Search results for "vector space"
showing 10 items of 287 documents
Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale
2002
L'objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l'arc atmosphérique optimal d'une navette spatiale (problème de rentrée sur Terre ou programme d'exploration de Mars). Le système décrivant les trajectoires est de dimension 6, le contrôle est l'angle de gîte cinématique et le coût est l'intégrale du flux thermique. Par ailleurs il y a des contraintes sur l'état (flux thermique, accélération normale et pression dynamique). Notre étude est essentiellement géométrique et fondée sur une évaluation de l'ensemble des états accessibles en tenant compte des contraintes sur l'état. On esquisse une analyse des extrémales du Principe du …
Topological Hopf algebras, quantum groups and deformation quantization
2003
After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and their doubles explains their dualities and provides a comprehensive framework. Relations with deformation quantization and applications to the deformation quantization of symmetric spaces are described
Scaling behavior of Tan's contact for trapped Lieb-Liniger bosons: From two to many
2018
We show that the contact parameter of N harmonically trapped interacting one-dimensional bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson solution, and that N-body effects can be almost factorized. The small deviations observed between our analytical results and density matrix renormalization group (DMRG) calculations are more pronounced when the interaction energy is maximal (i.e., at intermediate interaction strengths) but they remain bounded by the large-N local-density approximation obtained from the Lieb-Liniger equation of state stemming from the Bethe ansatz. The rescaled two-body solution is so close to the exact one…
Image difference detection under varying illumination based on vector space and correlations
2012
Abstract We propose two methods to detect differences in images independently of local changes of intensity. The methods are based on calculating geometrical operators when images are considered as vectors. Operators can be expressed in terms of correlations for the possibility of optical implementations. The methods are invariant to changes of the form af ( x , y ) + b , where a and b are arbitrary unknown parameters that may vary over the image f ( x , y ). Computer simulations show that the method works well when the illumination model is satisfied. Results from real images taken with a web camera show the robustness of the method.
Text Classification Using Novel “Anti-Bayesian” Techniques
2015
This paper presents a non-traditional “Anti-Bayesian” solution for the traditional Text Classification (TC) problem. Historically, all the recorded TC schemes work using the fundamental paradigm that once the statistical features are inferred from the syntactic/semantic indicators, the classifiers themselves are the well-established statistical ones. In this paper, we shall demonstrate that by virtue of the skewed distributions of the features, one could advantageously work with information latent in certain “non-central” quantiles (i.e., those distant from the mean) of the distributions. We, indeed, demonstrate that such classifiers exist and are attainable, and show that the design and im…
Limiting concepts in extensional flow
1975
A characteristic feature of extensional flows is their potential capability of determining a stable, oriented structure in liquid materials containing elongated particles. With reference to flexible linear macromolecules, either in solution or as polymer melts, the limiting conditions under which such an oriented structure is actually possible are critically reviewed. It is seen that orientation can be obtained either when entanglements are present, i.e. when the polymer molecules form some sort of network, or, if the molecules behave entirely individually, only under very special circumstances. Further, if the objective is the “freezing” of the oriented structure in a partly crystalline, h…
Single-pump heart-cutting two-dimensional liquid chromatography applied to the determination of fatty alcohol ethoxylates.
2014
Abstract A setup for heart-cutting bi-dimensional liquid chromatography (LC–LC), constructed with a chromatograph provided with a single pump, an auxiliary 6-port 2-position valve (V 6/2 ) and a column selector valve (V CS ), is described. The possible ways of connecting the two valves for LC–LC, namely with V 6/2 first followed by V CS and vice versa, are compared. The possibility of using the setups for preconcentration followed by the backwards transfer of the preconcentrated solutes to the detector or to a second column is also shown. The V 6/2 -first configuration for LC–LC was applied to the characterization of industrial fatty alcohol ethoxylates (FAEs) using UV–vis detection. For th…
Applying fully tensorial ICA to fMRI data
2016
There are two aspects in functional magnetic resonance imaging (fMRI) data that make them awkward to analyse with traditional multivariate methods - high order and high dimension. The first of these refers to the tensorial nature of observations as array-valued elements instead of vectors. Although this can be circumvented by vectorizing the array, doing so simultaneously loses all the structural information in the original observations. The second aspect refers to the high dimensionality along each dimension making the concept of dimension reduction a valuable tool in the processing of fMRI data. Different methods of tensor dimension reduction are currently gaining popUlarity in literature…
A blow-up result for a nonlinear wave equation on manifolds: the critical case
2021
We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.
Fundamental bounds on qubit reset
2020
Qubit reset is a basic prerequisite for operating quantum devices, requiring the export of entropy. The fastest and most accurate way to reset a qubit is obtained by coupling the qubit to an ancilla on demand. Here, we derive fundamental bounds on qubit reset in terms of maximum fidelity and minimum time, assuming control over the qubit and no control over the ancilla. Using the Cartan decomposition of the Lie algebra of qubit plus two-level ancilla, we identify the types of interaction and controls for which the qubit can be purified. For these configurations, we show that a time-optimal protocol consists of purity exchange between qubit and ancilla brought into resonance, where the maximu…