Search results for "integral"
showing 10 items of 902 documents
Kirkwood–Buff Integrals Using Molecular Simulation: Estimation of Surface Effects
2020
Kirkwood&ndash
Symmetry of minimizers with a level surface parallel to the boundary
2015
We consider the functional $$I_\Omega(v) = \int_\Omega [f(|Dv|) - v] dx,$$ where $\Omega$ is a bounded domain and $f$ is a convex function. Under general assumptions on $f$, G. Crasta [Cr1] has shown that if $I_\Omega$ admits a minimizer in $W_0^{1,1}(\Omega)$ depending only on the distance from the boundary of $\Omega$, then $\Omega$ must be a ball. With some restrictions on $f$, we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these results extend to more general settings, in particular to functionals that are not differenti…
Hollow system with fin. Transient Green function method combination for two hollow cylinders
2017
In this paper we develop mathematical model for three dimensional heat equation for the system with hollow wall and fin and construct its analytical solution for two hollow cylindrical sample. The method of solution is based on Green function method for one hollow cylinder. On the conjugation conditions between both hollow cylinders we construct solution for system wall with fin. As result we come to integral equation on the surface between both hollow cylinders. Solution is obtained in the form of second kind Fredholm integral equation. The generalizing of Green function method allows us to use Green function method for regular non-canonical domains.
Fixed point results on metric-type spaces
2014
Abstract In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.
A symmetric Galerkin BEM for plate bending analysis
2009
Abstract The Symmetric Galerkin Boundary Element Method is employed in thin plate bending analysis in accordance with the Love–Kirchhoff kinematical assumption. The equations are obtained through the stationary conditions of the total potential energy, written for a plate whose boundary is discretized in boundary elements. Since the matrix coefficients are made up as double integrals with high order singularities, a strategy is shown to compute these coefficients in closed form. Furthermore, in order to model the kinematical discontinuities and to weight the mechanical quantities along the boundary elements, the Lagrangian quadratic shape functions, rather than C 1 type (spline, Hermitian),…
Combining Defocus and Photoconsistency for Depth Map Estimation in 3D Integral Imaging
2017
This paper presents the application of a depth estimation method for scenes acquired using a Synthetic Aperture Integral Imaging (SAII) technique. SAII is an autostereoscopic technique consisting of an array of cameras that acquires images from different perspectives. The depth estimation method combines a defocus and a correspondence measure. This approach obtains consistent results and shows noticeable improvement in the depth estimation as compared to a minimum variance minimisation strategy, also tested in our scenes. Further improvements are obtained for both methods when they are fed into a regularisation approach that takes into account the depth in the spatial neighbourhood of a pix…
Fuzzy Integral Imaging Camera Calibration for Real Scale 3D Reconstructions
2014
In this paper, we present a quantitative analysis of the error in the reconstruction of a 3D scene which has been captured with Synthetic Aperture Integral Imaging system. The 3D information is obtained from 2D images for which the camera parameters are unknown. The model used for calibrating the Integral Imaging camera setup is based on fuzzy systems. These systems provide the opportunity for modeling of conditions which are inherently imprecisely defined. We demonstrate that the error in the 3D reconstruction not only depends on the number of cameras, but also to their relative positions. Our model is applied to a set of images captured experimentally from a real object. A true-color real…
Photoelastic Analysis of Partially Occluded Objects With an Integral-Imaging Polariscope
2014
Polariscopes are the basic instruments used for the analysis of the stress state of transparent materials. Polarized light passing through a 3D object carries the integrated effect of the stress field along the light path. Therefore, conventional polariscopes are not able to discern the stress state of objects involving multiple plates with mutual occlusions. In this paper we propose a novel experimental system for three-dimensional stress analysis based on the combination of a polariscope and Synthetic Aperture Integral Imaging technique. Experimental results show the system's ability to recover the information of the stress distribution of a set of plates located at different depths havin…
Non-invasive localization of atrial ectopic beats by using simulated body surface P-wave integral maps
2017
Non-invasive localization of continuous atrial ectopic beats remains a cornerstone for the treatment of atrial arrhythmias. The lack of accurate tools to guide electrophysiologists leads to an increase in the recurrence rate of ablation procedures. Existing approaches are based on the analysis of the P-waves main characteristics and the forward body surface potential maps (BSPMs) or on the inverse estimation of the electric activity of the heart from those BSPMs. These methods have not provided an efficient and systematic tool to localize ectopic triggers. In this work, we propose the use of machine learning techniques to spatially cluster and classify ectopic atrial foci into clearly diffe…
Tangent Measures, Densities, and Singular Integrals
1995
We introduce tangent measures in the sense of David Preiss. We discuss their applications to the density and rectifiability properties of general Borel measures in ℝ n as well as to the behaviour of certain singular integrals with respect to such measures.