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A COMMON FIXED POINT THEOREM IN AN M*-METRIC SPACE AND AN APPLICATION
Gharib M. Gharib,Abed Al-Rahman M. Malkawi,Ayat M. Rabaiah,Wasfi A. Shatanawi,Maha S. Alsauodi 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.2
In this paper, we introduce the concept of M*-metric spaces and how much the M*-metric and the b-metric spaces are related. Moreover, we introduce some ways of generating M*-metric spaces. Also, we investigate some types of convergence associated with M*-metric spaces. Some common fixed point for contraction and generalized contraction mappings in M*-metric spaces. Our work has been supported by many examples and an application.
MOA-2010-BLG-328Lb: A SUB-NEPTUNE ORBITING VERY LATE M DWARF?
Furusawa, K.,Udalski, A.,Sumi, T.,Bennett, D. P.,Bond, I. A.,Gould, A.,Jørgensen, U. G.,Snodgrass, C.,Prester, D. Dominis,Albrow, M. D.,Abe, F.,Botzler, C. S.,Chote, P.,Freeman, M.,Fukui, A.,Harris, P IOP Publishing 2013 The Astrophysical journal Vol.779 No.2
<P>We analyze the planetary microlensing event MOA-2010-BLG-328. The best fit yields host and planetary masses of M-h = 0.11 +/- 0.01 M-circle dot and M-p = 9.2 +/- 2.2 M-circle dot, corresponding to a very late M dwarf and sub-Neptune-mass planet, respectively. The system lies at D-L = 0.81 +/- 0.10 kpc with projected separation r(perpendicular to) = 0.92 +/- 0.16 AU. Because of the host's a priori unlikely close distance, as well as the unusual nature of the system, we consider the possibility that the microlens parallax signal, which determines the host mass and distance, is actually due to xallarap (source orbital motion) that is being misinterpreted as parallax. We show a result that favors the parallax solution, even given its close host distance. We show that future high-resolution astrometric measurements could decisively resolve the remaining ambiguity of these solutions.</P>
MOA-2011-BLG-293Lb: A TEST OF PURE SURVEY MICROLENSING PLANET DETECTIONS
Yee, J. C.,Shvartzvald, Y.,Gal-Yam, A.,Bond, I. A.,Udalski, A.,Kozłowski, S.,Han, C.,Gould, A.,Skowron, J.,Suzuki, D.,Abe, F.,Bennett, D. P.,Botzler, C. S.,Chote, P.,Freeman, M.,Fukui, A.,Furusawa, K. IOP Publishing 2012 The Astrophysical journal Vol.755 No.2
<P>Because of the development of large-format, wide-field cameras, microlensing surveys are now able to monitor millions of stars with sufficient cadence to detect planets. These new discoveries will span the full range of significance levels including planetary signals too small to be distinguished from the noise. At present, we do not understand where the threshold is for detecting planets. MOA-2011-BLG-293Lb is the first planet to be published from the new surveys, and it also has substantial follow-up observations. This planet is robustly detected in survey+follow-up data (Delta chi(2) similar to 5400). The planet/host mass ratio is q = (5.3 similar to 0.2) x 10(-3). The best-fit projected separation is s = 0.548 +/- 0.005 Einstein radii. However, due to the s <-> s(-1) degeneracy, projected separations of s-1 are only marginally disfavored at Delta chi(2) = 3. A Bayesian estimate of the host mass gives M-L = 0.43(-0.17)(+0.27) M-circle dot, with a sharp upper limit of M-L < 1.2 M-circle dot from upper limits on the lens flux. Hence, the planet mass is m(p) = 2.4(-0.9)(+1.5) M-Jup, and the physical projected separation is either r(perpendicular to) similar or equal to 1.0 AU or r(perpendicular to) similar or equal to 3.4 AU. We show that survey data alone predict this solution and are able to characterize the planet, but the Delta chi(2) is much smaller (Delta chi(2) similar to 500) than with the follow-up data. The Delta chi(2) for the survey data alone is smaller than for any other securely detected planet. This event suggests a means to probe the detection threshold, by analyzing a large sample of events like MOA-2011-BLG-293, which have both follow-up data and high-cadence survey data, to provide a guide for the interpretation of pure survey microlensing data.</P>
CAN THE MASSES OF ISOLATED PLANETARY-MASS GRAVITATIONAL LENSES BE MEASURED BY TERRESTRIAL PARALLAX?
