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# NGC 474

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 The SAURON project - VI. Line strength maps of 48 elliptical and lenticular galaxiesWe present absorption line strength maps of 48 representative ellipticaland lenticular galaxies obtained as part of a survey of nearby galaxiesusing our custom-built integral-field spectrograph, SAURON, operating onthe William Herschel Telescope. Using high-quality spectra, spatiallybinned to a constant signal-to-noise ratio, we measure four key age,metallicity and abundance ratio sensitive indices from the Lick/IDSsystem over a two-dimensional field extending up to approximately oneeffective radius. A discussion of calibrations and offsets is given,along with a description of error estimation and nebular emissioncorrection. We modify the classical Fe5270 index to define a new index,Fe5270S, which maximizes the useable spatial coverage ofSAURON. Maps of Hβ, Fe5015, Mgb and Fe5270S arepresented for each galaxy. We use the maps to compute average linestrengths integrated over circular apertures of one-eighth effectiveradius, and compare the resulting relations of index versus velocitydispersion with previous long-slit work. The metal line strength mapsshow generally negative gradients with increasing radius roughlyconsistent with the morphology of the light profiles. Remarkabledeviations from this general trend exist, particularly the Mgb isoindexcontours appear to be flatter than the isophotes of the surfacebrightness for about 40 per cent of our galaxies without significantdust features. Generally, these galaxies exhibit significant rotation.We infer from this that the fast-rotating component features a highermetallicity and/or an increased Mg/Fe ratio as compared to the galaxy asa whole. The Hβ maps are typically flat or show a mild positiveoutwards radial gradient, while a few galaxies show strong central peaksand/or elevated overall Hβ strength likely connected to recent starformation activity. For the most prominent post-starburst galaxies, eventhe metal line strength maps show a reversed gradient. The hot, warm and cold gas in Arp 227 - an evolving poor groupArp 227 represents a prototypical example of an interacting mixed pairof galaxies located in a low-density environment. We investigate the gasproperties of the pair in the X-ray, Hα, HI and CO bands. We alsodetect two additional members of the group in HI which indicates thatthe pair constitutes the dominant members of a loose group.The HI distribution shows a tail of gas that connects the spiral member,NGC 470, to the lenticular, NGC 474, showing that the two main membersare currently undergoing interaction. The Hα emission reveals thepresence of secondary components at the centre of NGC 470, superposed onthe main component tracing the rotation of the galaxy. This latter mapsa nearly unperturbed velocity field. The dominant, nearly unperturbedtrend of the kinematics is confirmed by CO observations, althoughrestricted to the centre of the galaxy. The X-ray luminosity of NGC 470is comparable with that of a normal' spiral galaxy. NGC 474 on theother hand is very gas-poor and has not been detected in Hα. ItsX-ray luminosity is consistent with the low end of the expected emissionfrom discrete sources.Arp 227 as a loose group shows several signatures of galaxy-galaxyinteraction. Our observations suggest the presence of signatures ofinteraction in the overall kinematics of the spiral companion. Theongoing interaction is clearly visible only in the outer HI halo of NGC470. While the large shell system of NGC 474 could be associated with anaccretion event, the secondary components in the Hα profile in thecentre of NGC 470 could be due to the interaction with the companion.The low X-ray luminosity of NGC 470 seems to be a characteristic ofdynamically young systems. All the above evidence suggest that Arp 227is an evolving group in the early phase of its evolution and that itsdrivers are the accretion of faint galaxies and the ongoing large-scaleinteraction between NGC 470 and 474. The SAURON project - V. Integral-field emission-line kinematics of 48 elliptical and lenticular galaxiesWe present the emission-line fluxes and kinematics of 48 representativeelliptical and lenticular galaxies obtained with our custom-builtintegral-field spectrograph, SAURON, operating on the William HerschelTelescope. Hβ, [OIII]λλ4959,5007 and[NI]λλ5198,5200 emission lines were measured using a newprocedure that simultaneously fits both the stellar spectrum and theemission lines. Using this technique we can detect emission lines downto an equivalent width of 0.1 Å set by the current limitations indescribing galaxy spectra with synthetic and real stellar templates,rather than by the quality of our spectra. Gas velocities and velocitydispersions are typically accurate to within 14 and 20 kms-1, respectively, and at worse to within 25 and 40 kms-1. The errors on the flux of the [OIII] and Hβ linesare on average 10 and 20 per cent, respectively, and never exceed 30 percent. Emission is clearly detected in 75 per cent of our samplegalaxies, and comes in a variety of resolved spatial distributions andkinematic behaviours. A mild dependence on the Hubble type and galacticenvironment is observed, with higher detection rates in lenticulargalaxies and field objects. More significant is the fact that only 55per cent of the galaxies in the Virgo cluster exhibit clearly detectedemission. The ionized-gas kinematics is rarely consistent with simplecoplanar circular motions. However, the gas almost never displayscompletely irregular kinematics, generally showing coherent motions withsmooth variations in angular momentum. In the majority of the cases, thegas kinematics is decoupled from the stellar kinematics, and in half ofthe objects this decoupling implies a recent acquisition of gaseousmaterial. Over the entire sample however, the distribution of the meanmisalignment values between stellar and gaseous angular momenta isinconsistent with a purely external origin. The distribution ofkinematic misalignment values is found to be strongly dependent on theapparent flattening and the level of rotational support of galaxies,with flatter, fast rotating objects hosting preferentially corotatinggaseous and stellar systems. In a third of the cases, the distributionand kinematics of the gas underscore the presence of non-axisymmetricperturbations of the gravitational potential. Consistent with previousstudies, the presence of dust features is always accompanied by gasemission while the converse is not always true. A considerable range ofvalues for the [OIII]/Hβ ratio is found both across the sample andwithin single galaxies. Despite the limitations of this ratio as anemission-line diagnostic, this finding suggests either that a variety ofmechanisms is responsible for the gas excitation in E and S0 galaxies orthat the metallicity of the interstellar material is quiteheterogeneous. Gas in early-type galaxies: cross-fuelling in late-type-early-type pairs?We present 12CO (J= 1-0) and 12CO (J= 2-1)observations of eight early-type galaxies, forming part of a sample ofinteracting galaxies, each consisting of one late- and one early-typesystem. All of the early-type galaxies observed are undetected in CO tolow levels, allowing us to place tight constraints on their moleculargas content. Additionally, we present HI absorption data for one system.The implications for possible gas transfer from the late- to theearly-type galaxy during the interaction are discussed. Stellar Populations in Nearby Lenticular GalaxiesWe have obtained two-dimensional spectral data for a sample of 58 nearbyS0 galaxies with the Multi-Pupil Fiber/Field Spectrograph of the 6 mtelescope of the Special Astrophysical Observatory of the RussianAcademy of Sciences. The Lick indices Hβ, Mg b, and arecalculated separately for the nuclei and for the bulges taken as therings between R=4'' and 7", and the luminosity-weighted ages,metallicities, and Mg/Fe ratios of the stellar populations are estimatedby comparing the data to single stellar population (SSP) models. Fourtypes of galaxy environments are considered: clusters, centers ofgroups, other places in groups, and the field. The nuclei are found tobe on average slightly younger than the bulges in any type ofenvironment, and the bulges of S0 galaxies in sparse environments areyounger than those in dense environments. The effect can be partlyattributed to the well-known age correlation with the stellar velocitydispersion in early-type galaxies (in our sample the galaxies in sparseenvironments are on average less massive than those in denseenvironments), but for the most massive S0 galaxies, withσ*=170-220 km s-1, the age dependence on theenvironment is still significant at the confidence level of 1.5 σ.Based on observations collected with the 6 m telescope (BTA) at theSpecial Astrophysical Observatory (SAO) of the Russian Academy ofSciences (RAS). Star Formation Histories of Nearby Elliptical Galaxies. II. Merger Remnant SampleThis work presents high signal-to-noise spectroscopic observations of asample of six suspected merger remnants, selected primarily on the basisof H I tidal debris detections. Single stellar population analysis ofthese galaxies indicates that their ages, metallicities, andα-enhancement ratios are consistent with those of a representativesample of nearby elliptical galaxies. The expected stellar population ofa recent merger remnant, a young age combined with low [α/Fe], isnot seen in any H I-selected galaxy. However, one galaxy (NGC 2534) isfound to deviate from the Z-plane in the sense expected for a mergerremnant. Another galaxy (NGC 7332), selected by other criteria, bestmatches the merger remnant expectations. Group, field and isolated early-type galaxies - II. Global trends from nuclear dataWe have derived ages, metallicities and enhanced-element ratios[α/Fe] for a sample of 83 early-type galaxies essentially ingroups, the field or isolated objects. The stellar-population propertiesderived for each galaxy correspond to the nuclear re/8aperture extraction. The median age found for Es is 5.8+/-0.6 Gyr andthe average metallicity is +0.37+/-0.03 dex. For S0s, the median age is3.0+/-0.6 Gyr and [Z/H]= 0.53+/-0.04 dex. We compare the distribution ofour galaxies in the Hβ-[MgFe] diagram with Fornax galaxies. Ourelliptical galaxies are 3-4 Gyr younger than Es in the Fornax cluster.We find that the galaxies lie in a plane defined by [Z/H]= 0.99logσ0- 0.46 log(age) - 1.60, or in linear terms Z~σ0× (age) -0.5. More massive (largerσ0) and older galaxies present, on average, large[α/Fe] values, and therefore must have undergone shorterstar-formation time-scales. Comparing group against field/isolatedgalaxies, it is not clear that environment plays an important role indetermining their stellar-population history. In particular, ourisolated galaxies show ages differing by more than 8 Gyr. Finally weexplore our large spectral coverage to derive log(O/H) metallicity fromthe Hα and NIIλ6584 and compare it with model-dependent[Z/H]. We find that the O/H abundances are similar for all galaxies, andwe can interpret it as if most chemical evolution has already finishedin these galaxies. Group, field and isolated early-type galaxies - I. Observations and nuclear dataThis is the first paper of a series on the investigation of stellarpopulation properties and galaxy evolution of an observationallyhomogeneous sample of early-type galaxies in groups, field and isolatedgalaxies.Here we present high signal-to-noise ratio (S/N) long-slit spectroscopyof 86 nearby elliptical and S0 galaxies. Eight of them are isolated,selected according to a rigorous criterion, which guarantees a genuinelow-density subsample. The present survey has the advantage of coveringa larger wavelength range than normally found in the literature, whichincludes [OIII]λ5007 and Hα, both lines important foremission correction. Among the 86 galaxies with S/N >= 15 (perresolution element, for re/8 central aperture), 57 have theirHβ-index corrected for emission (the average correction is 0.190Åin Hβ) and 42 galaxies reveal [OIII]λ5007 emission,of which 16 also show obvious Hα emission. Most of the galaxies inthe sample do not show obvious signs of disturbances nor tidal featuresin the morphologies, although 11 belong to the Arp catalogue of peculiargalaxies; only three of them (NGC 750, 751 and 3226) seem to be stronglyinteracting. We present the measurement of 25 central line-strengthindices calibrated to the Lick/IDS system. Kinematic information isobtained for the sample. We analyse the line-strength index versusvelocity dispersion relations for our sample of mainly low-densityenvironment galaxies, and compare the slope of the relations withcluster galaxies from the literature. Our main findings are that theindex-σ0 relations presented for low-density regionsare not significantly different from those of cluster E/S0s. The slopeof the index-σ0 relations does not seem to change forearly-type galaxies of different environmental densities, but thescatter of the relations seems larger for group, field and isolatedgalaxies than for cluster galaxies. The Central Region of Barred Galaxies: Molecular Environment, Starbursts, and Secular EvolutionStellar bars drive gas into the circumnuclear (CN) region of galaxies.To investigate the fate of the CN gas and star formation (SF), we studya sample of barred nonstarbursts and starbursts with high-resolution CO,optical, Hα, radio continuum, Brγ, and HST data, and findthe following. (1) The inner kiloparsec of bars differs markedly fromthe outer disk. It hosts molecular gas surface densitiesΣgas-m of 500-3500 Msolar pc-2,gas mass fractions of 10%-30%, and epicyclic frequencies of several100-1000 km s-1 kpc-1. Consequently, in the CNregion gravitational instabilities can only grow at high gas densitiesand on short timescales, explaining in part why powerful starburstsreside there. (2) Across the sample, we find bar pattern speeds withupper limits of 43-115 km s-1 pc-1 and outer innerLindblad resonance radii of >500 pc. (3) Barred starbursts andnonstarbursts have CN SF rates of 3-11 and 0.1-2 Msolaryr-1, despite similar CN gas masses. TheΣgas-m value in the starbursts is larger (1000-3500Msolar pc-2) and close to the Toomre criticaldensity over a large region. (4) Molecular gas makes up 10%-30% of theCN dynamical mass and fuels large CN SF rates in the starbursts,building young, massive, high-V/σ components. Implications forsecular evolution