectic manifolds. In this paper, we suppose that $M$ is a fibre bundle manifold equipped with a Poisson tensor tangential to the fibers. We show that in this case the construction of Cattaneo-Felder- Tomassini gives tangential (to the fibers) star products.

Isoperimetric inequality via Lipschitz regularity of Cheeger-harmonic functions

2014

Abstract Let ( X , d , μ ) be a complete, locally doubling metric measure space that supports a local weak L 2 -Poincare inequality. We show that optimal gradient estimates for Cheeger-harmonic functions imply local isoperimetric inequalities.

A note on topological dimension, Hausdorff measure, and rectifiability

2020

The purpose of this note is to record a consequence, for general metric spaces, of a recent result of David Bate. We prove the following fact: Let $X$ be a compact metric space of topological dimension $n$. Suppose that the $n$-dimensional Hausdorff measure of $X$, $\mathcal H^n(X)$, is finite. Suppose further that the lower n-density of the measure $\mathcal H^n$ is positive, $\mathcal H^n$-almost everywhere in $X$. Then $X$ contains an $n$-rectifiable subset of positive $\mathcal H^n$-measure. Moreover, the assumption on the lower density is unnecessary if one uses recently announced results of Cs\"ornyei-Jones.

The Calderón problem for the fractional Schrödinger equation

2020

We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where the measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension $\geq 2$ and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calder\'on problem.

Automorphism Groups of Certain Rational Hypersurfaces in Complex Four-Space

2014

The Russell cubic is a smooth contractible affine complex threefold which is not isomorphic to affine three-space. In previous articles, we discussed the structure of the automorphism group of this variety. Here we review some consequences of this structure and generalize some results to other hypersurfaces which arise as deformations of Koras–Russell threefolds.

Microlensing Discovery of a Population of Very Tight, Very Low Mass Binary Brown Dwarfs

2013

Although many models have been proposed, the physical mechanisms responsible for the formation of low-mass brown dwarfs (BDs) are poorly understood. The multiplicity properties and minimum mass of the BD mass function provide critical empirical diagnostics of these mechanisms. We present the discovery via gravitational microlensing of two very low mass, very tight binary systems. These binaries have directly and precisely measured total system masses of 0.025 M [SUB]⊙[/SUB] and 0.034 M [SUB]⊙[/SUB], and projected separations of 0.31 AU and 0.19 AU, making them the lowest-mass and tightest field BD binaries known. The discovery of a population of such binaries indicates that BD binaries can …

Differential branching fractions and isospin asymmetries of B -> K ((*)) μ(+) μ(-) decays

2014

The isospin asymmetries of $B \to K\mu^+\mu^-$ and $B \to K^{*}\mu^+\mu^-$ decays and the partial branching fractions of the $B^0 \to K^0\mu^+\mu^-$, $B^+ \to K^+\mu^+\mu^-$ and $B^+ \to K^{*+}\mu^+\mu^-$ decays are measured as functions of the dimuon mass squared, $q^2$. The data used correspond to an integrated luminosity of 3$~$fb$^{-1}$ from proton-proton collisions collected with the LHCb detector at centre-of-mass energies of 7$\,$TeV and 8$\,$TeV in 2011 and 2012, respectively. The isospin asymmetries are both consistent with the Standard Model expectations. The three measured branching fractions, while individually consistent, all favour lower values than their respective Standard M…