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Register a new userA Cepheid is No More: Hubbles Variable 19 in M33
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We report on the remarkable evolution in the light curve of a variable star discovered by Hubble (1926) in M33 and classified by him as a Cepheid. Early in the 20th century, the variable, designated as V19, exhibited a 54.7 day period, an intensity-weighted mean B magnitude of 19.59+/-0.23 mag, and a B amplitude of 1.1 mag. Its position in the P-L plane was consistent with the relation derived by Hubble from a total of 35 variables. Modern observations by the DIRECT project show a dramatic change in the properties of V19: its mean B magnitude has risen to 19.08 +/- 0.05 mag and its B amplitude has decreased to less than 0.1 mag. V19 does not appear to be a classical (Population I) Cepheid variable at present, and its nature remains a mystery. It is not clear how frequent such objects are nor how often they could be mistaken for classical Cepheids.
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We present a modern ephemeris and modern light curve of the first-discovered Cepheid variable in M31, Edwin Hubbles M31-V1. Observers of the American Association of Variable Star Observers undertook these observations during the latter half of 2010. The observations were in support of an outreach program by the Space Telescope Science Institutes Hubble Heritage project, but the resulting data are the first concentrated observations of M31-V1 made in modern times. AAVSO observers obtained 214 V-band, Rc-band, and unfiltered observations from which a current ephemeris was derived. The ephemeris derived from these observations is JD(Max) = 2455430.5(+/-0.5) + 31.4 (+/-0.1) E. The period derived from the 2010 data are in agreement with the historic values of the period, but the single season of data precludes a more precise determination of the period or measurement of the period change using these data alone. However, using an ephemeris based upon the period derived by Baade and Swope we are able to fit all of the observed data acceptably well. Continued observations in the modern era will be very valuable in linking these modern data with data from the 1920s-30s and 1950s, and will enable us to measure period change in this historic Cepheid. In particular, we strongly encourage intensive observations of this star around predicted times of maximum to constrain the date of maximum to better than 0.5 days.
We present a new luminous star in M33 located in the nuclear region. The star shows strong FeII and [FeII] forest, hydrogen emissions in the spectrum, as well as nebular lines. TiII and SiII lines were detected in absorption, their radial velocity shifted by ~ -30km/s relative to emission lines. The star is variable over seven years with 0.5 mag variations over a year. We studied its spectral energy distribution together with five confirmed Luminous Blue Variables and Var A in M33 using homogeneous data and methods. We found the stars bolometric luminosity to be log(L/Lsun)~6.27, a surface temperature of T~16000K and black body temperatures of two dust components of T~900 and 420K. The new star has properties intermediate between the LBVs and VarA (probable cool hypergiant). In the same time it has a hot photosphere, LBV-like luminosity and an extensive circumstellar material (strong [CaII] lines). In these seven luminous variables in M33 we find the total range of the hot component luminosities is 1.0 dex, but that of the dust componets is 2.0 dex. We conclude that the dust phenomenon in the luminous variables is temporary and variable, and that dust activity may follow strong eruptions.
Galaxies that contain bulges appear to contain central black holes whose masses correlate with the velocity dispersion of the bulge. We show that no corresponding relationship applies in the pure disk galaxy M33. Three-integral dynamical models fit Hubble Space Telescope WFPC2 photometry and STIS spectroscopy best if the central black hole mass is zero. The upper limit is 1500 M_sun. This is significantly below the mass expected from the velocity dispersion of the nucleus and far below any mass predicted from the disk kinematics. Our results suggest that supermassive black holes are associated only with galaxy bulges and not with their disks.
By the theorem of Mantel $[5]$ it is known that a graph with $n$ vertices and $lfloor frac{n^{2}}{4} rfloor+1$ edges must contain a triangle. A theorem of ErdH{o}s gives a strengthening: there are not only one, but at least $lfloorfrac{n}{2}rfloor$ triangles. We give a further improvement: if there is no vertex contained by all triangles then there are at least $n-2$ of them. There are some natural generalizations when $(a)$ complete graphs are considered (rather than triangles), $(b)$ the graph has $t$ extra edges (not only one) or $(c)$ it is supposed that there are no $s$ vertices such that every triangle contains one of them. We were not able to prove these generalizations, they are posed as conjectures.
Serverless computing, also known as Functions-as-a-Service, is a recent paradigm aimed at simplifying the programming of cloud applications. The idea is that developers design applications in terms of functions, which are then deployed on a cloud infrastructure. The infrastructure takes care of executing the functions whenever requested by remote clients, dealing automatically with distribution and scaling with respect to inbound traffic. While vendors already support a variety of programming languages for serverless computing (e.g. Go, Java, Javascript, Python), as far as we know there is no reference model yet to formally reason on this paradigm. In this paper, we propose the first formal programming model for serverless computing, which combines ideas from both the $lambda$-calculus (for functions) and the $pi$-calculus (for communication). To illustrate our proposal, we model a real-world serverless system. Thanks to our model, we are also able to capture and pinpoint the limitations of current vendor technologies, proposing possible amendments.
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