Search results for "vector [form factor]"

Type I vacuum solutions with aligned Papapetrou fields: an intrinsic characterization

2003

We show that Petrov type I vacuum solutions admitting a Killing vector whose Papapetrou field is aligned with a principal bivector of the Weyl tensor are the Kasner and Taub metrics, their counterpart with timelike orbits and their associated windmill-like solutions, as well as the Petrov homogeneous vacuum solution. We recover all these metrics by using an integration method based on an invariant classification which allows us to characterize every solution. In this way we obtain an intrinsic and explicit algorithm to identify them.

Covariant determination of the Weyl tensor geometry

2001

We give a covariant and deductive algorithm to determine, for every Petrov type, the geometric elements associated with the Weyl tensor: principal and other characteristic 2-forms, Debever null directions and canonical frames. We show the usefulness of these results by applying them in giving the explicit characterization of two families of metrics: static type I spacetimes and type III metrics with a hypersurface-orthogonal Killing vector. PACS numbers: 0240M, 0420C

Non-Linear Relativistic Evolution of Cosmological Perturbations in Irrotational Dust

2008

Confronting the impact parameter dependent JIMWLK evolution with HERA data

2018

The small-$x$ evolution of protons is determined from numerical solutions of the JIMWLK equations, starting from an initial condition at moderate $x$ for a finite size proton. The resulting dipole amplitude is used to calculate the total reduced cross section $\sigma_r$ and charm reduced cross section $\sigma_{rc}$, as well as diffractive vector meson production. We compare results to experimental data from HERA and discuss fundamental problems arising from the regime sensitive to non-perturbative physics. We emphasize that information on the gluonic content of the proton, gluon spatial distributions and correlations over wide ranges in $x$, which can in principle be constrained by our stud…

Flux of a Vector Field

2012

In this chapter we concentrate on aspects of vector calculus. A common physical application of this theory is the fluid flow problem of calculating the amount of fluid passing through a permeable surface. The abstract generalization of this leads us to the flux of a vector field through a regular 2-surface in \(\mathbb{R}^3\). More precisely, let the vector field F in \(\mathbb{R}^3\) represent the velocity vector field of a fluid. We immerse a permeable surface S in that fluid, and we are interested in the amount of fluid flow across the surface S per unit time. This is the flux integral of the vector field F across the surface S

Superconvergence phenomenon in the finite element method arising from averaging gradients

1984

We study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which at any nodal point is an average of gradients of linear elements on triangles incident with this nodal point. The convergence rate of the averaged gradient to an exact gradient in theL 2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.

A support vector domain method for change detection in multitemporal images

2010

This paper formulates the problem of distinguishing changed from unchanged pixels in multitemporal remote sensing images as a minimum enclosing ball (MEB) problem with changed pixels as target class. The definition of the sphere-shaped decision boundary with minimal volume that embraces changed pixels is approached in the context of the support vector formalism adopting a support vector domain description (SVDD) one-class classifier. SVDD maps the data into a high dimensional feature space where the spherical support of the high dimensional distribution of changed pixels is computed. Unlike the standard SVDD, the proposed formulation of the SVDD uses both target and outlier samples for defi…

Shape Description for Content-Based Image Retrieval

2000

The present work is focused on a global image characterization based on a description of the 2D displacements of the different shapes present in the image, which can be employed for CBIR applications.To this aim, a recognition system has been developed, that detects automatically image ROIs containing single objects, and classifies them as belonging to a particular class of shapes.In our approach we make use of the eigenvalues of the covariance matrix computed from the pixel rows of a single ROI. These quantities are arranged in a vector form, and are classified using Support Vector Machines (SVMs). The selected feature allows us to recognize shapes in a robust fashion, despite rotations or…

Cluster kernels for semisupervised classification of VHR urban images

2009

In this paper, we present and apply a semisupervised support vector machine based on cluster kernels for the problem of very high resolution image classification. In the proposed setting, a base kernel working with labeled samples only is deformed by a likelihood kernel encoding similarities between unlabeled examples. The resulting kernel is used to train a standard support vector machine (SVM) classifier. Experiments carried out on very high resolution (VHR) multispectral and hyperspectral images using very few labeled examples show the relevancy of the method in the context of urban image classification. Its simplicity and the small number of parameters involved make it versatile and wor…

Smartphone determination of fat in cured meat products

2017

Abstract A method has been developed to determine the fat content in different cold meat products by image processing using the camera of a mobile phone. Salchichon , chorizo , salami and cured ham pictures were taken with a Meizu M2 Mini mobile phone camera under fixed lighting conditions of the light emitting diode flash of the mobile phone. Images were treated with Matlab to obtain the mean pixels of average red, green and blue camera values colours (RGB) of the pixels and different data pretreatments were taken into account to correlate colour parameters with fat content values determined in a series of commercially available samples by the Soxhlet method. RGB values were used as input …