text:
• ### MagAO: Status and Science(1609.07683)

Sept. 25, 2016 astro-ph.IM
"MagAO" is the adaptive optics instrument at the Magellan Clay telescope at Las Campanas Observatory, Chile. MagAO has a 585-actuator adaptive secondary mirror and 1000-Hz pyramid wavefront sensor, operating on natural guide stars from $R$-magnitudes of -1 to 15. MagAO has been in on-sky operation for 166 nights since installation in 2012. MagAO's unique capabilities are simultaneous imaging in the visible and infrared with VisAO and Clio, excellent performance at an excellent site, and a lean operations model. Science results from MagAO include the first ground-based CCD image of an exoplanet, demonstration of the first accreting protoplanets, discovery of a new wide-orbit exoplanet, and the first empirical bolometric luminosity of an exoplanet. We describe the status, report the AO performance, and summarize the science results. New developments reported here include color corrections on red guide stars for the wavefront sensor, a new field stop stage to facilitate VisAO imaging of extended sources; and eyepiece observing at the visible-light diffraction limit of a 6.5-m telescope. We also discuss a recent hose failure that led to a glycol coolant leak, and the recovery of the adaptive secondary mirror (ASM) after this recent (Feb.\ 2016) incident.
• ### The numerical simulation tool for the MAORY multiconjugate adaptive optics system(1608.00386)

Aug. 1, 2016 astro-ph.IM
The Multiconjugate Adaptive Optics RelaY (MAORY) is and Adaptive Optics module to be mounted on the ESO European-Extremely Large Telescope (E-ELT). It is a hybrid Natural and Laser Guide System that will perform the correction of the atmospheric turbulence volume above the telescope feeding the Multi-AO Imaging Camera for Deep Observations Near Infrared spectro-imager (MICADO). We developed an end-to-end Monte- Carlo adaptive optics simulation tool to investigate the performance of a the MAORY and the calibration, acquisition, operation strategies. MAORY will implement Multiconjugate Adaptive Optics combining Laser Guide Stars (LGS) and Natural Guide Stars (NGS) measurements. The simulation tool implements the various aspect of the MAORY in an end to end fashion. The code has been developed using IDL and uses libraries in C++ and CUDA for efficiency improvements. Here we recall the code architecture, we describe the modeled instrument components and the control strategies implemented in the code.
• ### Magellan AO System $z'$, $Y_S$, and $L'$ Observations of the Very Wide 650 AU HD 106906 Planetary System(1604.06847)

April 23, 2016 astro-ph.EP
We analyze archival data from Bailey and co-workers from the $Magellan$ adaptive optics system and present the first 0.9 $\mu$m detection ($z' = 20.3\pm0.4$ mag; $\Delta z'=13.0\pm0.4$ mag) of the 11 $M_\mathrm{Jup}$ circumbinary planet HD 106906AB b, as well as the 1 and 3.8 $\mu$m detections of the debris disk around the binary. The disk has an east-west asymmetry in length and surface brightness, especially at 3.8 $\mu$m where the disk appears to be one-sided. The spectral energy distribution of b, when scaled to the $K_S$-band photometry, is consistent with 1800 K atmospheric models without significant dust reddening, unlike some young, very red, low-mass companions such as CT Cha B and 1RXS 1609 B. Therefore, the suggested circumplanetary disk of Kalas and co-workers might not contain much material, or might be closer to face-on. Finally, we suggest that the widest ($a\gtrsim100$ AU) low mass ratio ($M_\mathrm{p}/M_\mathrm{\star} \equiv q\lesssim0.01$) companions may have formed inside protoplanetary disks, but were later scattered by binary/planet interactions. Such a scattering event may have occurred for HD 106906AB b with its central binary star, but definitive proof at this time is elusive.
• ### Magellan Adaptive Optics first-light observations of the exoplanet beta Pic b. II. 3-5 micron direct imaging with MagAO+Clio, and the empirical bolometric luminosity of a self-luminous giant planet(1511.02894)

Nov. 9, 2015 astro-ph.EP, astro-ph.IM
Young giant exoplanets are a unique laboratory for understanding cool, low-gravity atmospheres. A quintessential example is the massive extrasolar planet $\beta$ Pic b, which is 9 AU from and embedded in the debris disk of the young nearby A6V star $\beta$ Pictoris. We observed the system with first light of the Magellan Adaptive Optics (MagAO) system. In Paper I we presented the first CCD detection of this planet with MagAO+VisAO. Here we present four MagAO+Clio images of $\beta$ Pic b at 3.1 $\mu$m, 3.3 $\mu$m, $L^\prime$, and $M^\prime$, including the first observation in the fundamental CH$_4$ band. To remove systematic errors from the spectral energy distribution (SED), we re-calibrate the literature photometry and combine it with our own data, for a total of 22 independent measurements at 16 passbands from 0.99--4.8 $\mu$m. Atmosphere models demonstrate the planet is cloudy but are degenerate in effective temperature and radius. The measured SED now covers $>$80\% of the planet's energy, so we approach the bolometric luminosity empirically. We calculate the luminosity by extending the measured SED with a blackbody and integrating to find log($L_{bol}$/$L_{Sun}$) $= -3.78\pm0.03$. From our bolometric luminosity and an age of 23$\pm$3 Myr, hot-start evolutionary tracks give a mass of 12.7$\pm$0.3 $M_{Jup}$, radius of 1.45$\pm$0.02 $R_{Jup}$, and $T_{eff}$ of 1708$\pm$23 K (model-dependent errors not included). Our empirically-determined luminosity is in agreement with values from atmospheric models (typically $-3.8$ dex), but brighter than values from the field-dwarf bolometric correction (typically $-3.9$ dex), illustrating the limitations in comparing young exoplanets to old brown dwarfs.
• ### New Extinction and Mass Estimates of the Low-mass Companion 1RXS 1609 B with the Magellan AO System: Evidence of an Inclined Dust Disk(1506.05816)

June 18, 2015 astro-ph.SR, astro-ph.EP
We used the Magellan adaptive optics system to image the 11 Myr substellar companion 1RXS 1609 B at the bluest wavelengths to date (z' and Ys). Comparison with synthetic spectra yields a higher temperature than previous studies of $T_\mathrm{eff}=2000\pm100\mathrm{K}$ and significant dust extinction of $A_V=4.5^{+0.5}_{-0.7}$ mag. Mass estimates based on the DUSTY tracks gives 0.012-0.015 Msun, making the companion likely a low-mass brown dwarf surrounded by a dusty disk. Our study suggests that 1RXS 1609 B is one of the 25% of Upper Scorpius low-mass members harboring disks, and it may have formed like a star and not a planet out at 320 AU.
• ### New Spatially Resolved Observations of the T Cha Transition Disk and Constraints on the Previously Claimed Substellar Companion(1501.01964)

Jan. 8, 2015 astro-ph.EP
We present multi-epoch non-redundant masking observations of the T Cha transition disk, taken at the VLT and Magellan in H, Ks, and L' bands. T Cha is one of a small number of transition disks that host companion candidates discovered by high-resolution imaging techniques, with a putative companion at a position angle of 78 degrees, separation of 62 mas, and contrast at L' of 5.1 mag. We find comparable binary parameters in our re-reduction of the initial detection images, and similar parameters in the 2011 L', 2013 NaCo L', and 2013 NaCo Ks data sets. We find a close-in companion signal in the 2012 NaCo L' dataset that cannot be explained by orbital motion, and a non-detection in the 2013 MagAO/Clio2 L' data. However, Monte-carlo simulations show that the best fits to the 2012 NaCo and 2013 MagAO/Clio2 followup data may be consistent with noise. There is also a significant probability of false non-detections in both of these data sets. We discuss physical scenarios that could cause the best fits, and argue that previous companion and scattering explanations are inconsistent with the results of the much larger dataset presented here.
• ### New Extinction and Mass Estimates from Optical Photometry of the Very Low Mass Brown Dwarf Companion CT Chamaeleontis B with the Magellan AO System(1501.01396)

Jan. 7, 2015 astro-ph.SR, astro-ph.EP
We used the Magellan adaptive optics (MagAO) system and its VisAO CCD camera to image the young low mass brown dwarf companion CT Chamaeleontis B for the first time at visible wavelengths. We detect it at r', i', z', and Ys. With our new photometry and Teff~2500 K derived from the shape its K-band spectrum, we find that CT Cha B has Av = 3.4+/-1.1 mag, and a mass of 14-24 Mj according to the DUSTY evolutionary tracks and its 1-5 Myr age. The overluminosity of our r' detection indicates that the companion has significant Halpha emission and a mass accretion rate ~6*10^-10 Msun/yr, similar to some substellar companions. Proper motion analysis shows that another point source within 2" of CT Cha A is not physical. This paper demonstrates how visible wavelength AO photometry (r', i', z', Ys) allows for a better estimate of extinction, luminosity, and mass accretion rate of young substellar companions.
• ### On the Morphology and Chemical Composition of the HR 4796A Debris Disk(1410.7753)

Oct. 28, 2014 astro-ph.SR, astro-ph.EP
[abridged] We present resolved images of the HR 4796A debris disk using the Magellan adaptive optics system paired with Clio-2 and VisAO. We detect the disk at 0.77 \microns, 0.91 \microns, 0.99 \microns, 2.15 \microns, 3.1 \microns, 3.3 \microns, and 3.8 \microns. We find that the deprojected center of the ring is offset from the star by 4.76$\pm$1.6 AU and that the deprojected eccentricity is 0.06$\pm$0.02, in general agreement with previous studies. We find that the average width of the ring is 14$^{+3}_{-2}%$, also comparable to previous measurements. Such a narrow ring precludes the existence of shepherding planets more massive than \about 4 \mj, comparable to hot-start planets we could have detected beyond \about 60 AU in projected separation. Combining our new scattered light data with archival HST/STIS and HST/NICMOS data at \about 0.5-2 \microns, along with previously unpublished Spitzer/MIPS thermal emission data and all other literature thermal data, we set out to constrain the chemical composition of the dust grains. After testing 19 individual root compositions and more than 8,400 unique mixtures of these compositions, we find that good fits to the scattered light alone and thermal emission alone are discrepant, suggesting that caution should be exercised if fitting to only one or the other. When we fit to both the scattered light and thermal emission simultaneously, we find mediocre fits (reduced chi-square \about 2). In general, however, we find that silicates and organics are the most favored, and that water ice is usually not favored. These results suggest that the common constituents of both interstellar dust and solar system comets also may reside around HR 4796A, though improved modeling is necessary to place better constraints on the exact chemical composition of the dust.
• ### A high resolution image of the inner-shell of the PCygni nebula in the infra-red [Fe II] line(1409.3721)