along the Hubble sequence are discussed. Testing galaxy evolution in the field: morphology and properties of the diffuse X-ray emission in shell galaxies.Not Available The SAURON project - III. Integral-field absorption-line kinematics of 48 elliptical and lenticular galaxiesWe present the stellar kinematics of 48 representative elliptical andlenticular galaxies obtained with our custom-built integral-fieldspectrograph SAURON operating on the William Herschel Telescope. Thedata were homogeneously processed through a dedicated reduction andanalysis pipeline. All resulting SAURON data cubes were spatially binnedto a constant minimum signal-to-noise ratio. We have measured thestellar kinematics with an optimized (penalized pixel-fitting) routinewhich fits the spectra in pixel space, via the use of optimal templates,and prevents the presence of emission lines to affect the measurements.We have thus generated maps of the mean stellar velocity V, the velocitydispersion σ, and the Gauss-Hermite moments h3 andh4 of the line-of-sight velocity distributions. The mapsextend to approximately one effective radius. Many objects displaykinematic twists, kinematically decoupled components, central stellardiscs, and other peculiarities, the nature of which will be discussed infuture papers of this series. Structure and kinematics of candidatedouble-barred galaxiesResults of optical and NIR spectral and photometric observations of asample of candidate double-barred galaxies are presented. Velocityfields and velocity dispersion maps of stars and ionized gas, continuumand emission-line images were constructed from integral-fieldspectroscopy observations carried out at the 6 m telescope (BTA) of SAORAS, with the MPFS spectrograph and the scanning Fabry-PerotInterferometer. NGC 2681 was also observed with thelong-slit spectrograph of the BTA. Optical and NIR images were obtainedat the BTA and at the 2.1 m telescope (OAN, México).High-resolution images were retrieved from the HST data archive.Morphological and kinematic features of all 13 sample objects aredescribed in detail. Attention is focused on the interpretation ofobserved non-circular motions of gas and stars in circumnuclear (onekiloparsec-scale) regions. We have shown first of all that these motionsare caused by the gravitational potential of a large-scale bar.NGC 3368 and NGC 3786 have nuclearbars only, their isophotal twist at larger radii being connected withthe bright spiral arms. Three cases of inner polar disks in our sample(NGC 2681, NGC 3368 andNGC 5850) are considered. We found ionized-gascounter-rotation in the central kiloparsec of the lenticular galaxyNGC 3945. Seven galaxies (NGC 470,NGC 2273, NGC 2681, NGC3945, NGC 5566, NGC5905, and NGC 6951) have inner mini-disksnested in large-scale bars. Minispiral structures occur often in thesenuclear disks. It is interesting that the majority of the observed,morphological and kinematical, features in the sample galaxies can beexplained without the secondary bar hypothesis. Thus we suggest that adynamically independent secondary bar is a rarer phenomenon than followsfrom isophotal analysis of the images only.Based on observations carried out at the 6 m telescope of the SpecialAstrophysical Observatory of the Russian Academy of Sciences, operatedunder the financial support of the Science Department of Russia(registration number 01-43), at the 2.1 m telescope of the ObservatorioAstronónico Nacional, San Pedro Martir, México, and fromthe data archive of the NASA/ESA Hubble Space Telescope at the SpaceTelescope Science Institute. STScI is operated by the association ofUniversities for Research in Astronomy, Inc. under NASA contract NAS5-26555.Tables 1 to 6 and Figures 2-13 and 15-18 are only available inelectronic form at http://www.edpsciences.org Properties of isolated disk galaxiesWe present a new sample of northern isolated galaxies, which are definedby the physical criterion that they were not affected by other galaxiesin their evolution during the last few Gyr. To find them we used thelogarithmic ratio, f, between inner and tidal forces acting upon thecandidate galaxy by a possible perturber. The analysis of thedistribution of the f-values for the galaxies in the Coma cluster leadus to adopt the criterion f ≤ -4.5 for isolated galaxies. Thecandidates were chosen from the CfA catalog of galaxies within thevolume defined by cz ≤5000 km s-1, galactic latitudehigher than 40o and declination ≥-2.5o. Theselection of the sample, based on redshift values (when available),magnitudes and sizes of the candidate galaxies and possible perturberspresent in the same field is discussed. The final list of selectedisolated galaxies includes 203 objects from the initial 1706. The listcontains only truly isolated galaxies in the sense defined, but it is byno means complete, since all the galaxies with possible companions underthe f-criterion but with unknown redshift were discarded. We alsoselected a sample of perturbed galaxies comprised of all the diskgalaxies from the initial list with companions (with known redshift)satisfying f ≥ -2 and \Delta(cz) ≤500 km s-1; a totalof 130 objects. The statistical comparison of both samples showssignificant differences in morphology, sizes, masses, luminosities andcolor indices. Confirming previous results, we found that late spiral,Sc-type galaxies are, in particular, more frequent among isolatedgalaxies, whereas Lenticular galaxies are more abundant among perturbedgalaxies. Isolated systems appear to be smaller, less luminous and bluerthan interacting objects. We also found that bars are twice as frequentamong perturbed galaxies compared to isolated galaxies, in particularfor early Spirals and Lenticulars. The perturbed galaxies have higherLFIR/LB and Mmol/LB ratios,but the atomic gas content is similar for the two samples. The analysisof the luminosity-size and mass-luminosity relations shows similartrends for both families, the main difference being the almost totalabsence of big, bright and massive galaxies among the family of isolatedsystems, together with the almost total absence of small, faint and lowmass galaxies among the perturbed systems. All these aspects indicatethat the evolution induced by interactions with neighbors would proceedfrom late, small, faint and low mass Spirals to earlier, bigger, moreluminous and more massive spiral and lenticular galaxies, producing atthe same time a larger fraction of barred galaxies but preserving thesame relations between global parameters. The properties we found forour sample of isolated galaxies appear similar to those of high redshiftgalaxies, suggesting that the present-day isolated galaxies could bequietly evolved, unused building blocks surviving in low densityenvironments.Tables \ref{t1} and \ref{t2} are only available in electronic form athttp://www.edpsciences.org First detection of cold dust in the northern shell of NGC 5128 (Centaurus A)Deep far-infrared (FIR) imaging data obtained with ISOPHOT at 90 μm,150 μm, and 200 μm detected the thermal emission from cold dust inthe northern shell region of NGC 5128 (Centaurus A), where previouslyneutral hydrogen and molecular gas has been found. A somewhat extendedFIR emission region is present in both the 150 μm and 200 μm map,while only an upper flux limit could be derived from the 90 μm data.The FIR spectral energy distribution can be reconciled with a modifiedblackbody spectrum with very cold dust color temperatures and emissivityindices in the range 13 K < TDust < 15.5 K and 2 >β > 1, respectively, where the data favor the low temperatureend. A representative value for the associated dust mass isMDust ≈ 7×104 Mȯ, whichtogether with the HI gas mass gives a gas-to-dust ratio of ≈300,close the average values of normal inactive spiral galaxies. This value,in conjunction with the atomic to molecular gas mass ratio typical for aspiral galaxy, indicates that the interstellar medium (ISM) from theinner part of a captured disk galaxy is likely the origin of theoutlying gas and dust. These observations are in agreement with recenttheoretical considerations that in galaxy interactions leading tostellar shell structures the less dissipative clumpy component of theISM from the captured galaxy can lead to gaseous shells. Alternatively,the outlying gas and dust could be a rotating ring structure resultingfrom an interaction or even late infall of tidal material of a merger inthe distant past. With all three components (atomic gas, molecular gas,dust) of the ISM present in the northern shell region, local starformation may account for the chains of young blue stars surrounding theregion to the east and north. The dust cloud may also be involved in thedisruption of the large scale radio jet before entering the brighterregion of the northern radio lobe.Based on observations with ISO, an ESA project with instruments fundedby ESA Member States (especially the PI countries: France, Germany, TheNetherlands and the UK) and with the participation of ISAS and NASA. Tidally Triggered Star Formation in Close Pairs of Galaxies. II. Constraints on Burst Strengths and AgesGalaxy-galaxy interactions rearrange the baryons in galaxies and triggersubstantial star formation; the aggregate effects of these interactionson the evolutionary histories of galaxies in the universe are poorlyunderstood. We combine B- and R-band photometry and optical spectroscopyto estimate the strengths and timescales of bursts of triggered starformation in the centers of 190 galaxies in pairs and compact groups.Based on an analysis of the measured colors and EW(Hα), wecharacterize the preexisting and triggered populations separately. Thebest-fitting burst scenarios assume stronger reddening corrections forline emission than for the continuum and continuous star formationlasting for >~100 Myr. The most realistic scenarios require aninitial mass function that is deficient in the highest mass stars. Thecolor of the preexisting stellar population is the most significantsource of uncertainty. Triggered star formation contributessubstantially (probably >~50%) to the R-band flux in the centralregions of several galaxies; tidal tails do not necessarily accompanythis star formation. Many of the galaxies in our sample have bluercenters than outskirts, suggesting that pre- or nonmerger interactionsmay lead to evolution along the Hubble sequence. These objects wouldappear blue and compact at higher redshifts; the older, redder outskirtsof the disks would be difficult to detect. Our data indicate thatgalaxies with larger separations on the sky contain weaker, and probablyolder, bursts of star formation on average. However, confirmation ofthese trends requires further constraints on the colors of the olderstellar populations and on the reddening for individual galaxies. Lensing and the Centers of Distant Early-Type GalaxiesGravitational lensing provides a unique probe of the inner 10-1000 pc ofdistant galaxies (z~0.2-1). Theoretical studies have predicted that eachstrong lens system should have a faint image near the center of the lensgalaxy, which should, in principle, be visible in radio lenses but hasnever been detected. We study the predicted core'' images using modelsderived from the stellar distributions in nearby early-type galaxies. Wefind that realistic lens galaxies produce a remarkably wide range ofcore images, with magnifications spanning some 6 orders of magnitude.More concentrated galaxies produce fainter core images, although notwith any model-independent relation between the galaxy properties andthe core images. Some real galaxies have diffuse cores that should yieldbright core images (magnification μcore>~0.1), but morecommon are galaxies that yield faint core images(μcore<~0.001). Thus, stellar mass distributions aloneare probably concentrated enough to explain the lack of observed coreimages. Observational sensitivity may need to improve by an order ofmagnitude before detections of core images become common. Two-imagelenses should tend to have brighter core images than four-image lenses,so they will be the better targets for finding core images andexploiting these tools for studying the central mass distributions ofdistant galaxies. Metallicity distributions of globular cluster systems in galaxiesWe collected a sample of 100 galaxies for which different observers havedetermined colour indices of globular cluster candidates. The sampleincludes representatives of galaxies of various morphological types anddifferent luminosities. Colour indices (in most cases (V-I), but also(B-I) and (C-T_1)) were transformed into metallicities [Fe/H] accordingto a relation by Kissler-Patig (1998). These data were analysed with theKMM software in order to estimate similarity of the distribution withuni- or bimodal Gaussian distribution. We found that 45 of 100 systemshave bimodal metallicity distributions. Mean metallicity of themetal-poor component for these galaxies is < [Fe/H]> = -1.40 +/-0.02, of the metal-rich component < [Fe/H]> = -0.69 +/- 0.03.Dispersions of the distributions are 0.15 and 0.18, respectively.Distribution of unimodal metallicities is rather wide. These data willbe analysed in a subsequent paper in order to find correlations withparameters of galaxies and galactic environment. Star Formation Histories of Early-Type Galaxies. I. Higher Order Balmer Lines as Age IndicatorsWe have obtained blue integrated spectra of 175 nearby early-typegalaxies, covering a wide range in galaxy velocity dispersion andemphasizing those with σ<100 km s-1. Galaxies havebeen observed both in the Virgo Cluster and in lower densityenvironments. The main goals are the evaluation of higher order Balmerlines as age indicators and differences in stellar populations as afunction of mass, environment, and morphology. In this first paper, ouremphasis is on presenting the methods used to characterize the behaviorof the Balmer lines through evolutionary population synthesis models.Lower σ galaxies exhibit a substantially greater intrinsicscatter, in a variety of line-strength indicators, than do higherσ galaxies, with the large intrinsic scatter setting in below aσ of 100 km s-1. Moreover, a greater contrast inscatter is present in the Balmer lines than in the lines of metalfeatures. Evolutionary synthesis modeling of the observed spectralindexes indicates that the strong Balmer lines found primarily among thelow-σ galaxies are caused by young age, rather than by lowmetallicity. Thus we find a trend between the population age and thecentral velocity dispersion, such that low-σ galaxies have