Isolated X-ray -- infrared sources in the region of interaction of the supernova remnant IC 443 with a molecular cloud

The nature of the extended hard X-ray source XMMU J061804.3+222732 and its surroundings is investigated using XMM-Newton, Chandra, and Spitzer observations. This source is located in an interaction region of the IC 443 supernova remnant with a neighboring molecular cloud. The X-ray emission consists of a number of bright clumps embedded in an extended structured non-thermal X-ray nebula larger than 30" in size. Some clumps show evidence for line emission at ~1.9 keV and ~3.7 keV at the 99% confidence level. Large-scale diffuse radio emission of IC 443 passes over the source region, with an enhancement near the source. An IR source of about 14" x 7" size is prominent in the 24 um, 70 um, and 2.2 um bands, adjacent to a putative Si K-shell X-ray line emission region. The observed IR/X-ray morphology and spectra are consistent with those expected for J/C-type shocks of different velocities driven by fragmented supernova ejecta colliding with the dense medium of a molecular cloud. The IR emission of the source detected by Spitzer can be attributed to both continuum emission from an HII region created by the ejecta fragment and line emission excited by shocks. This source region in IC 443 may be an example of a rather numerous population of hard X-ray/IR sources created by supernova explosions in the dense environment of star-forming regions. Alternative Galactic and extragalactic interpretations of the observed source are also discussed.Comment: The Astrophysical Journal, v. 677 (April 2008), in pres

Modified neural network operators and their convergence properties with summability methods

We study the approximation properties of Cardaliaguet-Euvrard type neural network operators. We first modify the operators in order to get the uniform convergence, later we use regular summability matrix methods in the approximation by means of these operators to get more general results than the classical ones. We also display some examples and show graphical illustrations supporting our approximation results by neural networks operators. At the end of the paper we extend the theory to the multivariate case