Sept. 12, 2014 astro-ph.SR, astro-ph.IM
We have obtained with the LBT Telescope AO system Near-Infrared camera PISCES images of the inner-shell of the nebula around the luminous blue variable star P Cygni in the [Fe II] emission line at 1.6435 {\mu}m. We have combined the images in order to cover a field of view of about 20" around P Cygni thus providing the high resolution (0".08) 2-D spatial distribution of the inner-shell of the P Cygni nebula in [Fe II]. We have identified several nebular emission regions which are characterized by an S/N>3. A comparison of our results with those available in the literature shows full consistency with the finding by Smith & Hartigan (2006) which are based on radial velocity measurements and their relatively good agreement with the extension of emission nebula in [NII] {\lambda}6584 found by Barlow et al. (1994). We have clearly detected extended emission also inside the radial distance R=7".8 and outside R=9".7 which are the nebular boundaries proposed by Smith & Hartigan (2006). New complementary spectroscopic observations to measure radial velocities and to derive the 3-D distribution of P Cygni nebula are planned.
• ### Into the Blue: AO Science with MagAO in the Visible(1407.5096)

We review astronomical results in the visible ({\lambda}<1{\mu}m) with adaptive optics. Other than a brief period in the early 1990s, there has been little astronomical science done in the visible with AO until recently. The most productive visible AO system to date is our 6.5m Magellan telescope AO system (MagAO). MagAO is an advanced Adaptive Secondary system at the Magellan 6.5m in Chile. This secondary has 585 actuators with < 1 msec response times (0.7 ms typically). We use a pyramid wavefront sensor. The relatively small actuator pitch (~23 cm/subap) allows moderate Strehls to be obtained in the visible (0.63-1.05 microns). We use a CCD AO science camera called "VisAO". On-sky long exposures (60s) achieve <30mas resolutions, 30% Strehls at 0.62 microns (r') with the VisAO camera in 0.5" seeing with bright R < 8 mag stars. These relatively high visible wavelength Strehls are made possible by our powerful combination of a next generation ASM and a Pyramid WFS with 378 controlled modes and 1000 Hz loop frequency. We'll review the key steps to having good performance in the visible and review the exciting new AO visible science opportunities and refereed publications in both broad-band (r,i,z,Y) and at Halpha for exoplanets, protoplanetary disks, young stars, and emission line jets. These examples highlight the power of visible AO to probe circumstellar regions/spatial resolutions that would otherwise require much larger diameter telescopes with classical infrared AO cameras.
• ### MagAO: Status and on-sky performance of the Magellan adaptive optics system(1407.5098)

MagAO is the new adaptive optics system with visible-light and infrared science cameras, located on the 6.5-m Magellan "Clay" telescope at Las Campanas Observatory, Chile. The instrument locks on natural guide stars (NGS) from 0$^\mathrm{th}$ to 16$^\mathrm{th}$ $R$-band magnitude, measures turbulence with a modulating pyramid wavefront sensor binnable from 28x28 to 7x7 subapertures, and uses a 585-actuator adaptive secondary mirror (ASM) to provide flat wavefronts to the two science cameras. MagAO is a mutated clone of the similar AO systems at the Large Binocular Telescope (LBT) at Mt. Graham, Arizona. The high-level AO loop controls up to 378 modes and operates at frame rates up to 1000 Hz. The instrument has two science cameras: VisAO operating from 0.5-1 $\mu$m and Clio2 operating from 1-5 $\mu$m. MagAO was installed in 2012 and successfully completed two commissioning runs in 2012-2013. In April 2014 we had our first science run that was open to the general Magellan community. Observers from Arizona, Carnegie, Australia, Harvard, MIT, Michigan, and Chile took observations in collaboration with the MagAO instrument team. Here we describe the MagAO instrument, describe our on-sky performance, and report our status as of summer 2014.
• ### Direct imaging of exoplanets in the habitable zone with adaptive optics(1407.5099)

July 18, 2014 astro-ph.EP, astro-ph.IM
One of the primary goals of exoplanet science is to find and characterize habitable planets, and direct imaging will play a key role in this effort. Though imaging a true Earth analog is likely out of reach from the ground, the coming generation of giant telescopes will find and characterize many planets in and near the habitable zones (HZs) of nearby stars. Radial velocity and transit searches indicate that such planets are common, but imaging them will require achieving extreme contrasts at very small angular separations, posing many challenges for adaptive optics (AO) system design. Giant planets in the HZ may even be within reach with the latest generation of high-contrast imagers for a handful of very nearby stars. Here we will review the definition of the HZ, and the characteristics of detectable planets there. We then review some of the ways that direct imaging in the HZ will be different from the typical exoplanet imaging survey today. Finally, we present preliminary results from our observations of the HZ of {\alpha} Centauri A with the Magellan AO system's VisAO and Clio2 cameras.
• ### On the use of asymmetric PSF on NIR images of crowded stellar fields(1407.2011)

July 8, 2014 astro-ph.IM
We present data collected using the camera PISCES coupled with the Firt Light Adaptive Optics (FLAO) mounted at the Large Binocular Telescope (LBT). The images were collected using two natural guide stars with an apparent magnitude of R<13 mag. During these observations the seeing was on average ~0.9". The AO performed very well: the images display a mean FWHM of 0.05 arcsec and of 0.06 arcsec in the J- and in the Ks-band, respectively. The Strehl ratio on the quoted images reaches 13-30% (J) and 50-65% (Ks), in the off and in the central pointings respectively. On the basis of this sample we have reached a J-band limiting magnitude of ~22.5 mag and the deepest Ks-band limiting magnitude ever obtained in a crowded stellar field: Ks~23 mag. J-band images display a complex change in the shape of the PSF when moving at larger radial distances from the natural guide star. In particular, the stellar images become more elongated in approaching the corners of the J-band images whereas the Ks-band images are more uniform. We discuss in detail the strategy used to perform accurate and deep photometry in these very challenging images. In particular we will focus our attention on the use of an updated version of ROMAFOT based on asymmetric and analytical Point Spread Functions. The quality of the photometry allowed us to properly identify a feature that clearly shows up in NIR bands: the main sequence knee (MSK). The MSK is independent of the evolutionary age, therefore the difference in magnitude with the canonical clock to constrain the cluster age, the main sequence turn off (MSTO), provides an estimate of the absolute age of the cluster. The key advantage of this new approach is that the error decreases by a factor of two when compared with the classical one. Combining ground-based Ks with space F606W photometry, we estimate the absolute age of M15 to be 13.70+-0.80 Gyr.
• ### Directly Imaged L-T Transition Exoplanets in the Mid-Infrared(1311.2085)

June 16, 2014 astro-ph.EP
Gas-giant planets emit a large fraction of their light in the mid-infrared ($\gtrsim$3$\mu$m), where photometry and spectroscopy are critical to our understanding of the bulk properties of extrasolar planets. Of particular importance are the L and M-band atmospheric windows (3-5$\mu$m), which are the longest wavelengths currently accessible to ground-based, high-contrast imagers. We present binocular LBT AO images of the HR 8799 planetary system in six narrow-band filters from 3-4$\mu$m, and a Magellan AO image of the 2M1207 planetary system in a broader 3.3$\mu$m band. These systems encompass the five known exoplanets with luminosities consistent with L$\rightarrow$T transition brown dwarfs. Our results show that the exoplanets are brighter and have shallower spectral slopes than equivalent temperature brown dwarfs in a wavelength range that contains the methane fundamental absorption feature (spanned by the narrowband filters and encompassed by the broader 3.3$\mu$m filter). For 2M1207 b, we find that thick clouds and non-equilibrium chemistry caused by vertical mixing can explain the object's appearance. For the HR 8799 planets, we present new models that suggest the atmospheres must have patchy clouds, along with non-equilibrium chemistry. Together, the presence of a heterogeneous surface and vertical mixing presents a picture of dynamic planetary atmospheres in which both horizontal and vertical motions influence the chemical and condensate profiles.
• ### Magellan Adaptive Optics first-light observations of the exoplanet $\beta$ Pic b. I. Direct imaging in the far-red optical with MagAO+VisAO and in the near-IR with NICI(1403.0560)

March 3, 2014 astro-ph.EP, astro-ph.IM
We present the first ground-based CCD ($\lambda < 1\mu$m) image of an extrasolar planet. Using MagAO's VisAO camera we detected the extrasolar giant planet (EGP) $\beta$ Pictoris b in $Y$-short ($Y_S$, 0.985 $\mu$m), at a separation of $0.470 \pm 0.010''$ and a contrast of $(1.63 \pm 0.49) \times 10^{-5}$. This detection has a signal-to-noise ratio of 4.1, with an empirically estimated upper-limit on false alarm probability of 1.0%. We also present new photometry from the NICI instrument on the Gemini-South telescope, in $CH_{4S,1\%}$ ($1.58$ $\mu m$), $K_S$ ($2.18\mu m$), and $K_{cont}$ (2.27 $\mu m$). A thorough analysis of our photometry combined with previous measurements yields an estimated near-IR spectral type of L$2.5\pm1.5$, consistent with previous estimates. We estimate log$(L_{bol}/L_{Sun})$ = $-3.86 \pm 0.04$, which is consistent with prior estimates for $\beta$ Pic b and with field early-L brown dwarfs. This yields a hot-start mass estimate of $11.9 \pm 0.7$ $M_{Jup}$ for an age of $21\pm4$ Myr, with an upper limit below the deuterium burning mass. Our $L_{bol}$ based hot-start estimate for temperature is $T_{eff}=1643\pm32$ K (not including model dependent uncertainty). Due to the large corresponding model-derived radius of $R=1.43\pm0.02$ $R_{Jup}$, this $T_{eff}$ is $\sim$$250$ K cooler than would be expected for a field L2.5 brown dwarf. Other young, low-gravity (large radius), ultracool dwarfs and directly-imaged EGPs also have lower effective temperatures than are implied by their spectral types. However, such objects tend to be anomalously red in the near-IR compared to field brown dwarfs. In contrast, $\beta$ Pic b has near-IR colors more typical of an early-L dwarf despite its lower inferred temperature.
• ### HD 106906 b: A planetary-mass companion outside a massive debris disk(1312.1265)

