Let A1 and A2 be expansive dilations, respectively, on R n and R. Let ~ A ≡ (A1, A2) and Ap( ~ A) be the class of product Muckenhoupt weights on R × R for p ∈ (1, ∞]. When p ∈ (1, ∞) and w ∈ Ap( ~ A), the authors characterize the weighted Lebesgue space L w (R × R) via the anisotropic Lusin-area function associated with ~ A. When p ∈ (0, 1], w ∈ A∞( ~ A), the authors introduce the weighted anis...

Thin films of nitromethane (CH3NO2) along with its isotopically labeled counterpart D3-nitromethane (CD3NO2) were photolyzed at discrete wavelength between 266 nm (4.7 eV) and 121 nm (10.2 eV) to explore the underlying mechanisms involved in the decomposition of model compounds of energetic materials in the condensed phase at 5 K. The chemical modifications of the ices were traced in situ via e...

Analysis of audio and musical information signals deals with the decomposition into atoms. This subject is most interesting and useful for the researchers who want to invent the inherent properties of the signal under decomposition and to construct a new version of it. Many algorithms have been proposed for the decomposition of audio and musical content and methodologies have been demonstrated ...

Let $$H_{p(\cdot ),q}$$ be the variable Lorentz–Hardy martingale spaces. In this paper, we give a new atomic decomposition for these spaces via simple $$L_r$$ -atoms $$(1<r \le \infty )$$ . Using decomposition, consider dual of Lorentz-Hardy case $$0<p(\cdot )\le 1$$ , $$0<q\le and )<2$$ $$1<q<\infty $$ respectively, prove that they are equivalent to BMO with exponent. Furthermore, also obtain ...

An in situ investigation of thermal decomposition reactions of trimethylindium (TMIn) in a vertical, upflow chemical vapor deposition reactor has been carried out using Raman spectroscopy. Monomethylindium (MMIn) and atomic indium were detected along with the precursor TMIn using N2 as the carrier gas. Atomic indium was identified by the peak at 2215 cm, which is equal to the difference between...

The main purpose of this paper is to establish a signal decomposition system aiming at mixed over-voltages in power systems. In an electric power system, over-voltage presents a great threat for the system safety. Analysis and identification of over-voltages is helpful to improve the stability and safety of power systems. Through statistical analysis of a collection of field over-voltage record...

A common aim of data modeling approaches is to produce schemas whose instantiations are always redundancy-free. This is especially useful when the implementation target is a relational database. This paper contrasts two very different approaches to attain a redundancy-free relational schema. The ObjectRole Modeling (ORM) approach emphasizes capturing semantics first in terms of atomic (elementa...

Topology-representing networks (TRNs) generate reduced models of biomolecules and thereby facilitate the 5tting of molecular fragments into large macromolecular complexes. The components of such complexes undergo a wide range of motions, and shapes observed at low resolution often deviate from the known atomic structures. What is required for the modeling of such motions is a combination of glo...

Applying the atomic sparse decomposition in the distribution network with harmonics and small current grounding to decompose the transient zero sequence current that appears after the single phase to ground fault is occurred. Based on dictionary of Gabor atoms and matching pursuit algorithm, the method extracts the atomic components iteratively from the feature signals and translated them to da...

We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and Density Functional Theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of domain decomposition methods. Using this approach, calculations have been successfully performed on several linear polymer chains con...