Weighted βγ\beta\gamma-summability of fuzzy functions of order θ\theta

The concept of weighted $\beta\gamma$ - summability of order $\theta$ in case of fuzzy functions is introduced and classified into ordinary and absolute sense. Several inclusion relations among the sets are investigated. Also we have found some suitable conditions to get its relation with the generalized statistical convergence. Finally we have proved a generalized version of Tauberian theorem

The embedded ring-like feature and star formation activities in G35.673-00.847

We present a multi-wavelength study to probe the star formation (SF) process in the molecular cloud linked with the G35.673-00.847 site (hereafter MCG35.6), which is traced in a velocity range of 53-62 km/s. Multi-wavelength images reveal a semi-ring-like feature (associated with ionized gas emission) and an embedded face-on ring-like feature (without the NVSS 1.4 GHz radio emission; where 1-sigma ~ 0.45 mJy/beam) in the MCG35.6. The semi-ring-like feature is originated by the ionizing feedback from a star with spectral type B0.5V-B0V. The central region of the ring-like feature does not contain detectable ionized gas emission, indicating that the ring-like feature is unlikely to be produced by the ionizing feedback from a massive star. Several embedded Herschel clumps and young stellar objects (YSOs) are identified in the MCG35.6, tracing the ongoing SF activities within the cloud. The polarization information from the Planck and GPIPS data trace the plane-of-sky magnetic field, which is oriented parallel to the major axis of the ring-like feature. At least five clumps (having M_clump ~ 740 - 1420 M_sun) seem to be distributed in an almost regularly spaced manner along the ring-like feature and contain noticeable YSOs. Based on the analysis of the polarization and molecular line data, three subregions containing the clumps are found to be magnetically supercritical in the ring-like feature. Altogether, the existence of the ring-like feature and the SF activities on its edges can be explained by the magnetic field mediated process as simulated by Li & Nakamura (2002).Comment: 26 pages, 12 figures, 5 tables. Accepted for publication in The Astrophysical Journa

Massive young stellar object W42-MME: The discovery of an infrared jet using VLT/NACO near-infrared images

We report on the discovery of an infrared jet from a deeply embedded infrared counterpart of 6.7 GHz methanol maser emission (MME) in W42 (i.e. W42-MME). We also investigate that W42-MME drives a parsec-scale H2 outflow, with detection of bow shock feature at ~0.52 pc to the north. The inner ~0.4 pc part of the H2 outflow has a position angle of ~18 deg and the position angle of ~40 deg is found farther away on either side of outflow from W42-MME. W42-MME is detected at wavelengths longer than 2.2 microns and is a massive young stellar object, with the estimated stellar mass of 19+-4 Msun. We map the inner circumstellar environment of W42-MME using VLT/NACO adaptive optics Ks and L' observations at resolutions ~0.2 arcsec and ~0.1 arcsec, respectively. We discover a collimated jet in the inner 4500 AU using the L' band, which contains prominent Br alpha line emission. The jet is located inside an envelope/cavity (extent ~10640 AU) that is tapered at both ends and is oriented along the north-south direction. Such observed morphology of outflow cavity around massive star is scarcely known and is very crucial for understanding the jet-outflow formation process in massive star formation. Along the flow axis, which is parallel to the previously known magnetic field, two blobs are found in both the NACO images at distances of ~11800 AU, located symmetrically from W42-MME. The observed W42-MME jet-outflow configuration can be used to constrain the jet launching and jet collimation models in massive star formation.Comment: 6 pages, 5 figures, Accepted for publication in The Astrophysical Journa

Embedded filaments in IRAS 05463+2652: early stage of fragmentation and star formation activities

We present a multi-wavelength data analysis of IRAS 05463+2652 (hereafter I05463+2652) to study star formation mechanisms. A shell-like structure around I05463+2652 is evident in the Herschel column density map, which is not associated with any ionized emission. Based on the Herschel sub-millimeter images, several parsec-scale filaments (including two elongated filaments, "s-fl" and "nw-fl" having lengths of ~6.4 pc and ~8.8 pc, respectively) are investigated in I05463+2652 site. Herschel temperature map depicts all these features in a temperature range of ~11-13 K. 39 clumps are identified and have masses between ~70-945 M$_\odot$. A majority of clumps (having M_clump >= 300 M$_\odot$) are distributed toward the shell-like structure. 175 young stellar objects (YSOs) are selected using the photometric 1-5 microns data and a majority of these YSOs are distributed toward the four areas of high column density >= 5 x 10^{21} cm^{-2}; A_V ~5.3 mag) in the shell-like structure, where massive clumps and a spatial association with filament(s) are also observed. The knowledge of observed masses per unit length of elongated filaments and critical mass length reveals that they are supercritical. The filament "nw-fl" is fragmented into five clumps (having M_clump ~100-545 M$_\odot$) and contains noticeable YSOs, while the other filament "s-fl" is fragmented into two clumps (having M_clump ~170-215 M$_\odot$) without YSOs. Together, these observational results favor the role of filaments in star formation process in I05480+2545. This study also reveals the filament "s-fl", containing two starless clumps, at an early stage of fragmentation.Comment: 13 pages, 6 figures, 1 table, Accepted for publication in The Astrophysical Journa