By using a coherent state quantizationà la Klauder-Berezin, phase operators are constructed in finite Hilbert subspaces of the Hilbert space of Fourier series. The study of infinite dimensional limits of mean values of some observables phase leads towards a simpler convergence to the canonical commutation relations.

One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

By using a coherent state quantization à la Klauder-Berezin, phase operators are constructed in finite Hilbert subspaces of the Hilbert space of Fourier series. The study of infinite dimensional limits of mean values of some observables leads towards a simpler convergence to the canonical commutation relations.

We express the Fourier coefficients of the Hilbert cusp form Lhf associated with mixed Hilbert cusp forms f and h in terms of the Fourier coefficients of a certain periodic function determined by f and h. We also obtain an expression of each Fourier coefficient of Lhf as an infinite series involving the Fourier coefficients of f and h.

In this paper, we propose algorithms which preserve energy in empirical mode decomposition (EMD), generating finite n number of band limited Intrinsic Mode Functions (IMFs). In the first energy preserving EMD (EPEMD) algorithm, a signal is decomposed into linearly independent (LI), non orthogonal yet energy preserving (LINOEP) IMFs and residue (EPIMFs). It is shown that a vector in an inner pro...

In type A, the q, t-Fuß-Catalan numbers can be defined as a bigraded Hilbert series of a module associated to the symmetric group. We generalize this construction to (finite) complex reflection groups and, based on computer experiments, we exhibit several conjectured algebraic and combinatorial properties of these polynomials with non-negative integer coefficients. We prove the conjectures for ...

Abstract: The Hilbert transform is a well-known tool of time series analysis that has been widely used to investigate oscillatory signals that resemble a noisy periodic oscillation, because it allows instantaneous phase and frequency to be estimated, which in turn uncovers interesting properties of the underlying process that generates the signal. Here we use this tool to analyze atmospheric da...

In this paper, a combined approach to damage diagnosis of systems is proposed. The intention is to identify the natural frequencies and the presence of damage. In a first step, the basic concept of the Hilbert Huang Transform is presented where the empirical mode decomposition is applied on the signal using a sifting process to obtain intrinsic mode functions exhibiting monocomponent behavior. ...