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# 7 Boo (7 Boötis)

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 Testing Stellar Models with an Improved Physical Orbit for 12 BootisIn a previous paper we reported on the binary system 12 Bootis and itsevolutionary state. In particular, the 12 Boo primary component is in arapid phase of evolution; hence accurate measurement of its physicalparameters makes it an interesting test case for stellar evolutionmodels. Here we report on a significantly improved determination of thephysical orbit of the double-lined spectroscopic binary system 12 Boo.We have a 12 Boo interferometry data set spanning 6 yr with the PalomarTestbed Interferometer, a smaller amount of data from the Navy PrototypeOptical Interferometer, and a radial velocity data set spanning 14 yrfrom the Harvard-Smithsonian Center for Astrophysics. We have updatedthe 12 Boo physical orbit model with our expanded interferometric andradial velocity data sets. The revised orbit is in good agreement withprevious results, and the physical parameters implied by a combined fitto our visibility and radial velocity data result in precise componentmasses and luminosities. In particular, the orbital parallax of thesystem is determined to be 27.72+/-0.15 mas, and masses of the twocomponents are determined to be 1.4160+/-0.0049 and 1.3740+/-0.0045Msolar, respectively. These mass determinations are moreprecise than those in the previous report by a factor of 4-5. Asindicated in the previous publication, even though the two componentsare nearly equal in mass, the system exhibits a significant brightnessdifference between the components in the near-infrared and visible. Weattribute this brightness difference to evolutionary differences betweenthe two components in their transition between main-sequence and giantevolutionary phases, and based on theoretical models, we can estimate asystem age of approximately 3.2 Gyr. Comparisons with stellar modelssuggest that the 12 Boo primary may be just entering the Hertzsprunggap, but that conclusion is highly dependent on details of the models.Such a dynamic evolutionary state makes the 12 Boo system a unique andimportant test for stellar models. CHARM2: An updated Catalog of High Angular Resolution MeasurementsWe present an update of the Catalog of High Angular ResolutionMeasurements (CHARM, Richichi & Percheron \cite{CHARM}, A&A,386, 492), which includes results available until July 2004. CHARM2 is acompilation of direct measurements by high angular resolution methods,as well as indirect estimates of stellar diameters. Its main goal is toprovide a reference list of sources which can be used for calibrationand verification observations with long-baseline optical and near-IRinterferometers. Single and binary stars are included, as are complexobjects from circumstellar shells to extragalactic sources. The presentupdate provides an increase of almost a factor of two over the previousedition. Additionally, it includes several corrections and improvements,as well as a cross-check with the valuable public release observationsof the ESO Very Large Telescope Interferometer (VLTI). A total of 8231entries for 3238 unique sources are now present in CHARM2. Thisrepresents an increase of a factor of 3.4 and 2.0, respectively, overthe contents of the previous version of CHARM.The catalog is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/431/773 Synthetic Lick Indices and Detection of α-enhanced Stars. II. F, G, and K Stars in the -1.0 < [Fe/H] < +0.50 RangeWe present an analysis of 402 F, G, and K solar neighborhood stars, withaccurate estimates of [Fe/H] in the range -1.0 to +0.5 dex, aimed at thedetection of α-enhanced stars and at the investigation of theirkinematical properties. The analysis is based on the comparison of 571sets of spectral indices in the Lick/IDS system, coming from fourdifferent observational data sets, with synthetic indices computed withsolar-scaled abundances and with α-element enhancement. We useselected combinations of indices to single out α-enhanced starswithout requiring previous knowledge of their main atmosphericparameters. By applying this approach to the total data set, we obtain alist of 60 bona fide α-enhanced stars and of 146 stars withsolar-scaled abundances. The properties of the detected α-enhancedand solar-scaled abundance stars with respect to their [Fe/H] values andkinematics are presented. A clear kinematic distinction betweensolar-scaled and α-enhanced stars was found, although a one-to-onecorrespondence to thin disk'' and thick disk'' components cannot besupported with the present data. J - K DENIS photometry of a VLTI-selected sample of bright southern starsWe present a photometric survey of bright southern stars carried outusing the DENIS instrument equipped with attenuating filters. Theobservations were carried out not using the survey mode of DENIS, butwith individual target pointings. This project was stimulated by theneed to obtain near-infrared photometry of stars to be used in earlycommissioning observations of the ESO Very Large TelescopeInterferometer, and in particular to establish a network of brightcalibrator sources.We stress that near-infrared photometry is peculiarly lacking for manybright stars. These stars are saturated in 2MASS as well as in regularDENIS observations. The only other observations available for brightinfrared stars are those of the Two Micron Sky Survey dating from overthirty years ago. These were restricted to declinations above≈-30°, and thus cover only about half of the sky accessible fromthe VLTI site.We note that the final 2MASS data release includes photometry of brightstars, obtained by means of point-spread function fitting. However, thismethod only achieves about 30% accuracy, which is not sufficient formost applications.In this work, we present photometry for over 600 stars, each with atleast one and up to eight measurements, in the J and K filters. Typicalaccuracy is at the level of 0\fm05 and 0\fm04 in the J and K_s bands,respectively.Based on observations collected at the European Southern Observatory, LaSilla.Tables 1 and 2 are only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/413/1037 Observational constraints for lithium depletion before the RGBPrecise Li abundances are determined for 54 giant stars mostly evolvingacross the Hertzsprung gap. We combine these data with rotationalvelocity and with information related to the deepening of the convectivezone of the stars to analyse their link to Li dilution in the referredspectral region. A sudden decline in Li abundance paralleling the onealready established in rotation is quite clear. Following similarresults for other stellar luminosity classes and spectral regions, thereis no linear relation between Li abundance and rotation, in spite of thefact that most of the fast rotators present high Li content. The effectsof convection in driving the Li dilution is also quite clear. Stars withhigh Li content are mostly those with an undeveloped convective zone,whereas stars with a developed convective zone present clear sign of Lidilution.Based on observations collected at ESO, La Silla, Chile, and at theObservatoire de Haute Provence, France, operated by the Centre Nationalde la Recherche Scientifique (CNRS). The Hamburg/RASS Catalogue of optical identifications. Northern high-galactic latitude ROSAT Bright Source Catalogue X-ray sourcesWe present the Hamburg/RASS Catalogue (HRC) of optical identificationsof X-ray sources at high-galactic latitude. The HRC includes all X-raysources from the ROSAT Bright Source Catalogue (RASS-BSC) with galacticlatitude |b| >=30degr and declination delta >=0degr . In thispart of the sky covering ~ 10 000 deg2 the RASS-BSC contains5341 X-ray sources. For the optical identification we used blue Schmidtprism and direct plates taken for the northern hemisphere Hamburg QuasarSurvey (HQS) which are now available in digitized form. The limitingmagnitudes are 18.5 and 20, respectively. For 82% of the selectedRASS-BSC an identification could be given. For the rest either nocounterpart was visible in the error circle or a plausibleidentification was not possible. With ~ 42% AGN represent the largestgroup of X-ray emitters, ~ 31% have a stellar counterpart, whereasgalaxies and cluster of galaxies comprise only ~ 4% and ~ 5%,respectively. In ~ 3% of the RASS-BSC sources no object was visible onour blue direct plates within 40\arcsec around the X-ray sourceposition. The catalogue is used as a source for the selection of(nearly) complete samples of the various classes of X-ray emitters. CHARM: A Catalog of High Angular Resolution MeasurementsThe Catalog of High Angular Resolution Measurements (CHARM) includesmost of the measurements obtained by the techniques of lunaroccultations and long-baseline interferometry at visual and infraredwavelengths, which have appeared in the literature or have otherwisebeen made public until mid-2001. A total of 2432 measurements of 1625sources are included, along with extensive auxiliary information. Inparticular, visual and infrared photometry is included for almost allthe sources. This has been partly extracted from currently availablecatalogs, and partly obtained specifically for CHARM. The main aim is toprovide a compilation of sources which could be used as calibrators orfor science verification purposes by the new generation of largeground-based facilities such as the ESO Very Large Interferometer andthe Keck Interferometer. The Catalog is available in electronic form atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/386/492, and from theauthors on CD-Rom. Activity Study in 3 Intermediate Mass Evolved StarsA spectroscopic CaII K&H and Hα study was carriedout for 3 single fast rotating evolved stars - HD145001, HD185958 andHD121107. Photometric UBV observations were also done. Data for theirX-ray behavior were analysed too. One of the stars appear to bechromospherically active. One of the rest two fast rotating giants seemsto be active from time to time, and the last one was found to beinactive, nevertheless its fast rotation. The situation of the stars onthe H-R diagram was found and their evolutionary status was determinedby using also