The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries — stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for decomposition have been proposed, including the method of frames (MOF), Matching pursuit (MP), and,...

A new proof is given of the atomic decomposition of Hardy spaces Hp, 0 < p ≤ 1, in the classical setting on Rn. The new method can be used to establish atomic decomposition of maximal Hardy spaces in general and nonclassical settings.

Throughout this paper by using the frame theory we give a short proof for atomic decomposition for weighted Bergman space. In fact we show that the weighted Bergman space L 2 a (dA α) admit an atomic decomposition i.e every analytic function in this space can be presented as a linear combination of " atoms " defined using the normalized reproducing kernel of this space .

A new proof is given of the atomic decomposition of Hardy spaces Hp, 0 < p ≤ 1, in the classical setting on Rn. The new method can be used to establish atomic decomposition of maximal Hardy spaces in general and nonclassical settings.

One of the great challenges of modern science is to faithfully model, and understand, matter at a wide range of scales. Starting with atoms, the vastness of the space of possible configurations poses a formidable challenge to any simulation of complex atomic and molecular systems. We introduce a computational method to reduce the complexity of atomic configuration space by systematically recogn...

We study the decomposition of an arbitrary Petri net into open nets. This means that shared places can be seen as message channels between components. We show that there exists a unique decomposition into atomic components which can be efficiently computed. We further show that every composition of components yields a component and that every component can be built from atomic components. Final...

In this paper, we present HyS, an application for fast atomic decomposition and module extraction of OWL-EL ontologies. HyS computes a hypergraph representation of the modular structure of an ontology. This hypergraph representation contains the atomic decomposition of the input ontology, and it allows to extract modules for a given signature. We provide an experimental evaluation of HyS with a...