Search results for " Operator"

Estimates for the Differences of Certain Positive Linear Operators

2020

The present paper deals with estimates for differences of certain positive linear operators defined on bounded or unbounded intervals. Our approach involves Baskakov type operators, the kth order Kantorovich modification of the Baskakov operators, the discrete operators associated with Baskakov operators, Meyer&ndash

Multi-agent control architecture for RFID cyberphysical robotic systems initial validation of tagged objects detection and identification using Playe…

2016

International audience; The objective of this paper is to describe and validate a multi-agent architecture proposed to control RFID Cyber-Physical Robotic Systems. This environment may contain human operators, robots (mobiles, manipulators, mobile manipulators, etc.), places (workrooms, walls, etc.) and other objects (tables, chairs, etc.). The proposed control architecture is composed of two types of agents dispatched on two levels. We find at the Organization level a Supervisory agent to allow operators to configure, manage and interact with the overall control system. At the Control level, we distinguish the Robots agents, to each robot (mobiles, manipulators or mobile manipulators) is a…

Inverse problems for a fractional conductivity equation

2020

This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint subsets of the exterior. Both the cases of infinitely many measurements and a single measurement are addressed. The results are based on a reduction from the fractional conductivity equation to the fractional Schr\"odinger equation, and as such represent extensions of previous works. Moreover, a simple application is shown in which the fractional conductivity equation is put into relation with a long jump random walk with weights.

Spherical harmonic expansion of fundamental solutions and their derivatives for homogenous elliptic operators

2017

In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansions…

A note on some fundamental results in complete gauge spaces and application

2015

We discuss the extension of some fundamental results in nonlinear analysis to the setting of gauge spaces. In particular, we establish Ekeland type and Caristi type results under suitable hypotheses for mappings and cyclic mappings. Our theorems generalize and complement some analogous results in the literature, also in the sense of ordered sets and oriented graphs. We apply our results to establishing the existence of solution to a second order nonlinear initial value problem.

INVESTIGATION, REALIZATION, AND ENTANGLEMENT CHARACTERIZATION OF COMPLEX OPTICAL QUANTUM STATES

2020

Suture intradermiche totali

2010

Two kind of total intradermal suture techniques are described in the present report. These procedures allow an effective reduction of post-operative pain of surgical wound, prevent infections, cut down tissutal trauma, achieve better aesthetic results, making easier postoperative patient''s management. From January 2001 to December 2007, 1,427 patients underwent surgical treatment and the wounds have been sewn with self-locking knots or intradermal skin closure with introflecting knots. This kind of procedures allow a sharp reduction of postoperative pain as well as the incidence of wound infections. Also the number of wound medication required after surgery is significantly reduced.

Unique continuation results for certain generalized ray transforms of symmetric tensor fields

2022

Let $I_{m}$ denote the Euclidean ray transform acting on compactly supported symmetric $m$-tensor field distributions $f$, and $I_{m}^{*}$ be its formal $L^2$ adjoint. We study a unique continuation result for the normal operator $N_{m}=I_{m}^{*}I_{m}$. More precisely, we show that if $N_{m}$ vanishes to infinite order at a point $x_0$ and if the Saint-Venant operator $W$ acting on $f$ vanishes on an open set containing $x_0$, then $f$ is a potential tensor field. This generalizes two recent works of Ilmavirta and M\"onkk\"onen who proved such unique continuation results for the ray transform of functions and vector fields/1-forms. One of the main contributions of this work is identifying t…

Multi-parameter analysis of the obstacle scattering problem

2022

Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Δu + k 2 u = 0. We show that the solution u and its far field pattern u ∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.

Quantitative Runge Approximation and Inverse Problems

2017

In this short note we provide a quantitative version of the classical Runge approximation property for second order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We show that these estimates are essentially optimal. As a model application we provide a new proof of the result from \cite{F07}, \cite{AK12} on stability for the Calder\'on problem with local data.