literature data for their chemical abundances. Thepossible reasons for activity in these evolved single stars werediscussed too. Photometric Variability in a Sample of 187 G and K GiantsWe have used three automatic photoelectric telescopes to obtainphotometric observations of 187 G, K, and (a few) M0 field giants. Wefind low-amplitude photometric variability on timescales of days toweeks on both sides of the coronal dividing line (CDL) in a total of 81or 43% of the 187 giants. About one-third of the variables haveamplitudes greater than 0.01 mag in V. In our sample the percentage ofvariable giants is a minimum for late-G spectral classes and increasesfor earlier and later classes; all K5 and M0 giants are variable. Wealso obtained high-resolution, red wavelength spectroscopic observationsof 147 of the giants, which we used to determine spectralclassifications, vsini values, and radial velocities. We acquiredadditional high-resolution, blue wavelength spectra of 48 of the giants,which we used to determine chromospheric emission fluxes. We analyzedthe photometric and spectroscopic observations to identify the cause(s)of photometric variability in our sample of giants. We show that thelight variations in the vast majority of G and K giant variables cannotbe due to rotation. For giants on the cool side of the CDL, we find thatthe variability mechanism is radial pulsation. Thus, the variabilitymechanism operating in M giants extends into the K giants up to aboutspectral class K2. On the hot side of the CDL, the variability mechanismis most likely nonradial, g-mode pulsation. The Visual Orbit and Evolutionary State of 12 BootisWe report on the determination of the visual orbit of the double-linedspectroscopic binary system 12 Bootis with data obtained by the PalomarTestbed Interferometer in 1998 and 1999. 12 Boo is a nearly equal-massdouble-lined binary system whose spectroscopic orbit is well known. Wehave estimated the visual orbit of 12 Boo from our interferometricvisibility data fitted both separately and in conjunction with archivaland CORAVEL radial velocity data. Our 12 Boo orbit is in good agreementwith the spectroscopic results, and the physical parameters implied by acombined fit to our visibility data and radial velocity data result inprecise component masses. In particular, the orbital parallax of thesystem is determined to be 27.09+/-0.41 mas, and masses of the twocomponents are determined to be 1.435+/-0.023 Msolar and1.409+/-0.020 Msolar, respectively. Somewhat remarkably, eventhough the two components are nearly equal mass, the system exhibits asignificant brightness difference between the components in thenear-infrared and visible. We attribute this brightness difference toevolutionary differences between the two components in their transitionbetween main-sequence and giant evolutionary phases, and based ontheoretical isochrones we can estimate a system age. Further, becausethe atmospheres of the two components are becoming more convective, wesuggest the system components are currently at or near synchronousrotation, and the system orbit is in the process of circularizing. Rotation and lithium in single giant starsIn the present work, we study the link between rotation and lithiumabundance in giant stars of luminosity class III, on the basis of alarge sample of 309 single stars of spectral type F, G and K. We havefound a trend for a link between the discontinuity in rotation at thespectral type G0III and the behavior of lithium abundances around thesame spectral type. The present work also shows that giant starspresenting the highest lithium contents, typically stars earlier thanG0III, are those with the highest rotation rates, pointing for adependence of lithium content on rotation, as observed for otherluminosity classes. Giant stars later than G0III present, as a rule, thelowest rotation rates and lithium contents. A large spread of about fivemagnitudes in lithium abundance is observed for the slow rotators.Finally, single giant stars with masses 1.5 < M/Msun<=2.5 show a clearest trend for a correlation between rotational velocityand lithium abundance. Based on observations collected at theObservatoire de Haute -- Provence (France) and at the European SouthernObservatory, La Silla (Chile). Table 2 is only available electronicallywith the On-Line publication athttp://link.springer.de/link/service/00230/ Ca II activity and rotation in F-K evolved starsCa II H and K high resolution observations for 60 evolved stars in thefield and in 5 open clusters are presented. From these spectrachromospheric fluxes are derived, and a homogeneous sample of more than100 giants is built adding data from the literature. In addition, formost stars, rotational velocities were derived from CORAVELobservations. By comparing chromospheric emission in the cluster starswe confirm the results of Pasquini & Brocato (1992): chromosphericactivity depends on the stellar effective temperature, and mass, whenintermediate mass stars (M ~ 4 Msun) are considered. TheHyades and the Praesepe clump giants show the same level of activity, asexpected from stars with similar masses and effective temperatures. Adifference of up to 0.4 dex in the chromospheric fluxes among the Hyadesgiants is recorded and this sets a clear limit to the intrinsic spreadof stellar activity in evolved giants. These differences in otherwisevery similar stars are likely due to stellar cycles and/or differencesin the stellar initial angular momentum. Among the field stars none ofthe giants with (V-R)o < 0.4 and Ia supergiants observedshows a signature of Ca II activity; this can be due either to the realabsence of a chromosphere, but also to other causes which preclude theappearance of Ca II reversal. By analyzing the whole sample we find thatchromospheric activity scales linearly with stellar rotational velocityand a high power of stellar effective temperature: F'k ~Teff7.7 (Vsini)0.9. This result can beinterpreted as the effect of two chromospheric components of differentnature: one mechanical and one magnetic. Alternatively, by using theHipparcos parallaxes and evolutionary tracks, we divide the sampleaccording to the stellar masses, and we follow the objects along anevolutionary track. For each range of masses activity can simply beexpressed as a function of only one parameter: either theTeff or the angular rotation Omega , with laws F'k~ Omega alpha , because angular velocity decreases witheffective temperature along an evolutionary track. By using theevolutionary tracks and the observed Vsini we investigate the evolutionof the angular momentum for evolved stars in the range 1-5Msun. For the 1.6-3 solar mass stars the data are consistentwith the IOmega =const law while lower and higher masses follow a lawsimilar to IOmega 2=const, where I is the computed stellarmomentum of inertia. We find it intriguing that Vsini remains almostconstant for 1Msun stars along their evolution; if a similarbehavior is shared by Pop II stars, this could explain the relativelyhigh degree of activity observed in Pop II giants. Finally, through theuse of models, we have verified the consistency of the F'k ~Omega alpha and the IOmega beta = Const lawsderived, finding an excellent agreement. This representation, albeitcrude (the models do not consider, for instance, mass losses) representsthe evolution of Ca II activity and of the angular momentum in asatisfactory way in most of the portion of HR diagram analyzed.Different predictions could be tested with observations in selectedclusters. Based on observations collected at ESO, La Silla. Tables 1-3are only available in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html The accretion of brown dwarfs and planets by giant stars - II. Solar-mass stars on the red giant branchThis paper extends our previous study of planet/brown dwarf accretion bygiant stars to solar-mass stars located on the red giant branch. Themodel assumes that the planet is dissipated at the bottom of theconvective envelope of the giant star. The evolution of the giant isthen followed in detail. We analyse the effects of different accretionrates and different initial conditions. The computations indicate thatthe accretion process is accompanied by a substantial expansion of thestar, and, in the case of high accretion rates, hot bottom burning canbe activated. The possible observational signatures that accompany theengulfing of a planet are also extensively investigated. They includethe ejection of a shell and a subsequent phase of IR emission, anincrease in the ^7Li surface abundance and a potential stellarmetallicity enrichment, spin-up of the star because of the deposition oforbital angular momentum, the possible generation of magnetic fields andthe related X-ray activity caused by the development of shear at thebase of the convective envelope, and the effects on the morphology ofthe horizontal branch in globular clusters. We propose that the IRexcess and high Li abundance observed in 4-8per cent of the G and Kgiants originate from the accretion of a giant planet, a brown dwarf ora very low-mass star. A catalog of rotational and radial velocities for evolved starsRotational and radial velocities have been measured for about 2000evolved stars of luminosity classes IV, III, II and Ib covering thespectral region F, G and K. The survey was carried out with the CORAVELspectrometer. The precision for the radial velocities is better than0.30 km s-1, whereas for the rotational velocity measurementsthe uncertainties are typically 1.0 km s-1 for subgiants andgiants and 2.0 km s-1 for class II giants and Ib supergiants.These data will add constraints to studies of the rotational behaviourof evolved stars as well as solid informations concerning the presenceof external rotational brakes, tidal interactions in evolved binarysystems and on the link between rotation, chemical abundance and stellaractivity. In this paper we present the rotational velocity v sin i andthe mean radial velocity for the stars of luminosity classes IV, III andII. Based on observations collected at the Haute--Provence Observatory,Saint--Michel, France and at the European Southern Observatory, LaSilla, Chile. Table \ref{tab5} also available in electronic form at CDSvia anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html Catalogs of temperatures and [Fe/H] averages for evolved G and K starsA catalog of mean values of [Fe/H] for evolved G and K stars isdescribed. The zero point for the catalog entries has been establishedby using differential analyses. Literature sources for those entries areincluded in the catalog. The mean values are given with rms errors andnumbers of degrees of freedom, and a simple example of the use of thesestatistical data is given. For a number of the stars with entries in thecatalog, temperatures have been determined. A separate catalogcontaining those data is briefly described. Catalog only available atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html Evolution of X-ray activity and rotation on G-K giantsThe recent availability of stellar parallaxes provided by the Hipparcosstar catalogue (ESA 1997) enables an accurate determination of thepositions of single field giants in a theoretical H-R diagram and areliable estimate of their masses. The present study combines these newastrometric data with previously published X-ray fluxes and rotationalvelocities. The results confirm the existence of a sharp decrease ofX-ray emission at spectral type K1 for 2.5 M_sun < M < 5 M_sungiants. The study shows that the rotational velocity of these starsreaches a minimum at the same location in the H-R diagram. However, notight relationship between X-ray luminosities and projected equatorialvelocities was found among the sample stars. I suggest that theseresults could reflect the importance of differential rotation indetermining the level of coronal emission among >= 2.5Msun G and K giants. The restoration of rigid rotation at thebottom of the red giant branch could prevent the maintenance of largescale magnetic fields, thus explaining the sharp decrease of coronalX-ray emission at spectral type K1. The ROSAT all-sky survey catalogue of optically bright late-type giants and supergiantsWe present X-ray data for all late-type (A, F, G, K, M) giants andsupergiants (luminosity classes I to III-IV) listed in the Bright StarCatalogue that have been detected in the ROSAT all-sky survey.Altogether, our catalogue contains 450 entries of X-ray emitting evolvedlate-type stars, which corresponds to an average detection rate of about11.7 percent. The selection of the sample stars, the data analysis, thecriteria for an accepted match between star and X-ray source, and thedetermination of X-ray fluxes are described. Catalogue only available atCDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html Rotational Velocities of Late-Type StarsA calibration based on the results of Gray has been used to determineprojected rotational velocities for 133 bright stars with spectral typesof F, G, or K, most of which appear in {\it The Bright Star Catalogue}.The vast majority have {\it v} sin {\it i} $\leq$ 10 km s$^{-1}$ and,thus, are slow rotators. With the new calibration, projected rotationalvelocities have been determined for a sample of 111 late-type stars,most of which are chromospherically active. Some of the stars have hadtheir rotational velocities measured for the first time. (SECTION:Stars) The Photometric Variability of Sun-like Stars: Observations and Results, 1984--1995Using differential Stromgren b, y photometry, we monitored thebrightness variations of 41 program stars and their 73 comparison starsfrom 1984 through 1995. The predominantly main-sequence program starsspanned ranges of temperature and mean chromospheric activity centeredon solar values. About 40% of all the stars showed measurablevariability, typically at levels below 0.01 mag (~1%), on bothnight-to-night and year-to-year timescales. The variability correlatedwith mean chromospheric activity and advancing spectral type. We presentdifferential light curves and statistical descriptions of ourobservations. HIPPARCOS distances of X-ray selected stars: implications on their nature as stellar population.We present the parallaxes, measured by Hipparcos, for a sample of X-rayselected stars. The stars belong to the stellar sample of the EinsteinExtended Medium Sensitivity Survey. They are all at galactic latitude|b|>20deg, and are generally far away from known star formingregions. Several of these stars show lithium abundance and activitylevel typical of very young stars with ages comparable to that of thePleiades. We show that the majority of our sample stars are on the mainsequence, with only =~20% being giants. We do not find a significantpresence of pre-main sequence stars in our sample, notwithstanding thefact that some of our stars have a considerable lithium abundance,showing that the stars observed are most likely young and activemain-sequence objects. The Einstein Extended Medium-Sensitivity Survey Second Epoch: Results for the StarsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1995ApJS...99..701F&db_key=AST Vitesses radiales. Catalogue WEB: Wilson Evans Batten. Subtittle: Radial velocities: The Wilson-Evans-Batten catalogue.We give a common version of the two catalogues of Mean Radial Velocitiesby Wilson (1963) and Evans (1978) to which we have added the catalogueof spectroscopic binary systems (Batten et al. 1989). For each star,when possible, we give: 1) an acronym to enter SIMBAD (Set ofIdentifications Measurements and Bibliography for Astronomical Data) ofthe CDS (Centre de Donnees Astronomiques de Strasbourg). 2) the numberHIC of the HIPPARCOS catalogue (Turon 1992). 3) the CCDM number(Catalogue des Composantes des etoiles Doubles et Multiples) byDommanget & Nys (1994). For the cluster stars, a precise study hasbeen done, on the identificator numbers. Numerous remarks point out theproblems we have had to deal with. Radio continuum emission from stars: a catalogue update.An updated version of my catalogue of radio stars is presented. Somestatistics and availability are discussed. The active dynamo stars: RS CVn, BY Dra, FK Com, Algol, W UMa, and T TauNot Available Chromospheric activity in G and K giants: the spectroscopic data baseI present high-resolution CCD spectra of CaII H and K emission lines of59 evolved stars of spectral type G and K and luminosity Class III,III-IV, and IV. This includes active stars like RS CVn binaries but alsoactive and inactive single stars. Most of the objects were observed forthe first time and several were discovered to be chromosphericallyactive. Spectra for ten stars of luminosity Class V are also given. Chromospheric activity in G and K giants and their rotation-activity relationWe obtained high-resolution CCD spectra of Ca II H and K emission linesof 59 evolved stars of spectral type G and K and luminosity class III,III-IV, and IV. Our sample includes active stars like RS CVn binariesbut also active and inactive single stars. Whenever possible wedetermine absolute emission line surface fluxes and use them,supplemented by previously published fluxes from high-resolutionspectra, to quantify the rotation-activity relation for evolved stars.We find that the Ca II surface fluxes from evolved stars scale linearlywith stellar rotational velocity and that the flux from the cooler starsdepends stronger upon rotation than the flux from the hotter stars, inagreement with previous findings for main-sequence stars. However, largescatter indicates that rotational velocity might not be the onlyrelevant parameter. We also present some evidence for the existence of a'basal' flux for evolved stars that scales approximately with the eightpower of the effective surface temperature. The photometric variability of K giantsWe have photometrically monitored 49 of the more than 200 K giants inthe Yale Catalog of Bright Stars (YCBS) which are named or suspectedvariable stars. Only two (HR 3275 and HR 5219) are clearly variable; afew more program stars and K- and M-giant comparison stars aremarginally variable. Most of these appear to be RS Canum Venaticorum orSR variables. Rotation and transition layer emission in cool giantsGray (1981, 1982) found that field giants with T(eff) less than about5500 K experience a steep decrease in rotational velocities coupled witha decrease in transition layer emission. This decrease may beattributable to fast magnetic braking or to redistribution of angularmomentum for rapidly increasing depths of the convection zones if theserotate with depth independent specific angular momentum. Additionalarguments in favor of the latter interpretation are presented. Theincrease of N/C abundances due to deep mixing occurs at the same pointas the decrease in v sin i. On the other hand, the ratios of the C IV toC II emission line fluxes decrease at this point indicating smallercontributions of MHD wave heating. The X-ray fluxes decrease at nearlythe same T(eff). Thus, no observations are found which would indicatelarger magnetic activity which could lead to fast magnetic braking.Theory predicts a rapid increase in the convection zone depth at theT(eff) where the decrease in v sin i is observed. This can explain theobserved phenomena. The Einstein Observatory Extended Medium-Sensitivity Survey. II - The optical identificationsThe optical identifications are presented of the Einstein ExtendedMedium-Sensitivity Survey (EMSS), including the methodology used tooptically identify the EMSS sources and the uncertainties involved withthat process. The optical properties of the classes of X-ray, optical,and radio data for each of the identified and, as yet, unidentifiedsources of the survey are described. A new class of X-ray emitters,cooling flow galaxies, is proposed. The criteria used to determinewhether the proposed optical counterpart to the X-ray source is aplausible identification are described. Plausibility is based on theoptical classification of the counterpart, e.g., AGN, cluster, G star,and the X-ray-to-optical flux ratios previously observed for theseclasses of X-ray emitters. Two independent schemes of opticalclassification of the counterparts are used to check the plausibility ofthese identifications; one is based on moderate-resolution opticalspectroscopy, and the other, on inferred X-ray luminosity and theoverall energy distribution.
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#### Observation and Astrometry data

