Search results for "Hilbert"

A novel identification procedure from ambient vibration data for buildings of the cultural heritage

Ambient modal identification, also known as Operational Modal Analysis (OMA), aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method based on appl…

THE HILBERT FUNCTION OF BIGRADED ALGEBRAS IN k[P1x P1]

2020

We classify the Hilbert functions of bigraded algebras in k[x1, x2, y1, y2] by introducing a numerical function called a Ferrers function.

A note on partial*–algebras and spaces of distributions

2014

Given a rigged Hilbert space (D,H,D'), the spaces D_{loc are considered. It is shown that, if D is a Hilbert *-algebra, D_{loc} carry out a natural structure of partial *-algebra. Furthermore, on D_{loc} it is defined a topology, so that D_{loc} is an interspace. Examples from distributions theory are considered.

MODULI DI BANACH SU C*-ALGEBRE: Rappresentazioni Hilbertiane ed in spazi Lp non commutativi

2006

La teoria delle *-rappresentazioni delle *-algebre localmente convesse o normate costituisce un argomento classico di cui dà conto una vasta letteratura. Le C*- algebre costituiscono sicuramente la classe di *-algebre di Banach per la quale la teoria delle rappresentazioni fornisce, probabilmente, i risultati più profondi ed importanti per le applicazioni. Nel 1964 R. Haag e D. Kastler formularono, in un celebre lavoro, il cosiddetto approccio algebrico alle teorie quantistiche per sistemi con infiniti gradi di libertà. In esso, ad una regione limitata dello spazio delle configurazioni del sistema, si associa la C*-algebra delle osservabili locali. L’unione di tutte queste C*-algebre costis…

Operators in rigged Hilbert spaces: toward a spectral analysis

Admissible perturbations of alpha-psi-pseudocontractive operators: convergence theorems

2015

In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we …

Incipient damage identification through characteristics of the analytical signal response

2008

The analytical signal is a complex representation of a time domain signal: the real part is the time domain signal itself, while the imaginary part is its Hilbert transform. It has been observed that damage, even at a very low level, yields clearly detectable variations of analytical signal quantities such as phase and instantaneous frequency. This observation can represent a step toward a quick and effective tool to recognize the presence of incipient damage where other frequency-based techniques fail. In this paper a damage identification procedure based on an adimensional functional of the square of the difference between the characteristics of the analytical theoretical and measured sig…

Event signal characterization for disturbance interpretation in power grid

2018

This paper presents the signal processing approach to detect and characterize the physical events that occur in power system using PMUs signals. A small window is applied so that the extracted spectral features belong to a stationary signal. This is based on applying empirical mode decomposition, followed by square root of spectral kurtosis (SRSK) for computation of statistical indices to indicate the event occurrence. Subsequently, features from these events are extracted using mel frequency cepstral coefficients on SRSK. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/re…

A Hybrid Frequency-Space Approach for Shape Measurement by Shadow Moiré Technique with Carrier Fringe Pattern

2006

In this paper, a novel methodology to process fringe pattern is presented. The core of the signal processing technique is the use of the direction information, a modulo 2pi quantity that locally informs about the direction along which fringes grow with maximum rate. By using this information, it was possible to perform adaptive, direction- and orientation-based operations on fringe images in order to remove unwanted effects, to enhance the contrast and to extract the phase information encoded. The method has been applied on shadow moire interferograms with carrier fringes in order to measure the surface of small objects. The developed algorithm allows to process fringes whose phase informat…

Smooth Feshbach map and operator-theoretic renormalization group methods

2003

Abstract A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map . It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel operator-theoretic renormalization group method is described and applied to analyze a general class of Hamiltonians on Fock space. The main advantage of the new renormalization group method over its predecessors is its technical simplicity, which it owes to the use of the smooth Feshbach map.