youngerluminosity-weighted mean ages. We have repeated this analysis usingseveral different Balmer lines and find consistent results from onespectral indicator to another. Redshift-Distance Survey of Early-Type Galaxies: Circular-Aperture PhotometryWe present R-band CCD photometry for 1332 early-type galaxies, observedas part of the ENEAR survey of peculiar motions using early-typegalaxies in the nearby universe. Circular apertures are used to tracethe surface brightness profiles, which are then fitted by atwo-component bulge-disk model. From the fits, we obtain the structuralparameters required to estimate galaxy distances using theDn-σ and fundamental plane relations. We find thatabout 12% of the galaxies are well represented by a pure r1/4law, while 87% are best fitted by a two-component model. There are 356repeated observations of 257 galaxies obtained during different runsthat are used to derive statistical corrections and bring the data to acommon system. We also use these repeated observations to estimate ourinternal errors. The accuracy of our measurements are tested by thecomparison of 354 galaxies in common with other authors. Typical errorsin our measurements are 0.011 dex for logDn, 0.064 dex forlogre, 0.086 mag arcsec-2 for<μe>, and 0.09 for mRC,comparable to those estimated by other authors. The photometric datareported here represent one of the largest high-quality and uniformall-sky samples currently available for early-type galaxies in thenearby universe, especially suitable for peculiar motion studies.Based on observations at Cerro Tololo Inter-American Observatory (CTIO),National Optical Astronomy Observatory, which is operated by theAssociation of Universities for Research in Astronomy, Inc., undercooperative agreement with the National Science Foundation (NSF);European Southern Observatory (ESO); Fred Lawrence Whipple Observatory(FLWO); and the MDM Observatory on Kitt Peak. A Search for H I in Five Elliptical Galaxies with Fine StructureWe report on VLA H I spectral line observations of five early-typegalaxies classified as optically peculiar because of the presence ofjets, ripples, or other optical fine structure. We detect H I within theprimary beam (30' half-power beamwidth) in four of the five systems.However, in only one case is this gas associated with the targetedelliptical galaxy. In the other cases the H I is associated with anearby gas-rich disk or dwarf galaxy. The one H I detection is for NGC7626, where we tentatively detect an H I cloud lying between 20 and 40kpc southwest of the galaxy center. Its origin is unclear. Our failureto detect obvious tidal H I features suggests that if thesefine-structure elliptical galaxies are remnants of disk galaxy mergers,either the progenitors were gas-poor or they are well evolved and anygaseous tidal features have dispersed and/or been converted into otherphases. Our targeted systems all reside in groups or clusters, and itseems likely that tidal H I is shorter lived in these environments thansuggested by studies of more isolated merger remnants. Core Radio and Optical Emission in the Nuclei of nearby FR I Radio GalaxiesIn this paper we analyze the relation between radio, optical continuumand Hα+[N II] emission from the cores of a sample of 21 nearbyFanaroff and Riley type I galaxies as observed with the VLBA and HST.The emission arises inside the inner tens of parsecs of the galaxies.Core radio emission is observed in 19/20 galaxies, optical corecontinuum emission is detected in 12/21 galaxies and Hα+[N II]core emission is detected in 20/21 galaxies. We confirm the recentlydetected linear correlation between radio and optical core emission inFR I galaxies and show that both core emissions also correlate withcentral Hα+[N II] emission. The tight correlations between radio,optical, and Hα+[N II] core emission constrain the bulk Lorentzfactor to γ~2-5 and γ<~2 for a continuous jet and a jetconsisting of discrete blobs, respectively, assuming jet-viewing anglesin the range 30°-90°. Radio and optical core emissions arelikely to be synchrotron radiation from the inner jet, possibly with asignificant contribution from emission by an accretion disk and/or flow.Elliptical galaxies with LINER nuclei without large-scale radio jetsseem to follow the core emission correlations found in FR I galaxies.This suggests that the central engines could be very similar for the twoclasses of active galactic nuclei. Based on observations with theNASA/ESA Hubble Space Telescope obtained at the Space Telescope ScienceInstitute, which is operated by the Association of Universities forResearch in Astronomy, Inc., under NASA contract NAS 5-26555. The SAURON project - II. Sample and early resultsEarly results are reported from the SAURON survey of the kinematics andstellar populations of a representative sample of nearby E, S0 and Sagalaxies. The survey is aimed at determining the intrinsic shape of thegalaxies, their orbital structure, the mass-to-light ratio as a functionof radius, the age and metallicity of the stellar populations, and thefrequency of kinematically decoupled cores and nuclear black holes. Theconstruction of the representative sample is described, and itsproperties are illustrated. A comparison with long-slit spectroscopicdata establishes that the SAURON measurements are comparable to, orbetter than, the highest-quality determinations. Comparisons arepresented for NGC 3384 and 4365, where stellar velocities and velocitydispersions are determined to a precision of 6kms-1, and theh3 and h4 parameters of the line-of-sight velocitydistribution to a precision of better than 0.02. Extraction of accurategas emission-line intensities, velocities and linewidths from the datacubes is illustrated for NGC 5813. Comparisons with published linestrengths for NGC 3384 and 5813 reveal uncertainties of <~0.1Åon the measurements of the Hβ, Mg b and Fe5270 indices.Integral-field mapping uniquely connects measurements of the kinematicsand stellar populations to the galaxy morphology. The maps presentedhere illustrate the rich stellar kinematics, gaseous kinematics, andline-strength distributions of early-type galaxies. The results includethe discovery of a thin, edge-on, disc in NGC 3623, confirm theaxisymmetric shape of the central region of M32, illustrate the LINERnucleus and surrounding counter-rotating star-forming ring in NGC 7742,and suggest a uniform stellar population in the decoupled core galaxyNGC 5813. Two-Dimensional Spectroscopy of Double-Barred GalaxiesWe describe the results of our spectroscopy for a sample of barredgalaxies whose inner regions exhibit an isophotal twist commonly calleda secondary bar. The line-of-sight velocity fields of the ionized gasand stars and the light-of-sight velocity dispersion fields of the starswere constructed from two-dimensional spectroscopy with the 6m SpecialAstrophysical Observatory telescope. We detected various types ofnon-circular motions of ionized gas: radial flows within large-scalebars, counter-rotation of the gas and stars at the center of NGC 3945, apolar gaseous disk in NGC 5850, etc. Our analysis of the optical andnear-infrared images (both ground-based and those from the Hubble SpaceTelescope) revealed circumnuclear minispirals in five objects. Thepresence of an inner (secondary) bar in the galaxy images is shown tohave no effect on the circumnuclear kinematics of the gas and stars.Thus, contrary to popular belief, the secondary bar is not a dynamicallydecoupled galactic structure. We conclude that the so-calleddouble-barred galaxies are not a separate type of galaxies but are acombination of objects with distinctly different morphology of theircircumnuclear regions. Bar Galaxies and Their EnvironmentsThe prints of the Palomar Sky Survey, luminosity classifications, andradial velocities were used to assign all northern Shapley-Ames galaxiesto either (1) field, (2) group, or (3) cluster environments. Thisinformation for 930 galaxies shows no evidence for a dependence of barfrequency on galaxy environment. This suggests that the formation of abar in a disk galaxy is mainly determined by the properties of theparent galaxy, rather than by the characteristics of its environment. The Colors of Globular ClustersA compilation has been made of available data on the ratio of the numberof metal-rich ([Fe/H]>-1.0) to metal-poor ([Fe/H]<-1.0) clustersin various globular cluster systems. Among early-type galaxies of typesE, E/S0, and S0, the ratio of blue to red globular clusters is found tovary by almost 2 orders of magnitude. The data suggest that cD galaxieshave the widest range of evolutionary histories. The fraction ofmetal-rich red clusters is largest among early-type galaxies and appearsto decrease toward later Hubble types. X-Ray-emitting QSOS Ejected from Arp 220Four compact ROSAT X-ray sources very close to the nearby ultraluminousinfrared galaxy Arp 220 (IC 4553) have been identified asmedium-redshift QSOs. The closest pair lying symmetrically across thegalaxy have almost identical redshifts z=1.25, 1.26. All of the evidencesuggests that these QSOs have been ejected from Arp 220 and have largeintrinsic redshifts. A Possible Relationship between Quasars and Clusters of GalaxiesThe distribution on the sky of clusters of galaxies shows significantassociation with relatively nearby, large, active galaxies. The patternis that of clusters paired equidistant across a central galaxy with theapparent magnitudes and redshifts of their constituent galaxies beingclosely matched. The clusters and the galaxies in them tend to be strongX-ray and radio emitters, and their redshifts occur at preferredredshift values. The central, low-redshift galaxies often show evidenceof ejection in the direction of these higher redshift clusters. In allthese respects the clusters resemble closely quasars which have beenincreasingly shown for the last 34 years to be similarly associated withactive parent galaxies. New, especially significant pairings of quasarsare presented here, which are, at the same time, associated with Abellclusters of galaxies. It is argued here that, empirically, the quasarsare ejected from active galaxies. They evolve to lower redshift withtime, forming stars, and fragmenting at the end of their developmentinto clusters of low-luminosity galaxies. The cluster galaxies can be atthe same distance as their lower redshift parents because they stillretain a component of their earlier, quasar intrinsic redshift. The Frequency of Active and Quiescent Galaxies with Companions: Implications for the Feeding of the NucleusWe analyze the idea that nuclear activity, either active galactic nuclei(AGNs) or star formation, can be triggered by interactions by studyingthe percentage of active, H II, and quiescent galaxies with companions.Our sample was selected from the Palomar survey and avoids selectionbiases faced by previous studies. This sample was split into fivedifferent groups, Seyfert galaxies, LINERs, transition galaxies, H IIgalaxies, and absorption-line galaxies. The comparison between the localgalaxy density distributions of the different groups showed that in mostcases there is no statistically significant difference among galaxies ofdifferent activity types, with the exception that absorption-linegalaxies are seen in higher density environments, since most of them arein the Virgo Cluster. The comparison of the percentage of galaxies withnearby companions showed that there is a higher percentage of LINERs,transition galaxies, and absorption-line galaxies with companions thanSeyfert and H II galaxies. However, we find that when we consider onlygalaxies of similar morphological types (elliptical or spiral), there isno difference in the percentage of galaxies with companions amongdifferent activity types, indicating that the former result was due tothe morphology-density effect. In addition, only small differences arefound when we consider galaxies with similar Hα luminosities. Thecomparison between H II galaxies of different Hα luminositiesshows that there is a significantly higher percentage of galaxies withcompanions among H II galaxies with L(Hα)>1039 ergss-1 than among those with L(Hα)<=1039ergs s-1, indicating that interactions increase the amount ofcircumnuclear star formation, in agreement with previous results. Thefact that we find that galaxies of different activity types have thesame percentage of companions suggests that interactions betweengalaxies is not a necessary condition to trigger the nuclear activity inAGNs. We compare our results with previous ones and discuss theirimplications. New Insights from Hubble Space Telescope Studies of Globular Cluster Systems. II. Analysis of 29 S0 SystemsWe examine the globular cluster systems (GCSs) of a sample of 34 S0galaxies from a WFPC2 snapshot survey in the V and I bands. Of these 34galaxies, 29 have measurable globular cluster systems. The mean color ofthe GCSs of individual galaxies vary from V-I=0.85 mag to V-I=1.17 mag.The average color of GCSs in all 29 S0 galaxies, V-I=1.00+/-0.07 mag, issimilar to the value of V-I=1.04+/-0.04 derived for ellipticals in acompanion paper. The mean metallicity of a cluster system is correlatedto the luminosity (or mass) of the host galaxy, but it is not dependenton the Hubble type. Our measurements of the local specific frequency, onthe other hand, confirm that the cluster formation efficiency is afunction of Hubble type. The mean local specific frequency of our samplewithin the WFPC2 field of view is 1.0+/-0.6, lower thanSN(Local)=2.4+/-1.8 derived for ellipticals in a similaranalysis. Although we are able to confirm a bimodal color distributionin only one galaxy from the shallow `snapshot'' images analyzed in thispaper, statistical tests suggest that 10%-20% of S0s are bimodal at thepresent level of photometric accuracy. There are no significant trendsin GCS properties with membership or location of the S0 host in a galaxycluster. We have measured the turnover luminosity of the globularcluster luminosity function (GCLF) for the richest few GCSs and find theGCLF distances to be in agreement with other estimates. The globularclusters in S0 galaxies have average half-light radii of ~2.6 pc, whichis similar to that of other galaxies, including our own. Based onobservations with the NASA/ESA Hubble Space Telescope, obtained at theSpace Telescope Science Institute, which is operated by the Associationof Universities for Research in Astronomy (AURA), Inc., under NASAcontract NAS 5-26555.
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#### Observation and Astrometry data

