Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory

In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.Nash equilibrium;noncooperative games

Approximate fixed point theorems in Banach spaces with applications in game theory

In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games

Ultraviolet Observations of Super-Chandrasekhar Mass Type Ia Supernova Candidates with Swift UVOT

Among Type Ia supernovae (SNe~Ia) exist a class of overluminous objects whose ejecta mass is inferred to be larger than the canonical Chandrasekhar mass. We present and discuss the UV/optical photometric light curves, colors, absolute magnitudes, and spectra of three candidate Super-Chandrasekhar mass SNe--2009dc, 2011aa, and 2012dn--observed with the Swift Ultraviolet/Optical Telescope. The light curves are at the broad end for SNe Ia, with the light curves of SN~2011aa being amongst the broadest ever observed. We find all three to have very blue colors which may provide a means of excluding these overluminous SNe from cosmological analysis, though there is some overlap with the bluest of "normal" SNe Ia. All three are overluminous in their UV absolute magnitudes compared to normal and broad SNe Ia, but SNe 2011aa and 2012dn are not optically overluminous compared to normal SNe Ia. The integrated luminosity curves of SNe 2011aa and 2012dn in the UVOT range (1600-6000 Angstroms) are only half as bright as SN~2009dc, implying a smaller 56Ni yield. While not enough to strongly affect the bolometric flux, the early time mid-UV flux makes a significant contribution at early times. The strong spectral features in the mid-UV spectra of SNe 2009dc and 2012dn suggest a higher temperature and lower opacity to be the cause of the UV excess rather than a hot, smooth blackbody from shock interaction. Further work is needed to determine the ejecta and 56Ni masses of SNe 2011aa and 2012dn and fully explain their high UV luminosities.Comment: 12 pages, 8 figures Accepted for publication in the Astrophysical Journal Data available on the Swift supernova website http://swift.gsfc.nasa.gov/docs/swift/sne/swift_sn.htm

The SkyMapper Transient Survey

The SkyMapper 1.3 m telescope at Siding Spring Observatory has now begun regular operations. Alongside the Southern Sky Survey, a comprehensive digital survey of the entire southern sky, SkyMapper will carry out a search for supernovae and other transients. The search strategy, covering a total footprint area of ~2000 deg2 with a cadence of $\leq 5$ days, is optimised for discovery and follow-up of low-redshift type Ia supernovae to constrain cosmic expansion and peculiar velocities. We describe the search operations and infrastructure, including a parallelised software pipeline to discover variable objects in difference imaging; simulations of the performance of the survey over its lifetime; public access to discovered transients; and some first results from the Science Verification data.Comment: 13 pages, 11 figures; submitted to PAS

A New Channel for the Detection of Planetary Systems Through Microlensing: II. Repeating Events

In the companion paper we began the task of systematically studying the detection of planets in wide orbits ($a > 1.5 R_E$) via microlensing surveys. In this paper we continue, focusing on repeating events. We find that, if all planetary systems are similar to our own Solar System, reasonable extensions of the present observing strategies would allow us to detect 3-6 repeating events per year along the direction to the Bulge. Indeed, if planetary systems with multiple planets are common, then future monitoring programs which lead to the discovery of thousands of stellar-lens events will likely discover events in which several different planets within a single system serve as lenses, with light curves exhibiting multiple repetitions. In this paper we discuss observing strategies to maximize the discovery of all wide-orbit planet-lens events. We also compare the likely detection rates of planets in wide orbits to those of planets located in the zone for resonant lensing. We find that, depending on the values of the planet masses and stellar radii of the lensed sources (which determine whether or not finite source size is important), and also on the sensitivity of the photometry used by observers, the detection of planets in wide orbits may be the primary route to the discovery of planets via microlensing. We also discuss how the combination of resonant and wide-orbit events can help us to learn about the distribution of planetary system properties (S 6.1). In addition, by determining the fraction of short-duration events due to planets, we indirectly derive information about the fraction of all short-duration events that may be due to low-mass MACHOs (S 6.2).Comment: 51 pages, 7 figures. To be published in the Astrophysical Journal, 20 February 1999. This completes the introduction to the discovery of planets in wide orbits begun in astro-ph/9808075, also to appear in ApJ on 20 February 199

A New Channel for the Detection of Planetary Systems Through Microlensing: I. Isolated Events Due to Planet Lenses