 Constellation: Bootes Right ascension: 13h53m12.90s Declination: +17Â°55'58.0" Apparent magnitude: 5.7 Distance: 209.644 parsecs Proper motion RA: -33.7 Proper motion Dec: 5.5 B-T magnitude: 6.759 V-T magnitude: 5.803

Catalogs and designations:
 Proper Names 7 Boötis   (Edit) Flamsteed 7 Boo HD 1989 HD 121107 TYCHO-2 2000 TYC 1470-940-1 USNO-A2.0 USNO-A2 1050-07030240 BSC 1991 HR 5225 HIP HIP 67787 → Request more catalogs and designations from VizieR


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# Interaction between 2 objects in Gazebo

I am working on a "pick and do" operation in ROS and simulating the same in Gazebo. I have model of a wrench, which is attached to my own gripper in URDF. The gripper in turn is attached to UR5. This setup has to rotate a knob on a panel. But as soon as the gripper touches the knob, the panel flies off even though the mass of the panel has been defined as 800kg in the sdf file. https://youtu.be/7vpE6pHe0x8

I tried the same setup by replacing my gripper with PR2 gripper (and without the wrench) and I getting decent results. So my guess is, again there seems to be some problem with the inertia of my gripper and the wrench. Would be great if anyone could help me in defining it correctly. Remove the .jpg at the end of the file name. C:\fakepath\gripper.stl.jpg

Gripper urdf : C:\fakepath\gripper.urdf.xacro.jpg

Panel sdf : C:\fakepath\model.sdf.jpg

Here's the video after making the panel model static. https://youtu.be/eP29QGYoQhY

edit retag close merge delete

The problem disappears after I enable kinematic property in Gazebo GUI for each link of UR5. Also, I can't do this with <gazebo reference="ur5_arm_wrist_3_link"> <selfcollide>1</selfcollide> <kinematic>1</kinematic> </gazebo> The only property which changes is selfCollide. How can I change this through URDF? I haven't found any documentation. I could save the world file with the entire setup. Can I load the world file instead of URDF for UR5 as well?

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# Lie Conformal Algebras With Structure Coefficients#

AUTHORS:

• Reimundo Heluani (2019-08-09): Initial implementation.

class sage.algebras.lie_conformal_algebras.lie_conformal_algebra_with_structure_coefs.LieConformalAlgebraWithStructureCoefficients(R, s_coeff, index_set=None, central_elements=None, category=None, element_class=None, prefix=None, names=None, latex_names=None, parity=None, **kwds)#

A Lie conformal algebra with a set of specified structure coefficients.

INPUT:

• R – a ring (Default: None); The base ring of this Lie conformal algebra. Behaviour is undefined if it is not a field of characteristic zero.

• s_coeff – Dictionary (Default: None); a dictionary containing the $$\lambda$$ brackets of the generators of this Lie conformal algebra. The family encodes a dictionary whose keys are pairs of either names or indices of the generators and the values are themselves dictionaries. For a pair of generators $$a$$ and $$b$$, the value of s_coeff[('a','b')] is a dictionary whose keys are positive integer numbers and the corresponding value for the key $$j$$ is a dictionary itself representing the j-th product $$a_{(j)}b$$. Thus, for a positive integer number $$j$$, the value of s_coeff[('a','b')][j] is a dictionary whose entries are pairs ('c',n) where 'c' is the name of a generator and $$n$$ is a positive number. The value for this key is the coefficient of $$\frac{T^{n}}{n!} c$$ in $$a_{(j)}b$$. For example the s_coeff for the Virasoro Lie conformal algebra is:

{('L','L'):{0:{('L',1):1}, 1:{('L',0):2}, 3:{('C',0):1/2}}}

Do not include central elements in this dictionary. Also, if the key ('a','b') is present, there is no need to include ('b','a') as it is defined by skew-symmetry. Any missing pair (besides the ones defined by skew-symmetry) is assumed to have vanishing $$\lambda$$-bracket.

• names – tuple of str (Default: None); The list of names for generators of this Lie conformal algebra. Do not include central elements in this list.

• central_elements – tuple of str (Default: None); A list of names for central elements of this Lie conformal algebra.

• index_set – enumerated set (Default: None); an indexing set for the generators of this Lie conformal algebra. Do not include central elements in this list.

• parity – tuple of $$0$$ or $$1$$ (Default: tuple of $$0$$);

a tuple specifying the parity of each non-central generator.

EXAMPLES:

• We construct the $$\beta-\gamma$$ system by directly giving the $$\lambda$$-brackets of the generators:

sage: betagamma_dict = {('b','a'):{0:{('K',0):1}}}
sage: V = LieConformalAlgebra(QQ, betagamma_dict, names=('a','b'), weights=(1,0), central_elements=('K',))
sage: V.category()
Category of H-graded finitely generated Lie conformal algebras with basis over Rational Field
sage: V.inject_variables()
Defining a, b, K
sage: a.bracket(b)
{0: -K}

• We construct the centerless Virasoro Lie conformal algebra:

sage: virdict =  {('L','L'):{0:{('L',1):1}, 1:{('L',0): 2}}}
sage: R = LieConformalAlgebra(QQbar, virdict, names='L')
sage: R.inject_variables()
Defining L
sage: L.bracket(L)
{0: TL, 1: 2*L}

• The construction checks that skew-symmetry is violated:

sage: wrongdict =  {('L','L'):{0:{('L',1):2}, 1:{('L',0): 2}}}
sage: LieConformalAlgebra(QQbar, wrongdict, names='L')
Traceback (most recent call last):
...
ValueError: two distinct values given for one and the same bracket. Skew-symmetry is not satisfied?

structure_coefficients()#

The structure coefficients of this Lie conformal algebra.

