Search results for "Approx"
showing 10 items of 922 documents
A new approximation procedure for fractals
2003
AbstractThis paper is based upon Hutchinson's theory of generating fractals as fixed points of a finite set of contractions, when considering this finite set of contractions as a contractive set-valued map.We approximate the fractal using some preselected parameters and we obtain formulae describing the “distance” between the “exact fractal” and the “approximate fractal” in terms of the preselected parameters. Some examples and also computation programs are given, showing how our procedure works.
Invariant approximation results in cone metric spaces
2011
Some sufficient conditions for the existence of fixed point of mappings satisfying generalized weak contractive conditions is obtained. A fixed point theorem for nonexpansive mappings is also obtained. As an application, some invariant approximation results are derived in cone metric spaces.
Resonance of minimizers forn-level quantum systems with an arbitrary cost
2004
We consider an optimal control problem describing a laser-induced population transfer on a n-level quantum system. For a convex cost depending only on the moduli of controls ( i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for n=2 and n=3): instead of looking for minimizers on the sphere one is reduced to look just for minimizers on the sphere . Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal mi…
Convergence of Markovian Stochastic Approximation with discontinuous dynamics
2016
This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H_{\theta_n}({X_{n+1}})$, where ${\left\{ {\theta}_n, n \in {\mathbb{N}} \right\}}$ is an ${\mathbb{R}}^d$-valued sequence, ${\left\{ {\gamma}_n, n \in {\mathbb{N}} \right\}}$ is a deterministic stepsize sequence, and ${\left\{ {X}_n, n \in {\mathbb{N}} \right\}}$ is a controlled Markov chain. We study the convergence under weak assumptions on smoothness-in-$\theta$ of the function $\theta \mapsto H_{\theta}({x})$. It is usually assumed that this function is continuous for any $x$; in this work, we relax this condition. Our results are illustrated by c…
Fronts propagating with signal dependent speed in limited diffusion and related Hamilton-Jacobi formulations
2021
We consider a class of limited diffusion equations and explore the formation of diffusion fronts as the result of a combination of diffusive and hyperbolic transport. We analyze a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion coefficient that depends on the unknown and on the gradient of the unknown. We explore the main features of the solution of the Hamilton-Jacobi equations that contain shocks and propose a suitable numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We analyze three model problems covering d…
Plasmon de surface de particules métalliques toroïdales
2006
This thesis deals with the optical properties of small metal torii. A method of resolution of the equation of Laplace in toroidal coordinates is introduced and the radiative properties of the metal toric nanoparticules are studied within the electrostatic framework. The study on the eigenmodes spatial distribution suggests that metal nanotorus can carry a non-zero magnetic dipole moment at optical frequencies. Analytical expressions for the extinction and scattering cross sections of the torus are also found and compared with numerical simulations and experimental results obtained with collaborations. The sensitivity of the plasmon frequency to the refraction index of the external medium an…
Nonlinear dynamical model of Costas loop and an approach to the analysis of its stability in the large
2015
The analysis of the stability and numerical simulation of Costas loop circuits for high-frequency signals is a challenging task. The problem lies in the fact that it is necessary to simultaneously observe very fast time scale of the input signals and slow time scale of phase difference between the input signals. To overcome this difficult situation it is possible, following the approach presented in the classical works of Gardner and Viterbi, to construct a mathematical model of Costas loop, in which only slow time change of signal?s phases and frequencies is considered. Such a construction, in turn, requires the computation of phase detector characteristic, depending on the waveforms of th…
Spurious finite-size instabilities in nuclear energy density functionals
2013
It is known that some well-established parametrizations of the EDF do not always provide converged results for nuclei and a qualitative link between this finding and the appearance of finite-size instabilities of SNM near saturation density when computed within the RPA has been pointed out. We seek for a quantitative and systematic connection between the impossibility to converge self-consistent calculations of nuclei and the occurrence of finite-size instabilities in SNM for the example of scalar-isovector (S=0, T=1) instabilities of the standard Skyrme EDF. We aim to establish a stability criterion based on computationally-friendly RPA calculations of SNM that is independent on the functi…
Muon capture revisited
1990
Abstract The problem of inclusive muon capture in nuclei is studied by calculating the capture rate in asymmetric infinite nuclear matter and using the local density approximation to evaluate the capture rates in nuclei. It is shown that the method is rather reliable and allows one to improve on approximations used in the past. The need for a strong nuclear renormalization is shown, reducing the capture rates by about a factor two in medium and heavy nuclei. By using standard effective interactions in the spin-isospin channel one can account for this renormalization and one finds a remarkable overall agreement with the measured capture rates for a large list of nuclei through the periodic t…
Strong-coupling expansion for the anharomonic oscillators −d2/dx 2+x 2+λx 2N
1992
A perturbation expansion based on a modified and scaled harmonic oscillator combined with Pade extrapolation techniques has been used to determine the expansion of the ground-state energy in fractional and negative powers of the coupling constant, valid for large values of λ.