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## Linear and non-linear Modified Gravity forecasts with future surveys

A new paper has been put on the arXiv by new CosmoStat member Valeria Pettorino, her PhD student Santiago Casas, in collaboration with Martin Kunz (Geneva) and Matteo Martinelli (Leiden).
The authors discuss forecasts in Modified Gravity cosmologies, described by two generic functions of time and space [Planck Dark Energy and Modified Gravity 2015Asaba et al 2013,Bull 2015Alonso et al 2016]. Their amplitude is constrained in different redshift bins. The authors elaborate on the impact of non-linear scales, showing that their inclusion (via a non-linear semi-analytical prescription applied to Modified Gravity) enables to highly reduce correlation among different redshift bins, even before any decorrelation procedure is applied. This is visually seen in the figure below (Fig.4 of arXiv), for the case of Galaxy Clustering: the correlation Matrix of the cosmological parameters (including the amplitudes of the Modified Gravity functions, binned in redshift)  is much more diagonal in the non-linear case (right panel) than in the linear one (left panel).

A decorrelation procedure (Zero-phase Component Analysis, ZCA) is anyway used to extract those combinations which are best constrained by future surveys such as Euclid. With respect to Principal Component Analysis, ZCA allows to find a new vector of uncorrelated variables that is as similar as possible to the original vector of variables.

The authors further consider two smooth time functions whose main allowed to depart from General Relativity only at late times (late-time parameterization) or able to detach also at early times (early-time parameterization). The Fisher Matrix forecasts for standard and Modified gravity parameters, for different surveys (Euclid, SKA1, SKA2) is shown in the plot below (extracted from Fig.15 of arXiv), in which Galaxy Clustering and Weak Lensing probes are combined. Left panel refers to linear analysis, right panel includes a non-linear treatment.

## Weak-lensing projections

A new paper has been put on the arXiv and submitted to MNRAS by CosmoStat member Martin Kilbinger.
The authors discuss various methods to calculate projections for weak gravitational lensing: Since lenses galaxies pick up matter inhomogeneities of the cosmic web along the line of sight while photons from the galaxies propagate through the Universe to the observer, these inhomogeneities have to be projected to a 2D observable, the cumulative shear or convergence. The full projection involves three-dimensional integrals over highly oscillating Bessel functions, and can be time-consuming to compute numerically to high accuracy. Most previous work have therefore used approximations such as the Limber approximation, that reduce the integrals to 1D, and thereby neglecing modes along the line of sight.

The authors show that these projections are more than adequate for present surveys. Sub-percent accuracy is reached for l>20, for example as shown by the pink curve, which is the ratio of the case 'ExtL1Hyb' to the full projection. The abbreviation means 'extended', corresponding to the improved approximation introduced by LoVerde & Afshordi (2008), first-order Limber, and hybrid, since this is a hybrid between flat-sky and spherical coordinates. This case has been used in most of the recent publications (e.g. for KiDS), whereas the cast 'L1Fl' (first-order Limber flat-sky) was popular for most publications since 2014.

These approximations are sufficient for the small areas of current observations coming from CFHTLenS, KiDS, and DES, and well below cosmic variance of even future surveys (the figure shows Euclid - 15,000 deg2 and Kids -1,500 deg2).

The paper then discusses the second-order Limber approximation, introduced in a general framework by LoVerde & Afshordi (2008), and applied to weak lensing in the current paper. The best 2nd-order case 'ExtL2Sph' reaches sub-percent accuracy down to l=3, sufficient for all future surveys.

The paper also computes the shear correlation function in real space, and shows that those approximations have a very minor influence.

The authors then go on to re-compute the cosmological constraints obtained in Kilbinger et al. (2013), and find virtually no change when chosing different approximations. Only the depreciated case 'ExtL1Fl' makes a noticeable difference, which is however still well within the statistical error bars. This case shows a particular slow convergence to the full projection.

The results of this paper are in contrast of the recent publication by Kitching et al. (2017), version 1, who find an order of magnitude larger effect. Those authors have since published a revised version, whose results are in agreement with ours. Note however that they conclude that errors from projection approximations of the types we discussed here (Limber, flat sky) could make up to 11% of the error budget of future surveys. This is however assuming the worst-case scenario including the depriciated cast 'ExtL1Fl', and we do not share their conclusion, but think that for example the projection 'ExtL2Sph' is sufficient for future surveys such as LSST and Euclid.

# First round of papers published

The XXL Survey is a deep X-ray survey observed with the XMM satellite, covering two fields of 25 deg2 each. Observations in many other wavelength, from radio to IR and optical, in both imaging and spectroscopy, complement the survey. The main science case is cosmology with X-ray selected galaxy clusters, but other fields such as galaxy evolution, AGNs, cluster physics, and the large-scale structure are being studied.

The main paper (Paper I) describing the survey and giving an overview of the science is arXiv:1512.04317 (Pierre et al. 2015). Paper IV (arxiv.org:1512.03857, Lieu et al. 2015) presents weak-lensing mass measurements of the brightest clusters in the Northern field, using CFHTLenS shapes and photometric redshifts.

## Review: Cosmology from cosmic shear observations

Martin Kilbinger, CEA Saclay, Service d'Astrophysique (SAp), France

Find on this page general information and updates for my recent review article (arXiv:1411.0155) on cosmic shear, Reports on Progress in Physics 78 (2015) 086901 (ads link for two-column format).

Fig. 7 of the review article: The quantity $\Sigma = \sigma_8 \left( \Omega_{\rm m}/0.3 \right)^\alpha$ as function of publication year.
Get the data in table format as pdf.

Updated figure!
02/2015: Added Stripe-82 and CFHTLenS peak counts
07/2015: Added DES-SV.
06/2016: Added DLS, two more CFHTLenS analyses, DES-SV peak counts, and KiDS-450.

In the video abstract of the article I talk about cosmic shear and the review for a broader audience.

Additional references, new papers
General papers, new reviews.

• Another weak-lensing review has been published by my colleagues Liping Fu and Zu-Hui Fan (behind a pay wall, not available on the arXiv).
• Rachel Mandelbaum's short, pedagogical review to instrumental systematics and WL

Sect. 2: Cosmological background

Sect. 5: Measuring weak lensing

• News on ensemble shape measurement methods:
An implementation of the Bernstein & Armstrong (2014) Bayesian shape method has been published at arXiv:1403.7669. The team that participated at the great3 challenge with the Bayesian inference method "MBI" published their pipeline and results paper, see arXiv:1411.2608.
• Okura & Futamase (arXiv:1405.1539) came up with an estimator of ellipticity that uses 0th instead of 2nd-order moments!
• arXiv:1409.6273 discusses atmospheric chromatic effects for LSST.
• Dust in spiral galaxies  as source of shape bias, but also astrophysical probe: arXiv:1411.6724.