Dec. 4, 2013 astro-ph.EP
We report the discovery of a planetary-mass companion, HD 106906 b, with the new Magellan Adaptive Optics (MagAO) + Clio2 system. The companion is detected with Clio2 in three bands: $J$, $K_S$, and $L^\prime$, and lies at a projected separation of 7.1'' (650 AU). It is confirmed to be comoving with its $13\pm2$ Myr-old F5 host using Hubble Space Telescope/Advanced Camera for Surveys astrometry over a time baseline of 8.3 yr. DUSTY and COND evolutionary models predict the companion's luminosity corresponds to a mass of $11\pm2 M_{Jup}$, making it one of the most widely separated planetary-mass companions known. We classify its Magellan/Folded-Port InfraRed Echellette $J/H/K$ spectrum as L$2.5\pm1$; the triangular $H$-band morphology suggests an intermediate surface gravity. HD 106906 A, a pre-main-sequence Lower Centaurus Crux member, was initially targeted because it hosts a massive debris disk detected via infrared excess emission in unresolved Spitzer imaging and spectroscopy. The disk emission is best fit by a single component at 95 K, corresponding to an inner edge of 15-20 AU and an outer edge of up to 120 AU. If the companion is on an eccentric ($e>0.65$) orbit, it could be interacting with the outer edge of the disk. Close-in, planet-like formation followed by scattering to the current location would likely disrupt the disk and is disfavored. Furthermore, we find no additional companions, though we could detect similar-mass objects at projected separations $>35$ AU. In situ formation in a binary-star-like process is more probable, although the companion-to-primary mass ratio, at $<1\%$, is unusually small.
• ### The First Circumstellar Disk Imaged in Silhouette with Adaptive Optics: MagAO Imaging of Orion 218-354(1308.4147)

Aug. 21, 2013 astro-ph.SR, astro-ph.EP
We present high resolution adaptive optics (AO) corrected images of the silhouette disk Orion 218-354 taken with Magellan AO (MagAO) and its visible light camera, VisAO, in simultaneous differential imaging (SDI) mode at H-alpha. This is the first image of a circumstellar disk seen in silhouette with adaptive optics and is among the first visible light adaptive optics results in the literature. We derive the disk extent, geometry, intensity and extinction profiles and find, in contrast with previous work, that the disk is likely optically-thin at H-alpha. Our data provide an estimate of the column density in primitive, ISM-like grains as a function of radius in the disk. We estimate that only ~10% of the total sub-mm derived disk mass lies in primitive, unprocessed grains. We use our data, Monte Carlo radiative transfer modeling and previous results from the literature to make the first self-consistent multiwavelength model of Orion 218-354. We find that we are able to reproduce the 1-1000micron SED with a ~2-540AU disk of the size, geometry, small vs. large grain proportion and radial mass profile indicated by our data. This inner radius is a factor of ~15 larger than the sublimation radius of the disk, suggesting that it is likely cleared in the very interior.
• ### The Gray Needle: Large Grains in the HD 15115 Debris Disk from LBT/PISCES/Ks and LBTI/LMIRcam/L' Adaptive Optics Imaging(1203.2619)

May 28, 2012 astro-ph.SR
We present diffraction-limited \ks band and \lprime adaptive optics images of the edge-on debris disk around the nearby F2 star HD 15115, obtained with a single 8.4 m primary mirror at the Large Binocular Telescope. At \ks band the disk is detected at signal-to-noise per resolution element (SNRE) \about 3-8 from \about 1-2\fasec 5 (45-113 AU) on the western side, and from \about 1.2-2\fasec 1 (63-90 AU) on the east. At \lprime the disk is detected at SNRE \about 2.5 from \about 1-1\fasec 45 (45-90 AU) on both sides, implying more symmetric disk structure at 3.8 \microns . At both wavelengths the disk has a bow-like shape and is offset from the star to the north by a few AU. A surface brightness asymmetry exists between the two sides of the disk at \ks band, but not at \lprime . The surface brightness at \ks band declines inside 1\asec (\about 45 AU), which may be indicative of a gap in the disk near 1\asec. The \ks - \lprime disk color, after removal of the stellar color, is mostly grey for both sides of the disk. This suggests that scattered light is coming from large dust grains, with 3-10 \microns -sized grains on the east side and 1-10 \microns dust grains on the west. This may suggest that the west side is composed of smaller dust grains than the east side, which would support the interpretation that the disk is being dynamically affected by interactions with the local interstellar medium.
• ### First Light LBT AO Images of HR 8799 bcde at 1.65 and 3.3 Microns: New Discrepancies between Young Planets and Old Brown Dwarfs(1203.2615)

April 27, 2012 astro-ph.EP, astro-ph.IM
As the only directly imaged multiple planet system, HR 8799 provides a unique opportunity to study the physical properties of several planets in parallel. In this paper, we image all four of the HR 8799 planets at H-band and 3.3 microns with the new LBT adaptive optics system, PISCES, and LBTI/LMIRCam. Our images offer an unprecedented view of the system, allowing us to obtain H and 3.3\$ micron photometry of the innermost planet (for the first time) and put strong upper-limits on the presence of a hypothetical fifth companion. We find that all four planets are unexpectedly bright at 3.3 microns compared to the equilibrium chemistry models used for field brown dwarfs, which predict that planets should be faint at 3.3 microns due to CH4 opacity. We attempt to model the planets with thick-cloudy, non-equilibrium chemistry atmospheres, but find that removing CH4 to fit the 3.3 micron photometry increases the predicted L' (3.8 microns) flux enough that it is inconsistent with observations. In an effort to fit the SED of the HR 8799 planets, we construct mixtures of cloudy atmospheres, which are intended to represent planets covered by clouds of varying opacity. In this scenario, regions with low opacity look hot and bright, while regions with high opacity look faint, similar to the patchy cloud structures on Jupiter and L/T transition brown-dwarfs. Our mixed cloud models reproduce all of the available data, but self-consistent models are still necessary to demonstrate their viability.
• ### Large Binocular Telescope Adaptive Optics System: New achievements and perspectives in adaptive optics(1203.2761)

March 13, 2012 astro-ph.IM
The Large Binocular Telescope (LBT) is a unique telescope featuring two co-mounted optical trains with 8.4m primary mirrors. The telescope Adaptive Optics (AO) system uses two innovative key components, namely an adaptive secondary mirror with 672 actuators and a high-order pyramid wave-front sensor. During the on-sky commissioning such a system reached performances never achieved before on large ground-based optical telescopes. Images with 40mas resolution and Strehl Ratios higher than 80% have been acquired in H band (1.6 micron). Such images showed a contrast as high as 10e-4. Based on these results, we compare the performances offered by a Natural Guide Star (NGS) system upgraded with the state-of-the-art technology and those delivered by existing Laser Guide Star (LGS) systems. The comparison, in terms of sky coverage and performances, suggests rethinking the current role ascribed to NGS and LGS in the next generation of AO systems for the 8-10 meter class telescopes and Extremely Large Telescopes (ELTs).
• ### Numerical control matrix rotation for the LINC-NIRVANA Multi-Conjugate Adaptive Optics system(1008.4475)

Aug. 26, 2010 astro-ph.IM
LINC-NIRVANA will realize the interferometric imaging focal station of the Large Binocular Telescope. A double Layer Oriented multi-conjugate adaptive optics system assists the two arms of the interferometer, supplying high order wave-front correction. In order to counterbalance the field rotation, mechanical derotation for the two ground wave-front sensors, and optical derotators for the mid-high layers sensors fix the positions of the focal planes with respect to the pyramids aboard the wave-front sensors. The derotation introduces pupil images rotation on the wavefront sensors: the projection of the deformable mirrors on the sensor consequently change. The proper adjustment of the control matrix will be applied in real-time through numerical computation of the new matrix. In this paper we investigate the temporal and computational aspects related to the pupils rotation, explicitly computing the wave-front errors that may be generated.


text:
# Reflection and Refraction

This is a continuation from the previous tutorial - Gaussian Beam.

The characteristics of reflection and refraction of an optical wave at the interface of two different media depend on the properties of the media. We first consider the simple case of reflection and refraction at the planar interface of two dielectric media that are linear, lossless, and isotropic. In this situation, the permittivities ε1 and ε2 of the two media are constant real scalars, while the permeabilities are simply equal to μ0 at optical frequencies. We assume that the optical wave is incident from medium 1 with a wavevector ki, while the reflected wave has a wavevector kr, and the transmitted wave has a wavevector kt.

Because an optical wave varies with exp(ikr - iωt), the condition that

$\tag{143}\mathbf{k}_\text{i}\cdot\mathbf{r}=\mathbf{k}_\text{r}\cdot\mathbf{r}=\mathbf{k}_\text{t}\cdot\mathbf{r}$

is required at the interface for the boundary conditions described by (17) - (20) [refer to the optical fields and Maxwell's equations tutorial] to be satisfied at all points along the interface at all times. This implies that the three vectors kikr, and kt lie in the same plane known as the plane of incidence, as shown in figure 16 and 17 below.

The projections of these three wavevectors on the interface are all equal so that

$\tag{144}k_i\sin{\theta_i}=k_r\sin{\theta_r}=k_t\sin{\theta_t}$

where θi is the angle of incidence, and θr and θt are the angle of reflection and the angle of refraction, respectively, for the reflected and transmitted waves. All three angles are measured with respect to the normal $$\hat{n}$$ of the interface, as is shown in figure 16 and 17.

Because ki = kr and ki/kt = n1/n2, (144) yields the relation

$\tag{145}\theta_i=\theta_r$

and the following familiar Snell law for refraction:

$\tag{146}n_1\sin{\theta_i}=n_2\sin{\theta_t}$

By expressing H in terms of k x E in the form of (86) [refer to the propagation in an isotropic medium tutorial] with appropriate values of k for the incident, reflected, and refracted fields, the amplitudes of the reflected and transmitted fields can be obtained from the boundary conditions in (17) and (18) [refer to the optical fields and Maxwell's equations tutorial]. There are two different modes of field polarization.

TE Polarization (s wave, σ wave)

The electric field is linearly polarized in a direction perpendicular to the plane of incidence while the magnetic field is polarized parallel to the plane of incidence, as shown in figure 16. This is called transverse electric (TE) polarization or perpendicular polarization. This wave is also called s polarized, or σ polarized. In this case, the reflection coefficient, r, and the transmission coefficient, t, of the electric field are given by the following Fresnel equations:

$\tag{147}r_s\equiv\frac{\mathcal{E}_r}{\mathcal{E}_i}\equiv\frac{n_1\cos\theta_i-n_2\cos\theta_t}{n_1\cos\theta_i+n_2\cos\theta_t}=\frac{n_1\cos\theta_i-\sqrt{n_2^2-n_1^2\sin^2\theta_i}}{n_1\cos\theta_i+\sqrt{n_2^2-n_1^2\sin^2\theta_i}}$

$\tag{148}t_s\equiv\frac{\mathcal{E}_t}{\mathcal{E}_i}=\frac{2n_1\cos\theta_i}{n_1\cos\theta_i+n_2\cos\theta_t}=\frac{2n_1\cos\theta_i}{n_1\cos\theta_i+\sqrt{n_2^2-n_1^2\sin^2\theta_i}}$

respectively. The intensity reflectance and transmittance, R and T, which are also known as reflectivity and transmissivity, respectively, are given by

$\tag{149}R_s\equiv\frac{I_r}{I_i}=\frac{|\bar{\mathbf{S}}_r\cdot\hat{n}|}{|\bar{\mathbf{S}}_i\cdot\hat{n}|}=\left|\frac{n_1\cos\theta_i-n_2\cos\theta_t}{n_1\cos\theta_i+n_2\cos\theta_t}\right|^2$

$\tag{150}T_s\equiv\frac{I_t}{I_i}=\frac{|\bar{\mathbf{S}}_t\cdot\hat{n}|}{|\bar{\mathbf{S}}_i\cdot\hat{n}|}=1-R_s$

TM Polarization (p wave, π wave)

The electric field is linearly polarized in a direction parallel to the plane of incidence while the magnetic field is polarized perpendicular to the plane of incidence, as shown in figure 17 below.