EXAMPLES:

sage: Vir = lie_conformal_algebras.Virasoro(AA)
sage: Vir.structure_coefficients()
Finite family {('L', 'L'): ((0, TL), (1, 2*L), (3, 1/2*C))}

sage: lie_conformal_algebras.NeveuSchwarz(QQ).structure_coefficients()
Finite family {('G', 'G'): ((0, 2*L), (2, 2/3*C)),  ('G', 'L'): ((0, 1/2*TG), (1, 3/2*G)),  ('L', 'G'): ((0, TG), (1, 3/2*G)),  ('L', 'L'): ((0, TL), (1, 2*L), (3, 1/2*C))}


text:
# Challanging Problem It is nessecary to solve quicly

1. Apr 30, 2008

### vip89

Challanging Problem " It is nessecary to solve quicly"

I have a problem :
A car moves along the real line from x = 0 at t = 0 to x = 1 at t = 1, with
differentiable position function x(t) and differentiable velocity function v(t) = x0(t).
The car
begins and ends the trip at a standstill; that is v = 0 at both the beginning and the end of
the trip. Let L be the maximum velocity attained during the trip. Prove that at some time
between the beginning and end of the trip, l v’ l > L^2/(L-1).

Can you verify that L > 1 ???

Thankx

2. Apr 30, 2008

### eok20

The average velocity is 1 and since the position function is continuous (since its differentiable) and v(0) = 0 = v(1), there must be some time at which the velocity is greater than 1 (for otherwise the average would be less than 1). Therefore L > 1.

I take it that v' is the derivative of the velocity function, i.e. the acceleration?

3. May 2, 2008

### vip89

Thnkx very much, but how do u know that The average velocity is 1??

4. May 2, 2008

### exk

L=1 simply by taking the slope of a straight line that connects the 2 endpoints.

5. May 2, 2008

### HallsofIvy

Staff Emeritus
The car went distance 1 in time 1: 1/1= average speed!

6. May 6, 2008

### vip89

How u jumped from "The average velocity is 1 and since the position function is continuous (since its differentiable) and v(0) = 0 = v(1)" To "L > 1."

Is it a rule ?Give me the sorce u got that from
If not ,how u profed it??

7. May 9, 2008

### vip89

tHESE R my trials
pls tell me wt I must do??

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8. May 10, 2008

### HallsofIvy

Staff Emeritus
Actually, it is NOT true that L> 1. If the car moved with constant velocity, then L would be 1. The average speed is 1. If that speed is not constant, then there must be sometime when the velocity was less than 1, some time when the velocity was greater than 1. What is true is that $]L\ge 1$.

9. May 10, 2008

### Redbelly98

Staff Emeritus
The velocity is zero at the beginning and end of the trip, which is less than the average. So it must be greater than the average for some portion of the trip.

10. May 10, 2008

### vip89

How I can complete the question??
I know that L>1
I think I must verify that the opposite of l v’ l > L^2/(L-1) is wrong
pls help me today?

11. May 10, 2008

### HallsofIvy

Staff Emeritus
Thanks. I didn't even think of that!!

12. May 10, 2008

### HallsofIvy

Staff Emeritus
Yes, that's a good idea! Notice that | |. You must take both acceleration and deceleration into account. Suppose the acceleration were never greater than L^2/(L-1). In fact, in order to make it simpler, suppose the acceleration were always equal to L^2/(L-1). How long would it take the car to reach speed L? If that is larger than 1/2, the car has less than 1/2 second left to go from L to 0. Assuming the deceleration is never less than -L^2/(L-1), how long will it take the car to go from speed L to 0?

13. May 10, 2008

### Redbelly98

Staff Emeritus
I tried (and failed) in an attempt to contradict the statement we're supposed to prove. Choosing a constant acceleration for 0<t<0.5, and the negative of that acceleration for 1/2<t<1, I got the following.

In order to have x=1 at t=1:

a = 4, t<0<1/2
a = -4, 1/2<0<1

v = 4t for t<0<1/2
v = 4(1-t) for 1/2<t<1

So L = 2 (maximum of v, occurs at t=1/2)

And |v'| = |a| is equal to L^2/(L-1) = 4, never greater than it.

But ... in this example v is not differentiable at t=1/2, so this doesn't disprove the statement after all.

p.s on a side note, I notice that it was "necessary to solve quickly" this problem more than 1 week ago. When is/was the actual deadline for this?

I prefer it when thread titles are actually descriptive of the question being asked. Too many threads titled "URGENT" or "solve quickly" or "very very important" can be trying on peoples' goodwill and patience.


text:
# Table format: Condense columns with siunitx

Brief background: I have created a table using the S column type provided by the siunitx package. This column type allows aligning the data and column headers just fine.

My problem: The table is too wide for my document, despite setting the width as \textwidth. I suspect this is because every column uses the same formatting and leaves room for a leading ( and a trailing ), even if it is not needed for each column.

MRE:

\documentclass[12pt,a4paper,titlepage,usenames]{article}

\usepackage[left=60mm,right=20mm,top=30mm,bottom=30mm]{geometry}
\usepackage{booktabs}
\usepackage{siunitx}
\usepackage{tabu}

\begin{document}

\begin{table}[h]
\sisetup{
table-space-text-pre={(},
table-space-text-post={)},
input-open-uncertainty = ,
input-close-uncertainty = ,
table-format=2.2,
table-text-alignment=right,
table-align-text-pre = false,
table-align-text-post = false
}
\scriptsize
\begin{tabular*}{\textwidth}{l@{\extracolsep{\fill}}  *{11}{S}}
\toprule
$i$ & {$\beta^{1i}$} & {$\beta^{2i}$} & {$\beta^{3i}$} & {$\beta^{4i}$} & {$E(c^i)$} & {$\sigma(\Delta c^i)$} & {$E(r^{e,i})$} & {$\sigma(r^i)$} & {$trn^i$} & {$Size^i$} & {$BM^i$} \\
& {$(\cdot 100)$} & {$(\cdot 100)$} & {$(\cdot 100)$} & {$(\cdot 100)$} & {$(\%)$} & {$(\%)$} & {$(\%)$} & {$(\%)$} & {$(\%)$} & {$(EUR)$} & \\

\midrule
1 & 1.43 & 0.00 & 0.00 & 0.00 & 0.26 & 0.00 & 0.96 & 1.97 & 0.50 & 28.45 & 3.14 \\
& (21.34) & (7.49) & (-6.67) & (-3.39) &  &  &  &  &  &  &  \\
3 & 1.41 & 0.00 & 0.00 & 0.00 & 0.25 & -0.00 & 0.66 & 1.78 & 0.83 & 61.16 & 0.88 \\
& (29.14) & (9.91) & (-7.12) & (-1.27) &  &  &  &  &  &  &  \\
5 & 1.30 & 0.00 & 0.00 & 0.00 & 0.25 & 0.00 & 1.56 & 2.11 & 14.69 & 5.45 & 0.00 \\
& (20.18) & (9.84) & (-4.12) & (-3.29) &  &  &  &  &  &  &  \\
\bottomrule

\end{tabular*}
\end{table}

\end{document}

This leads to: Where the two columns to the right overlap the tables edge.

My question: Can TEX figure out the correct column width automatically? How could I otherwise specify that for the columns on the right hand side, that not so much space for brackets is needed?

Thank you, C.

You can use individual table-format options for each S type column depending on its contents. S type columns without optional argument will use the table-format that is specified inside of the \sisetupcommand.

