Search results for "Parametric statistics"
showing 10 items of 354 documents
Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems
2020
We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is $$(p-1)$$-superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation-type result for the set of positive solutions as the parameter $$\lambda >0$$ varies. Also we prove the existence of a minimal positive solution $$u_\lambda ^*$$ and determine the monotonicity and continuity properties of the map $$\lambda \rightarrow u_\lambda ^*$$.
Multiple Solutions with Sign Information for a Class of Coercive (p, 2)-Equations
2019
We consider a nonlinear Dirichlet equation driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation). The hypotheses on the reaction f(z, x) are minimal and make the energy (Euler) functional of the problem coercive. We prove two multiplicity theorems producing three and four nontrivial smooth solutions, respectively, all with sign information. We apply our multiplicity results to the particular case of a class of parametric (p, 2)-equations.
Positive solutions for the Neumann p-Laplacian
2017
We examine parametric nonlinear Neumann problems driven by the p-Laplacian with asymptotically ( $$p-1$$ )-linear reaction term f(z, x) (as $$x\rightarrow +\infty $$ ). We determine the existence, nonexistence and minimality of positive solutions as the parameter $$\lambda >0$$ varies.
A multiplicity theorem for parametric superlinear (p,q)-equations
2020
We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.
Type I optical parametric oscillators above threshold are perfect squeezers for empty gauss-hermite modes at any pumping level
2007
A type I optical parametric oscillator pumped by a Gaussian beam above threshold and tuned to its first transverse mode family is shown to yield a perfectly squeezed, empty Gauss-Hermite mode at any pumping level.
Quantum fluctuations in cavity solitons
2005
Quantum fluctuations of degenerate optical parametric oscillators' cavity solitons (CS) are studied. We show that CSs are sources of perfectly squeezed light that exhibit photon fluctuations below the shot-noise level as well.
Parametric self-trapping in the presence of randomized quasi phase matching
2010
We report on experimental evidence of parametric spatial solitons in a quadratic crystal with randomized periodic ferroelectric poling. Two-color self-focusing via quadratic cascading overcomes the diffractive nature of both fundamental and frequency-doubled beams.
Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion
2001
International audience; We analyse theoretically and experimentally the Raman-assisted parametric coupling between non-phase-matched waves propagating in normally dispersive single-mode fibres. We perform a careful analysis of the wave-coupling behaviour, which shows that scalar and vector three-wave mixing (TWM) interactions induce a relatively small periodic power flow between a central-frequency pump at frequency ω0 and a pair of up-shifted (anti-Stokes) and down-shifted (Stokes) sidebands at frequencies View the MathML source and View the MathML source, respectively. For sufficiently high pump powers, the stimulated Raman scattering enters into play, causing a unilateral transfer of ene…
Laser driven parametric amplification in the xuv and soft-x-ray spectral range
2011
We present the first experimental realization of a new x-ray laser scheme based on strong-field parametric amplification of high-order harmonic radiation. With a simple semi-classical model, we can identify the most important experimental parameters, the spectral range and the small signal gain in gases. Using a single amplifier stage a small signal gain of 8000 has been obtained in Argon for the spectral range of 40-50 eV, using 350 fs, 7 mJ pulses at 1.05 µm. In Helium, we observed a small signal gain of 280 around 300 eV using 6 fs, 1.5 mJ pulses at 800 nm.
Centroid-based Cluster Analysis of HVSR Data for Seismic Microzonation
2014
Horizontal to Vertical Spectral Ratio (HVSR) datasets acquired for studies of seismic microzoning in various urban centers of Sicilian towns, have been used to test clustering analysis through a nonhierarchical centroid-based algorithm. In this context clustering techniques may be useful to identify areas with similar seismic behaviour through HVSR data. Centroid-based algorithms generally require the number of clusters, k, and the initial centroid coordinates to be specified in advance. This aspect is considered to be one of the biggest drawbacks of these algorithms. The proposed algorithm doesn’t limit the number of k clusters and choose the initial centroids automatically from the data s…