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Covariant integral quantization with rotational SO (3) symmetry is established for quantum motion on this group manifold. It can also be applied to Gabor signal analysis on this group. The corresponding phase space takes the form of a discrete-continuous hypercylinder. The central tool for implementing this procedure is the Weyl–Gabor operator, a non-unitary operator that operates on the Hilbert space of square-integrable functions on SO (3) . This operator serves as the counterpart to the unitary Weyl or displacement operator used in constructing standard Schrödinger–Glauber–Sudarshan coherent states. We unveil a diverse range of properties associated with the quantizations and their corresponding semi-classical phase-space portraits, which are derived from different weight functions on the considered discrete-continuous hypercylinder. Certain classes of these weight functions lead to families of coherent states. Moreover, our approach allows us to define a Wigner distribution, satisfying the standard marginality conditions, along with its related Wigner transform. [ABSTRACT FROM AUTHOR]

Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalized positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a covariant way. One of their advantages is their ability to circumvent problems due to the presence of singularities in the classical models. In this paper, we implement covariant integral quantizations for systems whose phase space is Z × S 1 , i.e., for systems moving on the circle. The symmetry group of this phase space is the discrete & compact version of the Weyl–Heisenberg group, namely the central extension of the abelian group Z × SO (2) . In this regard, the phase space is viewed as the right coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on L 2 (S 1) , is square integrable on the phase space. We show how to derive corresponding covariant integral quantizations from (weight) functions on the phase space and resulting resolution of the identity. As particular cases of the latter we recover quantizations with de Bièvre-del Olmo–Gonzales and Kowalski–Rembielevski–Papaloucas coherent states on the circle. Another straightforward outcome of our approach is the Mukunda Wigner transform. We also look at the specific cases of coherent states built from shifted gaussians, Von Mises, Poisson, and Fejér kernels. Applications to stellar representations are in progress. [ABSTRACT FROM AUTHOR]

Byline: Romain Murenzi, Mike Hughes It is evident that strategies need to be undertaken to reverse the decline of Africa's share of world trade. This paper argues that through the development of regional and sub-regional integration, coupled with the development of national science and technological innovative and entrepreneurship skills, the fortunes can be reversed. The study focuses on Rwanda and reviews the policies and strategies to acquire and create knowledge linked to knowledge transfer and innovation to stimulate and develop the national economy in particular encouraging the private sector as an engine of growth. It emphasises the importance of regional cooperation to open larger markets and economies of scale.

Covariant affine integral quantization of the half-plane is studied and applied to the motion of a particle on the half-line. We examine the consequences of different quantizer operators built from weight functions on the half-plane. To illustrate the procedure, we examine two particular choices of the weight function, yielding thermal density operators and affine inversion, respectively. The former gives rise to a temperature-dependent probability distribution on the half-plane whereas the latter yields the usual canonical quantization and a quasi-probability distribution (affine Wigner function) which is real, marginal in both momentum p and position q. [ABSTRACT FROM AUTHOR]

We develop a novel pose estimation technique for synthetic aperture radar image chips based on the 2-D continuous wavelet transform (CWT). The pose estimator exploits a fast approximation of the 2-D CWT so that its computational complexity is comparable to a principle component analysis (PCA) based approach. By incorporating energy from various scales, the CWT approach is more robust than the PCA method. Experiments over the MSTAR database confirm the robustness of the CWT method. [Copyright &y& Elsevier]