Search results for "Geometry"

Homeomorphisms of finite distortion: discrete length of radial images

2008

AbstractWe study homeomorphisms of finite exponentially integrable distortion of the unit ball Bn onto a domain Ω of finite volume. We show that under such a mapping the images of almost all radii (in terms of a gauge dimension) have finite discrete length. We also show that our dimension estimate is essentially sharp.

Rescaling principle for isolated essential singularities of quasiregular mappings

2012

We establish a rescaling theorem for isolated essential singularities of quasiregular mappings. As a consequence we show that the class of closed manifolds receiving a quasiregular mapping from a punctured unit ball with an essential singularity at the origin is exactly the class of closed quasiregularly elliptic manifolds, that is, closed manifolds receiving a non-constant quasiregular mapping from a Euclidean space.

On quasi-denting points, denting faces and the geometry of the unit ball ofd(w, 1)

1994

Spectral rigidity and invariant distributions on Anosov surfaces

2014

This article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity results are of independent interest and imply the existence of many geometric invariant distributions on the unit sphere bundle. In particular, we show that on any Anosov surface $(M,g)$, given a smooth function $f$ on $M$ there is a distribution in the Sobolev space $H^{-1}(SM)$ that is invariant under the geodesic flow and whose projection to $M$ i…

Strongly extreme points and approximation properties

2017

We show that if $x$ is a strongly extreme point of a bounded closed convex subset of a Banach space and the identity has a geometrically and topologically good enough local approximation at $x$, then $x$ is already a denting point. It turns out that such an approximation of the identity exists at any strongly extreme point of the unit ball of a Banach space with the unconditional compact approximation property. We also prove that every Banach space with a Schauder basis can be equivalently renormed to satisfy the sufficient conditions mentioned. In contrast to the above results we also construct a non-symmetric norm on $c_0$ for which all points on the unit sphere are strongly extreme, but …

Geometric mean and triangles inscribed in a semicircle in Banach spaces

2008

AbstractWe consider the triangles with vertices x, −x and y where x,y are points on the unit sphere of a normed space. Using the geometric means of the variable lengths of the sides of these triangles, we define two geometric constants for Banach spaces. These constants are closely related to the modulus of convexity of the space under consideration, and they seem to represent a useful tool to estimate the exact values of the James and Jordan–von Neumann constants of some Banach spaces.

Solutions to the 1-harmonic flow with values into a hyper-octant of the N-sphere

2013

Abstract We announce existence results for the 1-harmonic flow from a domain of R m into the first hyper-octant of the N -dimensional unit sphere, under homogeneous Neumann boundary conditions. The arguments rely on a notion of “geodesic representative” of a BV-vector field on its jump set.

Intruder Pattern Identification

2008

This paper considers the problem of intrusion detection in information systems as a classification problem. In particular the case of masquerader is treated. This kind of intrusion is one of the more difficult to discover because it may attack already open user sessions. Moreover, this problem is complex because of the large variability of user models and the lack of available data for the learning purpose. Here, flexible and robust similarity measures, suitable also for non-numeric data, are defined, they will be incorporated on a one-class training K N N and compared with several classification methods proposed in the literature using the Masquerading User Data set (www.schonlau.net) repr…

Effects of undergrowth removal and edge proximity on ground beetles and vascular plants in urban boreal forests

2019

A new tool for evaluating and/or selecting analytical methods: Summarizing the information in a hexagon

2019

Abstract A quantitative evaluation tool is proposed, which aims to assess optimal selection or/and testing of analytical methods. Objective criteria related to analytical performance, sustainability, environmental impact and economic cost are evaluated through the definition of penalty points divided into five different blocks, namely, figures of merit, toxicity and safety, residues, carbon footprint and economic cost. For each block, the overall qualification is scaled from 0 to 4 and it is depicted on a regular hexagonal pictogram that allows a user friendly comparison of analytical procedures. The present evaluation tool aims to be a guideline for evaluating and/or selecting analytical p…