Academic literature on the topic 'Matrice multiplicative de Hilbert'

In this paper, we obtain an efficient separability criterion for bipartite quantum pure state systems, which is based on the two-order minors of the coefficient matrix corresponding to quantum state. Then, we generalize this criterion to multipartite arbitrarily dimensional pure states. Our criterion is directly built upon coefficient matrices, but not density matrices or observables, so it has the advantage of being computed easily. Indeed, to judge separability for an arbitrary n-partite pure state in a d-dimensional Hilbert space, it only needs at most O(d) times operations of multiplication and comparison. Our criterion can be extended to mixed states. Compared with Yu's criteria, our methods are faster, and can be applied to any quantum state.

The singular value decomposition (SVD) is a basic tool for analyzing matrices. Regarding a general matrix as defining a linear operator and choosing appropriate orthonormal bases for the domain and co-domain allows the operator to be represented as multiplication by a diagonal matrix. It is well known that the SVD extends naturally to a compact linear operator mapping one Hilbert space to another; the resulting representation is known as the singular value expansion (SVE). It is less well known that a general bounded linear operator defined on Hilbert spaces also has a singular value expansion. This SVE allows a simple analysis of a variety of questions about the operator, such as whether it defines a well-posed linear operator equation and how to regularize the equation when it is not well posed.

Multiplicative unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki–Tatsuuma Duality Theorem characterizes abstractly C*-algebras acted on by unital endomorphisms that are intrinsically related to the regular representation of a multiplicative unitary. The relevant C*-algebras turn out to be simple and indeed separable if the corresponding multiplicative unitaries act on a separable Hilbert space. A categorical analogue provides internal characterizations of minimal representation categories of a multiplicative unitary. Endomorphisms of the Cuntz algebra related algebraically to the grading are discussed as is the notion of braided symmetry in a tensor C*-category.

The experiment tested the relative contribution of additive and multiplicative noise components in isometric force fluctuations. We implemented the Hilbert–Huang transform to analyze variability in the steady state region of isometric force time series generated by participants in three adult age categories: (1) young (20–24 yrs); (2) old (60–69 yrs); and older-old (75–90 yrs). Each participant generated isometric force output in response to constant target force levels (5–40% maximum voluntary contraction). The empirical mode decomposition component of the Hilbert–Huang transform was applied to each isometric force time series resulting in a set of intrinsic mode functions (IMFS). The amplitude modulation envelopes of the IMFS obtained from the modulus of the Hilbert transform were random sequences. These random sequences were the source of the multiplicative noise. Analyses showed significant age group differences in the multiplicative noise structure of the force output. The results provide preliminary evidence that multiplicative noise dominates additive noise in isometric force output and can discriminate among the force fluctuations of healthy adult participants of different ages.

Nous étudions deux problèmes. Le premier concerne les sections finies de l'inégalité multiplicative de Hilbert. Nous donnons le comportement asymptotique de la meilleure constante $lambda_n$ dans l'inégalité$$Big|sum_{i,j=2}^{n}frac{a_ioverline{a_j}}{ijlog(ij)}Big|leq lambda_n sum_{i=2}^n|a_i|^2.$$Nous donnons aussi le comportement asymptotique de la version $ell^p$ des sections finies de l'inégalité multiplicative de Hilbert.Le deuxième problème concerne l'appartenance des fonctions distance à l'algèbre des multiplicateurs de l'espace de Dirichlet. Les fonctions distance sont les fonctions extérieures dont les valeurs au bord ne dépendent que de la distance par rapport à un ensemble fermé du cercle unité de mesure nulle. Nous donnons une estimation de l'intégrale de Dirichlet d'une fonction distance pour qu'elle appartienne à l'algèbre des multiplicateurs
We study two problems. The first one concerns finite sections of the Hilbert multiplicative inequality. We give the asymptotic behaviour of the best constant $lambda_n$ in the inequality$$Big|sum_{i,j=2}^{n}frac{a_ioverline{a_j}}{ijlog(ij)}Big|leq lambda_n sum_{i=2}^n|a_i|^2.$$We also give the asymptotic behaviour of the $ell^p$ version of the finite sections of the Hilbert multiplicative inequality.The second problem concerns the membership of the multiplier algebra of the Dirichlet space of so-called distance functions, namely outer functions whose boundary values depend only on distance to a closed subset of measure zero. We establish an estimate for the Dirichlet integral of such function to belong to the multiplier algebras of the Dirichlet space

In this paper we deal with the `strength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according_to_M. Z. Nashed [15] the ill-posedness of type I if A is not compact, but we have R(A) 6= R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with noncompact operators A are not in general `less' ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete least-squares solutions and the growth rate of Galerkin matrices in both cases. Ill-posedness measures for compact operators A as discussed in [10] are derived from the decay rate of the nonincreasing sequence of singular values of A. Since singular values do not exist for noncompact operators A; we introduce stability rates in order to have a common measure for the compact and noncompact cases. Properties of these rates are illustrated by means of convolution equations in the compact case and by means of equations with multiplication operators in the noncompact case. Moreover using increasing rearrangements of the multiplier functions specific measures of ill-posedness called ill-posedness rates are considered for the multiplication operators. In this context, the character of sufficient conditions providing convergence rates of Tikhonov regularization are compared for compact operators and multiplication operators.