This is called transverse magnetic (TM) polarization or parallel polarization. This wave is also called p polarized, or π polarized. In this case, the reflection and transmission coefficients of the electric field are given by the following Fresnel equations:

$\tag{151}r_p\equiv\frac{\mathcal{E}_r}{\mathcal{E}_i}=\frac{n_2\cos\theta_i-n_1\cos\theta_t}{n_2\cos\theta_i+n_1\cos\theta_t}=\frac{n_2^2\cos\theta_i-n_1\sqrt{n_2^2-n_1^2\sin^2\theta_i}}{n_2^2\cos\theta_i+n_1\sqrt{n_2^2-n_1^2\sin^2\theta_i}}$

$\tag{152}t_p\equiv\frac{\mathcal{E}_t}{\mathcal{E}_i}=\frac{2n_1\cos\theta_i}{n_2\cos\theta_i+n_1\cos\theta_t}=\frac{2n_1n_2\cos\theta_i}{n_2^2\cos\theta_i+n_1\sqrt{n_2^2-n_1^2\sin^2\theta_i}}$

respectively. The intensity reflectance and transmittance for TM polarization are given, respectively, by

$\tag{153}R_p\equiv\frac{I_r}{I_i}=\left|\frac{n_2\cos\theta_i-n_1\cos\theta_t}{n_2\cos\theta_i+n_1\cos\theta_t}\right|^2$

$\tag{154}T_p\equiv\frac{I_t}{I_i}=1-R_p$

Several important characteristics of the reflection and refraction of an optical wave at an interface between two media are summarized.

1. For both TE and TM polarization, R = |r|2 and R + T = 1, but T  |t|2.

2. If n1 < n2, light is incident from a rare medium upon a dense medium. In this case, the reflection is called external reflection. If n1 > n2, light is incident from a dense medium on a rare medium, and the reflection is called internal reflection.

3. Normal incidence. In the case of normal incidence, θi = θt = 0. There is no difference between TE and TM polarizations, and

$\tag{155}R=\left|\frac{n_1-n_2}{n_1+n_2}\right|^2,\qquad T=1-R=\frac{4n_1n_2}{(n_1+n_2)^2}$

For the case of external reflection at normal incidence, there is a 180° phase reversal for the reflected electric field with respect to the incident field. For internal reflection, the phase of the reflected field is not reversed at normal incidence. However, the values of R and T do not depend on which side of the interface the wave comes from.

4. Brewster angle. For a TE wave, Rs increases monotonically with the angle of incidence. For a TM wave, Rp first decreases then increases as the angle of incidence increases. For the interface between two lossless media, Rp = 0 at an angle of incidence θi = θB, where

$\tag{156}\theta_B=\tan^{-1}\frac{n_2}{n_1}$

is known as the Brewster angle. When θi = θB, the angle of refraction for the transmitted wave is

$\tag{157}\theta_t=\frac{\pi}{2}-\theta_B$

It can be shown that this angle is the Brewster angle for the same wave incident from the other side of the interface. Figure 18(a) shows the reflectance of TE and TM waves as a function of the angle of incidence for external reflection at the interface between two media of refractive indices of 1 and 3.5.

These characteristics are very useful in practical device applications:

(a) At θi = θB, a TM-polarized wave is totally transmitted, resulting in a perfect lossless window for TM polarization - such windows are called Brewster windows and are useful as laser windows.

(b) At θi = θB, the reflected wave is completely TE polarized - linearly polarized light can be produced by a reflection-type polarizer based on this principle.

5. Critical angle. In the case of internal reflection with n1 > n2, total internal reflection occurs if the angle of incidence θi is larger than the angle

$\tag{158}\theta_c=\sin^{-1}\frac{n_2}{n_1}$

which is called the critical angle. The reflectance of TE and TM waves as a function of angle of incidence for internal reflection at the interface between two media of refractive indices of 1 and 3.5 is shown in figure 18(b). Note that the Brewster angle for internal reflection is always smaller than the critical angle.

6. If one or both media have a loss or gain, the indices of refraction become complex. In this situation, the reflectance of the TM wave has a minimum that does not reach zero, as shown in figure 19 for external reflection.

7. For wave propagation in a general direction in an anisotropic medium, there are two normal modes that have different indices of refraction. The refracted fields of these two normal modes can propagate in different directions, resulting in the phenomenon of double refraction. Meanwhile, the Poynting vector does not have to be in the plane of incidence.

8. Optical media are generally dispersive. Therefore, reflectance and transmittance, as well as the direction of the refracted wave, are generally frequency dependent.

Example

Water has an index of refraction n = 1.33. The index of refraction of ordinary glass is approximately n = 1.5. For most semiconductors, such as Si, GaAs, and InP, the index of refraction is often in the range between 3 and 4, depending on the optical wavelength and the material. Her we take a nominal value of n = 3.5 for a semiconductor. Find the reflectivities at normal incidence, the Brewster angles, and the critical angles for these media at their interfaces with air.

Using the formula given in (155) for the reflectivity at normal incidence, we find that R = 0.02 for water, R = 0.04 for ordinary glass, and R typically falls in the range of 0.3 and 0.32 for a semiconductor.

Using (156) for the Brewster angle, we find that θB ≈ 54° for water, θB ≈ 56° for ordinary glass, and θB is typically around 74° for a semiconductor.

Using (158) for the critical angle, we find that θc ≈ 49° for water, θc ≈ 42° for ordinary glass, and θc is around 17° for a semiconductor.

The next part continues with the Phase Velocity, Group Velocity, and Dispersion tutorial

format: plain


text:
# Properties

 Label 47190u Number of curves $4$ Conductor $47190$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 47190u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.y4 47190u1 $$[1, 0, 1, 132371, 40035752]$$ $$144794100308831/474439680000$$ $$-840498833940480000$$ $$[2]$$ $$737280$$ $$2.1225$$ $$\Gamma_0(N)$$-optimal
47190.y3 47190u2 $$[1, 0, 1, -1261549, 471035816]$$ $$125337052492018849/18404100000000$$ $$32603985800100000000$$ $$[2, 2]$$ $$1474560$$ $$2.4691$$
47190.y2 47190u3 $$[1, 0, 1, -5414269, -4384324408]$$ $$9908022260084596129/1047363281250000$$ $$1855467941894531250000$$ $$[2]$$ $$2949120$$ $$2.8157$$
47190.y1 47190u4 $$[1, 0, 1, -19411549, 32915975816]$$ $$456612868287073618849/12544848030000$$ $$22223963520874830000$$ $$[2]$$ $$2949120$$ $$2.8157$$

## Rank

sage: E.rank()

The elliptic curves in class 47190u have rank $$1$$.

## Complex multiplication

The elliptic curves in class 47190u do not have complex multiplication.

## Modular form 47190.2.a.u

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + q^{12} - q^{13} - q^{15} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.


text:
## Support Center

### Entering math symbols in the Lesson Space with LaTeX syntax

If you're studying math, you will probably need to enter mathematics expressions in chats with your tutor. To make this easier, we support LaTeX, a way of writing mathematics terms and equations with ordinary text. To use it in chats, put the symbols and equations you want to use between two sets of double-dollar signs, like this:

 $$x + y = z$$

Greek letters and other special characters are written with "commands" (a word preceded with a backslash):
 $$\alpha, \beta, \gamma, \omega, \pi$$

Functions are written similarly:
 $$\log(n), \cos(x), \tan(y)$$

Powers and indices are written with caret and underscore, with the value in braces:
 $$n^{2}, n_{4}$$

Fractions are written with a the "frac" command and the numerator and denominator in braces:
 $$\frac{x}{y + 1}$$

Roots are written similarly:
 $$\root{x + y}$$

Some examples with the above notation used in combination:
 $$\cos(2\omega) = \cos^{2}\omega - \sin^{2}\omega$$

 $$\sum_{i=1}^{10} t_i$$

 $$\int_0^\infty \mathrm{e}^{-x}\,\mathrm{d}x$$

LaTeX/Mathematics on Wikibooks
Online LaTeX editor
LaTeX Reference PDF
f9b39e144d88a2275522416c3b9767b4@instaedu.desk-mail.com
https://cdn.desk.com/
false
desk


text:
# Image of a quadratic form is a closed cone

Let $$Q : E \to F$$ be a quadratic form induced by a symmetric bilinear form $$B : E \times E \to F$$ defined in a finite dimensional real normed vector space $$E$$, with values in the normed vector space $$F \supseteq E$$ (continuous inclusion). I already know that the image $$C= Q(E)$$ is a cone in $$F$$. How do I prove that it is also closed? Also, is it true that the convex hull of $$C$$ is closed?

• Really? Do you have a counterexample in mind? What if the norms are induced by an inner product? May 25 at 0:08
• I'll post a counterexample. But in fact, I'm quite confused about the convexity now. (Probably because I should actually sleep rather than doing maths...) May 25 at 0:11
• May I ask whether you found out whether $Q(E)$ is always convex? May 26 at 17:28
• I didn't found out :( but I suspect it may not be always convex Jun 2 at 20:32
• Thanks for your response! Jun 2 at 20:38

In general, $$Q(E)$$ is not closed.
Counterexample. Let $$E = F = \mathbb{R}^2$$ and set $$B(x,y) := \begin{pmatrix} x_1y_1 \\ x_1y_2 + x_2y_1 \end{pmatrix}.$$ Then $$Q(x) := \begin{pmatrix} x_1^2 \\ 2x_1x_2 \end{pmatrix},$$ so $$Q(E)$$ is the open right half plane together with the origin.


text:
anonymous 4 years ago How are slopes of parallel and perpendicular lines determined and how are they related?

1. anonymous

Straight Line Equation: y=mx+c where m is the gradient The gradient of two parallel lines are equal. m1=m2 The gradient of perpendicular lines multiply to give -1. m1*m2=-1

2. anonymous

$m=\frac{y_2-y_1}{x_2-x_1}$ Use this to find the gradient if the equation is unknown :)


text:
# SCIP

Solving Constraint Integer Programs

cons_orbitope.h File Reference

## Detailed Description

constraint handler for (partitioning/packing/full) orbitope constraints w.r.t. the full symmetric group

Definition in file cons_orbitope.h.

#include "scip/def.h"
#include "scip/type_cons.h"
#include "scip/type_retcode.h"
#include "scip/type_scip.h"
#include "scip/type_var.h"

Go to the source code of this file.