Scripts

Fig. 3 (b), derivatives of the convergence power spectrum with respect to various cosmological parameters.
cs_review_scripts.tgz.

Comments and suggestions are welcome! Please write to me at martin.kilbinger@cea.fr.

Last updated 22 July 2015.

## New model on peak counts: paper published

A new, probabilistic model for weak-lensing peak counts has recently been proposed by CosmoStat group members Lin and Kilbinger (arXiv:1410.6955). It is based on drawing halos from the mass function and, via ray-tracing, generating weak-lensing maps to count peaks. These simulated maps can directly be compared to observations, making this a forward-modelling approach of the cluster mass function, in contrast to many other traditional methods using cluster probes such as X-ray, optical richness, or SZ observations.

The model prediction is in very good agreement with N-body simulations.

It is very flexible, and can potentially include astrophysical and observational effects, such as intrinsic alignment, halo triaxiality, masking, photo-z errors, etc. Moreover, the pdf of the number of peaks can be output by the model, allowing for a very general likelihood calculation, without e.g. assuming a Gaussian distribution of the observables.

The paper has been accepted for publication in A&A (20/01/2015). Reference: A&A, 576, A24.

The code corresponding to the model is available for download here.

## Daniel Machado's PhD defense at CEA Saclay (2 pm, Galilée room)

Title: "Improving automated redshift detection in the low signal-to-noise regime for Large Sky Surveys"

Abstract: "Large redshift surveys of galaxies are key to pinning down cosmological models. We present the Darth Fader algorithm which is dedicated to tackling redshift estimation in the low signal to noise regime, & can blindly differentiate spectra into separate categories as to whether they are likely to yield accurate redshift results, or not. We additionally present a new method for continuum subtraction that does not rely on modelling.

Results are shown for simulated data derived from the COSMOS Mock Catalogue. Further results are shown for a test of the algorithm on a subset of the WiggleZ catalogue, where redshifts have previously been determined by visual inspection."

## Review: Cosmology from cosmic shear observations

A review on cosmology from cosmic shear observations has been submitted to ROPP, and has the arXiv reference arXiv:1411.0115. Comments are very welcome! Check also the accompanying web page for more information, updates, and errata.

## Are the CMB anomalies real ?

A European team, involving researchers from the l'Ecole Polytechnique Fédérale de Lausanne (EPFL) and the Astrophysical Department Sap-AIM of CEA-Irfu, has found that some of the defects in the Cosmic Microwave Background of the universe present in the images obtained by the WMAP and Planck satellites may only be due to poor image reconstruction and incomplete subtraction of the contributions of our own galaxy. These results are published in the Journal of Cosmology and Astroparticle Physics August 2014.

## Release of Planck + WMAP CMB map using sparsity.

The LGMCA method has been used to reconstruct the Cosmic Microwave Background (CMB) image from WMAP 9 year and Planck-PR1 data. Based on the sparse modeling of signals - a framework recently developed in applied mathematics - the proposed component separation method is well-suited for the extraction of foreground emissions.

A joint WMAP9 year and Planck PR1 CMB has been reconstructed for the first time and produce a very high quality CMB map, especially on the galactic center where it is the most difficult due to the strong foreground emissions of our Galaxy. This webpage provides some comparisons between the PR1 and WPR1 maps and codes to recompute the map in the spirit of reproducible research.

# Fitting formulae of the reduced-shear power spectrum for weak lensing

## Reference

Martin Kilbinger, 2010, arXiv:1004.3493

## Description

We provide fitting formulae for the reduced-shear power-spectrum correction which is third-order in the lensing potential. This correction reaches up to 10% of the total lensing spectrum. Higher-order correction terms are one order of magnitude below the third-order term. The correction involves an integral over the matter bispectrum. We fit this integral with a combination of power-law functions and polynomials. We also fit the derivatives with respect to cosmological parameters. A Taylor-expansion around a fiducial (WMAP7) model provides accurate reduced-shear corrections within a region in parameter space containing the WMAP7 68% error elllipsoid.

## Results

Our fits are accurate to 1% for l<104, and to 2% for l<2·105, which reduces the bias by a factor of four compared to the case of no correction. This matches the precision lensing power spectrum predictions of recent N-body simulations.

## Download, install, and run the code

Download an example code which includes the fitting matrices. Use 'make' to compile the code. To use the code, you have to fill in Fmn(a) (eq. 10 from the paper) which involves the lensing efficiency, comoving distances and the redshift distribution(s).

The reduced-shear corrections are also implemented in the cosmology and lensing package 'nicaea'. This code provides all necessary functions to produce lensing observables (shear power spectrum and real-space second-order functions). The cosmology and redshift distributions are set via parameter files.

## Author

Martin Kilbinger (martin.kilbinger@cea.fr)

format: plain


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# OpenSSL - extract hash algorithm from signature data (PKCS#1 v 1.5)

PKCS#1 v 1.5 stores hash algorithm identifier that was used to digest the original message. I would like to know if and how to extract this information.

I am working on a buffer containing the signature bytes and a buffer with public key.

I know it can be done (e.g. openssl rsautl does it with -verify and -asn1parse), but there is no sensible documentation for asn1 functions in openssl.

The hash identifier of a given RSASSA-PKCS1-v1_5 signature can only be obtained using the signature's public key¹. It's revealed by performing the signature verification steps 1 and 2/a/b/c (which basically gets the signature as an integer, raises it to the power $$e$$ modulo $$N$$ extracted from the public key, and converts back to bytes), then parsing the Encoded Message, which should be as per section 9.2 step 5, that is $$\text{EM}=\mathtt{00}\mathbin\|\mathtt{01}\mathbin\|\mathtt{FF}\mathbin\|\ldots\|\mathtt{FF}\mathbin\|\mathtt{00}\mathbin\|T$$ where

• the left two bytes $$\mathtt{00}\mathbin\|\mathtt{01}$$ are fixed, and followed by $$f\ge8$$ bytes at $$\mathtt{FF}$$ then a $$\mathtt{00}$$ ($$f$$ is maximal, that is for a $$b$$-bit public modulus $$N$$ the length of $$T$$ is $$\left\lfloor(b-17)/8\right\rfloor-f$$ bytes).
• $$T$$ is ASN.1 DER encoded, containing the hash identifier and hash value.

The pragmatic approach to decode $$T$$ is to look at note 1 (or the table below, which comes from that).

MD2:         30 20 30 0C 06 08 2A 86 48 86 F7 0D 02 02 05 00 04 10 ∥ H
MD5:         30 20 30 0C 06 08 2A 86 48 86 F7 0D 02 05 05 00 04 10 ∥ H
SHA-1:       30 21 30 09 06 05 2B 0E 03 02 1A 05 00 04 14 ∥ H
SHA-224:     30 2D 30 0D 06 09 60 86 48 01 65 03 04 02 04 05 00 04 1C ∥ H
SHA-256:     30 31 30 0D 06 09 60 86 48 01 65 03 04 02 01 05 00 04 20 ∥ H
SHA-384:     30 41 30 0D 06 09 60 86 48 01 65 03 04 02 02 05 00 04 30 ∥ H
SHA-512:     30 51 30 0D 06 09 60 86 48 01 65 03 04 02 03 05 00 04 40 ∥ H
SHA-512/224: 30 2D 30 0D 06 09 60 86 48 01 65 03 04 02 05 05 00 04 1C ∥ H
SHA-512/256: 30 31 30 0D 06 09 60 86 48 01 65 03 04 02 06 05 00 04 20 ∥ H

If we dive into the fine print, this is a DigestInfoValue. For example, the last entry decodes as

• 30 31   Sequence of 49 bytes
• 30 0D   Sequence of 13 bytes
• 06 09   OID of 9 bytes
• 60 86 48 01 65 03 04 02 06
OID 2.16.840.1.101.3.4.2.6 meaning "SHA512-256 algorithm"
• 05 00   NULL for the Parameters field²
• 04 20   Octet string of 32 bytes
• (the hash H follows as 32 bytes).

See this for how OIDs are encoded, and links to the ASN.1 DER specification. Examples can be thrown at Lapo Luchini's useful ASN.1 decoder.

¹ Given a signature, it's possible to make a new public/private key pair that makes this signature valid with any desired hash identifier and matching any desired known message (not only the the original) when checked with this new public key.

² This field must be present and NULL when encoding and checking $$T$$ in the context of RSASSA-PKCS1-v1_5. In other contexts a parser must accept that it is missing for the SHA algorithms, see the Exception in appendix B.1 and the two paragraphs above.


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# If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0,

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If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0, [#permalink]  25 Sep 2013, 09:59
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If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0, what is the other factor of the equation?\

A. (x+2√3)
B. (x+4√3)
C. (x+6√3)
D. (x−2√3)
E. (x−6√3)

I tried to solve the equation by putting the value of x as (x−2√3) and got x= √48..and then I just got confused Can someone tell me the correct approach to the problem?

Thanks
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Sep 2013, 10:08, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0, [#permalink]  25 Sep 2013, 10:19
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bzb wrote:
If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0, what is the other factor of the equation?\

A. (x+2√3)
B. (x+4√3)
C. (x+6√3)
D. (x−2√3)
E. (x−6√3)

I tried to solve the equation by putting the value of x as (x−2√3) and got x= √48..and then I just got confused Can someone tell me the correct approach to the problem?

Thanks

Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:

$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.

So, we know that one of the roots of $$x^2+(4\sqrt{3})x-36=0$$ is $$2\sqrt{3}$$.

According to the theorem above $$2\sqrt{3}*x_2=\frac{c}{a}=\frac{-36}{1}$$ --> $$x_2=-\frac{18}{\sqrt{3}}=-6\sqrt{3}$$.

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Re: If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0, [#permalink]  23 Sep 2014, 21:33
Basic Formula:

(x+a) * (x+b) = x^2 + (a+b) * x + ab

Given equation:

$$x^2 + 4\sqrt{3} x - 36 = 0$$; one of the root = $$x - 2\sqrt{3}$$

Just observe & try to compare with the basic formula

1. Highlighted sign in the equation is +ve & middle sign of the root is -ve.

It means middle sign of the other root has to be +ve

Re-writing the equation as follow:

$$x^2 + (6\sqrt{3} - 2\sqrt{3}) x - (6\sqrt{3} * 2\sqrt{3}) = 0$$

$$x(x + 6\sqrt{3}) - 2\sqrt{3} (x + 6\sqrt{3}) = 0$$

$$(x + 6\sqrt{3}) (x - 2\sqrt{3}) = 0$$

$$Other root = x + 6\sqrt{3}$$

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Re: If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0,   [#permalink] 23 Sep 2014, 21:33
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I’ve been on a journey to get WPwatercooler.com to be on the fediverse and it hasn’t been as easy as I was thinking it was going to be. Folks that run a website and want to use Mastodon to build community around it have a few options for being presented on the Fediverse. This post isn’t going to help you solve this yet but I hope we can work out what needs to be done in order to do so.