In questo lavoro di tesi vengono presentati inizialmente i postulati della meccanica quantistica, passando poi alla descrizione di stati tramite vettori in uno spazio di Hilbert e, successivamente, alla descrizione tramite l’operatore densità associato al sistema. Introducendo quindi i concetti di qubit e di decomposizione di Schmidt, si mostra il fenomeno chiamato Entanglement, illustrando alcuni esempi. Nel quinto capitolo viene trattata l’Entropia di Von Neumann come stumento per quantificare l’Entanglement di un sistema, mentre nel sesto si discute il problema del paradosso EPR, accompagnato dal teorema di Bell. Viene presentato infine uno degli eseprimenti di Aspect, prova sperimentale della non validità della teoria a varibili nascoste locali di cui Einstein, Podolski e Rosen furono sostenitori.

Une spécification précise des variances-covariances d'erreur d'ébauche est essentielle pour la réussite du processus d'assimilation des données. Des travaux récents proposent d'estimer ces statistiques à partir d'un ensemble d'assimilations perturbées. Cette approche, héritée des méthodes de Monte Carlo, offre la possibilité de calculer des statistiques relatives à la situation météorologique du jour, et de s'affranchir des hypothèses et contraintes des méthodes d'estimation et de modélisation utilisées jusqu'à présent. Une difficulté majeure de cette approche, liée à la taille réduite de l'ensemble disponible, concerne le niveau de bruit d'échantillonnage relativement élevé qui affecte l'estimation des statistiques. Des méthodes de filtrage doivent donc être développées, afin de réduire ce bruit et d'améliorer la précision des estimations. Une première partie du travail est consacrée à la mise en oeuvre théorique puis pratique d'un filtrage spatial objectif des variances d'erreur ensemblistes, qui s'appuie sur le calcul du ratio bruit/signal de l'estimation. L'application de ce filtrage dans le cadre de l'assimilation variationnelle d'ensemble du modèle Arpège montre qu'il permet d'extraire des estimations bruitées une information riche et robuste, fortement liée aux processus dynamiques et physiques en cours. L'impact d'une extension des variances ensemblistes "du jour" à toutes les variables du système d'assimilation du modèle Arpège est ensuite examiné. Celui-ci s'avère globalement neutre à positif en termes de scores moyens de prévision. Des améliorations significatives sont par ailleurs obtenues pour la prévision d'évènements intenses. Une dernière étape s'intéresse à la représentation de l'erreur de modèle au sein de l'assimilation d'ensemble. Des diagnostics a posteriori sont utilisés pour estimer objectivement un coefficient d'inflation à appliquer aux perturbations d'ébauche de manière à simuler les effets de l'erreur de modélisation
A precise specification of background-error variances and covariances is essential to the success of the data assimilation process. Recent works suggest to estimate these statistics within an ensemble of perturbed assimilations. This approach, derived from Monte Carlo methods, offers the possibility to estimate flow-dependent statistics, and to get free of hypotheses and constraints related to estimation and modeling methods used so far. A major difficulty of this approach, induced by the finite ensemble size, is the relatively high level of sampling noise that affects the estimated statistics. Some filtering tools must then be developed, in order to reduce the noise and to improve the estimates accuracy. First investigations aim to design, from both theoretical and technical points of view, an objective spatial filtering of the ensemble-based error variances, which relies on a calculation of the noise/signal ratio of the estimation. The application of this filtering to the Arpège model ensemble variational assimilation shows its ability to extract from the noisy estimates a rich and robust information, closely linked to occurring dynamic and physical processes. The impact of extending the use of ensemble variances "of the day" to all variables in the assimilation system of the Arpège model is then examined. It turns out to be globally neutral to positive in terms of space and time-averaged forecast scores. On the other hand, significant improvements are obtained for the prediction of severe weather events. Finally, the representation of model error within the ensemble assimilation is considered. A posteriori diagnostics are used to objectively estimate an inflation coefficient, which is then applied to background perturbations in order to simulate the effects of model error

Il lavoro presentato si apre con una descrizione dei postulati della MQ al fine dell'introduzione delle particelle correlate o entangled.Sono messi in evidenza i tratti caratteristici del fenomeno ed i mezzi fisici per lo studio dello stesso.Si pone l'attenzione anche sul percorso storico che ha portato alla completa verifica teorica e sperimentale dell'entanglement.La tesi si chiude con l'introduzione di particolari regioni astrofisiche al fine di studiare un articolo presentato da J.Gomez che lega il fenomeno alle regioni presentate.