## Functions

SCIP_EXPORT SCIP_RETCODE SCIPincludeConshdlrOrbitope (SCIP *scip)

## Orbitope Constraints

This constraint handler can be used to handle symmetries in certain 0/1-programs. The principle structure is that some variables can be ordered in matrix form, such that permuting columns does not change the validity and objective function value of a solution. That is, the symmetry group of the program contains the full symmetric group obtained by permuting the columns of this matrix. These symmetries can be handled by so-called full orbitopes.

Moreover, if the variables in each row are contained in set packing or partitioning constraint, these symmetries can be handled by specialized packing or partitioning orbitopes.

In more mathematical terms the structure has to be as follows: There are 0/1-variables $$x_{ij}$$, $$i \in \{1, \dots, p\}$$, $$j \in \{1, \dots, q\}$$. The variables may be coupled through set packing or partitioning constraints:

$\sum_{j = 1}^q x_{ij} \leq 1 \quad \mbox{or} \quad \sum_{j = 1}^q x_{ij} = 1 \quad \mbox{for all }i = 1, \ldots, p.$

Permuting columns of $$x$$ does not change the validity and objective function value of any feasible solution.

We distinguish whether an orbitope is a model constraint or not. If it is a model constraint, then its information are copied to subSCIPs. Otherwise, the constraint was added just for the purpose of symmetry handling and we do not copy its information to subSCIPs.

enum  SCIP_OrbitopeType {
SCIP_ORBITOPETYPE_FULL = 0,
SCIP_ORBITOPETYPE_PARTITIONING = 1,
SCIP_ORBITOPETYPE_PACKING = 2
}

typedef enum SCIP_OrbitopeType SCIP_ORBITOPETYPE

SCIP_EXPORT SCIP_RETCODE SCIPcreateConsOrbitope (SCIP *scip, SCIP_CONS **cons, const char *name, SCIP_VAR ***vars, SCIP_ORBITOPETYPE orbitopetype, int nspcons, int nblocks, SCIP_Bool resolveprop, SCIP_Bool ismodelcons, SCIP_Bool initial, SCIP_Bool separate, SCIP_Bool enforce, SCIP_Bool check, SCIP_Bool propagate, SCIP_Bool local, SCIP_Bool modifiable, SCIP_Bool dynamic, SCIP_Bool removable, SCIP_Bool stickingatnode)

SCIP_EXPORT SCIP_RETCODE SCIPcreateConsBasicOrbitope (SCIP *scip, SCIP_CONS **cons, const char *name, SCIP_VAR ***vars, SCIP_ORBITOPETYPE orbitopetype, int nspcons, int nblocks, SCIP_Bool resolveprop, SCIP_Bool ismodelcons)


text:
# How do you graph abs(2x+1)?

As you know, $y = 2 x + 1$ graph looks like this.
An absolute value is always positive, so if $2 x + 1 < 0$, the sign of $y$ should change to positive. Thus, the point below the $x$-axis should reflect in the $x$-axis. Then the answer is


text:
# Bayesian COVID Probability

Last week, I got a call to come pick up my son from his preschool because he was identified as a close contact of someone that tested positive for COVID-19. Obviously, we were worried and trying to figure out how to keep the rest of the family safe. We also were staring down two weeks during which my son would be at home. Then, the next day, we were notified that the student had originally tested positive via an antigen rapid test, but had tested negative using RT-PCR nasal swab test.

# Estimating Negative Variance

A few weeks ago, my post-doc adviser, Mandy, asked me to examine a scenario. It was a basic random effects model of the form $W_{ijk} = X_{ik} + E_{ijk}, \quad i = 1,\ldots,n, \quad j = 1,\ldots,J, \quad k = 1,\ldots,K,$ in which the response for subject $i$ for replicate $j$ and component $k$ ($W_{ijk}$) is generated through a latent effect ($X_{ik}$) and some observational noise ($E_{ijk}$). The model can be applied to neuroimaging in which different unobserved structures or networks have some effect on blood oxygen levels.

# Bayesian Random Effects Models

Consider a scenario in which noisy data are observed, with variance driven by two primary sources: signal and noise. We can write the data generation as $W_{ij} = X_i + E_{ij}, \quad i = 1,\ldots, n, \quad j = 1,2$ Here, consider $X_i$ as the signal and $E_{ij}$ as the noise, with values generated from zero-mean normal distributions. $X_i \sim \text{Normal}(0,\sigma_x^2), \quad E_{ij} \sim \text{Normal}(0,\sigma_e^2)$

# Energy Use in California

The next few posts on this website will be based on emails that I have been sending to the Applied Mathematics and Statistics department every Monday as part of a reminder of the weekly doughnut social event that I help facilitate. In many of those emails, I include a data vizualization with very little explanation. I’ll include more here, like the motivation and the thought process, as well as the code and data source used to make the visualization.

# Word Clouds

Last summer, I was fortunate to be able to take a two-day short course with Abel Rodriguez here at UCSC. He based the course on the quarter-long Art of Data Visualization course that he had taught that winter quarter. It was super interesting, and it motivated me to try a few things on my own, including a word cloud. I use Google Voice, which saves all of my text messages in spreadsheet format.


text:
[CAS] Inconsistency with commands.
10-28-2016, 11:26 PM
Post: #1
 CH3791 Junior Member Posts: 40 Joined: May 2016
[CAS] Inconsistency with commands.
Sorry for yet another post guys but,

I am getting confused about the difference between uppercase and lowercase commands. For some cases there doesn't seem to be a difference.
STRING(); works the same as string();
LOCAL; works the same as local; **I think...**

But in other commands, they act a bit weird. I have found 2 so far:
Code:
#cas char_program(input):= BEGIN   return char(input); END; #end
Inputing 8730 returns an empty box. Apparently, I've used the wrong case for "CHAR". This is despite how in CAS mode, when you select the "CHAR" command from Toolbox > Catlg > "CHAR", it is given to you in lowercase. In this case, only CHAR works.

Code:
#cas expr_program(input):= BEGIN   return EXPR(input); END; #end
Inputing "a" returns "Error: Syntax Error". Instead of EXPR, expr is needed here. Although selecting "EXPR" from the CAS toolbox does give it in lowercase, it is displayed in uppercase in the catalog.

What is the difference between the cases, and how should I know which one to use?
10-29-2016, 06:19 AM
Post: #2
 parisse Senior Member Posts: 1,243 Joined: Dec 2013
RE: [CAS] Inconsistency with commands.
In CAS, you should use lowercase. char/asc is working in ASCII (8 bits char) extended to UTF8, while HOME is using UTF16 (16 bits char). For example
asc("a") returns a list of 1 integer
asc("é") returns a list of 2 integers
and char does the reverse.
Which means that the sqrt symbol is coded inside CAS with UTF8 corresponding to UTF16=8370, that is with 3 integers 226, 136, 154, that you get with asc.
10-29-2016, 08:01 AM
Post: #3
 CH3791 Junior Member Posts: 40 Joined: May 2016
RE: [CAS] Inconsistency with commands.
(10-29-2016 06:19 AM)parisse Wrote:  In CAS, you should use lowercase. char/asc is working in ASCII (8 bits char) extended to UTF8, while HOME is using UTF16 (16 bits char). For example
asc("a") returns a list of 1 integer
asc("é") returns a list of 2 integers
and char does the reverse.
Which means that the sqrt symbol is coded inside CAS with UTF8 corresponding to UTF16=8370, that is with 3 integers 226, 136, 154, that you get with asc.

Okk, thanks for clarifying.
 « Next Oldest | Next Newest »

User(s) browsing this thread: 1 Guest(s)


text:
RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 3, Pages 593–644 (Mi izv2143)

Nested matrix disks analytically depending parameter, and theorems on the invariance radii of limiting disks

S. A. Orlov

Abstract: In this work there is an investigation of a family of invertible (i.e. $W(b,\lambda)\not\equiv0$) analytic matrix-valued functions $W(b,\lambda)$ ($0<b<\infty$) which are $J$-contractive ($\Gamma(b,\lambda)\overset{\mathrm{def}}= J-W(b,\lambda)JW^*(b,\lambda)>0$, $J^*=J$, $J^2=I$) and which have monotonically increasing $J$-forms $\Gamma(b,\lambda)$ as $b\to\infty$. Invariance with respect to $\lambda$ of the rank of the matrix $R^2(\lambda)=\lim_{b\to\infty}\Gamma^{-1}(b,\lambda)$ is established, and conditions for convergence of $W(b,\lambda)$ are investigated. As a special case a theorem is obtained on the invariance of ranks of limiting radii of Weyl disks, which is fundamentally of significance in the theory of classical problems (the moment problem, the Nevanlinna–Pick problem, the Weyl problem on the number of square-integrable solutions of a system of differential equations, and so forth).
Bibliography: 17 titles.

Full text: PDF file (4567 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1976, 10:3, 565–613

Bibliographic databases:

UDC: 517.5+517.9
MSC: Primary 34B20, 15A03, 15A57; Secondary 15A21, 30A80, 15A45

Citation: S. A. Orlov, “Nested matrix disks analytically depending parameter, and theorems on the invariance radii of limiting disks”, Izv. Akad. Nauk SSSR Ser. Mat., 40:3 (1976), 593–644; Math. USSR-Izv., 10:3 (1976), 565–613

Citation in format AMSBIB
\Bibitem{Orl76} \by S.~A.~Orlov \paper Nested matrix disks analytically depending parameter, and theorems on the invariance radii of limiting disks \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1976 \vol 40 \issue 3 \pages 593--644 \mathnet{http://mi.mathnet.ru/izv2143} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=425671} \zmath{https://zbmath.org/?q=an:0337.34020} \transl \jour Math. USSR-Izv. \yr 1976 \vol 10 \issue 3 \pages 565--613 \crossref{https://doi.org/10.1070/IM1976v010n03ABEH001718}