2. Build your own Mastodon instance and make an account there and share your content
3. Use ActivityPub and allow people to follow your website on any Fediverse property

There is most likely more but for the most part its those 3 that you can select from.

I started out with WPwatercooler on Mastodon.online which can be found at https://mastodon.online/@wpwatercooler this works fine and people can follow it but I wanted to see if I could take it a step further and add WPwatercooler.com to the Fediverse directly and this is where ActivityPub comes in.

I installed these three plugins so that I could offer up ActivityPub via WebFinger and people on Mastodon will be able to find the website on there. I created 2 accounts on WPwatercooler.com one for each show wpwatercooler and devbranch and then I did a search for @[email protected] and @[email protected] on my Mastodon instance and was able to find them.

## The Problem

The thing I and other folks in our community ran into was that we could follow the accounts and if we tried a bunch sometimes it should register. Seems to be a caching issues I think. Let’s check and see.

## WebFinger

In part WebFinger is a protocol that allows for discovery of information about people and things identified by a URI. Information about a person might be discovered via an acct: URI, for example, which is a URI that looks like an email address.

Both of these accounts can be found by going to https://wpwatercooler.com/author/devbranch/ and https://wpwatercooler.com/author/wpwatercooler/ as you can see both of these are authors on the WPwatercooler website like I spoke about before. When someone tries and searches for @[email protected] on Mastodon it accesses https://wpwatercooler.com/.well-known/webfinger?resource=acct:[email protected] and as you can see from the url it looks at the domain name in the .well-known/webfinder and looks for the resource with the account name of [email protected]

Webfinger offers up a json output that looks like the following:

{
“subject”: “acct:[email protected]”,
“aliases”: [
“acct:[email protected]”,
“https://wpwatercooler.com/author/wpwatercooler/”,
“mailto:[email protected]”
],
{
“rel”: “http://webfinger.net/rel/profile-page”,
“href”: “https://wpwatercooler.com/author/wpwatercooler/”,
“type”: “text/html”
},
{
“rel”: “http://webfinger.net/rel/avatar”,
},
{
“rel”: “http://webfinger.net/rel/profile-page”,
“href”: “https://www.wpwatercooler.com”,
“type”: “text/html”
},
{
“rel”: “self”,
“type”: “application/activity+json”,
“href”: “https://wpwatercooler.com/author/wpwatercooler/”
},
{
“rel”: “http://nodeinfo.diaspora.software/ns/schema/2.0”,
“href”: “https://wpwatercooler.com/wp-json/nodeinfo/2.0”
},
{
“rel”: “http://nodeinfo.diaspora.software/ns/schema/1.1”,
“href”: “https://wpwatercooler.com/wp-json/nodeinfo/1.1”
},
{
“rel”: “http://nodeinfo.diaspora.software/ns/schema/1.0”,
“href”: “https://wpwatercooler.com/wp-json/nodeinfo/1.0”
},
{
“rel”: “https://feneas.org/ns/serviceinfo”,
“type”: “application/ld+json”,
“href”: “https://wpwatercooler.com/wp-json/serviceinfo/1.0”,
“properties”: {
“https://feneas.org/ns/serviceinfo#software.name”: “WPwatercooler”
}
},
{
“href”: “https://wpwatercooler.com/author/wpwatercooler/feed/ostatus/”,
“type”: “application/atom+xml”
},
{
“rel”: “http://ostatus.org/schema/1.0/subscribe”,
“template”: “https://wpwatercooler.com/?profile={uri}”
},
{
“rel”: “feed”,
“type”: “application/stream+json”,
“title”: “Activity-Streams 1.0 Feed”,
“href”: “https://wpwatercooler.com/author/wpwatercooler/feed/as1/”
},
{
“rel”: “feed”,
“type”: “application/activity+json”,
“title”: “Activity-Streams 2.0 Feed”,
“href”: “https://wpwatercooler.com/author/wpwatercooler/feed/as2/”
}
]
}

the section we’re interested in is

{
“rel”: “self”,
“type”: “application/activity+json”,
“href”: “https://wpwatercooler.com/author/wpwatercooler/”
},

This section has the author url and you can see that its using the type of application/activity+json instead of something like text/html so when it queries that url it passes along in the header Accept: application/activity+json and it should return it in that format.

Running the following command

$url -i -H “Accept: application/activity+json” “https://wpwatercooler.com/author/wpwatercooler” % Total % Received % Xferd Average Speed Time Time Time Current Dload Upload Total Spent Left Speed 0 0 0 0 0 0 0 0 —:—:— —:—:— —:—:— 0HTTP/2 200 date: Tue, 17 Jan 2023 17:42:34 GMT content-type: text/html; charset=UTF-8 last-modified: Tue, 17 Jan 2023 16:11:53 GMT cache-control: max-age=0 expires: Tue, 17 Jan 2023 16:40:07 GMT vary: Accept-Encoding age: 3746 x-cache: HIT cf-cache-status: DYNAMIC server-timing: cf-q-config;dur=9.0000003183377e-06 report-to: {“endpoints”:[{“url”:“https:\/\/a.nel.cloudflare.com\/report\/v3?s=hTOA5wCRdqy4Lkoey48CmI2UIbYym8HWAvtsssC4lRsXgli7%2BchgWImTY3ol%2FdS8gTcodIYZQ6cbSDMVZ1co5brwCJxEpkIdqJ%2FCEjwKcxOWhomHgfWISN9qzmkfkMd7tNo8fQORQ%3D%3D”}],“group”:“cf-nel”,“max_age”:604800} nel: {“success_fraction”:0,“report_to”:“cf-nel”,“max_age”:604800} server: cloudflare cf-ray: 78b0e3631e862ea3-LAX alt-svc: h3=“:443”; ma=86400, h3-29=“:443”; ma=86400 Cloudflare returns back text/html and outputs the author page and not the json we wanted. Talking with a few folks on Mastodon we found that people are having this issue with using Cloudflare and there isn’t anything we can do to resolve it sadly. I tried excluding the caching for the specific paths /author/(.*) and other such tricks and it keeps changing the content-type to text/html and not application/activity+json as requested. Looking online I’ve found a bunch of people using Cloudflare + ActivityPub running into this issue and other technologies that also use Accept: application/activity+json and finding that it only returns text/html. Bummer. The code that makes all that work can be found in the WordPress ActivityPub plugin class-activity-pub.php /** * Return a AS2 JSON version of an author, post or page. * * @param string$template The path to the template object.
*
* @return string The new path to the JSON template.
*/
public static function render_json_template( $template ) { if ( ! \is_author() && ! \is_singular() && ! \is_home() ) { return$template;
}

// check if user can publish posts
if ( \is_author() && ! user_can( \get_the_author_meta( 'ID' ), 'publish_posts' ) ) {
return $template; } if ( \is_author() ) {$json_template = ACTIVITYPUB_PLUGIN_DIR . '/templates/author-json.php';
} elseif ( \is_singular() ) {
$json_template = ACTIVITYPUB_PLUGIN_DIR . '/templates/post-json.php'; } elseif ( \is_home() ) {$json_template = ACTIVITYPUB_PLUGIN_DIR . '/templates/blog-json.php';
}

global $wp_query; if ( isset($wp_query->query_vars['activitypub'] ) ) {
return $json_template; } if ( ! isset($_SERVER['HTTP_ACCEPT'] ) ) {
return $template; }$accept_header = $_SERVER['HTTP_ACCEPT']; if ( \stristr($accept_header, 'application/activity+json' ) ||
\stristr( $accept_header, 'application/ld+json' ) ) { return$json_template;
}

// Accept header as an array.
$accept = \explode( ',', \trim($accept_header ) );

if (
\in_array( 'application/ld+json; profile=“https://www.w3.org/ns/activitystreams”', $accept, true ) || \in_array( 'application/activity+json',$accept, true ) ||
\in_array( 'application/ld+json', $accept, true ) || \in_array( 'application/json',$accept, true )
) {
return $json_template; } return$template;
}

## Can this be done?

After discussing this with @[email protected] and @[email protected] on mastodon in this tread https://simian.rodeo/@jasontucker/109701436056062907 we found that there is an endpoint that will return json https://wpwatercooler.com/author/wpwatercooler/activitypub

I’m wondering if instead we can force Webfinger to return that url with /activitypub at the end instead of expecting Cloudflare to return a non text/html content type. You can see this JSON output here https://wpwatercooler.com/author/wpwatercooler/activitypub/

“id”: “https://wpwatercooler.com/author/wpwatercooler/”,
“type”: “Person”,
“name”: “WPwatercooler Show”,
“summary”: “The world’s most influential WordPress podcast brought to you by Jason Tucker, Sé Reed & Jason Cosper”,
“url”: “https://wpwatercooler.com/author/wpwatercooler/”,
“icon”: {
“type”: “Image”,
},
“inbox”: “https://wpwatercooler.com/wp-json/activitypub/1.0/users/6260/inbox”,
“outbox”: “https://wpwatercooler.com/wp-json/activitypub/1.0/users/6260/outbox”,
“followers”: “https://wpwatercooler.com/wp-json/activitypub/1.0/users/6260/followers”,
“following”: “https://wpwatercooler.com/wp-json/activitypub/1.0/users/6260/following”,
“manuallyApprovesFollowers”: false,
“publicKey”: {
“id”: “https://wpwatercooler.com/author/wpwatercooler/#main-key”,
“owner”: “https://wpwatercooler.com/author/wpwatercooler/”,

What’s involved to make this work on Cloudflare? I’d love to hear in the comments and we can see about getting this combo of WordPress + CloudFlare + ActivityPub working, I’ve seen so many people complain about this not working with this very popular combo of technologies in the WordPress support forums.

## 11 responses to “What’s with ActivityPub + WordPress + Cloudflare not working?”

1. … liked this!

2. … reposted this!

3. Let me know what you think @tim @tomfinley

4. @jasontucker I am trying to read your post but it’s not loading for me, the page only half loads. Also what’s with the hashtags that are all hex codes? I’m so confused.

5. @shauny wow, that’s really weird

6. @shauny of course the first time I ever try to actually put code on my website, something funky like this happens

7. @shauny OK do you mind giving me a refresh?

8. @dustinrue well the real issue is that it’s not returning the correct content type

9. @jasontucker sorry was out. It’s working now. The long URLs add horizontal scrolling on mobile though, just FYI. I tried adding my site to the Fediverse but found that it’s probably better to just link to posts from a separate account, and track replies etc using webfinger. Less hassle!

10. @dustinrue yeah you can force the format by adding /activitypub to the end of the author url https://wpwatercooler.com/author/wpwatercooler/activitypub

11. @dustinrue yeah @tim and @tomfinley were also working out what the deal is here, Tim is using lightspeed and was having weird issues, i think this is a combo of cloudways hosting and their caching along with cloudflare for me.