Freeman, M.,Philpott, L. C.,Abe, F.,Albrow, M. D.,Bennett, D. P.,Bond, I. A.,Botzler, C. S.,Bray, J. C.,Cherrie, J. M.,Christie, G. W.,Dionnet, Z.,Gould, A.,Han, C.,Heyrovský,, D.,McCormick, J. IOP Publishing 2015 The Astrophysical journal Vol.799 No.2
<P>Recently Sumi et al. reported evidence for a large population of planetary-mass objects ( PMOs) that are either unbound or orbit host stars in orbits >= 10 AU. Their result was deduced from the statistical distribution of durations of gravitational microlensing events observed by the MOA collaboration during 2006 and 2007. Here we study the feasibility of measuring the mass of an individual PMO through microlensing by examining a particular event, MOA-2011-BLG-274. This event was unusual as the duration was short, the magnification high, the source-size effect large, and the angular Einstein radius small. Also, it was intensively monitored from widely separated locations under clear skies at low air masses. Choi et al. concluded that the lens of the event may have been a PMO but they did not attempt a measurement of its mass. We report here a re-analysis of the event using re-reduced data. We confirm the results of Choi et al. and attempt a measurement of the mass and distance of the lens using the terrestrial parallax effect. Evidence for terrestrial parallax is found at a 3 sigma level of confidence. The best fit to the data yields the mass and distance of the lens as 0.80 +/- 0.30 M-J and 0.80 +/- 0.25 kpc respectively. We exclude a host star to the lens out to a separation similar to 40 AU. Drawing on our analysis of MOA-2011-BLG-274 we propose observational strategies for future microlensing surveys to yield sharper results on PMOs including those down to super-Earth mass.</P>
OGLE-2013-BLG-0132Lb and OGLE-2013-BLG-1721Lb: Two Saturn-mass Planets Discovered around M-dwarfs
Mró,z, Przemek,Udalski, A.,Bond, I. A.,Skowron, J.,Sumi, T.,Han, C.,Szymań,ski, M. K.,Soszyń,ski, I.,Poleski, R.,Pietrukowicz, P.,Kozłowski, S.,Wyrzykowski, Ł.,Ulaczyk, K.,Abe, F.,Asak American Astronomical Society 2017 The Astronomical journal Vol.154 No.5
<P>We present the discovery of two planetary systems consisting of a Saturn-mass planet orbiting an M-dwarf, which were detected in faint microlensing events OGLE-2013-BLG-0132 and OGLE-2013-BLG-1721. The planetary anomalies were covered with high cadence by Optical Gravitational Lensing Experiment (OGLE) and Microlensing Observations in Astrophysics (MOA) photometric surveys. The light curve modeling indicates that the planet-to-host mass ratios are (5.15 +/- 0.28) x 10(-4) and (13.18 +/- 0.72) x 10(-4), respectively. Both events were too short and too faint to measure a reliable parallax signal and hence the lens mass. We therefore used a Bayesian analysis to estimate the masses of both planets: 0.29(-0.13) (+0.16) M-Jup (OGLE-2013-BLG-0132Lb) and 0.64(-0.31)(+0.35) M-Jup (OGLE-2013-BLG-1721Lb). Thanks to a high relative proper motion, OGLE-2013-BLG-0132 is a promising candidate for the high-resolution imaging follow-up. Both planets belong to an increasing sample of sub-Jupiter-mass planets orbiting M-dwarfs beyond the snow line.</P>
MICROLENSING DISCOVERY OF A POPULATION OF VERY TIGHT, VERY LOW MASS BINARY BROWN DWARFS
Choi, J.-Y.,Han, C.,Udalski, A.,Sumi, T.,Gaudi, B. S.,Gould, A.,Bennett, D. P.,Dominik, M.,Beaulieu, J.-P.,Tsapras, Y.,Bozza, V.,Abe, F.,Bond, I. A.,Botzler, C. S.,Chote, P.,Freeman, M.,Fukui, A.,Furu IOP Publishing 2013 The Astrophysical journal Vol.768 No.2