• http://mi.mathnet.ru/eng/izv2143
• http://mi.mathnet.ru/eng/izv/v40/i3/p593

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. V. Kovalishina, “Analytic theory of a class of interpolation problems”, Math. USSR-Izv., 22:3 (1984), 419–463
2. V. K. Dubovoi, “Multiplicities of one-sided shifts contained in a contraction operator”, Funct. Anal. Appl., 17:1 (1983), 55–56
3. D.B Hinton, J.K Shaw, “Hamiltonian systems of limit point or limit circle type with both endpoints singular”, Journal of Differential Equations, 50:3 (1983), 444
4. D. B. Hinton, A. Schneider, “On the Titchmarsh-Weyl Coefficients for SingularS-Hermitian Systems I”, Math Nachr, 163:1 (1993), 323
5. Christian Remling, “Geometric Characterization of Singular Self-Adjoint Boundary Conditions for Hamiltonian Systems”, Applicable Analysis, 60:1-2 (1996), 49
6. Fritz Gesztesy, Eduard Tsekanovskii, “On Matrix-Valued Herglotz Functions”, Math Nachr, 218:1 (2000), 61
7. Gesztesy F. Kiselev A. Makarov K., “Uniqueness Results for Matrix-Valued Schrodinger, Jacobi, and Dirac-Type Operators”, Math. Nachr., 239 (2002), 103–145
8. E. Andersson, “On the M-function and Borg–Marchenko theorems for vector-valued Sturm–Liouville equations”, J Math Phys (N Y ), 44:12 (2003), 6077
9. Yu. M. Dyukarev, “On the indeterminacy of interpolation problems for Nevanlinna functions”, Russian Math. (Iz. VUZ), 48:8 (2004), 24–36
10. Yu. M. Dyukarev, “Indeterminacy Criteria for the Stieltjes Matrix Moment Problem”, Math. Notes, 75:1 (2004), 66–82
11. Steve Clark, Fritz Gesztesy, “On Weyl–Titchmarsh theory for singular finite difference Hamiltonian systems”, Journal of Computational and Applied Mathematics, 171:1-2 (2004), 151
12. Yu. M. Dyukarev, “Indeterminacy of interpolation problems in the Stieltjes class”, Sb. Math., 196:3 (2005), 367–393
13. V. I. Khrabustovsky, “On the characteristic operators and projections and on the solutions of Weyl type of dissipative and accumulative operator systems. I. General case”, Zhurn. matem. fiz., anal., geom., 2:2 (2006), 149–175
14. Yu. M. Dyukarev, I. Yu. Serikova, “Complete indeterminacy of the Nevanlinna–Pick problem in the class $S[a,b]$”, Russian Math. (Iz. VUZ), 51:11 (2007), 17–29
15. D. B. Hinton, A. Schneider, “On the Titchmarsh-Weyl Coefficients for Singular S-Hermitian Systems II”, Math Nachr, 185:1 (2009), 67
16. V. I. Khrabustovskyi, “On the limit of regular dissipative and self-adjoint boundary value problems with nonseparated boundary conditions when an interval stretches to the semiaxis”, Zhurn. matem. fiz., anal., geom., 5:1 (2009), 54–81
17. Hermann Schulz-Baldes, “Geometry of Weyl theory for Jacobi matrices with matrix entries”, J Anal Math, 110:1 (2010), 129
18. Stephen Clark, Petr Zemánek, “On a Weyl–Titchmarsh theory for discrete symplectic systems on a half line”, Applied Mathematics and Computation, 217:7 (2010), 2952
19. V. M. Bruk, “On linear relations generated by a differential expression and by a Nevanlinna operator function”, Zhurn. matem. fiz., anal., geom., 7:2 (2011), 115–140
20. V. M. Bruk, “Linear relations generated by an integral equation with Nevanlinna operator measure”, Russian Math. (Iz. VUZ), 56:10 (2012), 1–14
21. B. Fritzsche, B. Kirstein, I. Ya. Roitberg, A. L. Sakhnovich, “Skew-Self-Adjoint Dirac System with a Rectangular Matrix Potential: Weyl Theory, Direct and Inverse Problems”, Integr. Equ. Oper. Theory, 2012
22. V. M. Bruk, “Invertible linear relations generated by an integral equation with a Nevanlinna measure”, Russian Math. (Iz. VUZ), 57:2 (2013), 13–24
23. A. M. Kholkin, F. S. Rofe-Beketov, “On Spectrum of Differential Operator with Block-Triangular Matrix Coefficients”, Zhurn. matem. fiz., anal., geom., 10:1 (2014), 44–63
24. Yu. M. Dyukarev, A. E. Choque Rivero, “Criterion for the Complete Indeterminacy of the Nevanlinna–Pick Matrix Problem”, Math. Notes, 96:5 (2014), 651–665
•  Number of views: This page: 383 Full text: 89 References: 23 First page: 1


text:
## Taiwanese Journal of Mathematics

### Traveling Waves for a Spatial SIRI Epidemic Model

#### Abstract

The aim of this paper is to study the traveling waves in a spatial SIRI epidemic model arising from herpes viral infection. We obtain the complete information about the existence and non-existence of traveling waves in the model. Namely, we prove that when the basic reproduction number $\mathcal{R}_0 \gt 1$, there exists a critical wave speed $c^* \gt 0$ such that for each $c \gt c^*$, the model admits positive traveling waves; and for $c \lt c^*$, the model has no non-negative and bounded traveling wave. We also give some numerical simulations to illustrate our analytic results.

#### Article information

Source
Taiwanese J. Math., Advance publication (2019), 26 pages.

Dates
First available in Project Euclid: 21 December 2018

https://projecteuclid.org/euclid.twjm/1545361214

Digital Object Identifier
doi:10.11650/tjm/181205

#### Citation

Xu, Zhiting; Xu, Yixin; Huang, Yehui. Traveling Waves for a Spatial SIRI Epidemic Model. Taiwanese J. Math., advance publication, 21 December 2018. doi:10.11650/tjm/181205. https://projecteuclid.org/euclid.twjm/1545361214

#### References

• S. Ai and R. Albashaireh, Traveling waves in spatial SIRS models, J. Dynam. Differential Equations 26 (2014), no. 1, 143–164.
• Z. Bai and S.-L. Wu, Traveling waves in a delayed SIR epidemic model with nonlinear incidence, Appl. Math. Comput. 263 (2015), 221–232.
• V. Capasso and G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model, Math. Biosci. 42 (1978), no. 1-2, 43–61.
• J. Chin, Control of Communicable Diseases Manual, American Public Health Association, Washington, 1999.
• A. Ducrot, M. Langlais and P. Magal, Qualitative analysis and travelling wave solutions for the SI model with vertical transmission, Commun. Pure Appl. Anal. 11 (2012), no. 1, 97–113.
• A. Ducrot and P. Magal, Travelling wave solutions for an infection-age structured epidemic model with external supplies, Nonlinearity 24 (2011), no. 10, 2891–2911.
• J. Fang and X.-Q. Zhao, Monotone wavefronts for partially degenerate reaction-diffusion systems, J. Dynam. Differential Equations. 21 (2009), no. 4, 663–680.
• S.-C. Fu, Traveling waves for a diffusive SIR model with delay, J. Math. Anal. Appl. 435 (2016), no. 1, 20–37.
• P. Georgescu and H. Zhang, A Lyapunov functional for a SIRI model with nonlinear incidence of infection and relapse, Appl. Math. Comput. 219 (2013), no. 16, 8496–8507.
• W. M. Hirsch, H. Hanisch and J.-P. Gabriel, Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior, Comm. Pure Appl. Math. 38 (1985), no. 6, 733–753.
• C.-H. Hsu and T.-S. Yang, Existence, uniqueness, monotonicity and asymptotic behaviour of travelling waves for epidemic models, Nonlinearity 26 (2013), no. 1, 121–139.
• W.-T. Li, G. Lin, C. Ma and F.-Y. Yang, Traveling wave solutions of a nonlocal delayed SIR model without outbreak threshold, Discrete Contin. Dyn. Syst. Ser. B 19 (2014), no. 2, 467–484.
• S. W. Martin, Livestock Disease Eradication: Evaluation of the Cooperative State-Federal Bovine Tuberculosis Eradication Program, National Academy Press, Washington, D.C., 1994.
• H. N. Moreira and Y. Wang, Global stability in an $S \to I \to R \to I$ model, SIAM Rev. 39 (1997), no. 3, 496–502.
• J. D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, third edition, Interdisciplinary Applied Mathematics 18, Springer-Verlag, New York, 2002.
• W. Pei, Q. Yang and Z. Xu, Traveling waves of a delayed epidemic model with spatial diffusion, Electron. J. Qual. Theory Differ. Equ. 2017 (2017), no. 82, 19 pp.
• L. Perko, Differential Equations and Dynamical Systems, third edition, Texts in Applied Mathematics 7, Springer-Verlag, New York, 2001.
• G. P. Sahu and J. Dhar, Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity, J. Math. Anal. Appl. 421 (2015), no. 2, 1651–1672.
• D. Tudor, A deterministic model for herpes infections in human and animal populations, SIAM Rev. 32 (1990), no. 1, 136–1139.
• H. Wang, Spreading speeds and traveling waves for non-cooperative reaction-diffusion systems, J. Nonlinear Sci. 21 (2011), no. 5, 747–783.
• H. Wang and X.-S. Wang, Traveling wave phenomena in a Kermack-McKendrick SIR model, J. Dynam. Differential Equations 28 (2016), no. 1, 143–166.
• X.-S. Wang, H. Wang and J. Wu, Traveling waves of diffusive predator-prey systems: disease outbreak propagation, Discrete Contin. Dyn. Syst. 32 (2012), no. 9, 3303–3324.
• Z.-C. Wang and J. Wu, Travelling waves of a diffusive Kermack-McKendrick epidemic model with non-local delayed transmission, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 466 (2010), no. 2113, 237–261.
• ––––, Traveling waves in a bio-reactor model with stage-structure, J. Math. Anal. Appl. 385 (2012), no. 2, 683–692.
• P. Weng and X.-Q. Zhao, Spreading speed and traveling waves for a multi-type SIS epidemic model, J. Differential Equations 229 (2006), no. 1, 270–296.
• C. Wu, Y. Yong, Q. Zhao, Y. Tian and Z. Xu, Epidemic waves of a spatial SIR model in combination with random dispersal and non-local dispersal, Appl. Math. Comput. 313 (2017), 122–143.
• Z. Xu, Traveling waves in a Kermack-McKendrick epidemic model with diffusion and latent period, Nonlinear Anal. 111 (2014), 66–81.
• ––––, Traveling waves for a diffusive SEIR epidemic model, Commun. Pure Appl. Anal. 15 (2016), no. 3, 871–892.
• ––––, Wave propagation in an infectious disease model, J. Math. Anal. Appl. 449 (2017), no. 1, 853–871.
• Z. Xu and D. Chen, An SIS epidemic model with diffusion, Appl. Math. J. Chinese Univ. Ser. B 32 (2017), no. 2, 127–146.
• Z. Xu, Y. Xu and Y. Huang, Stability and traveling waves of a vaccination model with nonlinear incidence, Comput. Math. Appl. 75 (2018), no. 2, 561–581.
• Q. Ye and Z. Li, Introduction to Reaction-diffusion Equations, Foundations of Modern Mathematics Series, Science Press, Beijing, 1990.
• Y. Q. Ye, S. L. Cai, L. S. Chen, K. C. Huang, D. J. Luo, Z. E. Ma, E. N. Wang, M. S. Wang and X. A. Yang, Theory of Limit Cycles, Translations of Methematical Monographs 66, American Mathematical Society, Providence, RI, 1986.
• T. Zhang, Minimal wave speed for a class of non-cooperative reaction-diffusion systems of three equations, J. Differential Equations 262 (2017), no. 9, 4724–4770.
• T. Zhang and W. Wang, Existence of traveling wave solutions for influenza model with treatment, J. Math. Anal. Appl. 419 (2014), no. 1, 469–495.
• Z. F. Zhang, T. R. Ding, W. Z. Huang and Z. X. Dong, Qualitative Theory of Differential Equations, Translations of Methematical Monographs 101, American Mathematical Society, Providence, RI, 1992.