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text:
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# Solution for A Hemispherical Bowl Made of Brass Has Inner Diameter 10.5 Cm. Find the Cost of Tin- Plating It on the Inside at the Rate of Rs. 4 per 100 Cm^2 - CBSE Class 9 - Mathematics

ConceptSurface Area of a Sphere

#### Question

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin- plating
it on the inside at the rate of Rs. 4 per 100 cm^2

#### Solution

Given
Inner diameter of hemisphere bowl -10.5cm

Radius -  (10.5)/2cm - 5.25 cm .

Surface area of hemispherical bowl - 2πr

- 2[22/7] × (5.25)^2 cm ^2

- 173 .25 cm^2

Cost of tin planning 100cm^2 area = Rs. 4

Cost of tin planning 173.25 cm^2 area = Rs .((4 xx173.25)/100)

= Rs. 6.93

Thus, The cost of tin plating the inner side of hemisphere bowl is Rs .6 93

Is there an error in this question or solution?

#### APPEARS IN

Solution A Hemispherical Bowl Made of Brass Has Inner Diameter 10.5 Cm. Find the Cost of Tin- Plating It on the Inside at the Rate of Rs. 4 per 100 Cm^2 Concept: Surface Area of a Sphere.
S


text:
Local properties of morphisms of schemes

In Hartshorne Proposition II.5.8, he shows, given a morphism $f \colon X \to Y$ where X and Y are schemes and $\mathcal{G}$ a quasi-coherent sheaf of $\mathcal{O}_{Y}$- modules, that $f^{*}\mathcal{G}$ is a quasi-coherent sheaf of $\mathcal{O}_{X}$-modules. Similarly, he shows that given $f$ quasicompact and separated, that the pushforward of a quasi-coherent sheaf is quasi-coherent.

My question concerns his reduction to the affine case. I understand that the quasi-coherent property is local, since it can be checked on an affine cover by definition, so for proving that the pullback of a quasi-coherent sheaf is quasi-coherent, one can assume $X$ to be affine. However, why is one allowed to also assume $Y$ to be affine as it is done in the proof, while for proving the pushforward, one can only assume $Y$ affine and not $X$?

If $U\subseteq X$ is an open set and $V\subseteq Y$ is any open set containing $f(U)$, then the restriction of $f^*\mathcal{G}$ to $U$ depends only on the restriction of $\mathcal{G}$ to $V$ (more precisely, $(f^*\mathcal{G})|_U=g^*(\mathcal{G}|_V)$, where $g:U\to V$ is the restriction of the morphism $f$ to a morphism $U\to V$). To show $f^*\mathcal{G}$ is quasicoherent, it suffices to show that $X$ has an open cover by affine open sets $U\subseteq X$ on which $(f^*\mathcal{G})|_U$ is quasicoherent. For each affine open $V\subseteq Y$, $f^{-1}(V)\subseteq X$ can be covered by affine open sets, and these sets taken over all $V$ will cover all of $X$. So it suffices to show $(f^*\mathcal{G})|_U$ is quasicoherent if $U\subseteq X$ is affine open and there exists an affine open $V\subseteq Y$ such that $f(U)\subseteq V$. But in that case, $(f^*\mathcal{G})|_U=g^*(\mathcal{G}|_V)$ as above, so you may as well replace $f$ by $g$ and assume $X=U$ and $Y=V$ are affine.
For the pushforward, if $V\subseteq Y$ is open, $(f_*\mathcal{F})|_V$ depends on the restriction of $\mathcal{F}$ to the set $f^{-1}(V)\subseteq X$, so you can replace $Y$ by $V$ and $X$ by $f^{-1}(V)$ to assume that $Y$ is affine. To assume that $X$ is affine as well as in the pullback case, you would need to have an open cover of $Y$ by affine open sets $V$ such that $f^{-1}(V)$ is affine as well. Such an open cover need not exist (for instance, if $Y$ has only one point and $X$ is not affine).
So in short, the difference between the two cases is that there always exists a cover of $X$ by affine open subsets $U$ such that $f(U)$ is contained in an affine open set, but there need not exist a cover of $Y$ by affine open subsets $V$ such that $f^{-1}(V)$ is affine.
• Thanks. Just a quick elementary question. Is it obvious that given $U \subseteq X$ an affine open, that there necessarily exists an affine open $V \subseteq Y$ such that $f(U) \subseteq V$? Does this simply follow from the definition of morphism of schemes and the gluing construction? – combustion1925 Feb 8 '16 at 23:38
• No, it's not obvious because it isn't even true. What is true is that there exists an open cover of $X$ by affine open sets $U$ which have this property (since you can take an affine open cover of $Y$, and then cover each of the sets $f^{-1}(V)$ by affine open sets). We're using here that to check that a sheaf is quasicoherent, it suffices to find an open cover such that its restriction to each set of the open cover is quasicoherent. – Eric Wofsey Feb 8 '16 at 23:40


text:
# Multiple Regression in Julia

Julia presents various ways to carry out multiple regressions. One easy way is to use the lm() function of the GLM package. In this post I will present how to use the lm() and run OLS on the following model

$y = \alpha + \beta_{1} x_{1} + \beta_{2} x_{2} + \beta_{3} x_{3}$

Our dependent variable $y$ will be my weekly average weight, the explanatory variable $x_{1}$ represents the sum of calories that I burned during the previous week, and variable $x_{2}$ is a binary variable that takes a value of 1 in case I was cycling the week earlier and 0 otherwise. For a more detailed description of the data see here.

# load a couple of packages
using Distributions
using GLM
using DataFrames
using DataArrays
using Taro
Taro.init()

# get data
path = "https://economictheoryblog.files.wordpress.com/2016/08/data.xlsx"
data = deleterows!(data,find(isna(data[:,1])|isna(data[:,2])))
data[:,1] = convert(DataArrays.DataArray{Float64,1},data[:,1])
data[:,2] = convert(DataArrays.DataArray{Float64,1},data[:,2])
data[:,3] = convert(DataArrays.DataArray{Float64,1},data[:,3])

# estimate the linear regression model
glm(@formula(weight ~ lag_calories + lag_cycling),


text:
# enthalpy of formation of ethyne

What is... (i) Deduce the equilibrium constant expression, Kc, for this reaction. [53] Consideration may include electrical classification and use of listed Group A electrical components in USA. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Now, if the enthalpy of formation of C2H6 is -85, the total enthalpy of formation on the left side is 2*(-85) = -170. Try: 2C(s) + H2(g) --> C2H2(g). The sublimation point at atmospheric pressure is −84.0 °C. Hess's law of heat summation states that if two or more thermochemical equations can be added together to give a final equation, then the heats of reaction can also be added to give a heat of reaction for the final equation. through a red hot tube and collecting the effluent. Unfortunately, this reaction would be virtually impossible to perform in the laboratory because carbon would react with hydrogen to form many different hydrocarbon products simultaneously. Oxyacetylene is the hottest burning common fuel gas. In the last section, we have seen how we can use calorimetry to determine the enthalpy … The two unchanged 2p orbitals form a pair of weaker π bonds. Postby Achang1L » Mon Jan 23, 2017 5:52 pm, Postby EllisJang2O » Tue Jan 24, 2017 3:34 pm, Postby Achang1L » Fri Feb 10, 2017 12:17 pm, Return to “Reaction Enthalpies (e.g., Using Hess’s Law, Bond Enthalpies, Standard Enthalpies of Formation)”, Users browsing this forum: No registered users and 0 guests, Calculate the standard enthalpy of formation of ethyne, the fuel used in oxyacetylene welding torches, from the information in Table 8.4 and given that. around the world. Acetylene is not especially toxic, but when generated from calcium carbide, it can contain toxic impurities such as traces of phosphine and arsine, which give it a distinct garlic-like smell. This colorless gas (lower hydrocarbons are generally gaseous in nature) is widely used as a fuel and a chemical building block. Pour autoriser Verizon Media et nos partenaires à traiter vos données personnelles, sélectionnez 'J'accepte' ou 'Gérer les paramètres' pour obtenir plus d’informations et pour gérer vos choix. However, enthalpy changes for combustion reactions are relatively easy to measure. The question does not state that there is a combustion reaction. it is worth 0.9% of the exam (2009 chemistry) much appreciated When 5.35 g ammonium chloride, $${\text{N}}{{\text{H}}_{\text{4}}}{\text{Cl(s)}}$$, is added... (i) Â  Â  Sketch and label an enthalpy level diagram for this reaction. Berthelot's empirical formula for acetylene (C4H2), as well as the alternative name "quadricarbure d'hydrogène" (hydrogen quadricarbide), were incorrect because chemists at that time used the wrong atomic mass for carbon (6 instead of 12). Likewise, the total enthalpy on the right must equal 2*(-394) + 6*(-286), which I found to be -2504. These solvents are used in pressurized gas cylinders. The development and advantages of arc-based welding processes have made oxy-fuel welding nearly extinct for many applications. Therefore, that reaction will be used as written. Â Â  Â ... (i) Â  Â  Calculate the amount, in mol, of anhydrous magnesium sulfate. When four moles of aluminium and four moles of iron combine with oxygen to form their oxides,... (i) Â  Â  Calculate the amount, in mol, of anhydrous magnesium sulfate. Informations sur votre appareil et sur votre connexion Internet, y compris votre adresse IP, Navigation et recherche lors de l’utilisation des sites Web et applications Verizon Media. National Post. Approximately 400,000 tonnes were produced by this method in 1983. Allow the gas to escape from the delivery-tube in the pneumatic trough until the issuing gas smells markedly of acetylene. The value of standard enthalpy of formation of acetylene at this temperature is: So, the enthalpy change in this reaction (which should be the standard enthalpy of combustion) is … Similarly, vinylpyrrolidone and vinylcarbazole are produced industrially by vinylation of 2-pyrrolidone and carbazole.[23][6]. Oxy-acetylene welding was a popular welding process in previous decades. The enthalpy of combustion of acetylene C2H2 is described by C2H2 (g) + (5/2)O2 (g) >>>>>CO2 (g) + H2O (l) Heat of Reaction (Rxn) = -1299kJ/mol. The standard enthalpy of formation (ΔHf°) at 398 K for methane, CH4(g) is 74.8 kJ mol^–1. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. For use in welding and cutting, the working pressures must be controlled by a regulator, since above 15 psi (100 kPa), if subjected to a shockwave (caused, for example, by a flashback), acetylene decomposes explosively into hydrogen and carbon. [7], As an alkyne, acetylene is unsaturated because its two carbon atoms are bonded together in a triple bond. An example will illustrate how Hess's law can be used. ), Standard enthalpy of formation for ethyne, Re: Standard enthalpy of formation for ethyne, Multimedia Attachments (click for details), How to Subscribe to a Forum, Subscribe to a Topic, and Bookmark a Topic (click for details), Accuracy, Precision, Mole, Other Definitions, Bohr Frequency Condition, H-Atom , Atomic Spectroscopy, Heisenberg Indeterminacy (Uncertainty) Equation, Wave Functions and s-, p-, d-, f- Orbitals, Electron Configurations for Multi-Electron Atoms, Polarisability of Anions, The Polarizing Power of Cations, Interionic and Intermolecular Forces (Ion-Ion, Ion-Dipole, Dipole-Dipole, Dipole-Induced Dipole, Dispersion/Induced Dipole-Induced Dipole/London Forces, Hydrogen Bonding), *Liquid Structure (Viscosity, Surface Tension, Liquid Crystals, Ionic Liquids), *Molecular Orbital Theory (Bond Order, Diamagnetism, Paramagnetism), Coordination Compounds and their Biological Importance, Shape, Structure, Coordination Number, Ligands, *Molecular Orbital Theory Applied To Transition Metals, Properties & Structures of Inorganic & Organic Acids, Properties & Structures of Inorganic & Organic Bases, Acidity & Basicity Constants and The Conjugate Seesaw, Calculating pH or pOH for Strong & Weak Acids & Bases, *Making Buffers & Calculating Buffer pH (Henderson-Hasselbalch Equation), *Biological Importance of Buffer Solutions, Administrative Questions and Class Announcements, Equilibrium Constants & Calculating Concentrations, Non-Equilibrium Conditions & The Reaction Quotient, Applying Le Chatelier's Principle to Changes in Chemical & Physical Conditions, Heat Capacities, Calorimeters & Calorimetry Calculations, Thermodynamic Systems (Open, Closed, Isolated), Thermodynamic Definitions (isochoric/isometric, isothermal, isobaric), Concepts & Calculations Using First Law of Thermodynamics, Concepts & Calculations Using Second Law of Thermodynamics, Third Law of Thermodynamics (For a Unique Ground State (W=1): S -> 0 as T -> 0) and Calculations Using Boltzmann Equation for Entropy, Entropy Changes Due to Changes in Volume and Temperature, Calculating Standard Reaction Entropies (e.g.