<P>Although many models have been proposed, the physical mechanisms responsible for the formation of low-mass brown dwarfs (BDs) are poorly understood. The multiplicity properties and minimum mass of the BD mass function provide critical empirical diagnostics of these mechanisms. We present the discovery via gravitational microlensing of two very low mass, very tight binary systems. These binaries have directly and precisely measured total system masses of 0.025 M-circle dot and 0.034 M-circle dot, and projected separations of 0.31 AU and 0.19 AU, making them the lowest-mass and tightest field BD binaries known. The discovery of a population of such binaries indicates that BD binaries can robustly form at least down to masses of similar to 0.02 M-circle dot. Future microlensing surveys will measure a mass-selected sample of BD binary systems, which can then be directly compared to similar samples of stellar binaries.</P>
Ground-based Parallax Confirmed by<i>Spitzer</i>: Binary Microlensing Event MOA-2015-BLG-020
Wang, Tianshu,Zhu, Wei,Mao, Shude,Bond, I. A.,Gould, A.,Udalski, A.,Sumi, T.,Bozza, V.,Ranc, C.,Cassan, A.,Yee, J. C.,Han, C.,Abe, F.,Asakura, Y.,Barry, R.,Bennett, D. P.,Bhattacharya, A.,Donachie, M. American Astronomical Society 2017 The Astrophysical journal Vol.845 No.2
<P>We present the analysis of the binary gravitational microlensing event MOA-2015-BLG-020. The event has a fairly long timescale (similar to 63 days) and thus the light curve deviates significantly from the lensing model that is based on the rectilinear lens-source relative motion. This enables us to measure the microlensing parallax through the annual parallax effect. The microlensing parallax parameters constrained by the ground-based data are confirmed by the Spitzer observations through the satellite parallax method. By additionally measuring the angular Einstein radius from the analysis of the resolved caustic crossing, the physical parameters of the lens are determined. It is found that the binary lens is composed of two dwarf stars with masses M-1= 0.606 +/- 0.028M(circle dot) and M-2= 0.125 +/- 0.006 M-circle dot in the Galactic disk. Assuming that the source star is at the same distance as the bulge red clump stars, we find the lens is at a distance D-L = 2.44 +/- 0.10 kpc. We also provide a summary and short discussion of all of the published microlensing events in which the annual parallax effect is confirmed by other independent observations.</P>
OGLE-2014-BLG-0289: Precise Characterization of a Quintuple-peak Gravitational Microlensing Event
Udalski, A.,Han, C.,Bozza, V.,Gould, A.,Bond, I. A.,Mró,z, P.,Skowron, J.,Wyrzykowski, Ł.,Szymań,ski, M. K.,Soszyń,ski, I.,Ulaczyk, K.,Poleski, R.,Pietrukowicz, P.,Kozłowski, S.,Abe, F American Astronomical Society 2018 The Astrophysical journal Vol.853 No.1
<P>We present the analysis of the binary-microlensing event OGLE-2014-BLG-0289. The event light curve exhibits five very unusual peaks, four of which were produced by caustic crossings and the other by a cusp approach. It is found that the quintuple-peak features of the light curve provide tight constraints on the source trajectory, enabling us to precisely and accurately measure the microlensing parallax pi(E). Furthermore, the three resolved caustics allow us to measure the angular Einstein radius theta(E). From the combination of pE and qE, the physical lens parameters are uniquely determined. It is found that the lens is a binary composed of two M dwarfs with masses M-1 = 0.52 +/- 0.04 M-circle dot and M-2 = 0.42 +/- 0.03 M-circle dot separated in projection by a(perpendicular to) = 6.4 +/- 0.5 au. The lens is located in the disk with a distance of D-L = 3.3 +/- 0.3 kpc. The reason for the absence of a lensing signal in the Spitzer data is that the time of observation corresponds to the flat region of the light curve.</P>