text:
### Top 3 Arxiv Papers Today in Complex Variables

##### #1. The growth of subharmonic functions along the imaginary axis
###### Anna E. Egorova, Bulat N. Khabibullin
Let $u\not\equiv -\infty$ and $M\not\equiv -\infty$ are two subharmonic functions in the complex plane $\mathbb C$ with the Riesz measures $\nu_u$ and $\mu_M$ such that $u(z)\leq O(|z|)$ and $M(z)\leq O(|z|)$ as $z\to \infty$. If the growth of a function $M$ in some sense exceeds the growth of a function $u$ on some straight line, then we can expect measure $\mu_M$ to dominate measure $\nu_u$ in some sense. We give quantitative forms of such dominance. The main results are illustrated by a new uniqueness theorem for entire functions of exponential type.
more | pdf | html
None.
###### Tweets
mathCVb: Anna E. Egorova, Bulat N. Khabibullin : The growth of subharmonic functions along the imaginary axis https://t.co/ge2iYYVSDK https://t.co/eDwcckwivE
None.
None.
###### Other stats
Sample Sizes : None.
Authors: 2
Total Words: 3995
Unqiue Words: 775

##### #2. Radii problems for normalized hyper-Bessel function
###### Evrim Toklu, Osman Kara
The main purpose of the present paper is to ascertain the radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B<A\leq 1,$ of normalized hyper-Bessel function.
more | pdf | html
None.
###### Tweets
mathCVb: Evrim Toklu, Osman Kara : Radii problems for normalized hyper-Bessel function https://t.co/ByyQ4PGxUq https://t.co/g8KQmJJeUf
None.
None.
###### Other stats
Sample Sizes : None.
Authors: 2
Total Words: 0
Unqiue Words: 0

##### #3. Orthogonal ring patterns
###### Alexander I. Bobenko, Tim Hoffmann, Thilo Rörig
We introduce orthogonal ring patterns consisting of pairs of concentric circles generalizing circle patterns. We show that orthogonal ring patterns are governed by the same equation as circle patterns. For every ring pattern there exists a one parameter family of patterns that interpolates between a circle pattern and its dual. We construct ring pattern analogues of the Doyle spiral, Erf and $z^{\alpha}$ functions. We also derive a variational principle and compute ring patterns based on Dirichlet and Neumann boundary conditions.
more | pdf | html
None.
###### Tweets
mathCVb: Alexander I. Bobenko, Tim Hoffmann, Thilo Rörig : Orthogonal ring patterns https://t.co/6gzzvNQE9c https://t.co/eiGXd45Kkr
None.
None.
###### Other stats
Sample Sizes : None.
Authors: 3
Total Words: 0
Unqiue Words: 0

Assert is a website where the best academic papers on arXiv (computer science, math, physics), bioRxiv (biology), BITSS (reproducibility), EarthArXiv (earth science), engrXiv (engineering), LawArXiv (law), PsyArXiv (psychology), SocArXiv (social science), and SportRxiv (sport research) bubble to the top each day.

Papers are scored (in real-time) based on how verifiable they are (as determined by their Github repos) and how interesting they are (based on Twitter).

To see top papers, follow us on twitter @assertpub_ (arXiv), @assert_pub (bioRxiv), and @assertpub_dev (everything else).

To see beautiful figures extracted from papers, follow us on Instagram.

Tracking 225,779 papers.

###### Search
Sort results based on if they are interesting or reproducible.
Interesting
Reproducible
Online
###### Stats
Tracking 225,779 papers.


text:
2.9.3 Typesetting mensural music

Mensural contexts

The predefined `MensuralVoice` and `MensuralStaff` contexts can be used to engrave a piece in mensural style. These contexts initialize all relevant context properties and grob properties to proper values, so you can immediately go ahead entering the chant, as the following excerpt demonstrates:

```\score {
<<
\new MensuralVoice = "discantus" \relative {
\hide Score.BarNumber {
c''1\melisma bes a g\melismaEnd
f\breve
\[ f1\melisma a c\breve d\melismaEnd \]
c\longa
c\breve\melisma a1 g1\melismaEnd
fis\longa^\signumcongruentiae
}
}
\new Lyrics \lyricsto "discantus" {
San -- ctus, San -- ctus, San -- ctus
}
>>
}
```

Music Glossary: mensural notation.

Mensural clefs

The following table shows all mensural clefs that are supported via the `\clef` command. Some of the clefs use the same glyph, but differ only with respect to the line they are printed on. In such cases, a trailing number in the name is used to enumerate these clefs, numbered from the lowest to the highest line. You can manually force a clef glyph to be typeset on an arbitrary line, as described in Clef. The note printed to the right side of each clef in the example column denotes the `c'` with respect to that clef.

Petrucci used C clefs with differently balanced left-side vertical beams, depending on which staff line it is printed.

 Description Supported Clefs Example mensural C clef `mensural-c1`, `mensural-c2`, `mensural-c3`, `mensural-c4`, `mensural-c5` mensural F clef `mensural-f` mensural G clef `mensural-g` black mensural C clef `blackmensural-c1`, `blackmensural-c2`, `blackmensural-c3`, `blackmensural-c4`, `blackmensural-c5` neomensural C clef `neomensural-c1`, `neomensural-c2`, `neomensural-c3`, `neomensural-c4` petrucci style C clefs, for use on different staff lines (the example shows the 2nd staff line C clef) `petrucci-c1`, `petrucci-c2`, `petrucci-c3`, `petrucci-c4`, `petrucci-c5` petrucci style F clefs, for use on different staff lines (the example shows the 3rd staff line F clef) `petrucci-f3`, `petrucci-f4`, `petrucci-f5` petrucci style G clef `petrucci-g`

Music Glossary: mensural notation, clef.

Notation Reference: Clef.

Known issues and warnings

The mensural g clef is mapped to the Petrucci g clef.

Mensural time signatures

There is limited support for mensuration signs (which are similar to, but not exactly the same as time signatures). The glyphs are hard-wired to particular time fractions. In other words, to get a particular mensuration sign with the `\time n/m` command, `n` and `m` have to be chosen according to the following table

Use the `style` property of grob `TimeSignature` to select ancient time signatures. Supported styles are `neomensural` and `mensural`. The above table uses the `neomensural` style. The following examples show the differences in style:

Time signature, gives a general introduction to the use of time signatures.

Music Glossary: mensural notation.

Notation Reference: Time signature.

Known issues and warnings

Ratios of note durations cannot change with the time signature, as those are not constant. For example, the ratio of 1 breve = 3 semibreves (tempus perfectum) can be made by hand, by setting

```breveTP = #(ly:make-duration -1 0 3/2)
…
{ c\breveTP f1 }
```

This sets `breveTP` to 3/2 times 2 = 3 times a whole note.

The `mensural68alt` and `neomensural68alt` symbols (alternate symbols for 6/8) are not addressable with `\time`. Use `\markup {\musicglyph #"timesig.mensural68alt" }` instead.

For ancient notation, a note head style other than the `default` style may be chosen. This is accomplished by setting the `style` property of the `NoteHead` object to `baroque`, `neomensural`, `mensural`, `petrucci`, `blackpetrucci` or `semipetrucci`.

The `baroque` style differs from the `default` style by:

• Providing a `maxima` note head, and
• Using a square shape for `\breve` note heads.

The `neomensural`, `mensural`, and `petrucci` styles differ from the `baroque` style by:

• Using rhomboidal heads for semibreves and all smaller durations, and
• Centering the stems on the note heads.

The `blackpetrucci` style produces note heads usable in black mensural notation or coloratio sections in white mensural notation. Because note head style does not influence flag count, in this style a semiminima should be notated as `a8*2`, not `a4`, otherwise it will look like a minima. The multiplier can be different if coloratio is used e.g. to notate triplets.

Use `semipetrucci` style to draw half-colored note heads (breves, longas and maximas).

The following example demonstrates the `petrucci` style:

```\set Score.skipBars = ##t
\autoBeamOff
a'\maxima a'\longa a'\breve a'1 a'2 a'4 a'8 a'16 a'
a'\breve*5/6
a'8*4/3 a'
a'\longa
```

Note head styles, gives an overview of all available note head styles.

Music Glossary: mensural notation, note head.

Mensural flags

Use the `flag-style` property of grob `Stem` to select ancient flags. Besides the `default` flag style, only the `mensural` style is supported.

```\override Flag.style = #'mensural
\override Stem.thickness = #1.0
\autoBeamOff
c8 d e f c16 d e f c32 d e f s8
c'8 d e f c16 d e f c32 d e f
```

Note that the innermost flare of each mensural flag is vertically aligned with a staff line.

There is no particular flag style for neo-mensural or Petrucci notation. There are no flags in Gregorian chant notation.

Music Glossary: mensural notation, flag.

Known issues and warnings

Vertically aligning each flag with a staff line assumes that stems always end either exactly on or exactly in the middle of two staff lines. This may not always be true when using advanced layout features of classical notation (which however are typically out of scope for mensural notation).

Mensural rests

Use the `style` property of grob `Rest` to select ancient rests. Supported ancient styles are `neomensural`, and `mensural`.

The following example demonstrates these styles:

```\set Score.skipBars = ##t
\override Rest.style = #'mensural
r\longa^"mensural" r\breve r1 r2 r4 r8 r16 s \break
\override Rest.style = #'neomensural
r\longa^"neomensural" r\breve r1 r2 r4 r8 r16
```

There are no 32nd and 64th rests specifically for the mensural or neo-mensural styles. Rests from the default style are used.

Music Glossary: mensural notation.

Notation Reference: Rests.

Snippets: Ancient notation.

Known issues and warnings

The glyph for the maxima rest in mensural style is actually a perfect longa rest; use two (or three) longa rests to print a maxima rest. Longa rests are not grouped automatically, so have to be done manually by using pitched rests.

Mensural accidentals and key signatures

The `mensural` style provides a sharp and a flat sign different from the default style. Mensural notation rarely used a natural sign: instead the appropriate sharp or flat is used. For example, a B natural in the key of F major would be indicated with a sharp. However, if specifically called for, the natural sign is taken from the `vaticana` style.

The style for accidentals and key signatures is controlled by the `glyph-name-alist` property of the grobs `Accidental` and `KeySignature`, respectively; e.g.:

```\override Staff.Accidental.glyph-name-alist =
#alteration-mensural-glyph-name-alist
```

Music Glossary: mensural notation, Pitch names, accidental, key signature.