\documentclass[12pt,a4paper,titlepage]{article}

\usepackage[left=60mm,right=20mm,top=30mm,bottom=30mm]{geometry}
\usepackage{booktabs}
\usepackage{siunitx}

\begin{document}

\begin{table}[h]
\sisetup{
table-space-text-pre={(},
table-space-text-post={)},
input-open-uncertainty = ,
input-close-uncertainty = ,
table-format=1.2,
table-text-alignment=right,
table-align-text-pre = false,
table-align-text-post = false
}
\scriptsize
\setlength{\tabcolsep}{0pt}
\begin{tabular*}{\textwidth}{l@{\extracolsep{\fill}}
S[table-format=2.2]
S
*{2}{S[table-format=-1.2]}
*{4}{S}
*{2}{S[table-format=2.2]}
S}
\toprule
$i$ & {$\beta^{1i}$} & {$\beta^{2i}$} & {$\beta^{3i}$} & {$\beta^{4i}$} & {$E(c^i)$} & {$\sigma(\Delta c^i)$} & {$E(r^{e,i})$} & {$\sigma(r^i)$} & {$trn^i$} & {$Size^i$} & {$BM^i$} \\
& {$(\cdot 100)$} & {$(\cdot 100)$} & {$(\cdot 100)$} & {$(\cdot 100)$} & {$(\%)$} & {$(\%)$} & {$(\%)$} & {$(\%)$} & {$(\%)$} & {$(EUR)$} & \\

\midrule
1 & 1.43 & 0.00 & 0.00 & 0.00 & 0.26 & 0.00 & 0.96 & 1.97 & 0.50 & 28.45 & 3.14 \\
& (21.34) & (7.49) & (-6.67) & (-3.39) &  &  &  &  &  &  &  \\
3 & 1.41 & 0.00 & 0.00 & 0.00 & 0.25 & -0.00 & 0.66 & 1.78 & 0.83 & 61.16 & 0.88 \\
& (29.14) & (9.91) & (-7.12) & (-1.27) &  &  &  &  &  &  &  \\
5 & 1.30 & 0.00 & 0.00 & 0.00 & 0.25 & 0.00 & 1.56 & 2.11 & 14.69 & 5.45 & 0.00 \\
& (20.18) & (9.84) & (-4.12) & (-3.29) &  &  &  &  &  &  &  \\
\bottomrule

\end{tabular*}
\end{table}

\end{document}

• +1. :-) I would suggest using text mode, though, or maybe \mathrm, for variable names such as trn, Size, BM, and especially EUR. – Mico Feb 5 at 6:05
• You're right. I'll change that. Admittedly, I did not look at the column headers too closely. – leandriis Feb 5 at 6:55
• Thank you for the suggestion. What would the benefit be of using text mode? – Chris937 Feb 5 at 10:07
• @Chris937 - Take, for instance, "EUR": Unless I'm baldly mistaken, it's the three-letter code for a currency. By typesetting EUR in math mode, the string is interpreted as the product of variables named E, U, and R; that just can't be right, can it? (E.g., look at the gap between U and R.) Give changing {$(EUR)$} to {(EUR)} a try to see for yourself what a difference it makes. – Mico Feb 5 at 10:24

I suggest to reduce \tabcolsep to 3.5pt and to apply @{\extracolsep{\fill}} from the first column:

\documentclass[12pt, a4paper, titlepage, usenames]{article}

\usepackage[left=60mm, right=20mm, vmargin=30mm, showframe]{geometry}
\usepackage{booktabs}
\usepackage{siunitx}

\begin{document}

\begin{table}[h]
\centering
\setlength{\tabcolsep}{3.5pt}
\sisetup{
table-space-text-pre={(},
table-space-text-post={)},
input-open-uncertainty = ,
input-close-uncertainty = ,
table-format=2.2,
table-text-alignment=right,
table-align-text-pre = false,
table-align-text-post = false
}
\scriptsize
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}l*{11}{S}}
\toprule
$i$ & {$\beta^{1i}$} & {$\beta^{2i}$} & {$\beta^{3i}$} & {$\beta^{4i}$} & {$E(c^i)$} & {$\sigma(\Delta c^i)$} & {$E(r^{e,i})$} & {$\sigma(r^i)$} & {$trn^i$} & {$Size^i$} & {$BM^i$} \\
& {$(\cdot 100)$} & {$(\cdot 100)$} & {$(\cdot 100)$} & {$(\cdot 100)$} & {$(\%)$} & {$(\%)$} & {$(\%)$} & {$(\%)$} & {$(\%)$} & {$(EUR)$} & \\

\midrule
1 & 1.43 & 0.00 & 0.00 & 0.00 & 0.26 & 0.00 & 0.96 & 1.97 & 0.50 & 28.45 & 3.14 \\
& (21.34) & (7.49) & (-6.67) & (-3.39) & & & & & & & \\
3 & 1.41 & 0.00 & 0.00 & 0.00 & 0.25 & -0.00 & 0.66 & 1.78 & 0.83 & 61.16 & 0.88 \\
& (29.14) & (9.91) & (-7.12) & (-1.27) & & & & & & & \\
5 & 1.30 & 0.00 & 0.00 & 0.00 & 0.25 & 0.00 & 1.56 & 2.11 & 14.69 & 5.45 & 0.00 \\
& (20.18) & (9.84) & (-4.12) & (-3.29) & & & & & & & \\
\bottomrule

\end{tabular*}
\end{table}

\end{document}


text:
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text:
• October 9th 2007, 05:12 PM
facesonfilm
Hey there. I am having difficulties with the Quadratic formula,
I know what goes where in the cases, but its just solving from there.
like in this equasion.

2x^2-5x=0

I know how to get it into the quadratic formula
this is what I got.
• October 9th 2007, 05:13 PM
Jhevon
Quote:

Originally Posted by facesonfilm
Hey there. I am having difficulties with the Quadratic formula,
I know what goes where in the cases, but its just solving from there.
like in this equasion.

2x^2-5x=0

I know how to get it into the quadratic formula
this is what I got.

that is wrong. c is zero here
• October 9th 2007, 05:23 PM
facesonfilm
I know C is zero there.. but isnt it in the form of Ax^2 + Bx + C?

so then when you plug it into the quadratic formula, you dont input a C.
• October 9th 2007, 05:38 PM
Jhevon
Quote:

Originally Posted by facesonfilm
I know C is zero there.. but isnt it in the form of Ax^2 + Bx + C?

so then when you plug it into the quadratic formula, you dont input a C.

you would not have the -4(2) under the square root. since that is -4ac and c is zero
• October 9th 2007, 05:39 PM
facesonfilm
so would the c (which is zero) make the whole 4ac equal zero?
• October 9th 2007, 05:43 PM
Jhevon
Quote:

Originally Posted by facesonfilm
so would the c (which is zero) make the whole 4ac equal zero?

umm, yes. zero times any number is zero
• October 9th 2007, 05:44 PM
facesonfilm
Oh kay, I didnt even catch that. Wow.
that sure makes me feel like a genius.
thanks alot!!
• October 9th 2007, 05:45 PM
SnipedYou
I'm surprised no one has pointed out that B is negative meaning that it should be

$\frac{5 \pm \sqrt{25}}{4}$

$\frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$

Making it

$-(-5)$ or just $5$
• October 9th 2007, 05:47 PM
Jhevon
Quote:

Originally Posted by SnipedYou
I'm surprised no one has pointed out that B is negative meaning that it should be

$\frac{5 \pm \sqrt{25}}{4}$

we would have gotten to that :D

we just had to deal with a more fundamental error first. anyway, so that we are all clear and on the same page:

the formula is: $x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}$

here $a = 2$, $b = -5$ and $c = 0$
• October 9th 2007, 05:49 PM
facesonfilm
So because I have a negitive with a negitive, it becomes a positive,
even in this case? Correct?
• October 9th 2007, 05:50 PM
Jhevon
Quote:

