相关论文: MRA Super-wavelets

New finite-dimensional representations of specific polynomial deformations of sl(2,R) are constructed. The corresponding generators can be, in particular, realized through linear differential operators preserving a finite-dimensional…

The deflection of ultra-high energy cosmic rays depends on the shape of the injection spectrum of the source and the pervasive cosmic magnetic fields. In this work it is applied the wavelet transform on the sphere to search for energy…

Wavelet and Gabor systems are based on translation-and-dilation and translation-and-modulation operators, respectively. They have been extensively studied. However, dilation-and-modulation systems have not, and they cannot be derived from…

We discuss R-symmetry in locally supersymmetric $N=2$ gauge theories coupled to hypermultiplets, which can be viewed as effective theories of heterotic string models. In this type of supergravities a suitable R-symmetry exists and can be…

We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…

We suggest that the static configurations of M-theory may be described by the matrix regularisation of the supermembrane theory in static regime. We compute the long range interaction between a M2-brane and an anti-M2-brane in agreement…

In theories with (sets of) two large extra dimensions and supersymmetry in the bulk, the presence of non-supersymmetric brane defects naturally induces a logarithmic potential for the volume of the transverse dimensions. Since the logarithm…

We construct maximal $\Lambda(p)$-subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents $p$. Our arguments combine restriction estimates and decoupling with old and new probabilistic estimates.

We discuss the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. We investigate which of the classical properties can be translated to this more general framework and the way in…

Tightly focused laser pulses as they diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we report on theoretical study of relativistic spherical wake waves and their…

In this work, we prove that certain L^2-unbounded transformations of orthogonal wavelet bases generate vaguelets. The L^2-unbounded functions involved in the transformations are assumed to be quasi-homogeneous at high frequencies. We…

Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…

Three-dimensional segmentation in magnetic resonance images (MRI), which reflects the true shape of the objects, is challenging since high-resolution isotropic MRIs are rare and typical MRIs are anisotropic, with the out-of-plane dimension…

Two classes of irreducible highest weight modules of the general linear Lie superalgebra $gl(1/\infty)$ are constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the algebra…

Diffusion-weighted magnetic resonance imaging (DW-MRI) can be used to characterise the microstructure of the nervous tissue, e.g. to delineate brain white matter connections in a non-invasive manner via fibre tracking. Magnetic Resonance…

In this paper, we study the convolution structure in the special affine Fourier domain to combine the advantages of the well known special affine Fourier and wavelet transforms into a novel integral transform coined as special affine…

We derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the…

We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional…

An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate…

For any symmetry group $H$ and any appropriate matrix dilation we give an explicit method for the construction of $H$-symmetric refinable interpolatory refinable masks which satisfy sum rule of arbitrary order $n$. For each such mask we…