We propose and evaluate the feasibility of a new strategy to search for planets via microlensing. This new strategy is designed to detect planets in "wide" orbits, i.e., with orbital separation, $a$ greater than $\sim 1.5 R_E$. Planets in wide orbits may provide the dominant channel for the microlensing discovery of planets, particularly low-mass (e.g., Earth-mass) planets. This paper concentrates on events in which a single planet serves as a lens, leading to an isolated event of short duration. We point out that a distribution of events due to lensing by stars with wide-orbit planets is necessarily accompanied by a distribution of shorter- duration events. The fraction of events in the latter distribution is proportional to the average value of $\sqrt{q}$, where $q$ is the ratio between \pl and stellar masses. The position of the peak or peaks also provides a measure of the mass ratios typical of planetary systems. We study detection strategies that can optimize our ability to discover isolated short-duration events due to lensing by planets, and find that monitoring employing sensitive photometry is particularly useful. If planetary systems similar to our own are common, even modest changes in detection strategy should lead to the discovery of a few isolated events of short duration every year. We therefore also address the issue of the contamination due to stellar populations of any microlensing signal due to low-mass MACHOs. We describe how, even for isolated events of short duration, it will be possible to test the hypothesis that the lens was a planet instead of a low-mass MACHO, if the central star of the planetary system contributes a measurable fraction of the baseline flux.Comment: 37 pages, 6 figure. To be published in the Astrophysical Journal. This is part one of a series of papers on microlensing by planetary systems containing wide-orbit planets; the series represents a reorganization and extension of astro-ph/971101

Very high energy observations of the BL Lac objects 3C 66A and OJ 287

Using the Solar Tower Atmospheric Cherenkov Effect Experiment (STACEE), we have observed the BL Lac objects 3C 66A and OJ 287. These are members of the class of low-frequency-peaked BL Lac objects (LBLs) and are two of the three LBLs predicted by Costamante and Ghisellini to be potential sources of very high energy (>100 GeV) gamma-ray emission. The third candidate, BL Lacertae, has recently been detected by the MAGIC collaboration. Our observations have not produced detections; we calculate a 99% CL upper limit of flux from 3C 66A of 0.15 Crab flux units and from OJ 287 our limit is 0.52 Crab. These limits assume a Crab-like energy spectrum with an effective energy threshold of 185 GeV.Comment: 24 pages, 15 figures, Accepted for publication in Astroparticle Physic

Type Ia supernova Hubble diagram with near-infrared and optical observations

We main goal of this paper is to test whether the NIR peak magnitudes of SNe Ia could be accurately estimated with only a single observation obtained close to maximum light, provided the time of B band maximum and the optical stretch parameter are known. We obtained multi-epoch UBVRI and single-epoch J and H photometric observations of 16 SNe Ia in the redshift range z=0.037-0.183, doubling the leverage of the current SN Ia NIR Hubble diagram and the number of SNe beyond redshift 0.04. This sample was analyzed together with 102 NIR and 458 optical light curves (LCs) of normal SNe Ia from the literature. The analysis of 45 well-sampled NIR LCs shows that a single template accurately describes them if its time axis is stretched with the optical stretch parameter. This allows us to estimate the NIR peak magnitudes even with one observation obtained within 10 days from B-band maximum. We find that the NIR Hubble residuals show weak correlation with DM_15 and E(B-V), and for the first time we report a possible dependence on the J_max-H_max color. The intrinsic NIR luminosity scatter of SNe Ia is estimated to be around 0.10 mag, which is smaller than what can be derived for a similarly heterogeneous sample at optical wavelengths. In conclusion, we find that SNe Ia are at least as good standard candles in the NIR as in the optical. We showed that it is feasible to extended the NIR SN Ia Hubble diagram to z=0.2 with very modest sampling of the NIR LCs, if complemented by well-sampled optical LCs. Our results suggest that the most efficient way to extend the NIR Hubble diagram to high redshift would be to obtain a single observation close to the NIR maximum. (abridged)Comment: 39 pages, 15 figures, accepted by A&

Very high-energy observations of the two high-frequency peaked BL Lac objects 1ES 1218+304 and H 1426+428

We present results of very-high-energy gamma-ray observations (E > 160 GeV) of two high-frequency-peaked BL Lac (HBL) objects, 1ES 1218+304 and H 1426+428, with the Solar Tower Atmospheric Cherenkov Effect Experiment (STACEE). Both sources are very-high-energy gamma-ray emitters above 100 GeV, detected using ground-based Cherenkov telescopes. STACEE observations of 1ES 1218+304 and H 1426+428 did not produce detections; we present 99% CL flux upper limits for both sources, assuming spectral indices measured mostly at higher energies

Correlated variability in the blazar 3C 454.3

The blazar 3C 454.3 was revealed by the Fermi Gamma-ray Space Telescope to be in an exceptionally high flux state in July 2008. Accordingly, we performed a multi-wavelength monitoring campaign on this blazar using IR and optical observations from the SMARTS telescopes, optical, UV and X-ray data from the Swift satellite, and public-release gamma-ray data from Fermi. We find an excellent correlation between the IR, optical, UV and gamma-ray light curves, with a time lag of less than one day. The amplitude of the infrared variability is comparable to that in gamma-rays, and larger than at optical or UV wavelengths. The X-ray flux is not strongly correlated with either the gamma-rays or longer wavelength data. These variability characteristics find a natural explanation in the external Compton model, in which electrons with Lorentz factor gamma~10^(3-4) radiate synchrotron emission in the infrared-optical and also scatter accretion disk or emission line photons to gamma-ray energies, while much cooler electrons (gamma~10^(1-2)) produce X-rays by scattering synchrotron or other ambient photons.Comment: 7 pages, 3 figures, submitted to ApJ Letter