Search results for "linear"
showing 10 items of 7165 documents
Multi-parameters rational solutions to the mKdV equation
2021
N-order solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6.
Variations of selective separability II: Discrete sets and the influence of convergence and maximality
2012
A space $X$ is called selectively separable(R-separable) if for every sequence of dense subspaces $(D_n : n\in\omega)$ one can pick finite (respectively, one-point) subsets $F_n\subset D_n$ such that $\bigcup_{n\in\omega}F_n$ is dense in $X$. These properties are much stronger than separability, but are equivalent to it in the presence of certain convergence properties. For example, we show that every Hausdorff separable radial space is R-separable and note that neither separable sequential nor separable Whyburn spaces have to be selectively separable. A space is called \emph{d-separable} if it has a dense $\sigma$-discrete subspace. We call a space $X$ D-separable if for every sequence of …
Quantization of Poisson Lie Groups and Applications
1996
LetG be a connected Poisson-Lie group. We discuss aspects of the question of Drinfel'd:can G be quantized? and give some answers. WhenG is semisimple (a case where the answer isyes), we introduce quantizable Poisson subalgebras ofC ∞(G), related to harmonic analysis onG; they are a generalization of F.R.T. models of quantum groups, and provide new examples of quantized Poisson algebras.
Evidence of oblate-prolate shape coexistence in the strongly-deformed nucleus 119Cs
2021
International audience; Prolate-oblate shape coexistence close to the ground state in the strongly-deformed proton-rich A≈120 nuclei is reported for the first time. One of the four reported bands in 119Cs, built on a 11/2− state at 670 keV, consists of nearly degenerate signature partners, and has properties which unequivocally indicate the strongly-coupled πh11/2[505]11/2− configuration associated with oblate shape. Together with the decoupled πh11/2[541]3/2− band built on the 11/2− prolate state at 110 keV, for which a half-life of T1/2=55(5)μs has been measured, the new bands bring evidence of shape coexistence at low spin in the proton-rich strongly deformed A≈120 nuclei, a phenomenon p…
Separation of uncorrelated stationary time series using autocovariance matrices
2014
Blind source separation (BSS) is a signal processing tool, which is widely used in various fields. Examples include biomedical signal separation, brain imaging and economic time series applications. In BSS, one assumes that the observed $p$ time series are linear combinations of $p$ latent uncorrelated weakly stationary time series. The aim is then to find an estimate for an unmixing matrix, which transforms the observed time series back to uncorrelated latent time series. In SOBI (Second Order Blind Identification) joint diagonalization of the covariance matrix and autocovariance matrices with several lags is used to estimate the unmixing matrix. The rows of an unmixing matrix can be deriv…
Roadmap on optical rogue waves and extreme events
2016
Nail Akhmediev et al. ; 38 págs.; 28 figs.
Adaptive synchronization of master-slave systems with mixed neutral and discrete time-delays and nonlinear perturbations
2011
This paper investigates the delay-dependent adaptive synchronization problem of the master and slave structure of linear systems with both constant neutral and time-varying discrete time-delays and nonlinear perturbations based on the Barbalat lemma and matching conditions. An adaption law which includes the master-slave parameters is obtained by using the Lyapunov functional method and inequality techniques to synchronize the master-slave systems without the knowledge of upper bounds of perturbation terms. Particularly, it is shown that the synchronization speed can be controlled by adjusting the update gain of the synchronization signal. A numerical example has been given to show the effe…
Gradient flows in random walk spaces
2021
El món digital ha comportat l'aparició de molts tipus de dades, de mida i complexitat creixents. De fet, els dispositius moderns ens permeten obtenir fàcilment imatges de major resolució, així com recopilar dades sobre cerques a la xarxa, anàlisis sanitàries, xarxes socials, sistemes d'informació geogràfica, etc. En conseqüència, l'estudi i el tractament d'aquests grans conjunts de dades té un gran interès i valor. En aquest sentit, els grafs ponderats proporcionen un espai de treball natural i flexible on representar les dades. En aquest context, un vèrtex representa una dada concreta i a cada aresta se li assigna un pes segons alguna mesura de semblança adequadament triada entre els vèrte…
A theoretical study of the 1B2u and 1B1u vibronic bands in benzene
2000
The two lowest bands, 1B2u and 1B1u, of the electronic spectrum of the benzene molecule have been studied theoretically using a new method to compute vibronic excitation energies and intensities. The complete active space (CAS) self-contained field (SCF) method (with six active π-orbitals) was used to compute harmonic force field for the ground state and the 1B2u and 1B1u electronic states. A linear approximation has been used for the transition dipole as a function of the nuclear displacement coordinates. Derivatives of the transition dipole were computed using a variant of the CASSCF state interaction method. Multiconfigurational second-order perturbation theory (CASPT2) was used to obtai…
Effects of rapid thermal annealing on the optical properties of low-loss 1.3μm GaInNAs∕GaAs saturable Bragg reflectors
2004
We report studies of the effect of rapid thermal annealing (RTA) on the optical properties of a low-loss 1.3 mum saturable Bragg reflector (SBR), consisting of a GaInNAs/GaAs single quantum well embedded in an AlAs/GaAs Bragg reflector grown monolithically on a GaAs substrate. RTA gives rise to a blueshift of the photoluminescence (PL) peak (and therefore of the excitonic absorption peak) and an enhancement of PL intensity, while the reflectivity properties including peak reflectivity and bandwidth are not degraded. Temperature dependent photoluminescence measurements show that the RTA-induced blueshift of photoluminescence consists of two components: one originating from the increase of op…