This paper studies how differentiable representations of certain subsemigroups of the Weyl-Heisenberg group may be obtained in suitably constructed rigged Hilbert spaces. These semigroup representations are induced from a continuous unitary representation of the Weyl-Heisenberg group in a Hilbert space. Aspects of the rigged Hilbert space formulation of time asymmetric quantum mechanics are als...

In order to distinguish the difference of non-stationary signals, the novel time-frequency analysis approach, i.e. Hilbert-Huang transform (HHT), is applied in this paper. Firstly, Hilbert-Huang transform is briefly introduced. Secondly, two different non-stationary signals are described in Empirical Mode Decomposition (EMD) and Hilbert spectra. With these results, the two signals that looked a...

The analytic signal method via the Hilbert transform is a key tool in signal analysis and processing, especially in the time-frquency analysis. Imaging and other applications to multidimensional signals call for extension of the method to higher dimensions. We justify the usage of partial Hilbert transforms to define multidimensional analytic signals from both engineering and mathematical persp...

We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the addition of probabilities of alternatives. Thus we obtain quantum interference without applying to wave or Hilbert space approach. The Hilbert space representa...

The rational solutions of the Painlevé-II equation appear in several applications and are known to have many remarkable algebraic and analytic properties. They also have several different representations, useful in different ways for establishing these properties. In particular, Riemann–Hilbert representations have proven to be useful for extracting the asymptotic behavior of the rational solut...

Wavelet transformation is one of the most practical mathematical transformations in the field of image processing, especially image and signal processing. Depending on the nature of the multiresolution analysis, Wavelet transformation become more accessible and powerful tools. In this paper, we refer to the mathematical foundations of this transformation.   Introduction: The...

For cable bridges, the cable tension force plays a crucial role in their construction, assessment and long-term structural health monitoring. Cable tension forces vary in real time with the change of the moving vehicle loads and environmental effects, and this continual variation in tension force may cause fatigue damage of a cable. Traditional vibration-based cable tension force estimation met...

We present an algorithm for grouping families of probability density functions (pdfs). We exploit the fact that under the square-root re-parametrization, the space of pdfs forms a Riemannian manifold, namely the unit Hilbert sphere. An immediate consequence of this re-parametrization is that different families of pdfs form different submanifolds of the unit Hilbert sphere. Therefore, the proble...