text:
## ganeshie8 one year ago why does this function work  function is_composite(n){ return "1".repeat(n).match(/^1?$|^(11+?)\1+$/); }  https://jsfiddle.net/dy8t4vou/

1. ganeshie8

@ParthKohli

2. ganeshie8

or anyone

3. dan815

woah lol what is that so cool

4. dan815

what language?

5. ganeshie8

javascript, try it in ur browser console

6. SolomonZelman

should be

7. SolomonZelman

don't really know what you are trying to make it look like if it is a latex question....

8. dan815

dang that looks so beautiful haha, i wish i knew what that syntax meant

9. SolomonZelman

i can't help. don't really get the result you desire to get.

10. SolomonZelman

screen shot or pic? (you can quite well draw it in colors and everything else with wio's extension for chrome which I am sure you have heard about...)

11. SolomonZelman

whatever. won't interrupt.

12. ganeshie8

|dw:1435258573923:dw|

13. ganeshie8

@SolomonZelman

14. dan815

how much of the syntax are u able to understand?

15. SolomonZelman

you want to make that picture $$\normalsize\color{blue}{ 4 }$$ $$\normalsize\color{blue}{ ^\text{______________________________________} }$$ $$\normalsize\color{blue}{ 6 }$$ $$\normalsize\color{blue}{ ^\text{______________________________________} }$$ $$\normalsize\color{blue}{ 8 }$$ $$\normalsize\color{blue}{ ^\text{______________________________________} }$$ $$\normalsize\color{blue}{ 9 }$$ $$\normalsize\color{blue}{ ^\text{______________________________________} }$$ $$\normalsize\color{blue}{ 10 }$$ $$\normalsize\color{blue}{ ^\text{______________________________________} }$$ $$\normalsize\color{blue}{ 12 }$$ $$\normalsize\color{blue}{ ^\text{______________________________________} }$$ ??

16. ParthKohli

I'm able to follow it till "why does this function work"

17. SolomonZelman

(I am not very good at this)

18. dan815

lool

19. ganeshie8

Haha typical programmer from math background

20. ParthKohli

It's just a function that takes parameter "n" and returns "1" if the function is composite and "0" if it's not, i.e., it's prime.

21. ganeshie8

You got it! you're ready to use the function !

22. ParthKohli

Looks like it checks if it contains certain keywords in its binary representation.

23. ganeshie8

thats very close, it actually converts the given number into unary number system

24. ParthKohli

Or hex representation? I don't know.

25. ParthKohli

Oh, unary...

26. ganeshie8

5 = 11111 3 = 111 etc

27. ganeshie8

"1".repeat(n) produces a string of "n" ones

28. ParthKohli

All the percentages and pluses and question-marks... oh dear.

29. ganeshie8

for simplicty, we can condence it further. below also works for n > 1 :  function is_composite(n){ return "1".repeat(n).match(/^(11+)\1+$/); }  30. ParthKohli The problem is that I don't really know what that is. What I think here is that you should first generate the number (parameter n) by repeating 1 'n' times, then start a number that is not 1 or the number itself, keep repeating it and reach the parameter. If such a number exists, then the thing is composite. 31. ParthKohli Like it should definitely be a loop, but I don't know where it mentions it being a loop. What I see is that the .match is attached to the .repeat so does the .repeat function tell it to repeat or what? 32. ganeshie8 consider an example in unary system 1111 is composite becuase it can be split as 11 11 33. ganeshie8 11111 is not composite because it cannot be split as 2 ones or 3 ones or 4 ones groups 34. ParthKohli Yeah, makes sense. Where does it say that in the program? :| 35. ganeshie8 match() is a string matching function 36. ganeshie8 it returns the match if it finds even groups of (11)+ otherwise it returns null 37. ParthKohli ? looks like it's a conditional operator. 38. ganeshie8 for example : "parthkohli".match(/java/) returns null 39. ganeshie8 "parthkohli".match(/art/) returns true 40. ParthKohli OK, I gotcha. Of course. This thing is looping over the size of the groups, right? So I'm sort of understanding this thing. I guess it says something like, "does it form even groups of this size? If not, proceed to the next size." Is that what (11)+ means? 41. ParthKohli 11+ I mean 42. ganeshie8 Exactly! 43. ganeshie8 $$a+$$ means 1 or more occurrences of $$a$$ 44. ParthKohli /^1?$|^(11+?)\1+$/ Could you walk us through each and every symbol above? Also, please do it quickly, because my battery is gonna finish in 10 minutes... 45. ganeshie8 lets look at the condensed expression /^(11+?)\1+$/

46. ganeshie8

^ matches start of string \$ matches end of string

47. ganeshie8

11+? matches "two" or more occurrences of "1"

48. ganeshie8

\1 backreferences the previous matched stuff in a parenthesis : (11+?)

49. ganeshie8

look up "regular expressions" for more details their syntax mostly same in almost all programming languages

50. ParthKohli

That is amazing. Wow.

51. ParthKohli

OK, good night then. Laterz.

52. ganeshie8

gnite!


text:
# Another Circle

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• Jun 2nd 2007, 03:23 PM
stones44
Another Circle
Circle with radius of 10 in
Chord AB is 14 in
Find measure of minor arc AB and then actual length of minor arc AB
• Jun 2nd 2007, 03:30 PM
Jhevon
Quote:

Originally Posted by stones44
Circle with radius of 10 in
Chord AB is 14 in
Find measure of minor arc AB and then actual length of minor arc AB

i'm a bit rusty on my circle theorems, so there may be an easier way to do this--but this is the first idea that came to me. see the diagram below

we can use the law of cosines to find the angle x. once we have that, we can use the length of arc formula to find the desired arc
• Jun 2nd 2007, 03:46 PM
Soroban
Hello, stones44!

Here's another way to determine that central angle $x = \angle AOB$.

In Jhevon's diagram, draw the apothem to chord AB.

Then: . $\sin\left(\frac{x}{2}\right) \:=\:\frac{7}{10}$

• Jun 2nd 2007, 03:54 PM
Jhevon
Quote:

Originally Posted by Soroban
Hello, stones44!

Here's another way to determine that central angle $x = \angle AOB$.

In Jhevon's diagram, draw the apothem to chord AB.

Then: . $\sin\left(\frac{x}{2}\right) \:=\:\frac{7}{10}$

Haha, i didn't see that. that's nice. and a lot simpler than using the cosine rule! As always Soroban does it better :D
• Jun 2nd 2007, 05:19 PM
Plato
Quote:

Originally Posted by Jhevon
That's nice. and a lot simpler than using the cosine rule!

While I agree Soroban's is standard and nice, I prefer the way you approached the problem.
Look: $x = \arccos \left( {\frac{{200 - 14^2 }}{{200}}} \right)$.
That is certainly calculator ready; and the actual arclength is 10x.
Don't sell yourself short.
• Jun 3rd 2007, 09:59 AM
Soroban
Hello, Jhevon!

Quote:

As always Soroban does it better.

I certainly am not "better" or "smarter" than you . . . just lazier.
. . I was not born with this gift; it took years of dedicated practice.

• Jun 3rd 2007, 02:10 PM
stones44
so actual arc length?

how is it 10x?
• Jun 3rd 2007, 02:26 PM
Soroban
Hello, stones44!

Quote:

so actual arc length?
how is it 10x?

The arc length formula is: . $s \:=\:r\theta$
. . where $r$ is the radius and $\theta$ is the central angle in radians.

Using Jhevon's approach: . $\cos x \:=\:0.02\quad\Rightarrow\quad x \:\approx\:1.55$ radians

Therefore: . $s \:=\:10(1.55) \:=\:15.5$ inches.

• Jun 3rd 2007, 05:34 PM
stones44
is there another way because I haven't learned that way
• Jun 3rd 2007, 05:40 PM
Jhevon
Quote:

Originally Posted by stones44
is there another way because I haven't learned that way

which way are you refering to? Soroban's way or my way? or both?--God forbid
• Jun 4th 2007, 04:16 AM
topsquark
Quote:

Originally Posted by stones44
is there another way because I haven't learned that way

If you are referring to arc length, no.

-Dan
• Jun 4th 2007, 07:41 AM
Jhevon
Quote:

Originally Posted by stones44
so actual arc length?

how is it 10x?

10 is the radius. and $x$ is the angle that subtends the arc. it may have been better for me to call it $\theta$. so you see the arc length formula is $s = r \theta$, and that's why it is 10x, since $r = 10$ and $\theta = x$. there is no other method as far as this part is concerned. if it is everything up to this point that you are unclear on, please be specific as to what the problem is
• Jun 4th 2007, 08:11 AM
Plato
Do you know the origin of the word radian? How large is one radian?
One radian is the measure of the central angle in any circle that intercepts an arc of the circle equal in length to the radius of the circle. So in any circle, if we have a central angle of 2.5 radians the intercepted arc has length 2.5r. If the circle has radius 10 then any central angle of .35 radians intercepts an arc of length 3.5.
• Jun 4th 2007, 02:24 PM
stones44
but if the measure of the arc is 88.8, meaning the central angle is 88.8, does that mean the length of the arc is 888? (with radius 10)
• Jun 4th 2007, 02:37 PM
Jhevon
Quote:

Originally Posted by stones44
but if the measure of the arc is 88.8, meaning the central angle is 88.8, does that mean the length of the arc is 888? (with radius 10)

no. you have the angle given in degrees here. you would use a different formula for that. in a circle, there are $2 \pi$ radians, and no more. anymore than that and it means you are making more than 1 revolution around the circle.

For degrees:

The length of arc $l$ is given by:

$l = \frac { \theta}{360} 2 \pi r$

where $\theta$ is the angle that subtends the arc in degrees
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