Notation Reference: Pitches, Accidentals, Automatic accidentals, Key signature.

Internals Reference: KeySignature.

Annotational accidentals (musica ficta)

In European music from before about 1600, singers were expected to chromatically alter notes at their own initiative according to certain rules. This is called musica ficta. In modern transcriptions, these accidentals are usually printed over the note.

Support for such suggested accidentals is included, and can be switched on by setting `suggestAccidentals` to true.

```fis gis
\set suggestAccidentals = ##t
ais bis
```

This will treat every subsequent accidental as musica ficta until it is unset with `\set suggestAccidentals = ##f`. A more practical way is to use `\once \set suggestAccidentals = ##t`, which can even be defined as a convenient shorthand:

```ficta = { \once \set suggestAccidentals = ##t }
\score { \relative
\new MensuralVoice  {
\once \set suggestAccidentals = ##t
bes'4 a2 g2 \ficta fis8 \ficta e! fis2 g1
}
}
```

Internals Reference: Accidental_engraver, AccidentalSuggestion.

White mensural ligatures

There is limited support for white mensural ligatures.

To engrave white mensural ligatures, in the layout block, replace the `Ligature_bracket_engraver` with the `Mensural_ligature_engraver` in the `Voice` context:

```\layout {
\context {
\Voice
\remove "Ligature_bracket_engraver"
\consists "Mensural_ligature_engraver"
}
}
```

There is no additional input language to describe the shape of a white mensural ligature. The shape is rather determined solely from the pitch and duration of the enclosed notes. While this approach may take a new user a while to get accustomed to, it has the great advantage that the full musical information of the ligature is known internally. This is not only required for correct MIDI output, but also allows for automatic transcription of the ligatures.

At certain places two consecutive notes can be represented either as two squares or as an oblique parallelogram (flexa shape). In such cases the default is the two squares, but a flexa can be required by setting the `ligature-flexa` property of the second note head. The length of a flexa can be set by the note head property `flexa-width`.

For example,

```\score {
\relative {
\set Score.timing = ##f
\set Score.defaultBarType = "-"
\override Staff.TimeSignature.style = #'mensural
\clef "petrucci-g"
\[ c''\maxima g \]
\[ d'\longa
c\breve f e d \]
\[ c\maxima d\longa \]
\[ e1 a, g\breve \]
}
\layout {
\context {
\Voice
\remove "Ligature_bracket_engraver"
\consists "Mensural_ligature_engraver"
}
}
}
```

Without replacing `Ligature_bracket_engraver` with `Mensural_ligature_engraver`, the same music looks as follows:

Music Glossary: ligature.

Notation Reference: Gregorian square neume ligatures, Ligatures.

Known issues and warnings

Horizontal spacing of ligatures may be poor. Accidentals may collide with previous notes.

Other languages: deutsch, español, français, italiano, 日本語.


text:
# Vertices of Attachment Question

#### cept

##### New member
I am currently reading "Graph Theory" by Tutte.

Just to make sure I understand the definition of vertex of attachment:

By Tutte's definition, "A vertex of attachment of H in G is a vertex of H that is incident with some edge of G that is not an edge of H. We write W(G, H) for the set of vertices of attachment of H in G..."

So if have a graph G(V) = {A, B, C, D} and G(E) = {a, b, c} drawn below

A ..a... B ....b ...C
0 ----- 0 -------0
|
|c
|
0
D

and subgraph H of G, where H(V) = {A, B} and H(E) = {a}

A.. a ....B
0-------0

then the set of vertices of attachment is: W(G, H) = { B }

Tutte futher writes:

"If H and K are subgraphs of G, let u write Q(G; H, K) for the set of all vertices x of G such that x belongs to W(G, H) and W(G, K) but not to W(G, H U K). Alternatively we may characterize x as incident with an edge of H not belonging to K and with an edge of K not belonging to H, but not incident with any edge of G outside both E(H) and E(K)."

I cannot picture this last statement.

QUESTION:
How can there be vertices of attachment that belong to W(G, H) and W(G, K), but not their union W(G, H U K)??


text:
## Canonical form for very small singular values

General discussions on the ideas behind the algorithm.
aeberharter
Posts: 3
Joined: 04 Nov 2019, 13:36

### Canonical form for very small singular values

The present algorithm to calculate the canonical form for infinite systems calculates the left and right dominant eigenvectors and takes the square root of each, which comes with a loss in precision.

It turns out that close to criticality and at large bond dimensions singular values eventually will become smaller than 1.e-8 which is about the domain where above mentioned precision loss becomes a problem and limits the effective bond dimension of the state.

Is there a method to circumvent this problem? Do you know an algorithm which is able to compute the canonical form with higher precision? I would be happy to implement it myself.
Johannes
Posts: 337
Joined: 21 Jul 2018, 12:52
Location: TU Munich

### Re: Canonical form for very small singular values

One alternative is to iteratively do QR decompositions (and RQ decompositions).
$$M M M M M = Q R M M M M = Q Q R M M M = ... = Q Q Q Q R$$
$$M M M M M = M M M M R' Q' = M M M R' Q' Q' = ... = R' Q' Q' Q' Q'$$
$$M M M M M M M M M M = Q Q Q Q Q R R' Q' Q' Q' Q' Q'$$,
hence you can simply SVD $$RR'$$ and should get the singular values. The $$Q, Q'$$ should give you the state in left/right canonical form.


text:
# How can I align the 3D cursor to a face / polygon with python

I'm currently trying to align the 3D Cursor to a face / polygon with python on Blender 2.8, to snap one object on the surface, but I don't know how can I achieve that, currently I'm using this as a test with the default cube, but it doesn't work as I expected:

import bpy
from bpy import context

scene= context.scene

obj = bpy.context.active_object
face = obj.data.polygons[0]

scene.cursor.location = face.normal
scene.cursor.rotation_euler = face.normal

rot = context.scene.cursor.rotation_euler.copy()
loc = context.scene.cursor.location.copy()

Yes, I know, I can do this with the Blender's snapping functions, but I would like to know how can achieve this with Python.

Hopefully, could someone please bring me some help?

Thank you so much!

So, an important thing to know here is that a normal is only a vector, so it, in a way, represents a single axis of the rotation. The script below pretty much guesses an x and y heading and uses the z direction as the up axis for the cursor. Here, I'm finding the location and normal of the selected face and assigning it to the location and up axis of the cursor. I've simplified this script a lot. It doesn't use the bmesh data, which means you may need to make your face selection in edit mode, and switch back to object mode and then back into edit mode before you run the script.

import bpy
import mathutils

C = bpy.context
cursor = C.scene.cursor
obj = C.active_object
p = obj.data.polygons

#get the normal and center of the selected face
normal = obj.data.polygons[p.active].normal
center = obj.data.polygons[p.active].center

#generate a quaternion rotation from the normal vector
up = normal.to_track_quat('X', 'Y')

#set the cursor to the center location and rotate it to match the up vector
cursor.location = center
cursor.rotation_quaternion = up

And then back in object mode again carry on with getting the cursor location and rotation and creating the primative like in your example above:

#get the object world matrix
mat = obj.matrix_world

#generate the location and rotation
rot = cursor.rotation_euler.copy()
loc = mat @ cursor.location.copy()

bpy.ops.object.mode_set(mode='OBJECT')
bpy.ops.mesh.primitive_plane_add(location = loc, rotation = rot)

You have to get the object world matrix and use it to offset the center location because any vertex, edge, or face location will be based on a distance from the object center, not the world center. Of course, you don't have to use the cursor as a step in between and can just apply the rotation and location of the face directly using:

rot = up
loc = mat @ center

• I think this works, but you should make it clear that the Cursor's rotation has to be in Quaternion mode – yarun can Jul 23 '19 at 4:38

Similarly,

Differs in that it uses live edit bmesh for getting the active face, and also atm it appears that setting the cursor matrix has no effect.

import bpy
import bmesh
from mathutils import Vector, Matrix

context = bpy.context
scene = context.scene
cursor = scene.cursor
ob = context.edit_object
mw = ob.matrix_world

me = ob.data
bm = bmesh.from_edit_mesh(me)

f = bm.select_history.active
o = mw @ f.calc_center_median()
f.normal_update()
norm = (o + mw @ f.normal) - o

q = norm.to_track_quat('Z', 'Y')

M = q.to_matrix().to_4x4()
M.translation = o
cursor.matrix = M # does not work!! bummer

cursor.location = o
if cursor.rotation_mode == 'QUATERNION':
cursor.rotation_quaternion = q
elif cursor.rotation_mode == 'AXIS_ANGLE':
cursor.rotation_axis_angle = q.to_axis_angle()
else:
cursor.rotation_euler = q.to_euler(cursor.rotation_mode)

Related:

On aligning the to the tangent to emulate NORMAL transform axis display

Align to face normal vector

Python: vertex normal according to World

• I tried your version but it does not seem to aling to the normals properly, please see the image imgur.com/qBoWJ6A.png – yarun can Sep 11 '19 at 3:53


text:
# Refresh Table¶

REFRESH TABLE [db_name.]table_name

Refresh all cached entries associated with the table. If the table was previously cached, then it would be cached lazily the next time it is scanned.


text:
# undisputed FrontEndTokenExecute

Thanks to this great topic, I've found the FrontEndToken that I was looking for: "DeleteGeneratedCells" (well, it is also written in Help but I've found it later :)

Question: I would love to execute it in NotebookObject without confirmation through the automatically displayed ChoiceDialog["Do You really want to..."].

Is it maybe a case of FrontEndTokenExecute parameters?

I suspect I can deal with it by setting some global options for Mathematica but I would rather leave them.

-
Related, perhaps duplicate: How to automate a FrontEnd return? – István Zachar Sep 12 '13 at 11:52
@IstvánZachar I would say it is very closely related because our purposes are a bit little different and acceptable solutions too. But we will see what community decides ;) – Kuba Sep 12 '13 at 11:55

Maybe you are looking for something like this. Make a list of the generated cells like this:

cells = Cells[GeneratedCell -> True];

Then delete them from the notebook using this

NotebookDelete[cells];

-
I had to check but it seems that for my needs this works well. And there is no ChoiceDialog[] so thank You for this answer :) – Kuba May 21 '13 at 18:16
@Kuba no problem, glad you like it :) – Jacob Akkerboom May 21 '13 at 18:17
I'm very happy to see answers using the under-utilized Cells function. But I'm not sure what you mean by your statement that this "doesn't use the front end". Both Cells and NotebookDelete require a front end to work properly, and they're implemented by causing the kernel to issue commands to the front end. Incidentally, code very similar to this is in the Applications Examples section of the Cells documentation. – John Fultz Sep 12 '13 at 5:48
@JohnFultz ah, yes, I have made this mistake in another Q&A as well, and fortunately there I was immediately corrected. I should have remembered this Q&A. Thank you – Jacob Akkerboom Sep 12 '13 at 10:00