Search results for "Hilbert"
showing 10 items of 331 documents
Input-to-State Stability of Lur’e Hyperbolic Distributed Complex-Valued Parameter Control Systems: LOI Approach
2013
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/364057 Open access In this work, input-to-state stability of Lur'e hyperbolic distributed complex-valued parameter control systems has been addressed. Using comparison principle, delay-dependent sufficient conditions for the input-to-state stability in complex Hilbert spaces are established in terms of linear operator inequalities. Finally, numerical computation illustrates our result.
Convergence rate of a relaxed inertial proximal algorithm for convex minimization
2018
International audience; In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim to solve monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for values which have similarities with the results based on the Nesterov accelerated gradient method. The joint adjustment of inertia, relaxation and proximal terms plays a central role. In doing so, we highlight inertial proximal algorithms that converge for general monotone inclusions, and which, in the case of convex minimization, give fast convergence rates of values in the worst case.
Abnormal textures identification based on digital Hilbert optics methods: fundamental transforms and models
2018
The article presents the abnormal textures identification technology based on structural and statistical models of amplitude-phase images (APIm)– multidimensional data arrays (semantic models) and statistical correlation analysis methods using the generalized discrete Hilbert transforms (DHT)– 2D Hilbert (Foucault) isotropic (HTI), anisotropic (HTA) and total transforms – AP-analysis (APA) to calculate the APIm. The identified fragments of textures are obtained as examples of experimental observation of real mammograms contains areas of pathological tissues. The DHT based information technology as conceptual chart description is discussed and illustrated with DHO domain images. As additiona…
A damage identification procedure based on Hilbert transform: Experimental validation
2010
SUMMARY This paper aims at validating the feasibility of an identification procedure, based on the use of the Hilbert transform, by means of experimental tests for shear-type multi-degree-of-freedom systems. Particularly, a three-degree-of-freedom frame will be studied either numerically or experimentally by means of a laboratory scale model built at the laboratory of the Structural, Aerospace and Geotechnical Engineering Department (DISAG) of University of Palermo. Several damage scenarios have been considered to prove the effectiveness of the procedure. Moreover, the experimental tests have been conducted by considering two different input loads: pulse forces, simulated by means of an ins…
What is Mathematics: Gödel's Theorem and Around (Edition 2015)
2015
Hyper-textbook for students in mathematical logic and foundations of mathematics. Edition 2015.
ON SOME GENERALIZATION OF SMOOTHING PROBLEMS
2015
The paper deals with the generalized smoothing problem in abstract Hilbert spaces. This generalized problem involves particular cases such as the interpolating problem, the smoothing problem with weights, the smoothing problem with obstacles, the problem on splines in convex sets and others. The theorem on the existence and characterization of a solution of the generalized problem is proved. It is shown how the theorem gives already known theorems in special cases as well as some new results.
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…
Empirical Mode Decomposition on Mismatch Negativity
2008
Empirical mode decomposition (EMD) has been applied in the various disciplines to extract the desired signal. The basic principle is to decompose a time series into intrinsic mode functions (IFMs) and each IFM corresponds to an oscillation phenomenon. A statistical description of the oscillatory activities of the EEG has been well known. It is desired to extract single oscillatory process from the EEG by EMD. Mismatch negativity (MMN) can be automatically elicited by the deviant stimulus in an oddball paradigm, in which physically the deviant stimulus occurs among repetitive and homogeneous stimuli. MMN thus reflects the ability of the brain to detect changes in auditory stimuli. So, the MM…
The Principles of Quantum Theory
2013
This chapter develops the formal framework of quantum mechanics: the mathematical tools, generalization and abstraction of the notion of state, representation theory, and a first version of the postulates on which quantum theory rests.
An EEMD Aided Comparison of Time Histories and Its Application in Vehicle Safety
2017
In the context of signal processing, the comparison of time histories is required for different purposes, especially for the model validation of vehicle safety. Most of the existing metrics focus on the mathematical value only. Therefore, they suffer the measuring errors, disturbance, and uncertainties and can hardly achieve a stable result with a clear physical interpretation. This paper proposes a novel scheme of time histories comparison to be used in vehicle safety analysis. More specifically, each signal for comparison is decomposed into a trend signal and several intrinsic mode functions (IMFs) by ensemble empirical mode decomposition. The trend signals reflect the general variation a…