Originally Posted by facesonfilm
So because I have a negitive with a negitive, it becomes a positive,
even in this case? Correct?

yes, the negative of a negative is a positive
• October 9th 2007, 05:52 PM
facesonfilm
okay, I wasn't 100 % on that because our teacher just gave us the formula today like 5 minutes before the bell so I was kinda foggy on that.
• October 10th 2007, 01:00 PM
shuggyboi
why dont you just factorise "2x^2 -5x = 0"

to "x(2x-5) = 0"

then x would have the values:

x = 0 and 2x-5 = 0
2x = 5
x =5/2

:confused:
• October 10th 2007, 01:04 PM
Jhevon
Quote:

Originally Posted by shuggyboi
why dont you just factorise "2x^2 -5x = 0"

to "x(2x-5) = 0"

then x would have the values:

x = 0 and 2x-5 = 0
2x = 5
x =5/2

:confused:

i think he was required to use the quadratic formula


text:
Articles under category:
Complexity
 Vol 15, Article 17 (pp 1-20) Separation of AC$^0[\oplus]$ Formulas and Circuits
 Vol 14, Article 5 (pp 1-27) Randomized Query Complexity of Sabotaged and Composed Functions
 Vol 13, Article 10 (pp 1-19) On the Hardness of Approximating Balanced Homogenous 3-Lin
 Vol 12, Article 9 (pp 1-23) [APRX-RND14 Spec Issue] Communication Complexity of Set-Disjointness for All Probabilities by Mika Göös and Thomas Watson
 Vol 11, Article 14 (pp 357-393) Non-Commutative Arithmetic Circuits with Division by Pavel Hrubeš and Avi Wigderson


text:
# If sin x= 4/5, how do you find cos x?

cosx= $\frac{3}{5}$
Use Trignometrical identity cosx = $\sqrt{1 - {\sin}^{2} x}$
cos x = $\sqrt{1 - \frac{16}{25}}$ =$\sqrt{\frac{9}{25}}$ = $\frac{3}{5}$ to be the value in the first quadranr.


text:
# What's the problem with these alphabetic collisions?

I'm reading Halmos' Naive Set Theory.

According to the usual and natural convention "for some $y\,(x\, \epsilon \, A)$" just means "$x\, \epsilon \, A"$. It's equally harmless if the letter used has already been used with "for some-" or "for all-." Recall that "for some $x \, (x\, \epsilon \, A)$ means the same as "for some $y\, (y\, \epsilon \, A)$; it follows that a judicious change of notation will always avert alphabetic collisions.

It seems they change the letter to avoid these alphabetic collisions, but what's the problem with it? For me, it's clearer when it's stated without the letter chaging, just as in the bold text. Where are these alphabetic collisions going to be harmful? In the past, I felt confused when I saw "for some $y\,(x\, \epsilon \, A)$", I thought it was a statament about two objects.

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This doesn't make sense. Can you give more context? –  Ted Nov 21 '12 at 16:59
The $>$ is a typo. –  Andres Caicedo Nov 21 '12 at 17:00
do you mean to use the symbol $\in$? –  Holdsworth88 Nov 21 '12 at 17:02
@Holdsworth88: The $\in$ symbol is known as $\epsilon$-relation. In fact the original notation used $\epsilon$ and you can find old papers which used it that way. Halmos' book is quite old nowadays. –  Asaf Karagila Nov 21 '12 at 17:04
I believe I have corrected two typos in the quoted text. –  Arthur Fischer Nov 21 '12 at 17:17


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Reducibity of n-ary semigroups: from quasitriviality towards idempotency - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

## Reducibity of n-ary semigroups: from quasitriviality towards idempotency

(1) , (2) , (2) , (3)
1
2
3
Miguel Couceiro
Jean-Luc Marichal
• Function : Author
• PersonId : 908349
Pierre Mathonet
• Function : Author

#### Abstract

Let $X$ be a nonempty set. Denote by $\mathcal{F}^n_k$ the class of associative operations $F\colon X^n\to X$ satisfying the condition $F(x_1,\ldots,x_n)\in\{x_1,\ldots,x_n\}$ whenever at least $k$ of the elements $x_1,\ldots,x_n$ are equal to each other. The elements of $\mathcal{F}^n_1$ are said to be quasitrivial and those of $\mathcal{F}^n_n$ are said to be idempotent. We show that $\mathcal{F}^n_1=\cdots =\mathcal{F}^n_{n-2}\varsubsetneq\mathcal{F}^n_{n-1}\varsubsetneq\mathcal{F}^n_n$. The class $\mathcal{F}^n_1$ was recently characterized by Couceiro and Devillet, who showed that its elements are reducible to binary associative operations. However, some elements of $\mathcal{F}^n_n$ are not reducible. In this paper, we characterize the class $\mathcal{F}^n_{n-1}\setminus\mathcal{F}^n_1$ and show that its elements are reducible. In particular, we show that each of these elements is an extension of an $n$-ary Abelian group operation whose exponent divides $n-1$.

#### Domains

Mathematics [math]

### Dates and versions

hal-02293908 , version 1 (22-09-2019)

### Identifiers

• HAL Id : hal-02293908 , version 1

### Cite

Miguel Couceiro, Jimmy Devillet, Jean-Luc Marichal, Pierre Mathonet. Reducibity of n-ary semigroups: from quasitriviality towards idempotency. 2019. ⟨hal-02293908⟩

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Definitions

# Hydrophobic effect

The hydrophobic effect is the property that non-polar molecules tend to form intermolecular aggregates in an aqueous medium and analogous intramolecular interactions. The name arises from the combination of water in Attic Greek hydro- and for fear phobos, which describes the apparent repulsion between water and hydrocarbons. At the macroscopic level, the hydrophobic effect is apparent when oil and water are mixed together and form separate layers or the beading of water on hydrophobic surfaces such as waxy leafs. At the molecular level, the hydrophobic effect is an important driving force for biological structures and responsible for protein folding, protein-protein interactions, formation of lipid bilayer membranes, nucleic acid structures, and protein-small molecule interactions.

According to the solvophobic theory of Reversed Phase Chromatography (RPC), the hydrophobic effect is driven by the loss of hydrogen bonding and the higher entropic cost of forming a cavity around nonpolar molecules. These losses can be minimized by forcing nonpolar molecules together (see Thermodynamics).

## Amphiphiles

Amphiphiles are molecules that have both hydrophobic and hydrophilic domains. Detergents are composed of amphiphiles that allow hydrophobic molecules to be solubilized in water by forming micelles and bilayers (as in soap bubbles). They are also important to cell membranes composed of amphiphilic phospholipids that prevent the internal aqueous environment of a cell from mixing with external water.

## Biological folding

In the case of protein folding, the hydrophobic effect is important to understand the structure of proteins that have hydrophobic amino acids, such as alanine, valine, leucine, isoleucine, phenylalanine, and methionine grouped together with the protein. Most folded proteins have a hydrophobic core in which side chain packing stabilizes the folded state, and charged or polar side chains on the solvent-exposed surface where they interact with surrounding water molecules. It is generally accepted that minimizing the number of hydrophobic side chains exposed to water is the principal driving force behind the folding process, although a recent theory has been proposed which reassesses the contributions made by hydrogen bonding.

The energetics of DNA tertiary structure assembly were determined to be primarily driven by the hydrophobic effect, as opposed to Watson-Crick base pairing (which is responsible for sequence selectivity), although there is also a significant contribution from stacking interactions between the aromatic bases.

