On the measurement of frequency and of its sample variance with high-resolution counters

A frequency counter measures the input frequency $\bar{\nu}$ averaged over a suitable time $\tau$, versus the reference clock. High resolution is achieved by interpolating the clock signal. Further increased resolution is obtained by averaging multiple frequency measurements highly overlapped. In the presence of additive white noise or white phase noise, the square uncertainty improves from $\smash{\sigma^2_\nu\propto1/\tau^2}$ to $\smash{\sigma^2_\nu\propto1/\tau^3}$. Surprisingly, when a file of contiguous data is fed into the formula of the two-sample (Allan) variance $\smash{\sigma^2_y(\tau)=\mathbb{E}\{\frac12(\bar{y}_{k+1}-\bar{y}_k) ^2\}}$ of the fractional frequency fluctuation $y$, the result is the \emph{modified} Allan variance mod $\sigma^2_y(\tau)$. But if a sufficient number of contiguous measures are averaged in order to get a longer $\tau$ and the data are fed into the same formula, the results is the (non-modified) Allan variance. Of course interpretation mistakes are around the corner if the counter internal process is not well understood.Comment: 14 pages, 5 figures, 1 table, 18 reference

Radio and infrared study of the star forming region IRAS 20286+4105

A multi-wavelength investigation of the star forming complex IRAS 20286+4105, located in the Cygnus-X region, is presented here. Near-infrared K-band data is used to revisit the cluster / stellar group identified in previous studies. The radio continuum observations, at 610 and 1280 MHz show the presence of a HII region possibly powered by a star of spectral type B0 - B0.5. The cometary morphology of the ionized region is explained by invoking the bow-shock model where the likely association with a nearby supernova remnant is also explored. A compact radio knot with non-thermal spectral index is detected towards the centre of the cloud. Mid-infrared data from the Spitzer Legacy Survey of the Cygnus-X region show the presence of six Class I YSOs inside the cloud. Thermal dust emission in this complex is modelled using Herschel far-infrared data to generate dust temperature and column density maps. Herschel images also show the presence of two clumps in this region, the masses of which are estimated to be {\sim} 175 M{\sun} and 30 M{\sun}. The mass-radius relation and the surface density of the clumps do not qualify them as massive star forming sites. An overall picture of a runaway star ionizing the cloud and a triggered population of intermediate-mass, Class I sources located toward the cloud centre emerges from this multiwavelength study. Variation in the dust emissivity spectral index is shown to exist in this region and is seen to have an inverse relation with the dust temperature.Comment: 20 pages, 16 figures, accepted for publication in MNRA

Star formation activity in the southern Galactic HII region G351.63-1.25

The southern Galactic high mass star-forming region, G351.6-1.3, is a HII region-molecular cloud complex with a luminosity of 2.0 x 10^5 L_sun, located at a distance of 2.4 kpc. In this paper, we focus on the investigation of the associated HII region, embedded cluster and the interstellar medium in the vicinity of G351.6-1.3. We address the identification of exciting source(s) as well as the census of stellar populations. The ionised gas distribution has been mapped using the Giant Metrewave Radio Telescope (GMRT), India at three continuum frequencies: 1280, 610 and 325 MHz. The HII region shows an elongated morphology and the 1280 MHz map comprises six resolved high density regions encompassed by diffuse emission spanning 1.4 pc x 1.0 pc. The zero age main-sequence (ZAMS) spectral type of the brightest radio core is O7.5. We have carried out near-infrared observations in the JHKs bands using the SIRIUS instrument on the 1.4 m Infrared Survey Facility (IRSF) telescope. The near-infrared images reveal the presence of a cluster embedded in nebulous fan-shaped emission. The log-normal slope of the K-band luminosity function of the embedded cluster is found to be 0.27 +- 0.03 and the fraction of the near-infrared excess stars is estimated to be 43%. These indicate that the age of the cluster is consistent with 1 Myr. The champagne flow model from a flat, thin molecular cloud is used to explain the morphology of radio emission with respect to the millimetre cloud and infrared brightness.Comment: 18 pages, 8 figures, To be published in MNRA

An audit cycle to improve an emergency surgery ambulatory clinic

Marés Deulovol, Frederic; Florensa Ferrer, Adolf;Vilaseca, JosepPla mig de l'escultura de bonze situada a la part inferior de l'Obelisc a Pi i Margall. Mesura 4,19 x 1,21 x 0,70 metres i és de escultura de bronze, obelisc aplacat de granit gris

Model breaking points conceptualized

Current curriculum initiatives (e.g. National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) advocate that models be used in the mathematics classroom. However, despite their apparent promise, there comes a point when models break, a point in the mathematical problem space where the model cannot, or arguable should not, be used. In this work, we explore the breaking point of the chip model for integer subtraction and the area model for fraction addition. Breaking is inevitable – either because no one model is robust enough to be applicable in a very large problem space and/or because the modifications required to keep the model functioning weaken or even eliminate its benefits. While models are often intended to serve as visual illustrations or embodiments of a concept, adaptions at the model breaking point can turn model use into nothing more than executing the graphical analogue to a not-well-understood procedure. The act of identifying model breaking points illuminates the affordances and constraints of the model. This provides students a unique opportunity to discriminate across mathematical models to develop a meta-level understanding of the relationship between models and the mathematics those models are intended to support

Infrared study of the southern galactic star-forming regions associated with IRAS 10049-5657 and IRAS 10031-5632

We investigate the physical conditions of the interstellar medium and stellar components in the regions of the southern Galactic star-forming complexes associated with IRAS 10049-5657 and IRAS 10031-5632. These regions have been mapped simultaneously in two far-infrared bands (λeff ~150 and 210 µm), with ~1' angular resolution using the Tata Institute of Fundamental Research 1 m balloon-borne telescope. Spatial distribution of the temperature of cool dust and optical depth at 200 µm have been obtained taking advantage of the similar beams in the two bands. The HIRES processed Infrared Astronomical Satellite (IRAS) maps at 12, 25, 60, and 100 µm have been used for comparison. Using the Two Micron All Sky Survey near-infrared sources, we find the stellar populations of the embedded young clusters. A rich cluster of OB stars is seen in the IRAS 10049-5657 region. The fits to the stellar density radial profile of the cluster associated with IRAS 10049-5657 have been explored with the inverse radius profile as well as the King's profile; the cluster radius is ~2 pc. The source in the cluster closest to the IRAS peak is IRA-7, which lies above the zero-age main-sequence curve of spectral type O5 in the color-magnitude diagram. Unlike IRAS 10049-5657, a small cluster comprising a few deeply embedded sources is seen at the location of IRAS 10031-5632. Self-consistent radiative transfer modeling aimed at extracting important physical and geometrical details of the two IRAS sources shows that the best-fit models are in good agreement with the observed spectral energy distributions. The geometric details of the associated cloud and optical depths (t100) have been estimated. A uniform density distribution of dust and gas is implied for both the sources. In addition, the infrared ionic fine-structure line emission from gas has been modeled for both the regions and compared with data from the IRAS low-resolution spectrometer. For IRAS 10049-5657, the observed and modeled luminosities for most lines agree within a factor of 4 while for IRAS 10031-5632 we find a discrepancy of a factor of 100 and it is likely that some basic assumptions of the model are not valid in this case