Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry

Based on the observation that the moduli of a link variable on a cyclic group modify Connes' distance on this group, we construct several action functionals for this link variable within the framework of noncommutative geometry. After solving the equations of motion, we find that one type of action gives nontrivial vacuum solution for gravity on this cyclic group in a broad range of coupling constants and that such solutions can be expressed with Chebyshev's polynomials.Comment: Latex 7 pages; no figures. Significant modifications being given, with references adde

Identification of Candidate Millisecond Pulsars from Fermi LAT Observations II

Following our work presented in Dai et al. (2016), we report our detailed data analysis for another 38 Fermi gamma-ray un-associated sources. These sources are selected from the Fermi Large Area Telescope (LAT) third source catalog on the basis of the properties of known gamma-ray millisecond pulsars (MSPs) and for the purpose of finding likely candidate MSPs. From our analysis of the LAT data, we identify that among the 38 sources, 28 of them are single point-like sources with clean background and their spectra show significant curvature. We also conduct analysis of archival X-ray data available for 24 of the 28 sources. In the fields of 10 sources, there are at least one X-ray object, and in those of the other 14 sources, no X-ray object is detected but probably due to the X-ray observations being short. We discuss the possible MSP nature for these sources. Six of them(J0514.6-4406, J1035.7-6720, J1624.2-4041, J1744.1-7619, J1946.4-5403, and J2039.6-5618) are most likely associated with pulsars because of multi-wavelength identifications including direct radio or gamma-ray detection of pulsations. To firmly establish the associations or verify the MSP nature for other sources, deep X-ray and/or optical observations are needed.Comment: 18 pages, 4 figure