## Thermodynamics

The transfer free energy of non-polar molecule from non-polar solvent to aqueous solvent is often used to quantify the hydrophobic effect. The transfer free energy of hydrophobic molecule, $Delta G_\left\{rm t\right\}$, is positive. The $Delta G_\left\{rm t\right\}$ can be decomposed to the enthalpy component $Delta H_\left\{rm t\right\}$ and entropy component $-TDelta S_\left\{rm t\right\}$ by the thermodynamic relation $G = H - TS$. In room temperature, $Delta H_\left\{rm t\right\}$ is approximately zero, and $Delta S_\left\{rm t\right\}$ is negative. In other words, the hydrophobic effect is entropy-driven at room temperature. The other characteristic thermodynamic quantity of the hydrophobic effect is heat capacity change in transfer, $Delta C_\left\{p, \left\{rm t\right\}\right\}$, which has a positive value, as contrasted with a negative value in the transfer of a hydrophilic molecule.

Another way of understanding the hydrophobic effect is the example of a hydrophobic substance in water. Pure water molecules adopt a structure which maximizes entropy (S). A hydrophobic molecule will disrupt this structure and decrease entropy, and creates a 'cavity' as it is unable to interact electrostatically with the water molecules. When more than one 'cavity' is present, the surface area of disruptions is high, meaning that there are fewer free water molecules. To counter this, the water molecules push the hydrophobic molecules together and form a 'cage' structure around them which will have a smaller surface area than the total surface area of the cavities. This maximizes the amount of free water and thus the entropy. Therefore the hydrophobic effect might also be understood as the "the lipophobicity of water".

## References

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# Exercise where lagrangian is needed?

I teach a general equilibrium class in my university and I want to have an exercise that is not too difficult where the Lagrangian multiplier is needed. I was under the impression that with Cobb Douglas and 3 goods I could force them to use it but in the end it turned out that they could easily solve it without it. Is there a rule of thumb or an exercise for what kind of problems force students to use the Lagrangian? To be clear, I want an example with exchange.

• You could just ask them to tell you what the Langrange multiplier's value is and to provide an interpretation for it. That way, you ensure they use the Lagrangian approach and that they understand what the multiplier means. – Ubiquitous Nov 10 '18 at 19:31

## 1 Answer

I think a situation in which corner solutions may occur would be more fruitful. Cobb-Douglass ensures an interior solution, so they can use the expenditure share trick pretty easily, for any number of goods. Perhaps a really simple CES function, like $$x^.5+y^.5+z^{.5}$$? Or, if you still want an interior solution, pick something that's not a well-known function, but where marginal utility becomes infinite as either good approaches 0, like $$\ln(x) - \frac{1}{\sqrt{y}} - \frac{1}{z}$$ You'll still get tidy derivatives, but substitution won't be possible.

• Thanks for the suggestion, i'm testing it now. – Dio Oct 11 '18 at 15:49
• I don't think the first one works, I can get demand function without using the lagrangian. Not sure where to post the latex. – Dio Oct 11 '18 at 16:24
• but anyway the procedure is quite simple, you do MRS_(y to x) and MRS_(z to x), then you solve for z and y, plug those into the budget, and solve for x. Then substitute the x back into each MRS and you got the demand for each. – Dio Oct 11 '18 at 16:29
• Well, unfortunately, if you want interior solutions , then the MRS/p rule is a fact of life- it's a characterization of any solution to the first order conditions, derived from using the Lagrangian. I misunderstood what you had meant about them avoiding a Lagrangian- I thought they had just learned the Cobb-Douglas trick. – Mathew Knudson Oct 11 '18 at 23:51


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# Maharashtra Board Class 5 Maths Solutions Chapter 5 Fractions Problem Set 19

Balbharti Maharashtra Board Class 5 Maths Solutions Chapter 5 Fractions Problem Set 19 Textbook Exercise Important Questions and Answers.

## Maharashtra State Board Class 5 Maths Solutions Chapter 5 Fractions Problem Set 19

Write the proper symbol from < , > , or = in the box.

=

>

<

=

>

>

>

>

>

>

=

=

>

>

<

>

Example (1) 3/7 + 2/7 = ?
Let us divide a strip into 7 equal parts. We shall colour 3 parts with one colour and 2 parts with another.
The part with one colour is 3/7, and that with the other colour is 2/7.
The total coloured part is shown by the fraction 5/7.
It means that, $$\frac{3}{7}+\frac{2}{7}=\frac{3+2}{7}=\frac{5}{7}$$

Example (2) Add : $$\frac{3}{8}+\frac{2}{8}+\frac{1}{8}$$
The total coloured part is $$\frac{3}{8}+\frac{2}{8}+\frac{1}{8}=\frac{3+2+1}{8}=\frac{6}{8}$$

When adding like fractions, we add the numerators of the two fractions and write the denominator as it is.
Example (3) Add : 2/6 + 4/6 $$\frac{2}{6}+\frac{4}{6}=\frac{2+4}{6}=\frac{6}{6}$$
However, we know that 6/6 means that all 6 of the 6 equal parts are taken. That is, 1 whole figure is taken. Therefore, 6/6 = 1.

Note that:
If the numerator and denominator of a fraction are equal, the fraction is equal to one.
That is why, $$\frac{7}{7}=1 ; \frac{10}{10}=1 ; \frac{2}{5}+\frac{3}{5}=\frac{2+3}{5}=\frac{5}{5}=1$$
Remember that, if we do not divide a figure into parts, but keep it whole, it can also be written as 1.
This tells us that $$1=\frac{1}{1}=\frac{2}{2}=\frac{3}{3}$$ and so on.
You also know that if the numerator and denominator of a fraction have a common divisor, then the fraction obtained by dividing them by that divisor is equivalent to the given fraction.
$$\frac{5}{5}=\frac{5 \div 5}{5 \div 5}=\frac{1}{1}=1$$


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 Title: Thermo-mechanical model of steel shell behavior in continuous slab casting Author(s): Moitra, Avijit Doctoral Committee Chair(s): Thomas, Brian G. Department / Program: Mechanical Science and Engineering Discipline: Mechanical Engineering Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Engineering, Mechanical Engineering, Metallurgy Engineering, Materials Science Abstract: The behavior of the solidifying shell in the early stages of solidification has an important influence on the final quality of continuously-cast steel slabs. In order to understand the thermal and mechanical behavior of the shell, a two-dimensional transient stepwise-coupled finite-element model has been developed. The model simulates a transverse section of the slab as it moves down through the mold and below and incorporates the effects of heat conduction, solidification, shrinkage, non-uniform superheat dissipation due to turbulent fluid flow, thermal distortion of the mold and the visco-plastic mechanical behavior of the steel. Coupling between the thermal and the mechanical portions of the model are based on the mutual dependence of heat transfer across the interface between the shell and the mold and the size of the gap. The effects of mold distortion and taper on the gap size are also included. The effect of fluid flow has been incorporated via a heat flux imposed at the solid-liquid interface, which is obtained from a separate fluid flow model. The high temperature creep and plasticity of the steel is incorporated through a unified constitutive law defining the inelastic strain rates as a function of temperature, composition, accumulated plastic strain and the stress state. The model has been successfully verified with analytical solutions and measurements of temperature and shell thickness on an operating caster. Non-uniform dissipation of superheat caused by asymmetrical fluid flow has been found to have a critical influence on shell growth in the mold, in places where the interfacial gap size is significant. Model results suggest that a simple linear taper necessary to compensate for the slab shrinkage is not sufficient for low carbon steels because of the non-linear shrinkage associated with the $\delta$-$\gamma$ phase transformation. Model simulations extending below the mold suggest that bulging of the shell between rollers is responsible for the formation of off-corner depressions when the off-corner region of the shell leaving the mold is relatively thinner than other places. The model developed in this work is an effective tool and can be judiciously used to understand the formation mechanisms of various defects in continuous slab casting. Issue Date: 1993 Type: Text Language: English URI: http://hdl.handle.net/2142/19269 Rights Information: Copyright 1993 Moitra, Avijit Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9411721 OCLC Identifier: (UMI)AAI9411721